diff options
Diffstat (limited to 'lib/liboqs/src/sig/falcon')
41 files changed, 23751 insertions, 0 deletions
diff --git a/lib/liboqs/src/sig/falcon/Makefile b/lib/liboqs/src/sig/falcon/Makefile new file mode 100644 index 000000000..fe090f3ff --- /dev/null +++ b/lib/liboqs/src/sig/falcon/Makefile @@ -0,0 +1,49 @@ +#! gmake +# +# This Source Code Form is subject to the terms of the Mozilla Public +# License, v. 2.0. If a copy of the MPL was not distributed with this +# file, You can obtain one at http://mozilla.org/MPL/2.0/. + +####################################################################### +# (1) Include initial platform-independent assignments (MANDATORY). # +####################################################################### + +include manifest.mn + +####################################################################### +# (2) Include "global" configuration information. (OPTIONAL) # +####################################################################### + +USE_GCOV = +include $(CORE_DEPTH)/coreconf/config.mk + +####################################################################### +# (3) Include "component" configuration information. (OPTIONAL) # +####################################################################### + + + +####################################################################### +# (4) Include "local" platform-dependent assignments (OPTIONAL). # +####################################################################### + +include config.mk + +####################################################################### +# (5) Execute "global" rules. (OPTIONAL) # +####################################################################### + +include $(CORE_DEPTH)/coreconf/rules.mk + +####################################################################### +# (6) Execute "component" rules. (OPTIONAL) # +####################################################################### + + + +####################################################################### +# (7) Execute "local" rules. (OPTIONAL). # +####################################################################### + +WARNING_CFLAGS = $(NULL) + diff --git a/lib/liboqs/src/sig/falcon/config.mk b/lib/liboqs/src/sig/falcon/config.mk new file mode 100644 index 000000000..b28c9ce64 --- /dev/null +++ b/lib/liboqs/src/sig/falcon/config.mk @@ -0,0 +1,17 @@ +# DO NOT EDIT: generated from config.mk.subdirs.template +# +# This Source Code Form is subject to the terms of the Mozilla Public +# License, v. 2.0. If a copy of the MPL was not distributed with this +# file, You can obtain one at http://mozilla.org/MPL/2.0/. + +# add fixes for platform integration issues here. +# +# liboqs programs expect the public include files to be in oqs/xxxx, +# So we put liboqs in it's own module, oqs, and point to the dist files +INCLUDES += -I$(CORE_DEPTH)/lib/liboqs/src/common/pqclean_shims -I$(CORE_DEPTH)/lib/liboqs/src/common/sha3/xkcp_low/KeccakP-1600/plain-64bits +DEFINES += + +ifeq ($(OS_ARCH), Darwin) +DEFINES += -DOQS_HAVE_ALIGNED_ALLOC -DOQS_HAVE_MEMALIGN -DOQS_HAVE_POSIX_MEMALIGN +endif + diff --git a/lib/liboqs/src/sig/falcon/falcon.gyp b/lib/liboqs/src/sig/falcon/falcon.gyp new file mode 100644 index 000000000..73050d6ae --- /dev/null +++ b/lib/liboqs/src/sig/falcon/falcon.gyp @@ -0,0 +1,40 @@ +# DO NOT EDIT: generated from subdir.gyp.template +# This Source Code Form is subject to the terms of the Mozilla Public +# License, v. 2.0. If a copy of the MPL was not distributed with this +# file, You can obtain one at http://mozilla.org/MPL/2.0/. +{ + 'includes': [ + '../../../../../coreconf/config.gypi' + ], + 'targets': [ + { + 'target_name': 'oqs_src_sig_falcon', + 'type': 'static_library', + 'sources': [ + 'sig_falcon_512.c', + 'sig_falcon_1024.c', + ], + 'dependencies': [ + '<(DEPTH)/exports.gyp:nss_exports' + ] + } + ], + 'target_defaults': { + 'defines': [ + ], + 'include_dirs': [ + '<(DEPTH)/lib/liboqs/src/common/pqclean_shims', + '<(DEPTH)/lib/liboqs/src/common/sha3/xkcp_low/KeccakP-1600/plain-64bits', + ], + [ 'OS=="mac"', { + 'defines': [ + 'OQS_HAVE_POSIX_MEMALIGN', + 'OQS_HAVE_ALIGNED_ALLOC', + 'OQS_HAVE_MEMALIGN' + ] + }] + }, + 'variables': { + 'module': 'oqs' + } +} diff --git a/lib/liboqs/src/sig/falcon/manifest.mn b/lib/liboqs/src/sig/falcon/manifest.mn new file mode 100644 index 000000000..a0f3f2ee9 --- /dev/null +++ b/lib/liboqs/src/sig/falcon/manifest.mn @@ -0,0 +1,24 @@ +# DO NOT EDIT: generated from manifest.mn.subdirs.template +# +# This Source Code Form is subject to the terms of the Mozilla Public +# License, v. 2.0. If a copy of the MPL was not distributed with this +# file, You can obtain one at http://mozilla.org/MPL/2.0/. +CORE_DEPTH = ../../../../.. + +MODULE = oqs + +LIBRARY_NAME = oqs_src_sig_falcon +SHARED_LIBRARY = $(NULL) + +CSRCS = \ + sig_falcon_512.c \ + sig_falcon_1024.c \ + $(NULL) + +# only add module debugging in opt builds if DEBUG_PKCS11 is set +ifdef DEBUG_PKCS11 + DEFINES += -DDEBUG_MODULE +endif + +# This part of the code, including all sub-dirs, can be optimized for size +export ALLOW_OPT_CODE_SIZE = 1 diff --git a/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/Makefile b/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/Makefile new file mode 100644 index 000000000..fe090f3ff --- /dev/null +++ b/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/Makefile @@ -0,0 +1,49 @@ +#! gmake +# +# This Source Code Form is subject to the terms of the Mozilla Public +# License, v. 2.0. If a copy of the MPL was not distributed with this +# file, You can obtain one at http://mozilla.org/MPL/2.0/. + +####################################################################### +# (1) Include initial platform-independent assignments (MANDATORY). # +####################################################################### + +include manifest.mn + +####################################################################### +# (2) Include "global" configuration information. (OPTIONAL) # +####################################################################### + +USE_GCOV = +include $(CORE_DEPTH)/coreconf/config.mk + +####################################################################### +# (3) Include "component" configuration information. (OPTIONAL) # +####################################################################### + + + +####################################################################### +# (4) Include "local" platform-dependent assignments (OPTIONAL). # +####################################################################### + +include config.mk + +####################################################################### +# (5) Execute "global" rules. (OPTIONAL) # +####################################################################### + +include $(CORE_DEPTH)/coreconf/rules.mk + +####################################################################### +# (6) Execute "component" rules. (OPTIONAL) # +####################################################################### + + + +####################################################################### +# (7) Execute "local" rules. (OPTIONAL). # +####################################################################### + +WARNING_CFLAGS = $(NULL) + diff --git a/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/api.h b/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/api.h new file mode 100644 index 000000000..7a1c6569c --- /dev/null +++ b/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/api.h @@ -0,0 +1,80 @@ +#ifndef PQCLEAN_FALCON1024_CLEAN_API_H +#define PQCLEAN_FALCON1024_CLEAN_API_H + +#include <stddef.h> +#include <stdint.h> + +#define PQCLEAN_FALCON1024_CLEAN_CRYPTO_SECRETKEYBYTES 2305 +#define PQCLEAN_FALCON1024_CLEAN_CRYPTO_PUBLICKEYBYTES 1793 +#define PQCLEAN_FALCON1024_CLEAN_CRYPTO_BYTES 1330 + +#define PQCLEAN_FALCON1024_CLEAN_CRYPTO_ALGNAME "Falcon-1024" + +/* + * Generate a new key pair. Public key goes into pk[], private key in sk[]. + * Key sizes are exact (in bytes): + * public (pk): PQCLEAN_FALCON1024_CLEAN_CRYPTO_PUBLICKEYBYTES + * private (sk): PQCLEAN_FALCON1024_CLEAN_CRYPTO_SECRETKEYBYTES + * + * Return value: 0 on success, -1 on error. + */ +int PQCLEAN_FALCON1024_CLEAN_crypto_sign_keypair( + uint8_t *pk, uint8_t *sk); + +/* + * Compute a signature on a provided message (m, mlen), with a given + * private key (sk). Signature is written in sig[], with length written + * into *siglen. Signature length is variable; maximum signature length + * (in bytes) is PQCLEAN_FALCON1024_CLEAN_CRYPTO_BYTES. + * + * sig[], m[] and sk[] may overlap each other arbitrarily. + * + * Return value: 0 on success, -1 on error. + */ +int PQCLEAN_FALCON1024_CLEAN_crypto_sign_signature( + uint8_t *sig, size_t *siglen, + const uint8_t *m, size_t mlen, const uint8_t *sk); + +/* + * Verify a signature (sig, siglen) on a message (m, mlen) with a given + * public key (pk). + * + * sig[], m[] and pk[] may overlap each other arbitrarily. + * + * Return value: 0 on success, -1 on error. + */ +int PQCLEAN_FALCON1024_CLEAN_crypto_sign_verify( + const uint8_t *sig, size_t siglen, + const uint8_t *m, size_t mlen, const uint8_t *pk); + +/* + * Compute a signature on a message and pack the signature and message + * into a single object, written into sm[]. The length of that output is + * written in *smlen; that length may be larger than the message length + * (mlen) by up to PQCLEAN_FALCON1024_CLEAN_CRYPTO_BYTES. + * + * sm[] and m[] may overlap each other arbitrarily; however, sm[] shall + * not overlap with sk[]. + * + * Return value: 0 on success, -1 on error. + */ +int PQCLEAN_FALCON1024_CLEAN_crypto_sign( + uint8_t *sm, size_t *smlen, + const uint8_t *m, size_t mlen, const uint8_t *sk); + +/* + * Open a signed message object (sm, smlen) and verify the signature; + * on success, the message itself is written into m[] and its length + * into *mlen. The message is shorter than the signed message object, + * but the size difference depends on the signature value; the difference + * may range up to PQCLEAN_FALCON1024_CLEAN_CRYPTO_BYTES. + * + * m[], sm[] and pk[] may overlap each other arbitrarily. + * + * Return value: 0 on success, -1 on error. + */ +int PQCLEAN_FALCON1024_CLEAN_crypto_sign_open( + uint8_t *m, size_t *mlen, + const uint8_t *sm, size_t smlen, const uint8_t *pk); + +#endif diff --git a/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/codec.c b/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/codec.c new file mode 100644 index 000000000..c5ab4938b --- /dev/null +++ b/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/codec.c @@ -0,0 +1,555 @@ +#include "inner.h" + +/* + * Encoding/decoding of keys and signatures. + * + * ==========================(LICENSE BEGIN)============================ + * + * Copyright (c) 2017-2019 Falcon Project + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the + * "Software"), to deal in the Software without restriction, including + * without limitation the rights to use, copy, modify, merge, publish, + * distribute, sublicense, and/or sell copies of the Software, and to + * permit persons to whom the Software is furnished to do so, subject to + * the following conditions: + * + * The above copyright notice and this permission notice shall be + * included in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, + * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF + * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. + * IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY + * CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, + * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE + * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. + * + * ===========================(LICENSE END)============================= + * + * @author Thomas Pornin <thomas.pornin@nccgroup.com> + */ + + +/* see inner.h */ +size_t +PQCLEAN_FALCON1024_CLEAN_modq_encode( + void *out, size_t max_out_len, + const uint16_t *x, unsigned logn) { + size_t n, out_len, u; + uint8_t *buf; + uint32_t acc; + int acc_len; + + n = (size_t)1 << logn; + for (u = 0; u < n; u ++) { + if (x[u] >= 12289) { + return 0; + } + } + out_len = ((n * 14) + 7) >> 3; + if (out == NULL) { + return out_len; + } + if (out_len > max_out_len) { + return 0; + } + buf = out; + acc = 0; + acc_len = 0; + for (u = 0; u < n; u ++) { + acc = (acc << 14) | x[u]; + acc_len += 14; + while (acc_len >= 8) { + acc_len -= 8; + *buf ++ = (uint8_t)(acc >> acc_len); + } + } + if (acc_len > 0) { + *buf = (uint8_t)(acc << (8 - acc_len)); + } + return out_len; +} + +/* see inner.h */ +size_t +PQCLEAN_FALCON1024_CLEAN_modq_decode( + uint16_t *x, unsigned logn, + const void *in, size_t max_in_len) { + size_t n, in_len, u; + const uint8_t *buf; + uint32_t acc; + int acc_len; + + n = (size_t)1 << logn; + in_len = ((n * 14) + 7) >> 3; + if (in_len > max_in_len) { + return 0; + } + buf = in; + acc = 0; + acc_len = 0; + u = 0; + while (u < n) { + acc = (acc << 8) | (*buf ++); + acc_len += 8; + if (acc_len >= 14) { + unsigned w; + + acc_len -= 14; + w = (acc >> acc_len) & 0x3FFF; + if (w >= 12289) { + return 0; + } + x[u ++] = (uint16_t)w; + } + } + if ((acc & (((uint32_t)1 << acc_len) - 1)) != 0) { + return 0; + } + return in_len; +} + +/* see inner.h */ +size_t +PQCLEAN_FALCON1024_CLEAN_trim_i16_encode( + void *out, size_t max_out_len, + const int16_t *x, unsigned logn, unsigned bits) { + size_t n, u, out_len; + int minv, maxv; + uint8_t *buf; + uint32_t acc, mask; + unsigned acc_len; + + n = (size_t)1 << logn; + maxv = (1 << (bits - 1)) - 1; + minv = -maxv; + for (u = 0; u < n; u ++) { + if (x[u] < minv || x[u] > maxv) { + return 0; + } + } + out_len = ((n * bits) + 7) >> 3; + if (out == NULL) { + return out_len; + } + if (out_len > max_out_len) { + return 0; + } + buf = out; + acc = 0; + acc_len = 0; + mask = ((uint32_t)1 << bits) - 1; + for (u = 0; u < n; u ++) { + acc = (acc << bits) | ((uint16_t)x[u] & mask); + acc_len += bits; + while (acc_len >= 8) { + acc_len -= 8; + *buf ++ = (uint8_t)(acc >> acc_len); + } + } + if (acc_len > 0) { + *buf ++ = (uint8_t)(acc << (8 - acc_len)); + } + return out_len; +} + +/* see inner.h */ +size_t +PQCLEAN_FALCON1024_CLEAN_trim_i16_decode( + int16_t *x, unsigned logn, unsigned bits, + const void *in, size_t max_in_len) { + size_t n, in_len; + const uint8_t *buf; + size_t u; + uint32_t acc, mask1, mask2; + unsigned acc_len; + + n = (size_t)1 << logn; + in_len = ((n * bits) + 7) >> 3; + if (in_len > max_in_len) { + return 0; + } + buf = in; + u = 0; + acc = 0; + acc_len = 0; + mask1 = ((uint32_t)1 << bits) - 1; + mask2 = (uint32_t)1 << (bits - 1); + while (u < n) { + acc = (acc << 8) | *buf ++; + acc_len += 8; + while (acc_len >= bits && u < n) { + uint32_t w; + + acc_len -= bits; + w = (acc >> acc_len) & mask1; + w |= -(w & mask2); + if (w == -mask2) { + /* + * The -2^(bits-1) value is forbidden. + */ + return 0; + } + w |= -(w & mask2); + x[u ++] = (int16_t) * (int32_t *)&w; + } + } + if ((acc & (((uint32_t)1 << acc_len) - 1)) != 0) { + /* + * Extra bits in the last byte must be zero. + */ + return 0; + } + return in_len; +} + +/* see inner.h */ +size_t +PQCLEAN_FALCON1024_CLEAN_trim_i8_encode( + void *out, size_t max_out_len, + const int8_t *x, unsigned logn, unsigned bits) { + size_t n, u, out_len; + int minv, maxv; + uint8_t *buf; + uint32_t acc, mask; + unsigned acc_len; + + n = (size_t)1 << logn; + maxv = (1 << (bits - 1)) - 1; + minv = -maxv; + for (u = 0; u < n; u ++) { + if (x[u] < minv || x[u] > maxv) { + return 0; + } + } + out_len = ((n * bits) + 7) >> 3; + if (out == NULL) { + return out_len; + } + if (out_len > max_out_len) { + return 0; + } + buf = out; + acc = 0; + acc_len = 0; + mask = ((uint32_t)1 << bits) - 1; + for (u = 0; u < n; u ++) { + acc = (acc << bits) | ((uint8_t)x[u] & mask); + acc_len += bits; + while (acc_len >= 8) { + acc_len -= 8; + *buf ++ = (uint8_t)(acc >> acc_len); + } + } + if (acc_len > 0) { + *buf ++ = (uint8_t)(acc << (8 - acc_len)); + } + return out_len; +} + +/* see inner.h */ +size_t +PQCLEAN_FALCON1024_CLEAN_trim_i8_decode( + int8_t *x, unsigned logn, unsigned bits, + const void *in, size_t max_in_len) { + size_t n, in_len; + const uint8_t *buf; + size_t u; + uint32_t acc, mask1, mask2; + unsigned acc_len; + + n = (size_t)1 << logn; + in_len = ((n * bits) + 7) >> 3; + if (in_len > max_in_len) { + return 0; + } + buf = in; + u = 0; + acc = 0; + acc_len = 0; + mask1 = ((uint32_t)1 << bits) - 1; + mask2 = (uint32_t)1 << (bits - 1); + while (u < n) { + acc = (acc << 8) | *buf ++; + acc_len += 8; + while (acc_len >= bits && u < n) { + uint32_t w; + + acc_len -= bits; + w = (acc >> acc_len) & mask1; + w |= -(w & mask2); + if (w == -mask2) { + /* + * The -2^(bits-1) value is forbidden. + */ + return 0; + } + x[u ++] = (int8_t) * (int32_t *)&w; + } + } + if ((acc & (((uint32_t)1 << acc_len) - 1)) != 0) { + /* + * Extra bits in the last byte must be zero. + */ + return 0; + } + return in_len; +} + +/* see inner.h */ +size_t +PQCLEAN_FALCON1024_CLEAN_comp_encode( + void *out, size_t max_out_len, + const int16_t *x, unsigned logn) { + uint8_t *buf; + size_t n, u, v; + uint32_t acc; + unsigned acc_len; + + n = (size_t)1 << logn; + buf = out; + + /* + * Make sure that all values are within the -2047..+2047 range. + */ + for (u = 0; u < n; u ++) { + if (x[u] < -2047 || x[u] > +2047) { + return 0; + } + } + + acc = 0; + acc_len = 0; + v = 0; + for (u = 0; u < n; u ++) { + int t; + unsigned w; + + /* + * Get sign and absolute value of next integer; push the + * sign bit. + */ + acc <<= 1; + t = x[u]; + if (t < 0) { + t = -t; + acc |= 1; + } + w = (unsigned)t; + + /* + * Push the low 7 bits of the absolute value. + */ + acc <<= 7; + acc |= w & 127u; + w >>= 7; + + /* + * We pushed exactly 8 bits. + */ + acc_len += 8; + + /* + * Push as many zeros as necessary, then a one. Since the + * absolute value is at most 2047, w can only range up to + * 15 at this point, thus we will add at most 16 bits + * here. With the 8 bits above and possibly up to 7 bits + * from previous iterations, we may go up to 31 bits, which + * will fit in the accumulator, which is an uint32_t. + */ + acc <<= (w + 1); + acc |= 1; + acc_len += w + 1; + + /* + * Produce all full bytes. + */ + while (acc_len >= 8) { + acc_len -= 8; + if (buf != NULL) { + if (v >= max_out_len) { + return 0; + } + buf[v] = (uint8_t)(acc >> acc_len); + } + v ++; + } + } + + /* + * Flush remaining bits (if any). + */ + if (acc_len > 0) { + if (buf != NULL) { + if (v >= max_out_len) { + return 0; + } + buf[v] = (uint8_t)(acc << (8 - acc_len)); + } + v ++; + } + + return v; +} + +/* see inner.h */ +size_t +PQCLEAN_FALCON1024_CLEAN_comp_decode( + int16_t *x, unsigned logn, + const void *in, size_t max_in_len) { + const uint8_t *buf; + size_t n, u, v; + uint32_t acc; + unsigned acc_len; + + n = (size_t)1 << logn; + buf = in; + acc = 0; + acc_len = 0; + v = 0; + for (u = 0; u < n; u ++) { + unsigned b, s, m; + + /* + * Get next eight bits: sign and low seven bits of the + * absolute value. + */ + if (v >= max_in_len) { + return 0; + } + acc = (acc << 8) | (uint32_t)buf[v ++]; + b = acc >> acc_len; + s = b & 128; + m = b & 127; + + /* + * Get next bits until a 1 is reached. + */ + for (;;) { + if (acc_len == 0) { + if (v >= max_in_len) { + return 0; + } + acc = (acc << 8) | (uint32_t)buf[v ++]; + acc_len = 8; + } + acc_len --; + if (((acc >> acc_len) & 1) != 0) { + break; + } + m += 128; + if (m > 2047) { + return 0; + } + } + x[u] = (int16_t) m; + if (s) { + x[u] = (int16_t) - x[u]; + } + } + return v; +} + +/* + * Key elements and signatures are polynomials with small integer + * coefficients. Here are some statistics gathered over many + * generated key pairs (10000 or more for each degree): + * + * log(n) n max(f,g) std(f,g) max(F,G) std(F,G) + * 1 2 129 56.31 143 60.02 + * 2 4 123 40.93 160 46.52 + * 3 8 97 28.97 159 38.01 + * 4 16 100 21.48 154 32.50 + * 5 32 71 15.41 151 29.36 + * 6 64 59 11.07 138 27.77 + * 7 128 39 7.91 144 27.00 + * 8 256 32 5.63 148 26.61 + * 9 512 22 4.00 137 26.46 + * 10 1024 15 2.84 146 26.41 + * + * We want a compact storage format for private key, and, as part of + * key generation, we are allowed to reject some keys which would + * otherwise be fine (this does not induce any noticeable vulnerability + * as long as we reject only a small proportion of possible keys). + * Hence, we enforce at key generation time maximum values for the + * elements of f, g, F and G, so that their encoding can be expressed + * in fixed-width values. Limits have been chosen so that generated + * keys are almost always within bounds, thus not impacting neither + * security or performance. + * + * IMPORTANT: the code assumes that all coefficients of f, g, F and G + * ultimately fit in the -127..+127 range. Thus, none of the elements + * of max_fg_bits[] and max_FG_bits[] shall be greater than 8. + */ + +const uint8_t PQCLEAN_FALCON1024_CLEAN_max_fg_bits[] = { + 0, /* unused */ + 8, + 8, + 8, + 8, + 8, + 7, + 7, + 6, + 6, + 5 +}; + +const uint8_t PQCLEAN_FALCON1024_CLEAN_max_FG_bits[] = { + 0, /* unused */ + 8, + 8, + 8, + 8, + 8, + 8, + 8, + 8, + 8, + 8 +}; + +/* + * When generating a new key pair, we can always reject keys which + * feature an abnormally large coefficient. This can also be done for + * signatures, albeit with some care: in case the signature process is + * used in a derandomized setup (explicitly seeded with the message and + * private key), we have to follow the specification faithfully, and the + * specification only enforces a limit on the L2 norm of the signature + * vector. The limit on the L2 norm implies that the absolute value of + * a coefficient of the signature cannot be more than the following: + * + * log(n) n max sig coeff (theoretical) + * 1 2 412 + * 2 4 583 + * 3 8 824 + * 4 16 1166 + * 5 32 1649 + * 6 64 2332 + * 7 128 3299 + * 8 256 4665 + * 9 512 6598 + * 10 1024 9331 + * + * However, the largest observed signature coefficients during our + * experiments was 1077 (in absolute value), hence we can assume that, + * with overwhelming probability, signature coefficients will fit + * in -2047..2047, i.e. 12 bits. + */ + +const uint8_t PQCLEAN_FALCON1024_CLEAN_max_sig_bits[] = { + 0, /* unused */ + 10, + 11, + 11, + 12, + 12, + 12, + 12, + 12, + 12, + 12 +}; diff --git a/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/common.c b/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/common.c new file mode 100644 index 000000000..2e3005b2b --- /dev/null +++ b/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/common.c @@ -0,0 +1,294 @@ +#include "inner.h" + +/* + * Support functions for signatures (hash-to-point, norm). + * + * ==========================(LICENSE BEGIN)============================ + * + * Copyright (c) 2017-2019 Falcon Project + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the + * "Software"), to deal in the Software without restriction, including + * without limitation the rights to use, copy, modify, merge, publish, + * distribute, sublicense, and/or sell copies of the Software, and to + * permit persons to whom the Software is furnished to do so, subject to + * the following conditions: + * + * The above copyright notice and this permission notice shall be + * included in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, + * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF + * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. + * IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY + * CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, + * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE + * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. + * + * ===========================(LICENSE END)============================= + * + * @author Thomas Pornin <thomas.pornin@nccgroup.com> + */ + + +/* see inner.h */ +void +PQCLEAN_FALCON1024_CLEAN_hash_to_point_vartime( + inner_shake256_context *sc, + uint16_t *x, unsigned logn) { + /* + * This is the straightforward per-the-spec implementation. It + * is not constant-time, thus it might reveal information on the + * plaintext (at least, enough to check the plaintext against a + * list of potential plaintexts) in a scenario where the + * attacker does not have access to the signature value or to + * the public key, but knows the nonce (without knowledge of the + * nonce, the hashed output cannot be matched against potential + * plaintexts). + */ + size_t n; + + n = (size_t)1 << logn; + while (n > 0) { + uint8_t buf[2]; + uint32_t w; + + inner_shake256_extract(sc, (void *)buf, sizeof buf); + w = ((unsigned)buf[0] << 8) | (unsigned)buf[1]; + if (w < 61445) { + while (w >= 12289) { + w -= 12289; + } + *x ++ = (uint16_t)w; + n --; + } + } +} + +/* see inner.h */ +void +PQCLEAN_FALCON1024_CLEAN_hash_to_point_ct( + inner_shake256_context *sc, + uint16_t *x, unsigned logn, uint8_t *tmp) { + /* + * Each 16-bit sample is a value in 0..65535. The value is + * kept if it falls in 0..61444 (because 61445 = 5*12289) + * and rejected otherwise; thus, each sample has probability + * about 0.93758 of being selected. + * + * We want to oversample enough to be sure that we will + * have enough values with probability at least 1 - 2^(-256). + * Depending on degree N, this leads to the following + * required oversampling: + * + * logn n oversampling + * 1 2 65 + * 2 4 67 + * 3 8 71 + * 4 16 77 + * 5 32 86 + * 6 64 100 + * 7 128 122 + * 8 256 154 + * 9 512 205 + * 10 1024 287 + * + * If logn >= 7, then the provided temporary buffer is large + * enough. Otherwise, we use a stack buffer of 63 entries + * (i.e. 126 bytes) for the values that do not fit in tmp[]. + */ + + static const uint16_t overtab[] = { + 0, /* unused */ + 65, + 67, + 71, + 77, + 86, + 100, + 122, + 154, + 205, + 287 + }; + + unsigned n, n2, u, m, p, over; + uint16_t *tt1, tt2[63]; + + /* + * We first generate m 16-bit value. Values 0..n-1 go to x[]. + * Values n..2*n-1 go to tt1[]. Values 2*n and later go to tt2[]. + * We also reduce modulo q the values; rejected values are set + * to 0xFFFF. + */ + n = 1U << logn; + n2 = n << 1; + over = overtab[logn]; + m = n + over; + tt1 = (uint16_t *)tmp; + for (u = 0; u < m; u ++) { + uint8_t buf[2]; + uint32_t w, wr; + + inner_shake256_extract(sc, buf, sizeof buf); + w = ((uint32_t)buf[0] << 8) | (uint32_t)buf[1]; + wr = w - ((uint32_t)24578 & (((w - 24578) >> 31) - 1)); + wr = wr - ((uint32_t)24578 & (((wr - 24578) >> 31) - 1)); + wr = wr - ((uint32_t)12289 & (((wr - 12289) >> 31) - 1)); + wr |= ((w - 61445) >> 31) - 1; + if (u < n) { + x[u] = (uint16_t)wr; + } else if (u < n2) { + tt1[u - n] = (uint16_t)wr; + } else { + tt2[u - n2] = (uint16_t)wr; + } + } + + /* + * Now we must "squeeze out" the invalid values. We do this in + * a logarithmic sequence of passes; each pass computes where a + * value should go, and moves it down by 'p' slots if necessary, + * where 'p' uses an increasing powers-of-two scale. It can be + * shown that in all cases where the loop decides that a value + * has to be moved down by p slots, the destination slot is + * "free" (i.e. contains an invalid value). + */ + for (p = 1; p <= over; p <<= 1) { + unsigned v; + + /* + * In the loop below: + * + * - v contains the index of the final destination of + * the value; it is recomputed dynamically based on + * whether values are valid or not. + * + * - u is the index of the value we consider ("source"); + * its address is s. + * + * - The loop may swap the value with the one at index + * u-p. The address of the swap destination is d. + */ + v = 0; + for (u = 0; u < m; u ++) { + uint16_t *s, *d; + unsigned j, sv, dv, mk; + + if (u < n) { + s = &x[u]; + } else if (u < n2) { + s = &tt1[u - n]; + } else { + s = &tt2[u - n2]; + } + sv = *s; + + /* + * The value in sv should ultimately go to + * address v, i.e. jump back by u-v slots. + */ + j = u - v; + + /* + * We increment v for the next iteration, but + * only if the source value is valid. The mask + * 'mk' is -1 if the value is valid, 0 otherwise, + * so we _subtract_ mk. + */ + mk = (sv >> 15) - 1U; + v -= mk; + + /* + * In this loop we consider jumps by p slots; if + * u < p then there is nothing more to do. + */ + if (u < p) { + continue; + } + + /* + * Destination for the swap: value at address u-p. + */ + if ((u - p) < n) { + d = &x[u - p]; + } else if ((u - p) < n2) { + d = &tt1[(u - p) - n]; + } else { + d = &tt2[(u - p) - n2]; + } + dv = *d; + + /* + * The swap should be performed only if the source + * is valid AND the jump j has its 'p' bit set. + */ + mk &= -(((j & p) + 0x1FF) >> 9); + + *s = (uint16_t)(sv ^ (mk & (sv ^ dv))); + *d = (uint16_t)(dv ^ (mk & (sv ^ dv))); + } + } +} + +/* see inner.h */ +int +PQCLEAN_FALCON1024_CLEAN_is_short( + const int16_t *s1, const int16_t *s2, unsigned logn) { + /* + * We use the l2-norm. Code below uses only 32-bit operations to + * compute the square of the norm with saturation to 2^32-1 if + * the value exceeds 2^31-1. + */ + size_t n, u; + uint32_t s, ng; + + n = (size_t)1 << logn; + s = 0; + ng = 0; + for (u = 0; u < n; u ++) { + int32_t z; + + z = s1[u]; + s += (uint32_t)(z * z); + ng |= s; + z = s2[u]; + s += (uint32_t)(z * z); + ng |= s; + } + s |= -(ng >> 31); + + /* + * Acceptance bound on the l2-norm is: + * 1.2*1.55*sqrt(q)*sqrt(2*N) + * Value 7085 is floor((1.2^2)*(1.55^2)*2*1024). + */ + return s < (((uint32_t)7085 * (uint32_t)12289) >> (10 - logn)); +} + +/* see inner.h */ +int +PQCLEAN_FALCON1024_CLEAN_is_short_half( + uint32_t sqn, const int16_t *s2, unsigned logn) { + size_t n, u; + uint32_t ng; + + n = (size_t)1 << logn; + ng = -(sqn >> 31); + for (u = 0; u < n; u ++) { + int32_t z; + + z = s2[u]; + sqn += (uint32_t)(z * z); + ng |= sqn; + } + sqn |= -(ng >> 31); + + /* + * Acceptance bound on the l2-norm is: + * 1.2*1.55*sqrt(q)*sqrt(2*N) + * Value 7085 is floor((1.2^2)*(1.55^2)*2*1024). + */ + return sqn < (((uint32_t)7085 * (uint32_t)12289) >> (10 - logn)); +} diff --git a/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/config.mk b/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/config.mk new file mode 100644 index 000000000..b28c9ce64 --- /dev/null +++ b/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/config.mk @@ -0,0 +1,17 @@ +# DO NOT EDIT: generated from config.mk.subdirs.template +# +# This Source Code Form is subject to the terms of the Mozilla Public +# License, v. 2.0. If a copy of the MPL was not distributed with this +# file, You can obtain one at http://mozilla.org/MPL/2.0/. + +# add fixes for platform integration issues here. +# +# liboqs programs expect the public include files to be in oqs/xxxx, +# So we put liboqs in it's own module, oqs, and point to the dist files +INCLUDES += -I$(CORE_DEPTH)/lib/liboqs/src/common/pqclean_shims -I$(CORE_DEPTH)/lib/liboqs/src/common/sha3/xkcp_low/KeccakP-1600/plain-64bits +DEFINES += + +ifeq ($(OS_ARCH), Darwin) +DEFINES += -DOQS_HAVE_ALIGNED_ALLOC -DOQS_HAVE_MEMALIGN -DOQS_HAVE_POSIX_MEMALIGN +endif + diff --git a/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/fft.c b/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/fft.c new file mode 100644 index 000000000..a25bac4ec --- /dev/null +++ b/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/fft.c @@ -0,0 +1,700 @@ +#include "inner.h" + +/* + * FFT code. + * + * ==========================(LICENSE BEGIN)============================ + * + * Copyright (c) 2017-2019 Falcon Project + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the + * "Software"), to deal in the Software without restriction, including + * without limitation the rights to use, copy, modify, merge, publish, + * distribute, sublicense, and/or sell copies of the Software, and to + * permit persons to whom the Software is furnished to do so, subject to + * the following conditions: + * + * The above copyright notice and this permission notice shall be + * included in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, + * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF + * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. + * IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY + * CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, + * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE + * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. + * + * ===========================(LICENSE END)============================= + * + * @author Thomas Pornin <thomas.pornin@nccgroup.com> + */ + + +/* + * Rules for complex number macros: + * -------------------------------- + * + * Operand order is: destination, source1, source2... + * + * Each operand is a real and an imaginary part. + * + * All overlaps are allowed. + */ + +/* + * Addition of two complex numbers (d = a + b). + */ +#define FPC_ADD(d_re, d_im, a_re, a_im, b_re, b_im) do { \ + fpr fpct_re, fpct_im; \ + fpct_re = fpr_add(a_re, b_re); \ + fpct_im = fpr_add(a_im, b_im); \ + (d_re) = fpct_re; \ + (d_im) = fpct_im; \ + } while (0) + +/* + * Subtraction of two complex numbers (d = a - b). + */ +#define FPC_SUB(d_re, d_im, a_re, a_im, b_re, b_im) do { \ + fpr fpct_re, fpct_im; \ + fpct_re = fpr_sub(a_re, b_re); \ + fpct_im = fpr_sub(a_im, b_im); \ + (d_re) = fpct_re; \ + (d_im) = fpct_im; \ + } while (0) + +/* + * Multplication of two complex numbers (d = a * b). + */ +#define FPC_MUL(d_re, d_im, a_re, a_im, b_re, b_im) do { \ + fpr fpct_a_re, fpct_a_im; \ + fpr fpct_b_re, fpct_b_im; \ + fpr fpct_d_re, fpct_d_im; \ + fpct_a_re = (a_re); \ + fpct_a_im = (a_im); \ + fpct_b_re = (b_re); \ + fpct_b_im = (b_im); \ + fpct_d_re = fpr_sub( \ + fpr_mul(fpct_a_re, fpct_b_re), \ + fpr_mul(fpct_a_im, fpct_b_im)); \ + fpct_d_im = fpr_add( \ + fpr_mul(fpct_a_re, fpct_b_im), \ + fpr_mul(fpct_a_im, fpct_b_re)); \ + (d_re) = fpct_d_re; \ + (d_im) = fpct_d_im; \ + } while (0) + +/* + * Squaring of a complex number (d = a * a). + */ +#define FPC_SQR(d_re, d_im, a_re, a_im) do { \ + fpr fpct_a_re, fpct_a_im; \ + fpr fpct_d_re, fpct_d_im; \ + fpct_a_re = (a_re); \ + fpct_a_im = (a_im); \ + fpct_d_re = fpr_sub(fpr_sqr(fpct_a_re), fpr_sqr(fpct_a_im)); \ + fpct_d_im = fpr_double(fpr_mul(fpct_a_re, fpct_a_im)); \ + (d_re) = fpct_d_re; \ + (d_im) = fpct_d_im; \ + } while (0) + +/* + * Inversion of a complex number (d = 1 / a). + */ +#define FPC_INV(d_re, d_im, a_re, a_im) do { \ + fpr fpct_a_re, fpct_a_im; \ + fpr fpct_d_re, fpct_d_im; \ + fpr fpct_m; \ + fpct_a_re = (a_re); \ + fpct_a_im = (a_im); \ + fpct_m = fpr_add(fpr_sqr(fpct_a_re), fpr_sqr(fpct_a_im)); \ + fpct_m = fpr_inv(fpct_m); \ + fpct_d_re = fpr_mul(fpct_a_re, fpct_m); \ + fpct_d_im = fpr_mul(fpr_neg(fpct_a_im), fpct_m); \ + (d_re) = fpct_d_re; \ + (d_im) = fpct_d_im; \ + } while (0) + +/* + * Division of complex numbers (d = a / b). + */ +#define FPC_DIV(d_re, d_im, a_re, a_im, b_re, b_im) do { \ + fpr fpct_a_re, fpct_a_im; \ + fpr fpct_b_re, fpct_b_im; \ + fpr fpct_d_re, fpct_d_im; \ + fpr fpct_m; \ + fpct_a_re = (a_re); \ + fpct_a_im = (a_im); \ + fpct_b_re = (b_re); \ + fpct_b_im = (b_im); \ + fpct_m = fpr_add(fpr_sqr(fpct_b_re), fpr_sqr(fpct_b_im)); \ + fpct_m = fpr_inv(fpct_m); \ + fpct_b_re = fpr_mul(fpct_b_re, fpct_m); \ + fpct_b_im = fpr_mul(fpr_neg(fpct_b_im), fpct_m); \ + fpct_d_re = fpr_sub( \ + fpr_mul(fpct_a_re, fpct_b_re), \ + fpr_mul(fpct_a_im, fpct_b_im)); \ + fpct_d_im = fpr_add( \ + fpr_mul(fpct_a_re, fpct_b_im), \ + fpr_mul(fpct_a_im, fpct_b_re)); \ + (d_re) = fpct_d_re; \ + (d_im) = fpct_d_im; \ + } while (0) + +/* + * Let w = exp(i*pi/N); w is a primitive 2N-th root of 1. We define the + * values w_j = w^(2j+1) for all j from 0 to N-1: these are the roots + * of X^N+1 in the field of complex numbers. A crucial property is that + * w_{N-1-j} = conj(w_j) = 1/w_j for all j. + * + * FFT representation of a polynomial f (taken modulo X^N+1) is the + * set of values f(w_j). Since f is real, conj(f(w_j)) = f(conj(w_j)), + * thus f(w_{N-1-j}) = conj(f(w_j)). We thus store only half the values, + * for j = 0 to N/2-1; the other half can be recomputed easily when (if) + * needed. A consequence is that FFT representation has the same size + * as normal representation: N/2 complex numbers use N real numbers (each + * complex number is the combination of a real and an imaginary part). + * + * We use a specific ordering which makes computations easier. Let rev() + * be the bit-reversal function over log(N) bits. For j in 0..N/2-1, we + * store the real and imaginary parts of f(w_j) in slots: + * + * Re(f(w_j)) -> slot rev(j)/2 + * Im(f(w_j)) -> slot rev(j)/2+N/2 + * + * (Note that rev(j) is even for j < N/2.) + */ + +/* see inner.h */ +void +PQCLEAN_FALCON1024_CLEAN_FFT(fpr *f, unsigned logn) { + /* + * FFT algorithm in bit-reversal order uses the following + * iterative algorithm: + * + * t = N + * for m = 1; m < N; m *= 2: + * ht = t/2 + * for i1 = 0; i1 < m; i1 ++: + * j1 = i1 * t + * s = GM[m + i1] + * for j = j1; j < (j1 + ht); j ++: + * x = f[j] + * y = s * f[j + ht] + * f[j] = x + y + * f[j + ht] = x - y + * t = ht + * + * GM[k] contains w^rev(k) for primitive root w = exp(i*pi/N). + * + * In the description above, f[] is supposed to contain complex + * numbers. In our in-memory representation, the real and + * imaginary parts of f[k] are in array slots k and k+N/2. + * + * We only keep the first half of the complex numbers. We can + * see that after the first iteration, the first and second halves + * of the array of complex numbers have separate lives, so we + * simply ignore the second part. + */ + + unsigned u; + size_t t, n, hn, m; + + /* + * First iteration: compute f[j] + i * f[j+N/2] for all j < N/2 + * (because GM[1] = w^rev(1) = w^(N/2) = i). + * In our chosen representation, this is a no-op: everything is + * already where it should be. + */ + + /* + * Subsequent iterations are truncated to use only the first + * half of values. + */ + n = (size_t)1 << logn; + hn = n >> 1; + t = hn; + for (u = 1, m = 2; u < logn; u ++, m <<= 1) { + size_t ht, hm, i1, j1; + + ht = t >> 1; + hm = m >> 1; + for (i1 = 0, j1 = 0; i1 < hm; i1 ++, j1 += t) { + size_t j, j2; + + j2 = j1 + ht; + fpr s_re, s_im; + + s_re = fpr_gm_tab[((m + i1) << 1) + 0]; + s_im = fpr_gm_tab[((m + i1) << 1) + 1]; + for (j = j1; j < j2; j ++) { + fpr x_re, x_im, y_re, y_im; + + x_re = f[j]; + x_im = f[j + hn]; + y_re = f[j + ht]; + y_im = f[j + ht + hn]; + FPC_MUL(y_re, y_im, y_re, y_im, s_re, s_im); + FPC_ADD(f[j], f[j + hn], + x_re, x_im, y_re, y_im); + FPC_SUB(f[j + ht], f[j + ht + hn], + x_re, x_im, y_re, y_im); + } + } + t = ht; + } +} + +/* see inner.h */ +void +PQCLEAN_FALCON1024_CLEAN_iFFT(fpr *f, unsigned logn) { + /* + * Inverse FFT algorithm in bit-reversal order uses the following + * iterative algorithm: + * + * t = 1 + * for m = N; m > 1; m /= 2: + * hm = m/2 + * dt = t*2 + * for i1 = 0; i1 < hm; i1 ++: + * j1 = i1 * dt + * s = iGM[hm + i1] + * for j = j1; j < (j1 + t); j ++: + * x = f[j] + * y = f[j + t] + * f[j] = x + y + * f[j + t] = s * (x - y) + * t = dt + * for i1 = 0; i1 < N; i1 ++: + * f[i1] = f[i1] / N + * + * iGM[k] contains (1/w)^rev(k) for primitive root w = exp(i*pi/N) + * (actually, iGM[k] = 1/GM[k] = conj(GM[k])). + * + * In the main loop (not counting the final division loop), in + * all iterations except the last, the first and second half of f[] + * (as an array of complex numbers) are separate. In our chosen + * representation, we do not keep the second half. + * + * The last iteration recombines the recomputed half with the + * implicit half, and should yield only real numbers since the + * target polynomial is real; moreover, s = i at that step. + * Thus, when considering x and y: + * y = conj(x) since the final f[j] must be real + * Therefore, f[j] is filled with 2*Re(x), and f[j + t] is + * filled with 2*Im(x). + * But we already have Re(x) and Im(x) in array slots j and j+t + * in our chosen representation. That last iteration is thus a + * simple doubling of the values in all the array. + * + * We make the last iteration a no-op by tweaking the final + * division into a division by N/2, not N. + */ + size_t u, n, hn, t, m; + + n = (size_t)1 << logn; + t = 1; + m = n; + hn = n >> 1; + for (u = logn; u > 1; u --) { + size_t hm, dt, i1, j1; + + hm = m >> 1; + dt = t << 1; + for (i1 = 0, j1 = 0; j1 < hn; i1 ++, j1 += dt) { + size_t j, j2; + + j2 = j1 + t; + fpr s_re, s_im; + + s_re = fpr_gm_tab[((hm + i1) << 1) + 0]; + s_im = fpr_neg(fpr_gm_tab[((hm + i1) << 1) + 1]); + for (j = j1; j < j2; j ++) { + fpr x_re, x_im, y_re, y_im; + + x_re = f[j]; + x_im = f[j + hn]; + y_re = f[j + t]; + y_im = f[j + t + hn]; + FPC_ADD(f[j], f[j + hn], + x_re, x_im, y_re, y_im); + FPC_SUB(x_re, x_im, x_re, x_im, y_re, y_im); + FPC_MUL(f[j + t], f[j + t + hn], + x_re, x_im, s_re, s_im); + } + } + t = dt; + m = hm; + } + + /* + * Last iteration is a no-op, provided that we divide by N/2 + * instead of N. We need to make a special case for logn = 0. + */ + if (logn > 0) { + fpr ni; + + ni = fpr_p2_tab[logn]; + for (u = 0; u < n; u ++) { + f[u] = fpr_mul(f[u], ni); + } + } +} + +/* see inner.h */ +void +PQCLEAN_FALCON1024_CLEAN_poly_add( + fpr *a, const fpr *b, unsigned logn) { + size_t n, u; + + n = (size_t)1 << logn; + for (u = 0; u < n; u ++) { + a[u] = fpr_add(a[u], b[u]); + } +} + +/* see inner.h */ +void +PQCLEAN_FALCON1024_CLEAN_poly_sub( + fpr *a, const fpr *b, unsigned logn) { + size_t n, u; + + n = (size_t)1 << logn; + for (u = 0; u < n; u ++) { + a[u] = fpr_sub(a[u], b[u]); + } +} + +/* see inner.h */ +void +PQCLEAN_FALCON1024_CLEAN_poly_neg(fpr *a, unsigned logn) { + size_t n, u; + + n = (size_t)1 << logn; + for (u = 0; u < n; u ++) { + a[u] = fpr_neg(a[u]); + } +} + +/* see inner.h */ +void +PQCLEAN_FALCON1024_CLEAN_poly_adj_fft(fpr *a, unsigned logn) { + size_t n, u; + + n = (size_t)1 << logn; + for (u = (n >> 1); u < n; u ++) { + a[u] = fpr_neg(a[u]); + } +} + +/* see inner.h */ +void +PQCLEAN_FALCON1024_CLEAN_poly_mul_fft( + fpr *a, const fpr *b, unsigned logn) { + size_t n, hn, u; + + n = (size_t)1 << logn; + hn = n >> 1; + for (u = 0; u < hn; u ++) { + fpr a_re, a_im, b_re, b_im; + + a_re = a[u]; + a_im = a[u + hn]; + b_re = b[u]; + b_im = b[u + hn]; + FPC_MUL(a[u], a[u + hn], a_re, a_im, b_re, b_im); + } +} + +/* see inner.h */ +void +PQCLEAN_FALCON1024_CLEAN_poly_muladj_fft( + fpr *a, const fpr *b, unsigned logn) { + size_t n, hn, u; + + n = (size_t)1 << logn; + hn = n >> 1; + for (u = 0; u < hn; u ++) { + fpr a_re, a_im, b_re, b_im; + + a_re = a[u]; + a_im = a[u + hn]; + b_re = b[u]; + b_im = fpr_neg(b[u + hn]); + FPC_MUL(a[u], a[u + hn], a_re, a_im, b_re, b_im); + } +} + +/* see inner.h */ +void +PQCLEAN_FALCON1024_CLEAN_poly_mulselfadj_fft(fpr *a, unsigned logn) { + /* + * Since each coefficient is multiplied with its own conjugate, + * the result contains only real values. + */ + size_t n, hn, u; + + n = (size_t)1 << logn; + hn = n >> 1; + for (u = 0; u < hn; u ++) { + fpr a_re, a_im; + + a_re = a[u]; + a_im = a[u + hn]; + a[u] = fpr_add(fpr_sqr(a_re), fpr_sqr(a_im)); + a[u + hn] = fpr_zero; + } +} + +/* see inner.h */ +void +PQCLEAN_FALCON1024_CLEAN_poly_mulconst(fpr *a, fpr x, unsigned logn) { + size_t n, u; + + n = (size_t)1 << logn; + for (u = 0; u < n; u ++) { + a[u] = fpr_mul(a[u], x); + } +} + +/* see inner.h */ +void +PQCLEAN_FALCON1024_CLEAN_poly_div_fft( + fpr *a, const fpr *b, unsigned logn) { + size_t n, hn, u; + + n = (size_t)1 << logn; + hn = n >> 1; + for (u = 0; u < hn; u ++) { + fpr a_re, a_im, b_re, b_im; + + a_re = a[u]; + a_im = a[u + hn]; + b_re = b[u]; + b_im = b[u + hn]; + FPC_DIV(a[u], a[u + hn], a_re, a_im, b_re, b_im); + } +} + +/* see inner.h */ +void +PQCLEAN_FALCON1024_CLEAN_poly_invnorm2_fft(fpr *d, + const fpr *a, const fpr *b, unsigned logn) { + size_t n, hn, u; + + n = (size_t)1 << logn; + hn = n >> 1; + for (u = 0; u < hn; u ++) { + fpr a_re, a_im; + fpr b_re, b_im; + + a_re = a[u]; + a_im = a[u + hn]; + b_re = b[u]; + b_im = b[u + hn]; + d[u] = fpr_inv(fpr_add( + fpr_add(fpr_sqr(a_re), fpr_sqr(a_im)), + fpr_add(fpr_sqr(b_re), fpr_sqr(b_im)))); + } +} + +/* see inner.h */ +void +PQCLEAN_FALCON1024_CLEAN_poly_add_muladj_fft(fpr *d, + const fpr *F, const fpr *G, + const fpr *f, const fpr *g, unsigned logn) { + size_t n, hn, u; + + n = (size_t)1 << logn; + hn = n >> 1; + for (u = 0; u < hn; u ++) { + fpr F_re, F_im, G_re, G_im; + fpr f_re, f_im, g_re, g_im; + fpr a_re, a_im, b_re, b_im; + + F_re = F[u]; + F_im = F[u + hn]; + G_re = G[u]; + G_im = G[u + hn]; + f_re = f[u]; + f_im = f[u + hn]; + g_re = g[u]; + g_im = g[u + hn]; + + FPC_MUL(a_re, a_im, F_re, F_im, f_re, fpr_neg(f_im)); + FPC_MUL(b_re, b_im, G_re, G_im, g_re, fpr_neg(g_im)); + d[u] = fpr_add(a_re, b_re); + d[u + hn] = fpr_add(a_im, b_im); + } +} + +/* see inner.h */ +void +PQCLEAN_FALCON1024_CLEAN_poly_mul_autoadj_fft( + fpr *a, const fpr *b, unsigned logn) { + size_t n, hn, u; + + n = (size_t)1 << logn; + hn = n >> 1; + for (u = 0; u < hn; u ++) { + a[u] = fpr_mul(a[u], b[u]); + a[u + hn] = fpr_mul(a[u + hn], b[u]); + } +} + +/* see inner.h */ +void +PQCLEAN_FALCON1024_CLEAN_poly_div_autoadj_fft( + fpr *a, const fpr *b, unsigned logn) { + size_t n, hn, u; + + n = (size_t)1 << logn; + hn = n >> 1; + for (u = 0; u < hn; u ++) { + fpr ib; + + ib = fpr_inv(b[u]); + a[u] = fpr_mul(a[u], ib); + a[u + hn] = fpr_mul(a[u + hn], ib); + } +} + +/* see inner.h */ +void +PQCLEAN_FALCON1024_CLEAN_poly_LDL_fft( + const fpr *g00, + fpr *g01, fpr *g11, unsigned logn) { + size_t n, hn, u; + + n = (size_t)1 << logn; + hn = n >> 1; + for (u = 0; u < hn; u ++) { + fpr g00_re, g00_im, g01_re, g01_im, g11_re, g11_im; + fpr mu_re, mu_im; + + g00_re = g00[u]; + g00_im = g00[u + hn]; + g01_re = g01[u]; + g01_im = g01[u + hn]; + g11_re = g11[u]; + g11_im = g11[u + hn]; + FPC_DIV(mu_re, mu_im, g01_re, g01_im, g00_re, g00_im); + FPC_MUL(g01_re, g01_im, mu_re, mu_im, g01_re, fpr_neg(g01_im)); + FPC_SUB(g11[u], g11[u + hn], g11_re, g11_im, g01_re, g01_im); + g01[u] = mu_re; + g01[u + hn] = fpr_neg(mu_im); + } +} + +/* see inner.h */ +void +PQCLEAN_FALCON1024_CLEAN_poly_LDLmv_fft( + fpr *d11, fpr *l10, + const fpr *g00, const fpr *g01, + const fpr *g11, unsigned logn) { + size_t n, hn, u; + + n = (size_t)1 << logn; + hn = n >> 1; + for (u = 0; u < hn; u ++) { + fpr g00_re, g00_im, g01_re, g01_im, g11_re, g11_im; + fpr mu_re, mu_im; + + g00_re = g00[u]; + g00_im = g00[u + hn]; + g01_re = g01[u]; + g01_im = g01[u + hn]; + g11_re = g11[u]; + g11_im = g11[u + hn]; + FPC_DIV(mu_re, mu_im, g01_re, g01_im, g00_re, g00_im); + FPC_MUL(g01_re, g01_im, mu_re, mu_im, g01_re, fpr_neg(g01_im)); + FPC_SUB(d11[u], d11[u + hn], g11_re, g11_im, g01_re, g01_im); + l10[u] = mu_re; + l10[u + hn] = fpr_neg(mu_im); + } +} + +/* see inner.h */ +void +PQCLEAN_FALCON1024_CLEAN_poly_split_fft( + fpr *f0, fpr *f1, + const fpr *f, unsigned logn) { + /* + * The FFT representation we use is in bit-reversed order + * (element i contains f(w^(rev(i))), where rev() is the + * bit-reversal function over the ring degree. This changes + * indexes with regards to the Falcon specification. + */ + size_t n, hn, qn, u; + + n = (size_t)1 << logn; + hn = n >> 1; + qn = hn >> 1; + + /* + * We process complex values by pairs. For logn = 1, there is only + * one complex value (the other one is the implicit conjugate), + * so we add the two lines below because the loop will be + * skipped. + */ + f0[0] = f[0]; + f1[0] = f[hn]; + + for (u = 0; u < qn; u ++) { + fpr a_re, a_im, b_re, b_im; + fpr t_re, t_im; + + a_re = f[(u << 1) + 0]; + a_im = f[(u << 1) + 0 + hn]; + b_re = f[(u << 1) + 1]; + b_im = f[(u << 1) + 1 + hn]; + + FPC_ADD(t_re, t_im, a_re, a_im, b_re, b_im); + f0[u] = fpr_half(t_re); + f0[u + qn] = fpr_half(t_im); + + FPC_SUB(t_re, t_im, a_re, a_im, b_re, b_im); + FPC_MUL(t_re, t_im, t_re, t_im, + fpr_gm_tab[((u + hn) << 1) + 0], + fpr_neg(fpr_gm_tab[((u + hn) << 1) + 1])); + f1[u] = fpr_half(t_re); + f1[u + qn] = fpr_half(t_im); + } +} + +/* see inner.h */ +void +PQCLEAN_FALCON1024_CLEAN_poly_merge_fft( + fpr *f, + const fpr *f0, const fpr *f1, unsigned logn) { + size_t n, hn, qn, u; + + n = (size_t)1 << logn; + hn = n >> 1; + qn = hn >> 1; + + /* + * An extra copy to handle the special case logn = 1. + */ + f[0] = f0[0]; + f[hn] = f1[0]; + + for (u = 0; u < qn; u ++) { + fpr a_re, a_im, b_re, b_im; + fpr t_re, t_im; + + a_re = f0[u]; + a_im = f0[u + qn]; + FPC_MUL(b_re, b_im, f1[u], f1[u + qn], + fpr_gm_tab[((u + hn) << 1) + 0], + fpr_gm_tab[((u + hn) << 1) + 1]); + FPC_ADD(t_re, t_im, a_re, a_im, b_re, b_im); + f[(u << 1) + 0] = t_re; + f[(u << 1) + 0 + hn] = t_im; + FPC_SUB(t_re, t_im, a_re, a_im, b_re, b_im); + f[(u << 1) + 1] = t_re; + f[(u << 1) + 1 + hn] = t_im; + } +} diff --git a/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/fpr.c b/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/fpr.c new file mode 100644 index 000000000..669c825ee --- /dev/null +++ b/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/fpr.c @@ -0,0 +1,1890 @@ +#include "inner.h" + +/* + * Floating-point operations. + * + * This file implements the non-inline functions declared in + * fpr.h, as well as the constants for FFT / iFFT. + * + * ==========================(LICENSE BEGIN)============================ + * + * Copyright (c) 2017-2019 Falcon Project + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the + * "Software"), to deal in the Software without restriction, including + * without limitation the rights to use, copy, modify, merge, publish, + * distribute, sublicense, and/or sell copies of the Software, and to + * permit persons to whom the Software is furnished to do so, subject to + * the following conditions: + * + * The above copyright notice and this permission notice shall be + * included in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, + * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF + * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. + * IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY + * CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, + * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE + * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. + * + * ===========================(LICENSE END)============================= + * + * @author Thomas Pornin <thomas.pornin@nccgroup.com> + */ + + + +/* + * Normalize a provided unsigned integer to the 2^63..2^64-1 range by + * left-shifting it if necessary. The exponent e is adjusted accordingly + * (i.e. if the value was left-shifted by n bits, then n is subtracted + * from e). If source m is 0, then it remains 0, but e is altered. + * Both m and e must be simple variables (no expressions allowed). + */ +#define FPR_NORM64(m, e) do { \ + uint32_t nt; \ + \ + (e) -= 63; \ + \ + nt = (uint32_t)((m) >> 32); \ + nt = (nt | -nt) >> 31; \ + (m) ^= ((m) ^ ((m) << 32)) & ((uint64_t)nt - 1); \ + (e) += (int)(nt << 5); \ + \ + nt = (uint32_t)((m) >> 48); \ + nt = (nt | -nt) >> 31; \ + (m) ^= ((m) ^ ((m) << 16)) & ((uint64_t)nt - 1); \ + (e) += (int)(nt << 4); \ + \ + nt = (uint32_t)((m) >> 56); \ + nt = (nt | -nt) >> 31; \ + (m) ^= ((m) ^ ((m) << 8)) & ((uint64_t)nt - 1); \ + (e) += (int)(nt << 3); \ + \ + nt = (uint32_t)((m) >> 60); \ + nt = (nt | -nt) >> 31; \ + (m) ^= ((m) ^ ((m) << 4)) & ((uint64_t)nt - 1); \ + (e) += (int)(nt << 2); \ + \ + nt = (uint32_t)((m) >> 62); \ + nt = (nt | -nt) >> 31; \ + (m) ^= ((m) ^ ((m) << 2)) & ((uint64_t)nt - 1); \ + (e) += (int)(nt << 1); \ + \ + nt = (uint32_t)((m) >> 63); \ + (m) ^= ((m) ^ ((m) << 1)) & ((uint64_t)nt - 1); \ + (e) += (int)(nt); \ + } while (0) + +uint64_t +fpr_ursh(uint64_t x, int n) { + x ^= (x ^ (x >> 32)) & -(uint64_t)(n >> 5); + return x >> (n & 31); +} + +int64_t +fpr_irsh(int64_t x, int n) { + x ^= (x ^ (x >> 32)) & -(int64_t)(n >> 5); + return x >> (n & 31); +} + +uint64_t +fpr_ulsh(uint64_t x, int n) { + x ^= (x ^ (x << 32)) & -(uint64_t)(n >> 5); + return x << (n & 31); +} + +fpr +FPR(int s, int e, uint64_t m) { + fpr x; + uint32_t t; + unsigned f; + + /* + * If e >= -1076, then the value is "normal"; otherwise, it + * should be a subnormal, which we clamp down to zero. + */ + e += 1076; + t = (uint32_t)e >> 31; + m &= (uint64_t)t - 1; + + /* + * If m = 0 then we want a zero; make e = 0 too, but conserve + * the sign. + */ + t = (uint32_t)(m >> 54); + e &= -(int)t; + + /* + * The 52 mantissa bits come from m. Value m has its top bit set + * (unless it is a zero); we leave it "as is": the top bit will + * increment the exponent by 1, except when m = 0, which is + * exactly what we want. + */ + x = (((uint64_t)s << 63) | (m >> 2)) + ((uint64_t)(uint32_t)e << 52); + + /* + * Rounding: if the low three bits of m are 011, 110 or 111, + * then the value should be incremented to get the next + * representable value. This implements the usual + * round-to-nearest rule (with preference to even values in case + * of a tie). Note that the increment may make a carry spill + * into the exponent field, which is again exactly what we want + * in that case. + */ + f = (unsigned)m & 7U; + x += (0xC8U >> f) & 1; + return x; +} + +fpr +fpr_scaled(int64_t i, int sc) { + /* + * To convert from int to float, we have to do the following: + * 1. Get the absolute value of the input, and its sign + * 2. Shift right or left the value as appropriate + * 3. Pack the result + * + * We can assume that the source integer is not -2^63. + */ + int s, e; + uint32_t t; + uint64_t m; + + /* + * Extract sign bit. + * We have: -i = 1 + ~i + */ + s = (int)((uint64_t)i >> 63); + i ^= -(int64_t)s; + i += s; + + /* + * For now we suppose that i != 0. + * Otherwise, we set m to i and left-shift it as much as needed + * to get a 1 in the top bit. We can do that in a logarithmic + * number of conditional shifts. + */ + m = (uint64_t)i; + e = 9 + sc; + FPR_NORM64(m, e); + + /* + * Now m is in the 2^63..2^64-1 range. We must divide it by 512; + * if one of the dropped bits is a 1, this should go into the + * "sticky bit". + */ + m |= ((uint32_t)m & 0x1FF) + 0x1FF; + m >>= 9; + + /* + * Corrective action: if i = 0 then all of the above was + * incorrect, and we clamp e and m down to zero. + */ + t = (uint32_t)((uint64_t)(i | -i) >> 63); + m &= -(uint64_t)t; + e &= -(int)t; + + /* + * Assemble back everything. The FPR() function will handle cases + * where e is too low. + */ + return FPR(s, e, m); +} + +fpr +fpr_of(int64_t i) { + return fpr_scaled(i, 0); +} + +int64_t +fpr_rint(fpr x) { + uint64_t m, d; + int e; + uint32_t s, dd, f; + + /* + * We assume that the value fits in -(2^63-1)..+(2^63-1). We can + * thus extract the mantissa as a 63-bit integer, then right-shift + * it as needed. + */ + m = ((x << 10) | ((uint64_t)1 << 62)) & (((uint64_t)1 << 63) - 1); + e = 1085 - ((int)(x >> 52) & 0x7FF); + + /* + * If a shift of more than 63 bits is needed, then simply set m + * to zero. This also covers the case of an input operand equal + * to zero. + */ + m &= -(uint64_t)((uint32_t)(e - 64) >> 31); + e &= 63; + + /* + * Right-shift m as needed. Shift count is e. Proper rounding + * mandates that: + * - If the highest dropped bit is zero, then round low. + * - If the highest dropped bit is one, and at least one of the + * other dropped bits is one, then round up. + * - If the highest dropped bit is one, and all other dropped + * bits are zero, then round up if the lowest kept bit is 1, + * or low otherwise (i.e. ties are broken by "rounding to even"). + * + * We thus first extract a word consisting of all the dropped bit + * AND the lowest kept bit; then we shrink it down to three bits, + * the lowest being "sticky". + */ + d = fpr_ulsh(m, 63 - e); + dd = (uint32_t)d | ((uint32_t)(d >> 32) & 0x1FFFFFFF); + f = (uint32_t)(d >> 61) | ((dd | -dd) >> 31); + m = fpr_ursh(m, e) + (uint64_t)((0xC8U >> f) & 1U); + + /* + * Apply the sign bit. + */ + s = (uint32_t)(x >> 63); + return ((int64_t)m ^ -(int64_t)s) + (int64_t)s; +} + +int64_t +fpr_floor(fpr x) { + uint64_t t; + int64_t xi; + int e, cc; + + /* + * We extract the integer as a _signed_ 64-bit integer with + * a scaling factor. Since we assume that the value fits + * in the -(2^63-1)..+(2^63-1) range, we can left-shift the + * absolute value to make it in the 2^62..2^63-1 range: we + * will only need a right-shift afterwards. + */ + e = (int)(x >> 52) & 0x7FF; + t = x >> 63; + xi = (int64_t)(((x << 10) | ((uint64_t)1 << 62)) + & (((uint64_t)1 << 63) - 1)); + xi = (xi ^ -(int64_t)t) + (int64_t)t; + cc = 1085 - e; + + /* + * We perform an arithmetic right-shift on the value. This + * applies floor() semantics on both positive and negative values + * (rounding toward minus infinity). + */ + xi = fpr_irsh(xi, cc & 63); + + /* + * If the true shift count was 64 or more, then we should instead + * replace xi with 0 (if nonnegative) or -1 (if negative). Edge + * case: -0 will be floored to -1, not 0 (whether this is correct + * is debatable; in any case, the other functions normalize zero + * to +0). + * + * For an input of zero, the non-shifted xi was incorrect (we used + * a top implicit bit of value 1, not 0), but this does not matter + * since this operation will clamp it down. + */ + xi ^= (xi ^ -(int64_t)t) & -(int64_t)((uint32_t)(63 - cc) >> 31); + return xi; +} + +int64_t +fpr_trunc(fpr x) { + uint64_t t, xu; + int e, cc; + + /* + * Extract the absolute value. Since we assume that the value + * fits in the -(2^63-1)..+(2^63-1) range, we can left-shift + * the absolute value into the 2^62..2^63-1 range, and then + * do a right shift afterwards. + */ + e = (int)(x >> 52) & 0x7FF; + xu = ((x << 10) | ((uint64_t)1 << 62)) & (((uint64_t)1 << 63) - 1); + cc = 1085 - e; + xu = fpr_ursh(xu, cc & 63); + + /* + * If the exponent is too low (cc > 63), then the shift was wrong + * and we must clamp the value to 0. This also covers the case + * of an input equal to zero. + */ + xu &= -(uint64_t)((uint32_t)(cc - 64) >> 31); + + /* + * Apply back the sign, if the source value is negative. + */ + t = x >> 63; + xu = (xu ^ -t) + t; + return *(int64_t *)&xu; +} + +fpr +fpr_add(fpr x, fpr y) { + uint64_t m, xu, yu, za; + uint32_t cs; + int ex, ey, sx, sy, cc; + + /* + * Make sure that the first operand (x) has the larger absolute + * value. This guarantees that the exponent of y is less than + * or equal to the exponent of x, and, if they are equal, then + * the mantissa of y will not be greater than the mantissa of x. + * + * After this swap, the result will have the sign x, except in + * the following edge case: abs(x) = abs(y), and x and y have + * opposite sign bits; in that case, the result shall be +0 + * even if the sign bit of x is 1. To handle this case properly, + * we do the swap is abs(x) = abs(y) AND the sign of x is 1. + */ + m = ((uint64_t)1 << 63) - 1; + za = (x & m) - (y & m); + cs = (uint32_t)(za >> 63) + | ((1U - (uint32_t)(-za >> 63)) & (uint32_t)(x >> 63)); + m = (x ^ y) & -(uint64_t)cs; + x ^= m; + y ^= m; + + /* + * Extract sign bits, exponents and mantissas. The mantissas are + * scaled up to 2^55..2^56-1, and the exponent is unbiased. If + * an operand is zero, its mantissa is set to 0 at this step, and + * its exponent will be -1078. + */ + ex = (int)(x >> 52); + sx = ex >> 11; + ex &= 0x7FF; + m = (uint64_t)(uint32_t)((ex + 0x7FF) >> 11) << 52; + xu = ((x & (((uint64_t)1 << 52) - 1)) | m) << 3; + ex -= 1078; + ey = (int)(y >> 52); + sy = ey >> 11; + ey &= 0x7FF; + m = (uint64_t)(uint32_t)((ey + 0x7FF) >> 11) << 52; + yu = ((y & (((uint64_t)1 << 52) - 1)) | m) << 3; + ey -= 1078; + + /* + * x has the larger exponent; hence, we only need to right-shift y. + * If the shift count is larger than 59 bits then we clamp the + * value to zero. + */ + cc = ex - ey; + yu &= -(uint64_t)((uint32_t)(cc - 60) >> 31); + cc &= 63; + + /* + * The lowest bit of yu is "sticky". + */ + m = fpr_ulsh(1, cc) - 1; + yu |= (yu & m) + m; + yu = fpr_ursh(yu, cc); + + /* + * If the operands have the same sign, then we add the mantissas; + * otherwise, we subtract the mantissas. + */ + xu += yu - ((yu << 1) & -(uint64_t)(sx ^ sy)); + + /* + * The result may be smaller, or slightly larger. We normalize + * it to the 2^63..2^64-1 range (if xu is zero, then it stays + * at zero). + */ + FPR_NORM64(xu, ex); + + /* + * Scale down the value to 2^54..s^55-1, handling the last bit + * as sticky. + */ + xu |= ((uint32_t)xu & 0x1FF) + 0x1FF; + xu >>= 9; + ex += 9; + + /* + * In general, the result has the sign of x. However, if the + * result is exactly zero, then the following situations may + * be encountered: + * x > 0, y = -x -> result should be +0 + * x < 0, y = -x -> result should be +0 + * x = +0, y = +0 -> result should be +0 + * x = -0, y = +0 -> result should be +0 + * x = +0, y = -0 -> result should be +0 + * x = -0, y = -0 -> result should be -0 + * + * But at the conditional swap step at the start of the + * function, we ensured that if abs(x) = abs(y) and the + * sign of x was 1, then x and y were swapped. Thus, the + * two following cases cannot actually happen: + * x < 0, y = -x + * x = -0, y = +0 + * In all other cases, the sign bit of x is conserved, which + * is what the FPR() function does. The FPR() function also + * properly clamps values to zero when the exponent is too + * low, but does not alter the sign in that case. + */ + return FPR(sx, ex, xu); +} + +fpr +fpr_sub(fpr x, fpr y) { + y ^= (uint64_t)1 << 63; + return fpr_add(x, y); +} + +fpr +fpr_neg(fpr x) { + x ^= (uint64_t)1 << 63; + return x; +} + +fpr +fpr_half(fpr x) { + /* + * To divide a value by 2, we just have to subtract 1 from its + * exponent, but we have to take care of zero. + */ + uint32_t t; + + x -= (uint64_t)1 << 52; + t = (((uint32_t)(x >> 52) & 0x7FF) + 1) >> 11; + x &= (uint64_t)t - 1; + return x; +} + +fpr +fpr_double(fpr x) { + /* + * To double a value, we just increment by one the exponent. We + * don't care about infinites or NaNs; however, 0 is a + * special case. + */ + x += (uint64_t)((((unsigned)(x >> 52) & 0x7FFU) + 0x7FFU) >> 11) << 52; + return x; +} + +fpr +fpr_mul(fpr x, fpr y) { + uint64_t xu, yu, w, zu, zv; + uint32_t x0, x1, y0, y1, z0, z1, z2; + int ex, ey, d, e, s; + + /* + * Extract absolute values as scaled unsigned integers. We + * don't extract exponents yet. + */ + xu = (x & (((uint64_t)1 << 52) - 1)) | ((uint64_t)1 << 52); + yu = (y & (((uint64_t)1 << 52) - 1)) | ((uint64_t)1 << 52); + + /* + * We have two 53-bit integers to multiply; we need to split + * each into a lower half and a upper half. Moreover, we + * prefer to have lower halves to be of 25 bits each, for + * reasons explained later on. + */ + x0 = (uint32_t)xu & 0x01FFFFFF; + x1 = (uint32_t)(xu >> 25); + y0 = (uint32_t)yu & 0x01FFFFFF; + y1 = (uint32_t)(yu >> 25); + w = (uint64_t)x0 * (uint64_t)y0; + z0 = (uint32_t)w & 0x01FFFFFF; + z1 = (uint32_t)(w >> 25); + w = (uint64_t)x0 * (uint64_t)y1; + z1 += (uint32_t)w & 0x01FFFFFF; + z2 = (uint32_t)(w >> 25); + w = (uint64_t)x1 * (uint64_t)y0; + z1 += (uint32_t)w & 0x01FFFFFF; + z2 += (uint32_t)(w >> 25); + zu = (uint64_t)x1 * (uint64_t)y1; + z2 += (z1 >> 25); + z1 &= 0x01FFFFFF; + zu += z2; + + /* + * Since xu and yu are both in the 2^52..2^53-1 range, the + * product is in the 2^104..2^106-1 range. We first reassemble + * it and round it into the 2^54..2^56-1 range; the bottom bit + * is made "sticky". Since the low limbs z0 and z1 are 25 bits + * each, we just take the upper part (zu), and consider z0 and + * z1 only for purposes of stickiness. + * (This is the reason why we chose 25-bit limbs above.) + */ + zu |= ((z0 | z1) + 0x01FFFFFF) >> 25; + + /* + * We normalize zu to the 2^54..s^55-1 range: it could be one + * bit too large at this point. This is done with a conditional + * right-shift that takes into account the sticky bit. + */ + zv = (zu >> 1) | (zu & 1); + w = zu >> 55; + zu ^= (zu ^ zv) & -w; + + /* + * Get the aggregate scaling factor: + * + * - Each exponent is biased by 1023. + * + * - Integral mantissas are scaled by 2^52, hence an + * extra 52 bias for each exponent. + * + * - However, we right-shifted z by 50 bits, and then + * by 0 or 1 extra bit (depending on the value of w). + * + * In total, we must add the exponents, then subtract + * 2 * (1023 + 52), then add 50 + w. + */ + ex = (int)((x >> 52) & 0x7FF); + ey = (int)((y >> 52) & 0x7FF); + e = ex + ey - 2100 + (int)w; + + /* + * Sign bit is the XOR of the operand sign bits. + */ + s = (int)((x ^ y) >> 63); + + /* + * Corrective actions for zeros: if either of the operands is + * zero, then the computations above were wrong. Test for zero + * is whether ex or ey is zero. We just have to set the mantissa + * (zu) to zero, the FPR() function will normalize e. + */ + d = ((ex + 0x7FF) & (ey + 0x7FF)) >> 11; + zu &= -(uint64_t)d; + + /* + * FPR() packs the result and applies proper rounding. + */ + return FPR(s, e, zu); +} + +fpr +fpr_sqr(fpr x) { + return fpr_mul(x, x); +} + +fpr +fpr_div(fpr x, fpr y) { + uint64_t xu, yu, q, q2, w; + int i, ex, ey, e, d, s; + + /* + * Extract mantissas of x and y (unsigned). + */ + xu = (x & (((uint64_t)1 << 52) - 1)) | ((uint64_t)1 << 52); + yu = (y & (((uint64_t)1 << 52) - 1)) | ((uint64_t)1 << 52); + + /* + * Perform bit-by-bit division of xu by yu. We run it for 55 bits. + */ + q = 0; + for (i = 0; i < 55; i ++) { + /* + * If yu is less than or equal xu, then subtract it and + * push a 1 in the quotient; otherwise, leave xu unchanged + * and push a 0. + */ + uint64_t b; + + b = ((xu - yu) >> 63) - 1; + xu -= b & yu; + q |= b & 1; + xu <<= 1; + q <<= 1; + } + + /* + * We got 55 bits in the quotient, followed by an extra zero. We + * want that 56th bit to be "sticky": it should be a 1 if and + * only if the remainder (xu) is non-zero. + */ + q |= (xu | -xu) >> 63; + + /* + * Quotient is at most 2^56-1. Its top bit may be zero, but in + * that case the next-to-top bit will be a one, since the + * initial xu and yu were both in the 2^52..2^53-1 range. + * We perform a conditional shift to normalize q to the + * 2^54..2^55-1 range (with the bottom bit being sticky). + */ + q2 = (q >> 1) | (q & 1); + w = q >> 55; + q ^= (q ^ q2) & -w; + + /* + * Extract exponents to compute the scaling factor: + * + * - Each exponent is biased and we scaled them up by + * 52 bits; but these biases will cancel out. + * + * - The division loop produced a 55-bit shifted result, + * so we must scale it down by 55 bits. + * + * - If w = 1, we right-shifted the integer by 1 bit, + * hence we must add 1 to the scaling. + */ + ex = (int)((x >> 52) & 0x7FF); + ey = (int)((y >> 52) & 0x7FF); + e = ex - ey - 55 + (int)w; + + /* + * Sign is the XOR of the signs of the operands. + */ + s = (int)((x ^ y) >> 63); + + /* + * Corrective actions for zeros: if x = 0, then the computation + * is wrong, and we must clamp e and q to 0. We do not care + * about the case y = 0 (as per assumptions in this module, + * the caller does not perform divisions by zero). + */ + d = (ex + 0x7FF) >> 11; + s &= d; + e &= -d; + q &= -(uint64_t)d; + + /* + * FPR() packs the result and applies proper rounding. + */ + return FPR(s, e, q); +} + +fpr +fpr_inv(fpr x) { + return fpr_div(4607182418800017408u, x); +} + +fpr +fpr_sqrt(fpr x) { + uint64_t xu, q, s, r; + int ex, e; + + /* + * Extract the mantissa and the exponent. We don't care about + * the sign: by assumption, the operand is nonnegative. + * We want the "true" exponent corresponding to a mantissa + * in the 1..2 range. + */ + xu = (x & (((uint64_t)1 << 52) - 1)) | ((uint64_t)1 << 52); + ex = (int)((x >> 52) & 0x7FF); + e = ex - 1023; + + /* + * If the exponent is odd, double the mantissa and decrement + * the exponent. The exponent is then halved to account for + * the square root. + */ + xu += xu & -(uint64_t)(e & 1); + e >>= 1; + + /* + * Double the mantissa. + */ + xu <<= 1; + + /* + * We now have a mantissa in the 2^53..2^55-1 range. It + * represents a value between 1 (inclusive) and 4 (exclusive) + * in fixed point notation (with 53 fractional bits). We + * compute the square root bit by bit. + */ + q = 0; + s = 0; + r = (uint64_t)1 << 53; + for (int i = 0; i < 54; i ++) { + uint64_t t, b; + + t = s + r; + b = ((xu - t) >> 63) - 1; + s += (r << 1) & b; + xu -= t & b; + q += r & b; + xu <<= 1; + r >>= 1; + } + + /* + * Now, q is a rounded-low 54-bit value, with a leading 1, + * 52 fractional digits, and an additional guard bit. We add + * an extra sticky bit to account for what remains of the operand. + */ + q <<= 1; + q |= (xu | -xu) >> 63; + + /* + * Result q is in the 2^54..2^55-1 range; we bias the exponent + * by 54 bits (the value e at that point contains the "true" + * exponent, but q is now considered an integer, i.e. scaled + * up. + */ + e -= 54; + + /* + * Corrective action for an operand of value zero. + */ + q &= -(uint64_t)((ex + 0x7FF) >> 11); + + /* + * Apply rounding and back result. + */ + return FPR(0, e, q); +} + +int +fpr_lt(fpr x, fpr y) { + /* + * If both x and y are positive, then a signed comparison yields + * the proper result: + * - For positive values, the order is preserved. + * - The sign bit is at the same place as in integers, so + * sign is preserved. + * Moreover, we can compute [x < y] as sgn(x-y) and the computation + * of x-y will not overflow. + * + * If the signs differ, then sgn(x) gives the proper result. + * + * If both x and y are negative, then the order is reversed. + * Hence [x < y] = sgn(y-x). We must compute this separately from + * sgn(x-y); simply inverting sgn(x-y) would not handle the edge + * case x = y properly. + */ + int cc0, cc1; + int64_t sx; + int64_t sy; + + sx = *(int64_t *)&x; + sy = *(int64_t *)&y; + sy &= ~((sx ^ sy) >> 63); /* set sy=0 if signs differ */ + + cc0 = (int)((sx - sy) >> 63) & 1; /* Neither subtraction overflows when */ + cc1 = (int)((sy - sx) >> 63) & 1; /* the signs are the same. */ + + return cc0 ^ ((cc0 ^ cc1) & (int)((x & y) >> 63)); +} + +uint64_t +fpr_expm_p63(fpr x, fpr ccs) { + /* + * Polynomial approximation of exp(-x) is taken from FACCT: + * https://eprint.iacr.org/2018/1234 + * Specifically, values are extracted from the implementation + * referenced from the FACCT article, and available at: + * https://github.com/raykzhao/gaussian + * Here, the coefficients have been scaled up by 2^63 and + * converted to integers. + * + * Tests over more than 24 billions of random inputs in the + * 0..log(2) range have never shown a deviation larger than + * 2^(-50) from the true mathematical value. + */ + static const uint64_t C[] = { + 0x00000004741183A3u, + 0x00000036548CFC06u, + 0x0000024FDCBF140Au, + 0x0000171D939DE045u, + 0x0000D00CF58F6F84u, + 0x000680681CF796E3u, + 0x002D82D8305B0FEAu, + 0x011111110E066FD0u, + 0x0555555555070F00u, + 0x155555555581FF00u, + 0x400000000002B400u, + 0x7FFFFFFFFFFF4800u, + 0x8000000000000000u + }; + + uint64_t z, y; + size_t u; + uint32_t z0, z1, y0, y1; + uint64_t a, b; + + y = C[0]; + z = (uint64_t)fpr_trunc(fpr_mul(x, fpr_ptwo63)) << 1; + for (u = 1; u < (sizeof C) / sizeof(C[0]); u ++) { + /* + * Compute product z * y over 128 bits, but keep only + * the top 64 bits. + * + * TODO: On some architectures/compilers we could use + * some intrinsics (__umulh() on MSVC) or other compiler + * extensions (unsigned __int128 on GCC / Clang) for + * improved speed; however, most 64-bit architectures + * also have appropriate IEEE754 floating-point support, + * which is better. + */ + uint64_t c; + + z0 = (uint32_t)z; + z1 = (uint32_t)(z >> 32); + y0 = (uint32_t)y; + y1 = (uint32_t)(y >> 32); + a = ((uint64_t)z0 * (uint64_t)y1) + + (((uint64_t)z0 * (uint64_t)y0) >> 32); + b = ((uint64_t)z1 * (uint64_t)y0); + c = (a >> 32) + (b >> 32); + c += (((uint64_t)(uint32_t)a + (uint64_t)(uint32_t)b) >> 32); + c += (uint64_t)z1 * (uint64_t)y1; + y = C[u] - c; + } + + /* + * The scaling factor must be applied at the end. Since y is now + * in fixed-point notation, we have to convert the factor to the + * same format, and do an extra integer multiplication. + */ + z = (uint64_t)fpr_trunc(fpr_mul(ccs, fpr_ptwo63)) << 1; + z0 = (uint32_t)z; + z1 = (uint32_t)(z >> 32); + y0 = (uint32_t)y; + y1 = (uint32_t)(y >> 32); + a = ((uint64_t)z0 * (uint64_t)y1) + + (((uint64_t)z0 * (uint64_t)y0) >> 32); + b = ((uint64_t)z1 * (uint64_t)y0); + y = (a >> 32) + (b >> 32); + y += (((uint64_t)(uint32_t)a + (uint64_t)(uint32_t)b) >> 32); + y += (uint64_t)z1 * (uint64_t)y1; + + return y; +} + +const fpr fpr_gm_tab[] = { + 0, 0, + 9223372036854775808U, 4607182418800017408U, + 4604544271217802189U, 4604544271217802189U, + 13827916308072577997U, 4604544271217802189U, + 4606496786581982534U, 4600565431771507043U, + 13823937468626282851U, 4606496786581982534U, + 4600565431771507043U, 4606496786581982534U, + 13829868823436758342U, 4600565431771507043U, + 4607009347991985328U, 4596196889902818827U, + 13819568926757594635U, 4607009347991985328U, + 4603179351334086856U, 4605664432017547683U, + 13829036468872323491U, 4603179351334086856U, + 4605664432017547683U, 4603179351334086856U, + 13826551388188862664U, 4605664432017547683U, + 4596196889902818827U, 4607009347991985328U, + 13830381384846761136U, 4596196889902818827U, + 4607139046673687846U, 4591727299969791020U, + 13815099336824566828U, 4607139046673687846U, + 4603889326261607894U, 4605137878724712257U, + 13828509915579488065U, 4603889326261607894U, + 4606118860100255153U, 4602163548591158843U, + 13825535585445934651U, 4606118860100255153U, + 4598900923775164166U, 4606794571824115162U, + 13830166608678890970U, 4598900923775164166U, + 4606794571824115162U, 4598900923775164166U, + 13822272960629939974U, 4606794571824115162U, + 4602163548591158843U, 4606118860100255153U, + 13829490896955030961U, 4602163548591158843U, + 4605137878724712257U, 4603889326261607894U, + 13827261363116383702U, 4605137878724712257U, + 4591727299969791020U, 4607139046673687846U, + 13830511083528463654U, 4591727299969791020U, + 4607171569234046334U, 4587232218149935124U, + 13810604255004710932U, 4607171569234046334U, + 4604224084862889120U, 4604849113969373103U, + 13828221150824148911U, 4604224084862889120U, + 4606317631232591731U, 4601373767755717824U, + 13824745804610493632U, 4606317631232591731U, + 4599740487990714333U, 4606655894547498725U, + 13830027931402274533U, 4599740487990714333U, + 4606912484326125783U, 4597922303871901467U, + 13821294340726677275U, 4606912484326125783U, + 4602805845399633902U, 4605900952042040894U, + 13829272988896816702U, 4602805845399633902U, + 4605409869824231233U, 4603540801876750389U, + 13826912838731526197U, 4605409869824231233U, + 4594454542771183930U, 4607084929468638487U, + 13830456966323414295U, 4594454542771183930U, + 4607084929468638487U, 4594454542771183930U, + 13817826579625959738U, 4607084929468638487U, + 4603540801876750389U, 4605409869824231233U, + 13828781906679007041U, 4603540801876750389U, + 4605900952042040894U, 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4604563781218984604U, 4604524701268679793U, + 13827896738123455601U, 4604563781218984604U, + 4569220649180767418U, 4607182376410422530U, + 13830554413265198338U, 4569220649180767418U +}; + +const fpr fpr_p2_tab[] = { + 4611686018427387904U, + 4607182418800017408U, + 4602678819172646912U, + 4598175219545276416U, + 4593671619917905920U, + 4589168020290535424U, + 4584664420663164928U, + 4580160821035794432U, + 4575657221408423936U, + 4571153621781053440U, + 4566650022153682944U +}; diff --git a/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/fpr.h b/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/fpr.h new file mode 100644 index 000000000..a1c122275 --- /dev/null +++ b/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/fpr.h @@ -0,0 +1,253 @@ +#ifndef PQCLEAN_FALCON1024_CLEAN_FPR_H +#define PQCLEAN_FALCON1024_CLEAN_FPR_H + +/* + * Floating-point operations. + * + * ==========================(LICENSE BEGIN)============================ + * + * Copyright (c) 2017-2019 Falcon Project + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the + * "Software"), to deal in the Software without restriction, including + * without limitation the rights to use, copy, modify, merge, publish, + * distribute, sublicense, and/or sell copies of the Software, and to + * permit persons to whom the Software is furnished to do so, subject to + * the following conditions: + * + * The above copyright notice and this permission notice shall be + * included in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, + * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF + * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. + * IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY + * CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, + * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE + * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. + * + * ===========================(LICENSE END)============================= + * + * @author Thomas Pornin <thomas.pornin@nccgroup.com> + */ + + +/* ====================================================================== */ +/* + * Custom floating-point implementation with integer arithmetics. We + * use IEEE-754 "binary64" format, with some simplifications: + * + * - Top bit is s = 1 for negative, 0 for positive. + * + * - Exponent e uses the next 11 bits (bits 52 to 62, inclusive). + * + * - Mantissa m uses the 52 low bits. + * + * Encoded value is, in general: (-1)^s * 2^(e-1023) * (1 + m*2^(-52)) + * i.e. the mantissa really is a 53-bit number (less than 2.0, but not + * less than 1.0), but the top bit (equal to 1 by definition) is omitted + * in the encoding. + * + * In IEEE-754, there are some special values: + * + * - If e = 2047, then the value is either an infinite (m = 0) or + * a NaN (m != 0). + * + * - If e = 0, then the value is either a zero (m = 0) or a subnormal, + * aka "denormalized number" (m != 0). + * + * Of these, we only need the zeros. The caller is responsible for not + * providing operands that would lead to infinites, NaNs or subnormals. + * If inputs are such that values go out of range, then indeterminate + * values are returned (it would still be deterministic, but no specific + * value may be relied upon). + * + * At the C level, the three parts are stored in a 64-bit unsigned + * word. + * + * One may note that a property of the IEEE-754 format is that order + * is preserved for positive values: if two positive floating-point + * values x and y are such that x < y, then their respective encodings + * as _signed_ 64-bit integers i64(x) and i64(y) will be such that + * i64(x) < i64(y). For negative values, order is reversed: if x < 0, + * y < 0, and x < y, then ia64(x) > ia64(y). + * + * IMPORTANT ASSUMPTIONS: + * ====================== + * + * For proper computations, and constant-time behaviour, we assume the + * following: + * + * - 32x32->64 multiplication (unsigned) has an execution time that + * is independent of its operands. This is true of most modern + * x86 and ARM cores. Notable exceptions are the ARM Cortex M0, M0+ + * and M3 (in the M0 and M0+, this is done in software, so it depends + * on that routine), and the PowerPC cores from the G3/G4 lines. + * For more info, see: https://www.bearssl.org/ctmul.html + * + * - Left-shifts and right-shifts of 32-bit values have an execution + * time which does not depend on the shifted value nor on the + * shift count. An historical exception is the Pentium IV, but most + * modern CPU have barrel shifters. Some small microcontrollers + * might have varying-time shifts (not the ARM Cortex M*, though). + * + * - Right-shift of a signed negative value performs a sign extension. + * As per the C standard, this operation returns an + * implementation-defined result (this is NOT an "undefined + * behaviour"). On most/all systems, an arithmetic shift is + * performed, because this is what makes most sense. + */ + +/* + * Normally we should declare the 'fpr' type to be a struct or union + * around the internal 64-bit value; however, we want to use the + * direct 64-bit integer type to enable a lighter call convention on + * ARM platforms. This means that direct (invalid) use of operators + * such as '*' or '+' will not be caught by the compiler. We rely on + * the "normal" (non-emulated) code to detect such instances. + */ +typedef uint64_t fpr; + +/* + * For computations, we split values into an integral mantissa in the + * 2^54..2^55 range, and an (adjusted) exponent. The lowest bit is + * "sticky" (it is set to 1 if any of the bits below it is 1); when + * re-encoding, the low two bits are dropped, but may induce an + * increment in the value for proper rounding. + */ + +/* + * Right-shift a 64-bit unsigned value by a possibly secret shift count. + * We assumed that the underlying architecture had a barrel shifter for + * 32-bit shifts, but for 64-bit shifts on a 32-bit system, this will + * typically invoke a software routine that is not necessarily + * constant-time; hence the function below. + * + * Shift count n MUST be in the 0..63 range. + */ +#define fpr_ursh PQCLEAN_FALCON1024_CLEAN_fpr_ursh +uint64_t fpr_ursh(uint64_t x, int n); + +/* + * Right-shift a 64-bit signed value by a possibly secret shift count + * (see fpr_ursh() for the rationale). + * + * Shift count n MUST be in the 0..63 range. + */ +#define fpr_irsh PQCLEAN_FALCON1024_CLEAN_fpr_irsh +int64_t fpr_irsh(int64_t x, int n); + +/* + * Left-shift a 64-bit unsigned value by a possibly secret shift count + * (see fpr_ursh() for the rationale). + * + * Shift count n MUST be in the 0..63 range. + */ +#define fpr_ulsh PQCLEAN_FALCON1024_CLEAN_fpr_ulsh +uint64_t fpr_ulsh(uint64_t x, int n); + +/* + * Expectations: + * s = 0 or 1 + * exponent e is "arbitrary" and unbiased + * 2^54 <= m < 2^55 + * Numerical value is (-1)^2 * m * 2^e + * + * Exponents which are too low lead to value zero. If the exponent is + * too large, the returned value is indeterminate. + * + * If m = 0, then a zero is returned (using the provided sign). + * If e < -1076, then a zero is returned (regardless of the value of m). + * If e >= -1076 and e != 0, m must be within the expected range + * (2^54 to 2^55-1). + */ +#define FPR PQCLEAN_FALCON1024_CLEAN_FPR +fpr FPR(int s, int e, uint64_t m); + + +#define fpr_scaled PQCLEAN_FALCON1024_CLEAN_fpr_scaled +fpr fpr_scaled(int64_t i, int sc); + +#define fpr_of PQCLEAN_FALCON1024_CLEAN_fpr_of +fpr fpr_of(int64_t i); + +static const fpr fpr_q = 4667981563525332992; +static const fpr fpr_inverse_of_q = 4545632735260551042; +static const fpr fpr_inv_2sqrsigma0 = 4594603506513722306; +static const fpr fpr_inv_sigma = 4573359825155195350; +static const fpr fpr_sigma_min_9 = 4608495221497168882; +static const fpr fpr_sigma_min_10 = 4608586345619182117; +static const fpr fpr_log2 = 4604418534313441775; +static const fpr fpr_inv_log2 = 4609176140021203710; +static const fpr fpr_bnorm_max = 4670353323383631276; +static const fpr fpr_zero = 0; +static const fpr fpr_one = 4607182418800017408; +static const fpr fpr_two = 4611686018427387904; +static const fpr fpr_onehalf = 4602678819172646912; +static const fpr fpr_invsqrt2 = 4604544271217802189; +static const fpr fpr_invsqrt8 = 4600040671590431693; +static const fpr fpr_ptwo31 = 4746794007248502784; +static const fpr fpr_ptwo31m1 = 4746794007244308480; +static const fpr fpr_mtwo31m1 = 13970166044099084288U; +static const fpr fpr_ptwo63m1 = 4890909195324358656; +static const fpr fpr_mtwo63m1 = 14114281232179134464U; +static const fpr fpr_ptwo63 = 4890909195324358656; + +#define fpr_rint PQCLEAN_FALCON1024_CLEAN_fpr_rint +int64_t fpr_rint(fpr x); + +#define fpr_floor PQCLEAN_FALCON1024_CLEAN_fpr_floor +int64_t fpr_floor(fpr x); + +#define fpr_trunc PQCLEAN_FALCON1024_CLEAN_fpr_trunc +int64_t fpr_trunc(fpr x); + +#define fpr_add PQCLEAN_FALCON1024_CLEAN_fpr_add +fpr fpr_add(fpr x, fpr y); + +#define fpr_sub PQCLEAN_FALCON1024_CLEAN_fpr_sub +fpr fpr_sub(fpr x, fpr y); + +#define fpr_neg PQCLEAN_FALCON1024_CLEAN_fpr_neg +fpr fpr_neg(fpr x); + +#define fpr_half PQCLEAN_FALCON1024_CLEAN_fpr_half +fpr fpr_half(fpr x); + +#define fpr_double PQCLEAN_FALCON1024_CLEAN_fpr_double +fpr fpr_double(fpr x); + +#define fpr_mul PQCLEAN_FALCON1024_CLEAN_fpr_mul +fpr fpr_mul(fpr x, fpr y); + +#define fpr_sqr PQCLEAN_FALCON1024_CLEAN_fpr_sqr +fpr fpr_sqr(fpr x); + +#define fpr_div PQCLEAN_FALCON1024_CLEAN_fpr_div +fpr fpr_div(fpr x, fpr y); + +#define fpr_inv PQCLEAN_FALCON1024_CLEAN_fpr_inv +fpr fpr_inv(fpr x); + +#define fpr_sqrt PQCLEAN_FALCON1024_CLEAN_fpr_sqrt +fpr fpr_sqrt(fpr x); + +#define fpr_lt PQCLEAN_FALCON1024_CLEAN_fpr_lt +int fpr_lt(fpr x, fpr y); + +/* + * Compute exp(x) for x such that |x| <= ln 2. We want a precision of 50 + * bits or so. + */ +#define fpr_expm_p63 PQCLEAN_FALCON1024_CLEAN_fpr_expm_p63 +uint64_t fpr_expm_p63(fpr x, fpr ccs); + +#define fpr_gm_tab PQCLEAN_FALCON1024_CLEAN_fpr_gm_tab +extern const fpr fpr_gm_tab[]; + +#define fpr_p2_tab PQCLEAN_FALCON1024_CLEAN_fpr_p2_tab +extern const fpr fpr_p2_tab[]; + +/* ====================================================================== */ +#endif diff --git a/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/inner.c b/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/inner.c new file mode 100755 index 000000000..f5c269eda --- /dev/null +++ b/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/inner.c @@ -0,0 +1,70 @@ +#include "inner.h" + +/* + * ==========================(LICENSE BEGIN)============================ + * + * Copyright (c) 2017-2019 Falcon Project + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the + * "Software"), to deal in the Software without restriction, including + * without limitation the rights to use, copy, modify, merge, publish, + * distribute, sublicense, and/or sell copies of the Software, and to + * permit persons to whom the Software is furnished to do so, subject to + * the following conditions: + * + * The above copyright notice and this permission notice shall be + * included in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, + * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF + * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. + * IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY + * CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, + * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE + * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. + * + * ===========================(LICENSE END)============================= + */ + +unsigned set_fpu_cw(unsigned x) { + return x; +} + + +uint64_t prng_get_u64(prng *p) { + size_t u; + + /* + * If there are less than 9 bytes in the buffer, we refill it. + * This means that we may drop the last few bytes, but this allows + * for faster extraction code. Also, it means that we never leave + * an empty buffer. + */ + u = p->ptr; + if (u >= (sizeof p->buf.d) - 9) { + PQCLEAN_FALCON1024_CLEAN_prng_refill(p); + u = 0; + } + p->ptr = u + 8; + + return (uint64_t)p->buf.d[u + 0] + | ((uint64_t)p->buf.d[u + 1] << 8) + | ((uint64_t)p->buf.d[u + 2] << 16) + | ((uint64_t)p->buf.d[u + 3] << 24) + | ((uint64_t)p->buf.d[u + 4] << 32) + | ((uint64_t)p->buf.d[u + 5] << 40) + | ((uint64_t)p->buf.d[u + 6] << 48) + | ((uint64_t)p->buf.d[u + 7] << 56); +} + + +unsigned prng_get_u8(prng *p) { + unsigned v; + + v = p->buf.d[p->ptr ++]; + if (p->ptr == sizeof p->buf.d) { + PQCLEAN_FALCON1024_CLEAN_prng_refill(p); + } + return v; +} diff --git a/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/inner.h b/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/inner.h new file mode 100644 index 000000000..886f51a67 --- /dev/null +++ b/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/inner.h @@ -0,0 +1,794 @@ +#ifndef PQCLEAN_FALCON1024_CLEAN_INNER_H +#define PQCLEAN_FALCON1024_CLEAN_INNER_H + + +/* + * Internal functions for Falcon. This is not the API intended to be + * used by applications; instead, this internal API provides all the + * primitives on which wrappers build to provide external APIs. + * + * ==========================(LICENSE BEGIN)============================ + * + * Copyright (c) 2017-2019 Falcon Project + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the + * "Software"), to deal in the Software without restriction, including + * without limitation the rights to use, copy, modify, merge, publish, + * distribute, sublicense, and/or sell copies of the Software, and to + * permit persons to whom the Software is furnished to do so, subject to + * the following conditions: + * + * The above copyright notice and this permission notice shall be + * included in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, + * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF + * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. + * IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY + * CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, + * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE + * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. + * + * ===========================(LICENSE END)============================= + * + * @author Thomas Pornin <thomas.pornin@nccgroup.com> + */ + +/* + * IMPORTANT API RULES + * ------------------- + * + * This API has some non-trivial usage rules: + * + * + * - All public functions (i.e. the non-static ones) must be referenced + * with the PQCLEAN_FALCON1024_CLEAN_ macro (e.g. PQCLEAN_FALCON1024_CLEAN_verify_raw for the verify_raw() + * function). That macro adds a prefix to the name, which is + * configurable with the FALCON_PREFIX macro. This allows compiling + * the code into a specific "namespace" and potentially including + * several versions of this code into a single application (e.g. to + * have an AVX2 and a non-AVX2 variants and select the one to use at + * runtime based on availability of AVX2 opcodes). + * + * - Functions that need temporary buffers expects them as a final + * tmp[] array of type uint8_t*, with a size which is documented for + * each function. However, most have some alignment requirements, + * because they will use the array to store 16-bit, 32-bit or 64-bit + * values (e.g. uint64_t or double). The caller must ensure proper + * alignment. What happens on unaligned access depends on the + * underlying architecture, ranging from a slight time penalty + * to immediate termination of the process. + * + * - Some functions rely on specific rounding rules and precision for + * floating-point numbers. On some systems (in particular 32-bit x86 + * with the 387 FPU), this requires setting an hardware control + * word. The caller MUST use set_fpu_cw() to ensure proper precision: + * + * oldcw = set_fpu_cw(2); + * PQCLEAN_FALCON1024_CLEAN_sign_dyn(...); + * set_fpu_cw(oldcw); + * + * On systems where the native floating-point precision is already + * proper, or integer-based emulation is used, the set_fpu_cw() + * function does nothing, so it can be called systematically. + */ +#include "fips202.h" +#include "fpr.h" +#include <stdint.h> +#include <stdlib.h> +#include <string.h> + + + + + +/* + * Some computations with floating-point elements, in particular + * rounding to the nearest integer, rely on operations using _exactly_ + * the precision of IEEE-754 binary64 type (i.e. 52 bits). On 32-bit + * x86, the 387 FPU may be used (depending on the target OS) and, in + * that case, may use more precision bits (i.e. 64 bits, for an 80-bit + * total type length); to prevent miscomputations, we define an explicit + * function that modifies the precision in the FPU control word. + * + * set_fpu_cw() sets the precision to the provided value, and returns + * the previously set precision; callers are supposed to restore the + * previous precision on exit. The correct (52-bit) precision is + * configured with the value "2". On unsupported compilers, or on + * targets other than 32-bit x86, or when the native 'double' type is + * not used, the set_fpu_cw() function does nothing at all. + */ +#define set_fpu_cw PQCLEAN_FALCON1024_CLEAN_set_fpu_cw +unsigned set_fpu_cw(unsigned x); + + +/* ==================================================================== */ +/* + * SHAKE256 implementation (shake.c). + * + * API is defined to be easily replaced with the fips202.h API defined + * as part of PQClean. + */ + + + +#define inner_shake256_context shake256incctx +#define inner_shake256_init(sc) shake256_inc_init(sc) +#define inner_shake256_inject(sc, in, len) shake256_inc_absorb(sc, in, len) +#define inner_shake256_flip(sc) shake256_inc_finalize(sc) +#define inner_shake256_extract(sc, out, len) shake256_inc_squeeze(out, len, sc) +#define inner_shake256_ctx_release(sc) shake256_inc_ctx_release(sc) + + +/* ==================================================================== */ +/* + * Encoding/decoding functions (codec.c). + * + * Encoding functions take as parameters an output buffer (out) with + * a given maximum length (max_out_len); returned value is the actual + * number of bytes which have been written. If the output buffer is + * not large enough, then 0 is returned (some bytes may have been + * written to the buffer). If 'out' is NULL, then 'max_out_len' is + * ignored; instead, the function computes and returns the actual + * required output length (in bytes). + * + * Decoding functions take as parameters an input buffer (in) with + * its maximum length (max_in_len); returned value is the actual number + * of bytes that have been read from the buffer. If the provided length + * is too short, then 0 is returned. + * + * Values to encode or decode are vectors of integers, with N = 2^logn + * elements. + * + * Three encoding formats are defined: + * + * - modq: sequence of values modulo 12289, each encoded over exactly + * 14 bits. The encoder and decoder verify that integers are within + * the valid range (0..12288). Values are arrays of uint16. + * + * - trim: sequence of signed integers, a specified number of bits + * each. The number of bits is provided as parameter and includes + * the sign bit. Each integer x must be such that |x| < 2^(bits-1) + * (which means that the -2^(bits-1) value is forbidden); encode and + * decode functions check that property. Values are arrays of + * int16_t or int8_t, corresponding to names 'trim_i16' and + * 'trim_i8', respectively. + * + * - comp: variable-length encoding for signed integers; each integer + * uses a minimum of 9 bits, possibly more. This is normally used + * only for signatures. + * + */ + +size_t PQCLEAN_FALCON1024_CLEAN_modq_encode(void *out, size_t max_out_len, + const uint16_t *x, unsigned logn); +size_t PQCLEAN_FALCON1024_CLEAN_trim_i16_encode(void *out, size_t max_out_len, + const int16_t *x, unsigned logn, unsigned bits); +size_t PQCLEAN_FALCON1024_CLEAN_trim_i8_encode(void *out, size_t max_out_len, + const int8_t *x, unsigned logn, unsigned bits); +size_t PQCLEAN_FALCON1024_CLEAN_comp_encode(void *out, size_t max_out_len, + const int16_t *x, unsigned logn); + +size_t PQCLEAN_FALCON1024_CLEAN_modq_decode(uint16_t *x, unsigned logn, + const void *in, size_t max_in_len); +size_t PQCLEAN_FALCON1024_CLEAN_trim_i16_decode(int16_t *x, unsigned logn, unsigned bits, + const void *in, size_t max_in_len); +size_t PQCLEAN_FALCON1024_CLEAN_trim_i8_decode(int8_t *x, unsigned logn, unsigned bits, + const void *in, size_t max_in_len); +size_t PQCLEAN_FALCON1024_CLEAN_comp_decode(int16_t *x, unsigned logn, + const void *in, size_t max_in_len); + +/* + * Number of bits for key elements, indexed by logn (1 to 10). This + * is at most 8 bits for all degrees, but some degrees may have shorter + * elements. + */ +extern const uint8_t PQCLEAN_FALCON1024_CLEAN_max_fg_bits[]; +extern const uint8_t PQCLEAN_FALCON1024_CLEAN_max_FG_bits[]; + +/* + * Maximum size, in bits, of elements in a signature, indexed by logn + * (1 to 10). The size includes the sign bit. + */ +extern const uint8_t PQCLEAN_FALCON1024_CLEAN_max_sig_bits[]; + +/* ==================================================================== */ +/* + * Support functions used for both signature generation and signature + * verification (common.c). + */ + +/* + * From a SHAKE256 context (must be already flipped), produce a new + * point. This is the non-constant-time version, which may leak enough + * information to serve as a stop condition on a brute force attack on + * the hashed message (provided that the nonce value is known). + */ +void PQCLEAN_FALCON1024_CLEAN_hash_to_point_vartime(inner_shake256_context *sc, + uint16_t *x, unsigned logn); + +/* + * From a SHAKE256 context (must be already flipped), produce a new + * point. The temporary buffer (tmp) must have room for 2*2^logn bytes. + * This function is constant-time but is typically more expensive than + * PQCLEAN_FALCON1024_CLEAN_hash_to_point_vartime(). + * + * tmp[] must have 16-bit alignment. + */ +void PQCLEAN_FALCON1024_CLEAN_hash_to_point_ct(inner_shake256_context *sc, + uint16_t *x, unsigned logn, uint8_t *tmp); + +/* + * Tell whether a given vector (2N coordinates, in two halves) is + * acceptable as a signature. This compares the appropriate norm of the + * vector with the acceptance bound. Returned value is 1 on success + * (vector is short enough to be acceptable), 0 otherwise. + */ +int PQCLEAN_FALCON1024_CLEAN_is_short(const int16_t *s1, const int16_t *s2, unsigned logn); + +/* + * Tell whether a given vector (2N coordinates, in two halves) is + * acceptable as a signature. Instead of the first half s1, this + * function receives the "saturated squared norm" of s1, i.e. the + * sum of the squares of the coordinates of s1 (saturated at 2^32-1 + * if the sum exceeds 2^31-1). + * + * Returned value is 1 on success (vector is short enough to be + * acceptable), 0 otherwise. + */ +int PQCLEAN_FALCON1024_CLEAN_is_short_half(uint32_t sqn, const int16_t *s2, unsigned logn); + +/* ==================================================================== */ +/* + * Signature verification functions (vrfy.c). + */ + +/* + * Convert a public key to NTT + Montgomery format. Conversion is done + * in place. + */ +void PQCLEAN_FALCON1024_CLEAN_to_ntt_monty(uint16_t *h, unsigned logn); + +/* + * Internal signature verification code: + * c0[] contains the hashed nonce+message + * s2[] is the decoded signature + * h[] contains the public key, in NTT + Montgomery format + * logn is the degree log + * tmp[] temporary, must have at least 2*2^logn bytes + * Returned value is 1 on success, 0 on error. + * + * tmp[] must have 16-bit alignment. + */ +int PQCLEAN_FALCON1024_CLEAN_verify_raw(const uint16_t *c0, const int16_t *s2, + const uint16_t *h, unsigned logn, uint8_t *tmp); + +/* + * Compute the public key h[], given the private key elements f[] and + * g[]. This computes h = g/f mod phi mod q, where phi is the polynomial + * modulus. This function returns 1 on success, 0 on error (an error is + * reported if f is not invertible mod phi mod q). + * + * The tmp[] array must have room for at least 2*2^logn elements. + * tmp[] must have 16-bit alignment. + */ +int PQCLEAN_FALCON1024_CLEAN_compute_public(uint16_t *h, + const int8_t *f, const int8_t *g, unsigned logn, uint8_t *tmp); + +/* + * Recompute the fourth private key element. Private key consists in + * four polynomials with small coefficients f, g, F and G, which are + * such that fG - gF = q mod phi; furthermore, f is invertible modulo + * phi and modulo q. This function recomputes G from f, g and F. + * + * The tmp[] array must have room for at least 4*2^logn bytes. + * + * Returned value is 1 in success, 0 on error (f not invertible). + * tmp[] must have 16-bit alignment. + */ +int PQCLEAN_FALCON1024_CLEAN_complete_private(int8_t *G, + const int8_t *f, const int8_t *g, const int8_t *F, + unsigned logn, uint8_t *tmp); + +/* + * Test whether a given polynomial is invertible modulo phi and q. + * Polynomial coefficients are small integers. + * + * tmp[] must have 16-bit alignment. + */ +int PQCLEAN_FALCON1024_CLEAN_is_invertible( + const int16_t *s2, unsigned logn, uint8_t *tmp); + +/* + * Count the number of elements of value zero in the NTT representation + * of the given polynomial: this is the number of primitive 2n-th roots + * of unity (modulo q = 12289) that are roots of the provided polynomial + * (taken modulo q). + * + * tmp[] must have 16-bit alignment. + */ +int PQCLEAN_FALCON1024_CLEAN_count_nttzero(const int16_t *sig, unsigned logn, uint8_t *tmp); + +/* + * Internal signature verification with public key recovery: + * h[] receives the public key (NOT in NTT/Montgomery format) + * c0[] contains the hashed nonce+message + * s1[] is the first signature half + * s2[] is the second signature half + * logn is the degree log + * tmp[] temporary, must have at least 2*2^logn bytes + * Returned value is 1 on success, 0 on error. Success is returned if + * the signature is a short enough vector; in that case, the public + * key has been written to h[]. However, the caller must still + * verify that h[] is the correct value (e.g. with regards to a known + * hash of the public key). + * + * h[] may not overlap with any of the other arrays. + * + * tmp[] must have 16-bit alignment. + */ +int PQCLEAN_FALCON1024_CLEAN_verify_recover(uint16_t *h, + const uint16_t *c0, const int16_t *s1, const int16_t *s2, + unsigned logn, uint8_t *tmp); + +/* ==================================================================== */ +/* + * Implementation of floating-point real numbers (fpr.h, fpr.c). + */ + +/* + * Real numbers are implemented by an extra header file, included below. + * This is meant to support pluggable implementations. The default + * implementation relies on the C type 'double'. + * + * The included file must define the following types, functions and + * constants: + * + * fpr + * type for a real number + * + * fpr fpr_of(int64_t i) + * cast an integer into a real number; source must be in the + * -(2^63-1)..+(2^63-1) range + * + * fpr fpr_scaled(int64_t i, int sc) + * compute i*2^sc as a real number; source 'i' must be in the + * -(2^63-1)..+(2^63-1) range + * + * fpr fpr_ldexp(fpr x, int e) + * compute x*2^e + * + * int64_t fpr_rint(fpr x) + * round x to the nearest integer; x must be in the -(2^63-1) + * to +(2^63-1) range + * + * int64_t fpr_trunc(fpr x) + * round to an integer; this rounds towards zero; value must + * be in the -(2^63-1) to +(2^63-1) range + * + * fpr fpr_add(fpr x, fpr y) + * compute x + y + * + * fpr fpr_sub(fpr x, fpr y) + * compute x - y + * + * fpr fpr_neg(fpr x) + * compute -x + * + * fpr fpr_half(fpr x) + * compute x/2 + * + * fpr fpr_double(fpr x) + * compute x*2 + * + * fpr fpr_mul(fpr x, fpr y) + * compute x * y + * + * fpr fpr_sqr(fpr x) + * compute x * x + * + * fpr fpr_inv(fpr x) + * compute 1/x + * + * fpr fpr_div(fpr x, fpr y) + * compute x/y + * + * fpr fpr_sqrt(fpr x) + * compute the square root of x + * + * int fpr_lt(fpr x, fpr y) + * return 1 if x < y, 0 otherwise + * + * uint64_t fpr_expm_p63(fpr x) + * return exp(x), assuming that 0 <= x < log(2). Returned value + * is scaled to 63 bits (i.e. it really returns 2^63*exp(-x), + * rounded to the nearest integer). Computation should have a + * precision of at least 45 bits. + * + * const fpr fpr_gm_tab[] + * array of constants for FFT / iFFT + * + * const fpr fpr_p2_tab[] + * precomputed powers of 2 (by index, 0 to 10) + * + * Constants of type 'fpr': + * + * fpr fpr_q 12289 + * fpr fpr_inverse_of_q 1/12289 + * fpr fpr_inv_2sqrsigma0 1/(2*(1.8205^2)) + * fpr fpr_inv_sigma 1/(1.55*sqrt(12289)) + * fpr fpr_sigma_min_9 1.291500756233514568549480827642 + * fpr fpr_sigma_min_10 1.311734375905083682667395805765 + * fpr fpr_log2 log(2) + * fpr fpr_inv_log2 1/log(2) + * fpr fpr_bnorm_max 16822.4121 + * fpr fpr_zero 0 + * fpr fpr_one 1 + * fpr fpr_two 2 + * fpr fpr_onehalf 0.5 + * fpr fpr_ptwo31 2^31 + * fpr fpr_ptwo31m1 2^31-1 + * fpr fpr_mtwo31m1 -(2^31-1) + * fpr fpr_ptwo63m1 2^63-1 + * fpr fpr_mtwo63m1 -(2^63-1) + * fpr fpr_ptwo63 2^63 + */ + +/* ==================================================================== */ +/* + * RNG (rng.c). + * + * A PRNG based on ChaCha20 is implemented; it is seeded from a SHAKE256 + * context (flipped) and is used for bulk pseudorandom generation. + * A system-dependent seed generator is also provided. + */ + +/* + * Obtain a random seed from the system RNG. + * + * Returned value is 1 on success, 0 on error. + */ +int PQCLEAN_FALCON1024_CLEAN_get_seed(void *seed, size_t seed_len); + +/* + * Structure for a PRNG. This includes a large buffer so that values + * get generated in advance. The 'state' is used to keep the current + * PRNG algorithm state (contents depend on the selected algorithm). + * + * The unions with 'dummy_u64' are there to ensure proper alignment for + * 64-bit direct access. + */ +typedef struct { + union { + uint8_t d[512]; /* MUST be 512, exactly */ + uint64_t dummy_u64; + } buf; + size_t ptr; + union { + uint8_t d[256]; + uint64_t dummy_u64; + } state; + int type; +} prng; + +/* + * Instantiate a PRNG. That PRNG will feed over the provided SHAKE256 + * context (in "flipped" state) to obtain its initial state. + */ +void PQCLEAN_FALCON1024_CLEAN_prng_init(prng *p, inner_shake256_context *src); + +/* + * Refill the PRNG buffer. This is normally invoked automatically, and + * is declared here only so that prng_get_u64() may be inlined. + */ +void PQCLEAN_FALCON1024_CLEAN_prng_refill(prng *p); + +/* + * Get some bytes from a PRNG. + */ +void PQCLEAN_FALCON1024_CLEAN_prng_get_bytes(prng *p, void *dst, size_t len); + +/* + * Get a 64-bit random value from a PRNG. + */ +#define prng_get_u64 PQCLEAN_FALCON1024_CLEAN_prng_get_u64 +uint64_t prng_get_u64(prng *p); + +/* + * Get an 8-bit random value from a PRNG. + */ +#define prng_get_u8 PQCLEAN_FALCON1024_CLEAN_prng_get_u8 +unsigned prng_get_u8(prng *p); + +/* ==================================================================== */ +/* + * FFT (falcon-fft.c). + * + * A real polynomial is represented as an array of N 'fpr' elements. + * The FFT representation of a real polynomial contains N/2 complex + * elements; each is stored as two real numbers, for the real and + * imaginary parts, respectively. See falcon-fft.c for details on the + * internal representation. + */ + +/* + * Compute FFT in-place: the source array should contain a real + * polynomial (N coefficients); its storage area is reused to store + * the FFT representation of that polynomial (N/2 complex numbers). + * + * 'logn' MUST lie between 1 and 10 (inclusive). + */ +void PQCLEAN_FALCON1024_CLEAN_FFT(fpr *f, unsigned logn); + +/* + * Compute the inverse FFT in-place: the source array should contain the + * FFT representation of a real polynomial (N/2 elements); the resulting + * real polynomial (N coefficients of type 'fpr') is written over the + * array. + * + * 'logn' MUST lie between 1 and 10 (inclusive). + */ +void PQCLEAN_FALCON1024_CLEAN_iFFT(fpr *f, unsigned logn); + +/* + * Add polynomial b to polynomial a. a and b MUST NOT overlap. This + * function works in both normal and FFT representations. + */ +void PQCLEAN_FALCON1024_CLEAN_poly_add(fpr *a, const fpr *b, unsigned logn); + +/* + * Subtract polynomial b from polynomial a. a and b MUST NOT overlap. This + * function works in both normal and FFT representations. + */ +void PQCLEAN_FALCON1024_CLEAN_poly_sub(fpr *a, const fpr *b, unsigned logn); + +/* + * Negate polynomial a. This function works in both normal and FFT + * representations. + */ +void PQCLEAN_FALCON1024_CLEAN_poly_neg(fpr *a, unsigned logn); + +/* + * Compute adjoint of polynomial a. This function works only in FFT + * representation. + */ +void PQCLEAN_FALCON1024_CLEAN_poly_adj_fft(fpr *a, unsigned logn); + +/* + * Multiply polynomial a with polynomial b. a and b MUST NOT overlap. + * This function works only in FFT representation. + */ +void PQCLEAN_FALCON1024_CLEAN_poly_mul_fft(fpr *a, const fpr *b, unsigned logn); + +/* + * Multiply polynomial a with the adjoint of polynomial b. a and b MUST NOT + * overlap. This function works only in FFT representation. + */ +void PQCLEAN_FALCON1024_CLEAN_poly_muladj_fft(fpr *a, const fpr *b, unsigned logn); + +/* + * Multiply polynomial with its own adjoint. This function works only in FFT + * representation. + */ +void PQCLEAN_FALCON1024_CLEAN_poly_mulselfadj_fft(fpr *a, unsigned logn); + +/* + * Multiply polynomial with a real constant. This function works in both + * normal and FFT representations. + */ +void PQCLEAN_FALCON1024_CLEAN_poly_mulconst(fpr *a, fpr x, unsigned logn); + +/* + * Divide polynomial a by polynomial b, modulo X^N+1 (FFT representation). + * a and b MUST NOT overlap. + */ +void PQCLEAN_FALCON1024_CLEAN_poly_div_fft(fpr *a, const fpr *b, unsigned logn); + +/* + * Given f and g (in FFT representation), compute 1/(f*adj(f)+g*adj(g)) + * (also in FFT representation). Since the result is auto-adjoint, all its + * coordinates in FFT representation are real; as such, only the first N/2 + * values of d[] are filled (the imaginary parts are skipped). + * + * Array d MUST NOT overlap with either a or b. + */ +void PQCLEAN_FALCON1024_CLEAN_poly_invnorm2_fft(fpr *d, + const fpr *a, const fpr *b, unsigned logn); + +/* + * Given F, G, f and g (in FFT representation), compute F*adj(f)+G*adj(g) + * (also in FFT representation). Destination d MUST NOT overlap with + * any of the source arrays. + */ +void PQCLEAN_FALCON1024_CLEAN_poly_add_muladj_fft(fpr *d, + const fpr *F, const fpr *G, + const fpr *f, const fpr *g, unsigned logn); + +/* + * Multiply polynomial a by polynomial b, where b is autoadjoint. Both + * a and b are in FFT representation. Since b is autoadjoint, all its + * FFT coefficients are real, and the array b contains only N/2 elements. + * a and b MUST NOT overlap. + */ +void PQCLEAN_FALCON1024_CLEAN_poly_mul_autoadj_fft(fpr *a, + const fpr *b, unsigned logn); + +/* + * Divide polynomial a by polynomial b, where b is autoadjoint. Both + * a and b are in FFT representation. Since b is autoadjoint, all its + * FFT coefficients are real, and the array b contains only N/2 elements. + * a and b MUST NOT overlap. + */ +void PQCLEAN_FALCON1024_CLEAN_poly_div_autoadj_fft(fpr *a, + const fpr *b, unsigned logn); + +/* + * Perform an LDL decomposition of an auto-adjoint matrix G, in FFT + * representation. On input, g00, g01 and g11 are provided (where the + * matrix G = [[g00, g01], [adj(g01), g11]]). On output, the d00, l10 + * and d11 values are written in g00, g01 and g11, respectively + * (with D = [[d00, 0], [0, d11]] and L = [[1, 0], [l10, 1]]). + * (In fact, d00 = g00, so the g00 operand is left unmodified.) + */ +void PQCLEAN_FALCON1024_CLEAN_poly_LDL_fft(const fpr *g00, + fpr *g01, fpr *g11, unsigned logn); + +/* + * Perform an LDL decomposition of an auto-adjoint matrix G, in FFT + * representation. This is identical to poly_LDL_fft() except that + * g00, g01 and g11 are unmodified; the outputs d11 and l10 are written + * in two other separate buffers provided as extra parameters. + */ +void PQCLEAN_FALCON1024_CLEAN_poly_LDLmv_fft(fpr *d11, fpr *l10, + const fpr *g00, const fpr *g01, + const fpr *g11, unsigned logn); + +/* + * Apply "split" operation on a polynomial in FFT representation: + * f = f0(x^2) + x*f1(x^2), for half-size polynomials f0 and f1 + * (polynomials modulo X^(N/2)+1). f0, f1 and f MUST NOT overlap. + */ +void PQCLEAN_FALCON1024_CLEAN_poly_split_fft(fpr *f0, fpr *f1, + const fpr *f, unsigned logn); + +/* + * Apply "merge" operation on two polynomials in FFT representation: + * given f0 and f1, polynomials moduo X^(N/2)+1, this function computes + * f = f0(x^2) + x*f1(x^2), in FFT representation modulo X^N+1. + * f MUST NOT overlap with either f0 or f1. + */ +void PQCLEAN_FALCON1024_CLEAN_poly_merge_fft(fpr *f, + const fpr *f0, const fpr *f1, unsigned logn); + +/* ==================================================================== */ +/* + * Key pair generation. + */ + +/* + * Required sizes of the temporary buffer (in bytes). + * + * This size is 28*2^logn bytes, except for degrees 2 and 4 (logn = 1 + * or 2) where it is slightly greater. + */ +#define FALCON_KEYGEN_TEMP_1 136 +#define FALCON_KEYGEN_TEMP_2 272 +#define FALCON_KEYGEN_TEMP_3 224 +#define FALCON_KEYGEN_TEMP_4 448 +#define FALCON_KEYGEN_TEMP_5 896 +#define FALCON_KEYGEN_TEMP_6 1792 +#define FALCON_KEYGEN_TEMP_7 3584 +#define FALCON_KEYGEN_TEMP_8 7168 +#define FALCON_KEYGEN_TEMP_9 14336 +#define FALCON_KEYGEN_TEMP_10 28672 + +/* + * Generate a new key pair. Randomness is extracted from the provided + * SHAKE256 context, which must have already been seeded and flipped. + * The tmp[] array must have suitable size (see FALCON_KEYGEN_TEMP_* + * macros) and be aligned for the uint32_t, uint64_t and fpr types. + * + * The private key elements are written in f, g, F and G, and the + * public key is written in h. Either or both of G and h may be NULL, + * in which case the corresponding element is not returned (they can + * be recomputed from f, g and F). + * + * tmp[] must have 64-bit alignment. + * This function uses floating-point rounding (see set_fpu_cw()). + */ +void PQCLEAN_FALCON1024_CLEAN_keygen(inner_shake256_context *rng, + int8_t *f, int8_t *g, int8_t *F, int8_t *G, uint16_t *h, + unsigned logn, uint8_t *tmp); + +/* ==================================================================== */ +/* + * Signature generation. + */ + +/* + * Expand a private key into the B0 matrix in FFT representation and + * the LDL tree. All the values are written in 'expanded_key', for + * a total of (8*logn+40)*2^logn bytes. + * + * The tmp[] array must have room for at least 48*2^logn bytes. + * + * tmp[] must have 64-bit alignment. + * This function uses floating-point rounding (see set_fpu_cw()). + */ +void PQCLEAN_FALCON1024_CLEAN_expand_privkey(fpr *expanded_key, + const int8_t *f, const int8_t *g, const int8_t *F, const int8_t *G, + unsigned logn, uint8_t *tmp); + +/* + * Compute a signature over the provided hashed message (hm); the + * signature value is one short vector. This function uses an + * expanded key (as generated by PQCLEAN_FALCON1024_CLEAN_expand_privkey()). + * + * The sig[] and hm[] buffers may overlap. + * + * On successful output, the start of the tmp[] buffer contains the s1 + * vector (as int16_t elements). + * + * The minimal size (in bytes) of tmp[] is 48*2^logn bytes. + * + * tmp[] must have 64-bit alignment. + * This function uses floating-point rounding (see set_fpu_cw()). + */ +void PQCLEAN_FALCON1024_CLEAN_sign_tree(int16_t *sig, inner_shake256_context *rng, + const fpr *expanded_key, + const uint16_t *hm, unsigned logn, uint8_t *tmp); + +/* + * Compute a signature over the provided hashed message (hm); the + * signature value is one short vector. This function uses a raw + * key and dynamically recompute the B0 matrix and LDL tree; this + * saves RAM since there is no needed for an expanded key, but + * increases the signature cost. + * + * The sig[] and hm[] buffers may overlap. + * + * On successful output, the start of the tmp[] buffer contains the s1 + * vector (as int16_t elements). + * + * The minimal size (in bytes) of tmp[] is 72*2^logn bytes. + * + * tmp[] must have 64-bit alignment. + * This function uses floating-point rounding (see set_fpu_cw()). + */ +void PQCLEAN_FALCON1024_CLEAN_sign_dyn(int16_t *sig, inner_shake256_context *rng, + const int8_t *f, const int8_t *g, + const int8_t *F, const int8_t *G, + const uint16_t *hm, unsigned logn, uint8_t *tmp); + +/* + * Internal sampler engine. Exported for tests. + * + * sampler_context wraps around a source of random numbers (PRNG) and + * the sigma_min value (nominally dependent on the degree). + * + * sampler() takes as parameters: + * ctx pointer to the sampler_context structure + * mu center for the distribution + * isigma inverse of the distribution standard deviation + * It returns an integer sampled along the Gaussian distribution centered + * on mu and of standard deviation sigma = 1/isigma. + * + * gaussian0_sampler() takes as parameter a pointer to a PRNG, and + * returns an integer sampled along a half-Gaussian with standard + * deviation sigma0 = 1.8205 (center is 0, returned value is + * nonnegative). + */ + +typedef struct { + prng p; + fpr sigma_min; +} sampler_context; + +int PQCLEAN_FALCON1024_CLEAN_sampler(void *ctx, fpr mu, fpr isigma); + +int PQCLEAN_FALCON1024_CLEAN_gaussian0_sampler(prng *p); + +/* ==================================================================== */ + +#endif diff --git a/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/keygen.c b/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/keygen.c new file mode 100644 index 000000000..2d47412d0 --- /dev/null +++ b/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/keygen.c @@ -0,0 +1,4231 @@ +#include "inner.h" + +/* + * Falcon key pair generation. + * + * ==========================(LICENSE BEGIN)============================ + * + * Copyright (c) 2017-2019 Falcon Project + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the + * "Software"), to deal in the Software without restriction, including + * without limitation the rights to use, copy, modify, merge, publish, + * distribute, sublicense, and/or sell copies of the Software, and to + * permit persons to whom the Software is furnished to do so, subject to + * the following conditions: + * + * The above copyright notice and this permission notice shall be + * included in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, + * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF + * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. + * IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY + * CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, + * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE + * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. + * + * ===========================(LICENSE END)============================= + * + * @author Thomas Pornin <thomas.pornin@nccgroup.com> + */ + + +#define MKN(logn) ((size_t)1 << (logn)) + +/* ==================================================================== */ +/* + * Modular arithmetics. + * + * We implement a few functions for computing modulo a small integer p. + * + * All functions require that 2^30 < p < 2^31. Moreover, operands must + * be in the 0..p-1 range. + * + * Modular addition and subtraction work for all such p. + * + * Montgomery multiplication requires that p is odd, and must be provided + * with an additional value p0i = -1/p mod 2^31. See below for some basics + * on Montgomery multiplication. + * + * Division computes an inverse modulo p by an exponentiation (with + * exponent p-2): this works only if p is prime. Multiplication + * requirements also apply, i.e. p must be odd and p0i must be provided. + * + * The NTT and inverse NTT need all of the above, and also that + * p = 1 mod 2048. + * + * ----------------------------------------------------------------------- + * + * We use Montgomery representation with 31-bit values: + * + * Let R = 2^31 mod p. When 2^30 < p < 2^31, R = 2^31 - p. + * Montgomery representation of an integer x modulo p is x*R mod p. + * + * Montgomery multiplication computes (x*y)/R mod p for + * operands x and y. Therefore: + * + * - if operands are x*R and y*R (Montgomery representations of x and + * y), then Montgomery multiplication computes (x*R*y*R)/R = (x*y)*R + * mod p, which is the Montgomery representation of the product x*y; + * + * - if operands are x*R and y (or x and y*R), then Montgomery + * multiplication returns x*y mod p: mixed-representation + * multiplications yield results in normal representation. + * + * To convert to Montgomery representation, we multiply by R, which is done + * by Montgomery-multiplying by R^2. Stand-alone conversion back from + * Montgomery representation is Montgomery-multiplication by 1. + */ + +/* + * Precomputed small primes. Each element contains the following: + * + * p The prime itself. + * + * g A primitive root of phi = X^N+1 (in field Z_p). + * + * s The inverse of the product of all previous primes in the array, + * computed modulo p and in Montgomery representation. + * + * All primes are such that p = 1 mod 2048, and are lower than 2^31. They + * are listed in decreasing order. + */ + +typedef struct { + uint32_t p; + uint32_t g; + uint32_t s; +} small_prime; + +static const small_prime PRIMES[] = { + { 2147473409, 383167813, 10239 }, + { 2147389441, 211808905, 471403745 }, + { 2147387393, 37672282, 1329335065 }, + { 2147377153, 1977035326, 968223422 }, + { 2147358721, 1067163706, 132460015 }, + { 2147352577, 1606082042, 598693809 }, + { 2147346433, 2033915641, 1056257184 }, + { 2147338241, 1653770625, 421286710 }, + { 2147309569, 631200819, 1111201074 }, + { 2147297281, 2038364663, 1042003613 }, + { 2147295233, 1962540515, 19440033 }, + { 2147239937, 2100082663, 353296760 }, + { 2147235841, 1991153006, 1703918027 }, + { 2147217409, 516405114, 1258919613 }, + { 2147205121, 409347988, 1089726929 }, + { 2147196929, 927788991, 1946238668 }, + { 2147178497, 1136922411, 1347028164 }, + { 2147100673, 868626236, 701164723 }, + { 2147082241, 1897279176, 617820870 }, + { 2147074049, 1888819123, 158382189 }, + { 2147051521, 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273612548 }, + { 2136850433, 111208983, 1181257116 }, + { 2136809473, 1627275942, 1680317971 }, + { 2136764417, 1574888217, 14011331 }, + { 2136741889, 14011055, 1129154251 }, + { 2136727553, 35862563, 1838555253 }, + { 2136721409, 310235666, 1363928244 }, + { 2136698881, 1612429202, 1560383828 }, + { 2136649729, 1138540131, 800014364 }, + { 2136606721, 602323503, 1433096652 }, + { 2136563713, 182209265, 1919611038 }, + { 2136555521, 324156477, 165591039 }, + { 2136549377, 195513113, 217165345 }, + { 2136526849, 1050768046, 939647887 }, + { 2136508417, 1886286237, 1619926572 }, + { 2136477697, 609647664, 35065157 }, + { 2136471553, 679352216, 1452259468 }, + { 2136457217, 128630031, 824816521 }, + { 2136422401, 19787464, 1526049830 }, + { 2136420353, 698316836, 1530623527 }, + { 2136371201, 1651862373, 1804812805 }, + { 2136334337, 326596005, 336977082 }, + { 2136322049, 63253370, 1904972151 }, + { 2136297473, 312176076, 172182411 }, + { 2136248321, 381261841, 369032670 }, + { 2136242177, 358688773, 1640007994 }, + { 2136229889, 512677188, 75585225 }, + { 2136219649, 2095003250, 1970086149 }, + { 2136207361, 1909650722, 537760675 }, + { 2136176641, 1334616195, 1533487619 }, + { 2136158209, 2096285632, 1793285210 }, + { 2136143873, 1897347517, 293843959 }, + { 2136133633, 923586222, 1022655978 }, + { 2136096769, 1464868191, 1515074410 }, + { 2136094721, 2020679520, 2061636104 }, + { 2136076289, 290798503, 1814726809 }, + { 2136041473, 156415894, 1250757633 }, + { 2135996417, 297459940, 1132158924 }, + { 2135955457, 538755304, 1688831340 }, + { 0, 0, 0 } +}; + +/* + * Reduce a small signed integer modulo a small prime. The source + * value x MUST be such that -p < x < p. + */ +static inline uint32_t +modp_set(int32_t x, uint32_t p) { + uint32_t w; + + w = (uint32_t)x; + w += p & -(w >> 31); + return w; +} + +/* + * Normalize a modular integer around 0. + */ +static inline int32_t +modp_norm(uint32_t x, uint32_t p) { + return (int32_t)(x - (p & (((x - ((p + 1) >> 1)) >> 31) - 1))); +} + +/* + * Compute -1/p mod 2^31. This works for all odd integers p that fit + * on 31 bits. + */ +static uint32_t +modp_ninv31(uint32_t p) { + uint32_t y; + + y = 2 - p; + y *= 2 - p * y; + y *= 2 - p * y; + y *= 2 - p * y; + y *= 2 - p * y; + return (uint32_t)0x7FFFFFFF & -y; +} + +/* + * Compute R = 2^31 mod p. + */ +static inline uint32_t +modp_R(uint32_t p) { + /* + * Since 2^30 < p < 2^31, we know that 2^31 mod p is simply + * 2^31 - p. + */ + return ((uint32_t)1 << 31) - p; +} + +/* + * Addition modulo p. + */ +static inline uint32_t +modp_add(uint32_t a, uint32_t b, uint32_t p) { + uint32_t d; + + d = a + b - p; + d += p & -(d >> 31); + return d; +} + +/* + * Subtraction modulo p. + */ +static inline uint32_t +modp_sub(uint32_t a, uint32_t b, uint32_t p) { + uint32_t d; + + d = a - b; + d += p & -(d >> 31); + return d; +} + +/* + * Halving modulo p. + */ +/* unused +static inline uint32_t +modp_half(uint32_t a, uint32_t p) +{ + a += p & -(a & 1); + return a >> 1; +} +*/ + +/* + * Montgomery multiplication modulo p. The 'p0i' value is -1/p mod 2^31. + * It is required that p is an odd integer. + */ +static inline uint32_t +modp_montymul(uint32_t a, uint32_t b, uint32_t p, uint32_t p0i) { + uint64_t z, w; + uint32_t d; + + z = (uint64_t)a * (uint64_t)b; + w = ((z * p0i) & (uint64_t)0x7FFFFFFF) * p; + d = (uint32_t)((z + w) >> 31) - p; + d += p & -(d >> 31); + return d; +} + +/* + * Compute R2 = 2^62 mod p. + */ +static uint32_t +modp_R2(uint32_t p, uint32_t p0i) { + uint32_t z; + + /* + * Compute z = 2^31 mod p (this is the value 1 in Montgomery + * representation), then double it with an addition. + */ + z = modp_R(p); + z = modp_add(z, z, p); + + /* + * Square it five times to obtain 2^32 in Montgomery representation + * (i.e. 2^63 mod p). + */ + z = modp_montymul(z, z, p, p0i); + z = modp_montymul(z, z, p, p0i); + z = modp_montymul(z, z, p, p0i); + z = modp_montymul(z, z, p, p0i); + z = modp_montymul(z, z, p, p0i); + + /* + * Halve the value mod p to get 2^62. + */ + z = (z + (p & -(z & 1))) >> 1; + return z; +} + +/* + * Compute 2^(31*x) modulo p. This works for integers x up to 2^11. + * p must be prime such that 2^30 < p < 2^31; p0i must be equal to + * -1/p mod 2^31; R2 must be equal to 2^62 mod p. + */ +static inline uint32_t +modp_Rx(unsigned x, uint32_t p, uint32_t p0i, uint32_t R2) { + int i; + uint32_t r, z; + + /* + * 2^(31*x) = (2^31)*(2^(31*(x-1))); i.e. we want the Montgomery + * representation of (2^31)^e mod p, where e = x-1. + * R2 is 2^31 in Montgomery representation. + */ + x --; + r = R2; + z = modp_R(p); + for (i = 0; (1U << i) <= x; i ++) { + if ((x & (1U << i)) != 0) { + z = modp_montymul(z, r, p, p0i); + } + r = modp_montymul(r, r, p, p0i); + } + return z; +} + +/* + * Division modulo p. If the divisor (b) is 0, then 0 is returned. + * This function computes proper results only when p is prime. + * Parameters: + * a dividend + * b divisor + * p odd prime modulus + * p0i -1/p mod 2^31 + * R 2^31 mod R + */ +static uint32_t +modp_div(uint32_t a, uint32_t b, uint32_t p, uint32_t p0i, uint32_t R) { + uint32_t z, e; + int i; + + e = p - 2; + z = R; + for (i = 30; i >= 0; i --) { + uint32_t z2; + + z = modp_montymul(z, z, p, p0i); + z2 = modp_montymul(z, b, p, p0i); + z ^= (z ^ z2) & -(uint32_t)((e >> i) & 1); + } + + /* + * The loop above just assumed that b was in Montgomery + * representation, i.e. really contained b*R; under that + * assumption, it returns 1/b in Montgomery representation, + * which is R/b. But we gave it b in normal representation, + * so the loop really returned R/(b/R) = R^2/b. + * + * We want a/b, so we need one Montgomery multiplication with a, + * which also remove one of the R factors, and another such + * multiplication to remove the second R factor. + */ + z = modp_montymul(z, 1, p, p0i); + return modp_montymul(a, z, p, p0i); +} + +/* + * Bit-reversal index table. + */ +static const uint16_t REV10[] = { + 0, 512, 256, 768, 128, 640, 384, 896, 64, 576, 320, 832, + 192, 704, 448, 960, 32, 544, 288, 800, 160, 672, 416, 928, + 96, 608, 352, 864, 224, 736, 480, 992, 16, 528, 272, 784, + 144, 656, 400, 912, 80, 592, 336, 848, 208, 720, 464, 976, + 48, 560, 304, 816, 176, 688, 432, 944, 112, 624, 368, 880, + 240, 752, 496, 1008, 8, 520, 264, 776, 136, 648, 392, 904, + 72, 584, 328, 840, 200, 712, 456, 968, 40, 552, 296, 808, + 168, 680, 424, 936, 104, 616, 360, 872, 232, 744, 488, 1000, + 24, 536, 280, 792, 152, 664, 408, 920, 88, 600, 344, 856, + 216, 728, 472, 984, 56, 568, 312, 824, 184, 696, 440, 952, + 120, 632, 376, 888, 248, 760, 504, 1016, 4, 516, 260, 772, + 132, 644, 388, 900, 68, 580, 324, 836, 196, 708, 452, 964, + 36, 548, 292, 804, 164, 676, 420, 932, 100, 612, 356, 868, + 228, 740, 484, 996, 20, 532, 276, 788, 148, 660, 404, 916, + 84, 596, 340, 852, 212, 724, 468, 980, 52, 564, 308, 820, + 180, 692, 436, 948, 116, 628, 372, 884, 244, 756, 500, 1012, + 12, 524, 268, 780, 140, 652, 396, 908, 76, 588, 332, 844, + 204, 716, 460, 972, 44, 556, 300, 812, 172, 684, 428, 940, + 108, 620, 364, 876, 236, 748, 492, 1004, 28, 540, 284, 796, + 156, 668, 412, 924, 92, 604, 348, 860, 220, 732, 476, 988, + 60, 572, 316, 828, 188, 700, 444, 956, 124, 636, 380, 892, + 252, 764, 508, 1020, 2, 514, 258, 770, 130, 642, 386, 898, + 66, 578, 322, 834, 194, 706, 450, 962, 34, 546, 290, 802, + 162, 674, 418, 930, 98, 610, 354, 866, 226, 738, 482, 994, + 18, 530, 274, 786, 146, 658, 402, 914, 82, 594, 338, 850, + 210, 722, 466, 978, 50, 562, 306, 818, 178, 690, 434, 946, + 114, 626, 370, 882, 242, 754, 498, 1010, 10, 522, 266, 778, + 138, 650, 394, 906, 74, 586, 330, 842, 202, 714, 458, 970, + 42, 554, 298, 810, 170, 682, 426, 938, 106, 618, 362, 874, + 234, 746, 490, 1002, 26, 538, 282, 794, 154, 666, 410, 922, + 90, 602, 346, 858, 218, 730, 474, 986, 58, 570, 314, 826, + 186, 698, 442, 954, 122, 634, 378, 890, 250, 762, 506, 1018, + 6, 518, 262, 774, 134, 646, 390, 902, 70, 582, 326, 838, + 198, 710, 454, 966, 38, 550, 294, 806, 166, 678, 422, 934, + 102, 614, 358, 870, 230, 742, 486, 998, 22, 534, 278, 790, + 150, 662, 406, 918, 86, 598, 342, 854, 214, 726, 470, 982, + 54, 566, 310, 822, 182, 694, 438, 950, 118, 630, 374, 886, + 246, 758, 502, 1014, 14, 526, 270, 782, 142, 654, 398, 910, + 78, 590, 334, 846, 206, 718, 462, 974, 46, 558, 302, 814, + 174, 686, 430, 942, 110, 622, 366, 878, 238, 750, 494, 1006, + 30, 542, 286, 798, 158, 670, 414, 926, 94, 606, 350, 862, + 222, 734, 478, 990, 62, 574, 318, 830, 190, 702, 446, 958, + 126, 638, 382, 894, 254, 766, 510, 1022, 1, 513, 257, 769, + 129, 641, 385, 897, 65, 577, 321, 833, 193, 705, 449, 961, + 33, 545, 289, 801, 161, 673, 417, 929, 97, 609, 353, 865, + 225, 737, 481, 993, 17, 529, 273, 785, 145, 657, 401, 913, + 81, 593, 337, 849, 209, 721, 465, 977, 49, 561, 305, 817, + 177, 689, 433, 945, 113, 625, 369, 881, 241, 753, 497, 1009, + 9, 521, 265, 777, 137, 649, 393, 905, 73, 585, 329, 841, + 201, 713, 457, 969, 41, 553, 297, 809, 169, 681, 425, 937, + 105, 617, 361, 873, 233, 745, 489, 1001, 25, 537, 281, 793, + 153, 665, 409, 921, 89, 601, 345, 857, 217, 729, 473, 985, + 57, 569, 313, 825, 185, 697, 441, 953, 121, 633, 377, 889, + 249, 761, 505, 1017, 5, 517, 261, 773, 133, 645, 389, 901, + 69, 581, 325, 837, 197, 709, 453, 965, 37, 549, 293, 805, + 165, 677, 421, 933, 101, 613, 357, 869, 229, 741, 485, 997, + 21, 533, 277, 789, 149, 661, 405, 917, 85, 597, 341, 853, + 213, 725, 469, 981, 53, 565, 309, 821, 181, 693, 437, 949, + 117, 629, 373, 885, 245, 757, 501, 1013, 13, 525, 269, 781, + 141, 653, 397, 909, 77, 589, 333, 845, 205, 717, 461, 973, + 45, 557, 301, 813, 173, 685, 429, 941, 109, 621, 365, 877, + 237, 749, 493, 1005, 29, 541, 285, 797, 157, 669, 413, 925, + 93, 605, 349, 861, 221, 733, 477, 989, 61, 573, 317, 829, + 189, 701, 445, 957, 125, 637, 381, 893, 253, 765, 509, 1021, + 3, 515, 259, 771, 131, 643, 387, 899, 67, 579, 323, 835, + 195, 707, 451, 963, 35, 547, 291, 803, 163, 675, 419, 931, + 99, 611, 355, 867, 227, 739, 483, 995, 19, 531, 275, 787, + 147, 659, 403, 915, 83, 595, 339, 851, 211, 723, 467, 979, + 51, 563, 307, 819, 179, 691, 435, 947, 115, 627, 371, 883, + 243, 755, 499, 1011, 11, 523, 267, 779, 139, 651, 395, 907, + 75, 587, 331, 843, 203, 715, 459, 971, 43, 555, 299, 811, + 171, 683, 427, 939, 107, 619, 363, 875, 235, 747, 491, 1003, + 27, 539, 283, 795, 155, 667, 411, 923, 91, 603, 347, 859, + 219, 731, 475, 987, 59, 571, 315, 827, 187, 699, 443, 955, + 123, 635, 379, 891, 251, 763, 507, 1019, 7, 519, 263, 775, + 135, 647, 391, 903, 71, 583, 327, 839, 199, 711, 455, 967, + 39, 551, 295, 807, 167, 679, 423, 935, 103, 615, 359, 871, + 231, 743, 487, 999, 23, 535, 279, 791, 151, 663, 407, 919, + 87, 599, 343, 855, 215, 727, 471, 983, 55, 567, 311, 823, + 183, 695, 439, 951, 119, 631, 375, 887, 247, 759, 503, 1015, + 15, 527, 271, 783, 143, 655, 399, 911, 79, 591, 335, 847, + 207, 719, 463, 975, 47, 559, 303, 815, 175, 687, 431, 943, + 111, 623, 367, 879, 239, 751, 495, 1007, 31, 543, 287, 799, + 159, 671, 415, 927, 95, 607, 351, 863, 223, 735, 479, 991, + 63, 575, 319, 831, 191, 703, 447, 959, 127, 639, 383, 895, + 255, 767, 511, 1023 +}; + +/* + * Compute the roots for NTT and inverse NTT (binary case). Input + * parameter g is a primitive 2048-th root of 1 modulo p (i.e. g^1024 = + * -1 mod p). This fills gm[] and igm[] with powers of g and 1/g: + * gm[rev(i)] = g^i mod p + * igm[rev(i)] = (1/g)^i mod p + * where rev() is the "bit reversal" function over 10 bits. It fills + * the arrays only up to N = 2^logn values. + * + * The values stored in gm[] and igm[] are in Montgomery representation. + * + * p must be a prime such that p = 1 mod 2048. + */ +static void +modp_mkgm2(uint32_t *gm, uint32_t *igm, unsigned logn, + uint32_t g, uint32_t p, uint32_t p0i) { + size_t u, n; + unsigned k; + uint32_t ig, x1, x2, R2; + + n = (size_t)1 << logn; + + /* + * We want g such that g^(2N) = 1 mod p, but the provided + * generator has order 2048. We must square it a few times. + */ + R2 = modp_R2(p, p0i); + g = modp_montymul(g, R2, p, p0i); + for (k = logn; k < 10; k ++) { + g = modp_montymul(g, g, p, p0i); + } + + ig = modp_div(R2, g, p, p0i, modp_R(p)); + k = 10 - logn; + x1 = x2 = modp_R(p); + for (u = 0; u < n; u ++) { + size_t v; + + v = REV10[u << k]; + gm[v] = x1; + igm[v] = x2; + x1 = modp_montymul(x1, g, p, p0i); + x2 = modp_montymul(x2, ig, p, p0i); + } +} + +/* + * Compute the NTT over a polynomial (binary case). Polynomial elements + * are a[0], a[stride], a[2 * stride]... + */ +static void +modp_NTT2_ext(uint32_t *a, size_t stride, const uint32_t *gm, unsigned logn, + uint32_t p, uint32_t p0i) { + size_t t, m, n; + + if (logn == 0) { + return; + } + n = (size_t)1 << logn; + t = n; + for (m = 1; m < n; m <<= 1) { + size_t ht, u, v1; + + ht = t >> 1; + for (u = 0, v1 = 0; u < m; u ++, v1 += t) { + uint32_t s; + size_t v; + uint32_t *r1, *r2; + + s = gm[m + u]; + r1 = a + v1 * stride; + r2 = r1 + ht * stride; + for (v = 0; v < ht; v ++, r1 += stride, r2 += stride) { + uint32_t x, y; + + x = *r1; + y = modp_montymul(*r2, s, p, p0i); + *r1 = modp_add(x, y, p); + *r2 = modp_sub(x, y, p); + } + } + t = ht; + } +} + +/* + * Compute the inverse NTT over a polynomial (binary case). + */ +static void +modp_iNTT2_ext(uint32_t *a, size_t stride, const uint32_t *igm, unsigned logn, + uint32_t p, uint32_t p0i) { + size_t t, m, n, k; + uint32_t ni; + uint32_t *r; + + if (logn == 0) { + return; + } + n = (size_t)1 << logn; + t = 1; + for (m = n; m > 1; m >>= 1) { + size_t hm, dt, u, v1; + + hm = m >> 1; + dt = t << 1; + for (u = 0, v1 = 0; u < hm; u ++, v1 += dt) { + uint32_t s; + size_t v; + uint32_t *r1, *r2; + + s = igm[hm + u]; + r1 = a + v1 * stride; + r2 = r1 + t * stride; + for (v = 0; v < t; v ++, r1 += stride, r2 += stride) { + uint32_t x, y; + + x = *r1; + y = *r2; + *r1 = modp_add(x, y, p); + *r2 = modp_montymul( + modp_sub(x, y, p), s, p, p0i);; + } + } + t = dt; + } + + /* + * We need 1/n in Montgomery representation, i.e. R/n. Since + * 1 <= logn <= 10, R/n is an integer; morever, R/n <= 2^30 < p, + * thus a simple shift will do. + */ + ni = (uint32_t)1 << (31 - logn); + for (k = 0, r = a; k < n; k ++, r += stride) { + *r = modp_montymul(*r, ni, p, p0i); + } +} + +/* + * Simplified macros for NTT and iNTT (binary case) when the elements + * are consecutive in RAM. + */ +#define modp_NTT2(a, gm, logn, p, p0i) modp_NTT2_ext(a, 1, gm, logn, p, p0i) +#define modp_iNTT2(a, igm, logn, p, p0i) modp_iNTT2_ext(a, 1, igm, logn, p, p0i) + +/* + * Given polynomial f in NTT representation modulo p, compute f' of degree + * less than N/2 such that f' = f0^2 - X*f1^2, where f0 and f1 are + * polynomials of degree less than N/2 such that f = f0(X^2) + X*f1(X^2). + * + * The new polynomial is written "in place" over the first N/2 elements + * of f. + * + * If applied logn times successively on a given polynomial, the resulting + * degree-0 polynomial is the resultant of f and X^N+1 modulo p. + * + * This function applies only to the binary case; it is invoked from + * solve_NTRU_binary_depth1(). + */ +static void +modp_poly_rec_res(uint32_t *f, unsigned logn, + uint32_t p, uint32_t p0i, uint32_t R2) { + size_t hn, u; + + hn = (size_t)1 << (logn - 1); + for (u = 0; u < hn; u ++) { + uint32_t w0, w1; + + w0 = f[(u << 1) + 0]; + w1 = f[(u << 1) + 1]; + f[u] = modp_montymul(modp_montymul(w0, w1, p, p0i), R2, p, p0i); + } +} + +/* ==================================================================== */ +/* + * Custom bignum implementation. + * + * This is a very reduced set of functionalities. We need to do the + * following operations: + * + * - Rebuild the resultant and the polynomial coefficients from their + * values modulo small primes (of length 31 bits each). + * + * - Compute an extended GCD between the two computed resultants. + * + * - Extract top bits and add scaled values during the successive steps + * of Babai rounding. + * + * When rebuilding values using CRT, we must also recompute the product + * of the small prime factors. We always do it one small factor at a + * time, so the "complicated" operations can be done modulo the small + * prime with the modp_* functions. CRT coefficients (inverses) are + * precomputed. + * + * All values are positive until the last step: when the polynomial + * coefficients have been rebuilt, we normalize them around 0. But then, + * only additions and subtractions on the upper few bits are needed + * afterwards. + * + * We keep big integers as arrays of 31-bit words (in uint32_t values); + * the top bit of each uint32_t is kept equal to 0. Using 31-bit words + * makes it easier to keep track of carries. When negative values are + * used, two's complement is used. + */ + +/* + * Subtract integer b from integer a. Both integers are supposed to have + * the same size. The carry (0 or 1) is returned. Source arrays a and b + * MUST be distinct. + * + * The operation is performed as described above if ctr = 1. If + * ctl = 0, the value a[] is unmodified, but all memory accesses are + * still performed, and the carry is computed and returned. + */ +static uint32_t +zint_sub(uint32_t *a, const uint32_t *b, size_t len, + uint32_t ctl) { + size_t u; + uint32_t cc, m; + + cc = 0; + m = -ctl; + for (u = 0; u < len; u ++) { + uint32_t aw, w; + + aw = a[u]; + w = aw - b[u] - cc; + cc = w >> 31; + aw ^= ((w & 0x7FFFFFFF) ^ aw) & m; + a[u] = aw; + } + return cc; +} + +/* + * Mutiply the provided big integer m with a small value x. + * This function assumes that x < 2^31. The carry word is returned. + */ +static uint32_t +zint_mul_small(uint32_t *m, size_t mlen, uint32_t x) { + size_t u; + uint32_t cc; + + cc = 0; + for (u = 0; u < mlen; u ++) { + uint64_t z; + + z = (uint64_t)m[u] * (uint64_t)x + cc; + m[u] = (uint32_t)z & 0x7FFFFFFF; + cc = (uint32_t)(z >> 31); + } + return cc; +} + +/* + * Reduce a big integer d modulo a small integer p. + * Rules: + * d is unsigned + * p is prime + * 2^30 < p < 2^31 + * p0i = -(1/p) mod 2^31 + * R2 = 2^62 mod p + */ +static uint32_t +zint_mod_small_unsigned(const uint32_t *d, size_t dlen, + uint32_t p, uint32_t p0i, uint32_t R2) { + uint32_t x; + size_t u; + + /* + * Algorithm: we inject words one by one, starting with the high + * word. Each step is: + * - multiply x by 2^31 + * - add new word + */ + x = 0; + u = dlen; + while (u -- > 0) { + uint32_t w; + + x = modp_montymul(x, R2, p, p0i); + w = d[u] - p; + w += p & -(w >> 31); + x = modp_add(x, w, p); + } + return x; +} + +/* + * Similar to zint_mod_small_unsigned(), except that d may be signed. + * Extra parameter is Rx = 2^(31*dlen) mod p. + */ +static uint32_t +zint_mod_small_signed(const uint32_t *d, size_t dlen, + uint32_t p, uint32_t p0i, uint32_t R2, uint32_t Rx) { + uint32_t z; + + if (dlen == 0) { + return 0; + } + z = zint_mod_small_unsigned(d, dlen, p, p0i, R2); + z = modp_sub(z, Rx & -(d[dlen - 1] >> 30), p); + return z; +} + +/* + * Add y*s to x. x and y initially have length 'len' words; the new x + * has length 'len+1' words. 's' must fit on 31 bits. x[] and y[] must + * not overlap. + */ +static void +zint_add_mul_small(uint32_t *x, + const uint32_t *y, size_t len, uint32_t s) { + size_t u; + uint32_t cc; + + cc = 0; + for (u = 0; u < len; u ++) { + uint32_t xw, yw; + uint64_t z; + + xw = x[u]; + yw = y[u]; + z = (uint64_t)yw * (uint64_t)s + (uint64_t)xw + (uint64_t)cc; + x[u] = (uint32_t)z & 0x7FFFFFFF; + cc = (uint32_t)(z >> 31); + } + x[len] = cc; +} + +/* + * Normalize a modular integer around 0: if x > p/2, then x is replaced + * with x - p (signed encoding with two's complement); otherwise, x is + * untouched. The two integers x and p are encoded over the same length. + */ +static void +zint_norm_zero(uint32_t *x, const uint32_t *p, size_t len) { + size_t u; + uint32_t r, bb; + + /* + * Compare x with p/2. We use the shifted version of p, and p + * is odd, so we really compare with (p-1)/2; we want to perform + * the subtraction if and only if x > (p-1)/2. + */ + r = 0; + bb = 0; + u = len; + while (u -- > 0) { + uint32_t wx, wp, cc; + + /* + * Get the two words to compare in wx and wp (both over + * 31 bits exactly). + */ + wx = x[u]; + wp = (p[u] >> 1) | (bb << 30); + bb = p[u] & 1; + + /* + * We set cc to -1, 0 or 1, depending on whether wp is + * lower than, equal to, or greater than wx. + */ + cc = wp - wx; + cc = ((-cc) >> 31) | -(cc >> 31); + + /* + * If r != 0 then it is either 1 or -1, and we keep its + * value. Otherwise, if r = 0, then we replace it with cc. + */ + r |= cc & ((r & 1) - 1); + } + + /* + * At this point, r = -1, 0 or 1, depending on whether (p-1)/2 + * is lower than, equal to, or greater than x. We thus want to + * do the subtraction only if r = -1. + */ + zint_sub(x, p, len, r >> 31); +} + +/* + * Rebuild integers from their RNS representation. There are 'num' + * integers, and each consists in 'xlen' words. 'xx' points at that + * first word of the first integer; subsequent integers are accessed + * by adding 'xstride' repeatedly. + * + * The words of an integer are the RNS representation of that integer, + * using the provided 'primes' are moduli. This function replaces + * each integer with its multi-word value (little-endian order). + * + * If "normalize_signed" is non-zero, then the returned value is + * normalized to the -m/2..m/2 interval (where m is the product of all + * small prime moduli); two's complement is used for negative values. + */ +static void +zint_rebuild_CRT(uint32_t *xx, size_t xlen, size_t xstride, + size_t num, const small_prime *primes, int normalize_signed, + uint32_t *tmp) { + size_t u; + uint32_t *x; + + tmp[0] = primes[0].p; + for (u = 1; u < xlen; u ++) { + /* + * At the entry of each loop iteration: + * - the first u words of each array have been + * reassembled; + * - the first u words of tmp[] contains the + * product of the prime moduli processed so far. + * + * We call 'q' the product of all previous primes. + */ + uint32_t p, p0i, s, R2; + size_t v; + + p = primes[u].p; + s = primes[u].s; + p0i = modp_ninv31(p); + R2 = modp_R2(p, p0i); + + for (v = 0, x = xx; v < num; v ++, x += xstride) { + uint32_t xp, xq, xr; + /* + * xp = the integer x modulo the prime p for this + * iteration + * xq = (x mod q) mod p + */ + xp = x[u]; + xq = zint_mod_small_unsigned(x, u, p, p0i, R2); + + /* + * New value is (x mod q) + q * (s * (xp - xq) mod p) + */ + xr = modp_montymul(s, modp_sub(xp, xq, p), p, p0i); + zint_add_mul_small(x, tmp, u, xr); + } + + /* + * Update product of primes in tmp[]. + */ + tmp[u] = zint_mul_small(tmp, u, p); + } + + /* + * Normalize the reconstructed values around 0. + */ + if (normalize_signed) { + for (u = 0, x = xx; u < num; u ++, x += xstride) { + zint_norm_zero(x, tmp, xlen); + } + } +} + +/* + * Negate a big integer conditionally: value a is replaced with -a if + * and only if ctl = 1. Control value ctl must be 0 or 1. + */ +static void +zint_negate(uint32_t *a, size_t len, uint32_t ctl) { + size_t u; + uint32_t cc, m; + + /* + * If ctl = 1 then we flip the bits of a by XORing with + * 0x7FFFFFFF, and we add 1 to the value. If ctl = 0 then we XOR + * with 0 and add 0, which leaves the value unchanged. + */ + cc = ctl; + m = -ctl >> 1; + for (u = 0; u < len; u ++) { + uint32_t aw; + + aw = a[u]; + aw = (aw ^ m) + cc; + a[u] = aw & 0x7FFFFFFF; + cc = aw >> 31; + } +} + +/* + * Replace a with (a*xa+b*xb)/(2^31) and b with (a*ya+b*yb)/(2^31). + * The low bits are dropped (the caller should compute the coefficients + * such that these dropped bits are all zeros). If either or both + * yields a negative value, then the value is negated. + * + * Returned value is: + * 0 both values were positive + * 1 new a had to be negated + * 2 new b had to be negated + * 3 both new a and new b had to be negated + * + * Coefficients xa, xb, ya and yb may use the full signed 32-bit range. + */ +static uint32_t +zint_co_reduce(uint32_t *a, uint32_t *b, size_t len, + int64_t xa, int64_t xb, int64_t ya, int64_t yb) { + size_t u; + int64_t cca, ccb; + uint32_t nega, negb; + + cca = 0; + ccb = 0; + for (u = 0; u < len; u ++) { + uint32_t wa, wb; + uint64_t za, zb; + + wa = a[u]; + wb = b[u]; + za = wa * (uint64_t)xa + wb * (uint64_t)xb + (uint64_t)cca; + zb = wa * (uint64_t)ya + wb * (uint64_t)yb + (uint64_t)ccb; + if (u > 0) { + a[u - 1] = (uint32_t)za & 0x7FFFFFFF; + b[u - 1] = (uint32_t)zb & 0x7FFFFFFF; + } + cca = *(int64_t *)&za >> 31; + ccb = *(int64_t *)&zb >> 31; + } + a[len - 1] = (uint32_t)cca; + b[len - 1] = (uint32_t)ccb; + + nega = (uint32_t)((uint64_t)cca >> 63); + negb = (uint32_t)((uint64_t)ccb >> 63); + zint_negate(a, len, nega); + zint_negate(b, len, negb); + return nega | (negb << 1); +} + +/* + * Finish modular reduction. Rules on input parameters: + * + * if neg = 1, then -m <= a < 0 + * if neg = 0, then 0 <= a < 2*m + * + * If neg = 0, then the top word of a[] is allowed to use 32 bits. + * + * Modulus m must be odd. + */ +static void +zint_finish_mod(uint32_t *a, size_t len, const uint32_t *m, uint32_t neg) { + size_t u; + uint32_t cc, xm, ym; + + /* + * First pass: compare a (assumed nonnegative) with m. Note that + * if the top word uses 32 bits, subtracting m must yield a + * value less than 2^31 since a < 2*m. + */ + cc = 0; + for (u = 0; u < len; u ++) { + cc = (a[u] - m[u] - cc) >> 31; + } + + /* + * If neg = 1 then we must add m (regardless of cc) + * If neg = 0 and cc = 0 then we must subtract m + * If neg = 0 and cc = 1 then we must do nothing + * + * In the loop below, we conditionally subtract either m or -m + * from a. Word xm is a word of m (if neg = 0) or -m (if neg = 1); + * but if neg = 0 and cc = 1, then ym = 0 and it forces mw to 0. + */ + xm = -neg >> 1; + ym = -(neg | (1 - cc)); + cc = neg; + for (u = 0; u < len; u ++) { + uint32_t aw, mw; + + aw = a[u]; + mw = (m[u] ^ xm) & ym; + aw = aw - mw - cc; + a[u] = aw & 0x7FFFFFFF; + cc = aw >> 31; + } +} + +/* + * Replace a with (a*xa+b*xb)/(2^31) mod m, and b with + * (a*ya+b*yb)/(2^31) mod m. Modulus m must be odd; m0i = -1/m[0] mod 2^31. + */ +static void +zint_co_reduce_mod(uint32_t *a, uint32_t *b, const uint32_t *m, size_t len, + uint32_t m0i, int64_t xa, int64_t xb, int64_t ya, int64_t yb) { + size_t u; + int64_t cca, ccb; + uint32_t fa, fb; + + /* + * These are actually four combined Montgomery multiplications. + */ + cca = 0; + ccb = 0; + fa = ((a[0] * (uint32_t)xa + b[0] * (uint32_t)xb) * m0i) & 0x7FFFFFFF; + fb = ((a[0] * (uint32_t)ya + b[0] * (uint32_t)yb) * m0i) & 0x7FFFFFFF; + for (u = 0; u < len; u ++) { + uint32_t wa, wb; + uint64_t za, zb; + + wa = a[u]; + wb = b[u]; + za = wa * (uint64_t)xa + wb * (uint64_t)xb + + m[u] * (uint64_t)fa + (uint64_t)cca; + zb = wa * (uint64_t)ya + wb * (uint64_t)yb + + m[u] * (uint64_t)fb + (uint64_t)ccb; + if (u > 0) { + a[u - 1] = (uint32_t)za & 0x7FFFFFFF; + b[u - 1] = (uint32_t)zb & 0x7FFFFFFF; + } + cca = *(int64_t *)&za >> 31; + ccb = *(int64_t *)&zb >> 31; + } + a[len - 1] = (uint32_t)cca; + b[len - 1] = (uint32_t)ccb; + + /* + * At this point: + * -m <= a < 2*m + * -m <= b < 2*m + * (this is a case of Montgomery reduction) + * The top words of 'a' and 'b' may have a 32-th bit set. + * We want to add or subtract the modulus, as required. + */ + zint_finish_mod(a, len, m, (uint32_t)((uint64_t)cca >> 63)); + zint_finish_mod(b, len, m, (uint32_t)((uint64_t)ccb >> 63)); +} + +/* + * Compute a GCD between two positive big integers x and y. The two + * integers must be odd. Returned value is 1 if the GCD is 1, 0 + * otherwise. When 1 is returned, arrays u and v are filled with values + * such that: + * 0 <= u <= y + * 0 <= v <= x + * x*u - y*v = 1 + * x[] and y[] are unmodified. Both input values must have the same + * encoded length. Temporary array must be large enough to accommodate 4 + * extra values of that length. Arrays u, v and tmp may not overlap with + * each other, or with either x or y. + */ +static int +zint_bezout(uint32_t *u, uint32_t *v, + const uint32_t *x, const uint32_t *y, + size_t len, uint32_t *tmp) { + /* + * Algorithm is an extended binary GCD. We maintain 6 values + * a, b, u0, u1, v0 and v1 with the following invariants: + * + * a = x*u0 - y*v0 + * b = x*u1 - y*v1 + * 0 <= a <= x + * 0 <= b <= y + * 0 <= u0 < y + * 0 <= v0 < x + * 0 <= u1 <= y + * 0 <= v1 < x + * + * Initial values are: + * + * a = x u0 = 1 v0 = 0 + * b = y u1 = y v1 = x-1 + * + * Each iteration reduces either a or b, and maintains the + * invariants. Algorithm stops when a = b, at which point their + * common value is GCD(a,b) and (u0,v0) (or (u1,v1)) contains + * the values (u,v) we want to return. + * + * The formal definition of the algorithm is a sequence of steps: + * + * - If a is even, then: + * a <- a/2 + * u0 <- u0/2 mod y + * v0 <- v0/2 mod x + * + * - Otherwise, if b is even, then: + * b <- b/2 + * u1 <- u1/2 mod y + * v1 <- v1/2 mod x + * + * - Otherwise, if a > b, then: + * a <- (a-b)/2 + * u0 <- (u0-u1)/2 mod y + * v0 <- (v0-v1)/2 mod x + * + * - Otherwise: + * b <- (b-a)/2 + * u1 <- (u1-u0)/2 mod y + * v1 <- (v1-v0)/2 mod y + * + * We can show that the operations above preserve the invariants: + * + * - If a is even, then u0 and v0 are either both even or both + * odd (since a = x*u0 - y*v0, and x and y are both odd). + * If u0 and v0 are both even, then (u0,v0) <- (u0/2,v0/2). + * Otherwise, (u0,v0) <- ((u0+y)/2,(v0+x)/2). Either way, + * the a = x*u0 - y*v0 invariant is preserved. + * + * - The same holds for the case where b is even. + * + * - If a and b are odd, and a > b, then: + * + * a-b = x*(u0-u1) - y*(v0-v1) + * + * In that situation, if u0 < u1, then x*(u0-u1) < 0, but + * a-b > 0; therefore, it must be that v0 < v1, and the + * first part of the update is: (u0,v0) <- (u0-u1+y,v0-v1+x), + * which preserves the invariants. Otherwise, if u0 > u1, + * then u0-u1 >= 1, thus x*(u0-u1) >= x. But a <= x and + * b >= 0, hence a-b <= x. It follows that, in that case, + * v0-v1 >= 0. The first part of the update is then: + * (u0,v0) <- (u0-u1,v0-v1), which again preserves the + * invariants. + * + * Either way, once the subtraction is done, the new value of + * a, which is the difference of two odd values, is even, + * and the remaining of this step is a subcase of the + * first algorithm case (i.e. when a is even). + * + * - If a and b are odd, and b > a, then the a similar + * argument holds. + * + * The values a and b start at x and y, respectively. Since x + * and y are odd, their GCD is odd, and it is easily seen that + * all steps conserve the GCD (GCD(a-b,b) = GCD(a, b); + * GCD(a/2,b) = GCD(a,b) if GCD(a,b) is odd). Moreover, either a + * or b is reduced by at least one bit at each iteration, so + * the algorithm necessarily converges on the case a = b, at + * which point the common value is the GCD. + * + * In the algorithm expressed above, when a = b, the fourth case + * applies, and sets b = 0. Since a contains the GCD of x and y, + * which are both odd, a must be odd, and subsequent iterations + * (if any) will simply divide b by 2 repeatedly, which has no + * consequence. Thus, the algorithm can run for more iterations + * than necessary; the final GCD will be in a, and the (u,v) + * coefficients will be (u0,v0). + * + * + * The presentation above is bit-by-bit. It can be sped up by + * noticing that all decisions are taken based on the low bits + * and high bits of a and b. We can extract the two top words + * and low word of each of a and b, and compute reduction + * parameters pa, pb, qa and qb such that the new values for + * a and b are: + * a' = (a*pa + b*pb) / (2^31) + * b' = (a*qa + b*qb) / (2^31) + * the two divisions being exact. The coefficients are obtained + * just from the extracted words, and may be slightly off, requiring + * an optional correction: if a' < 0, then we replace pa with -pa + * and pb with -pb. Each such step will reduce the total length + * (sum of lengths of a and b) by at least 30 bits at each + * iteration. + */ + uint32_t *u0, *u1, *v0, *v1, *a, *b; + uint32_t x0i, y0i; + uint32_t num, rc; + size_t j; + + if (len == 0) { + return 0; + } + + /* + * u0 and v0 are the u and v result buffers; the four other + * values (u1, v1, a and b) are taken from tmp[]. + */ + u0 = u; + v0 = v; + u1 = tmp; + v1 = u1 + len; + a = v1 + len; + b = a + len; + + /* + * We'll need the Montgomery reduction coefficients. + */ + x0i = modp_ninv31(x[0]); + y0i = modp_ninv31(y[0]); + + /* + * Initialize a, b, u0, u1, v0 and v1. + * a = x u0 = 1 v0 = 0 + * b = y u1 = y v1 = x-1 + * Note that x is odd, so computing x-1 is easy. + */ + memcpy(a, x, len * sizeof * x); + memcpy(b, y, len * sizeof * y); + u0[0] = 1; + memset(u0 + 1, 0, (len - 1) * sizeof * u0); + memset(v0, 0, len * sizeof * v0); + memcpy(u1, y, len * sizeof * u1); + memcpy(v1, x, len * sizeof * v1); + v1[0] --; + + /* + * Each input operand may be as large as 31*len bits, and we + * reduce the total length by at least 30 bits at each iteration. + */ + for (num = 62 * (uint32_t)len + 30; num >= 30; num -= 30) { + uint32_t c0, c1; + uint32_t a0, a1, b0, b1; + uint64_t a_hi, b_hi; + uint32_t a_lo, b_lo; + int64_t pa, pb, qa, qb; + int i; + uint32_t r; + + /* + * Extract the top words of a and b. If j is the highest + * index >= 1 such that a[j] != 0 or b[j] != 0, then we + * want (a[j] << 31) + a[j-1] and (b[j] << 31) + b[j-1]. + * If a and b are down to one word each, then we use + * a[0] and b[0]. + */ + c0 = (uint32_t) -1; + c1 = (uint32_t) -1; + a0 = 0; + a1 = 0; + b0 = 0; + b1 = 0; + j = len; + while (j -- > 0) { + uint32_t aw, bw; + + aw = a[j]; + bw = b[j]; + a0 ^= (a0 ^ aw) & c0; + a1 ^= (a1 ^ aw) & c1; + b0 ^= (b0 ^ bw) & c0; + b1 ^= (b1 ^ bw) & c1; + c1 = c0; + c0 &= (((aw | bw) + 0x7FFFFFFF) >> 31) - (uint32_t)1; + } + + /* + * If c1 = 0, then we grabbed two words for a and b. + * If c1 != 0 but c0 = 0, then we grabbed one word. It + * is not possible that c1 != 0 and c0 != 0, because that + * would mean that both integers are zero. + */ + a1 |= a0 & c1; + a0 &= ~c1; + b1 |= b0 & c1; + b0 &= ~c1; + a_hi = ((uint64_t)a0 << 31) + a1; + b_hi = ((uint64_t)b0 << 31) + b1; + a_lo = a[0]; + b_lo = b[0]; + + /* + * Compute reduction factors: + * + * a' = a*pa + b*pb + * b' = a*qa + b*qb + * + * such that a' and b' are both multiple of 2^31, but are + * only marginally larger than a and b. + */ + pa = 1; + pb = 0; + qa = 0; + qb = 1; + for (i = 0; i < 31; i ++) { + /* + * At each iteration: + * + * a <- (a-b)/2 if: a is odd, b is odd, a_hi > b_hi + * b <- (b-a)/2 if: a is odd, b is odd, a_hi <= b_hi + * a <- a/2 if: a is even + * b <- b/2 if: a is odd, b is even + * + * We multiply a_lo and b_lo by 2 at each + * iteration, thus a division by 2 really is a + * non-multiplication by 2. + */ + uint32_t rt, oa, ob, cAB, cBA, cA; + uint64_t rz; + + /* + * rt = 1 if a_hi > b_hi, 0 otherwise. + */ + rz = b_hi - a_hi; + rt = (uint32_t)((rz ^ ((a_hi ^ b_hi) + & (a_hi ^ rz))) >> 63); + + /* + * cAB = 1 if b must be subtracted from a + * cBA = 1 if a must be subtracted from b + * cA = 1 if a must be divided by 2 + * + * Rules: + * + * cAB and cBA cannot both be 1. + * If a is not divided by 2, b is. + */ + oa = (a_lo >> i) & 1; + ob = (b_lo >> i) & 1; + cAB = oa & ob & rt; + cBA = oa & ob & ~rt; + cA = cAB | (oa ^ 1); + + /* + * Conditional subtractions. + */ + a_lo -= b_lo & -cAB; + a_hi -= b_hi & -(uint64_t)cAB; + pa -= qa & -(int64_t)cAB; + pb -= qb & -(int64_t)cAB; + b_lo -= a_lo & -cBA; + b_hi -= a_hi & -(uint64_t)cBA; + qa -= pa & -(int64_t)cBA; + qb -= pb & -(int64_t)cBA; + + /* + * Shifting. + */ + a_lo += a_lo & (cA - 1); + pa += pa & ((int64_t)cA - 1); + pb += pb & ((int64_t)cA - 1); + a_hi ^= (a_hi ^ (a_hi >> 1)) & -(uint64_t)cA; + b_lo += b_lo & -cA; + qa += qa & -(int64_t)cA; + qb += qb & -(int64_t)cA; + b_hi ^= (b_hi ^ (b_hi >> 1)) & ((uint64_t)cA - 1); + } + + /* + * Apply the computed parameters to our values. We + * may have to correct pa and pb depending on the + * returned value of zint_co_reduce() (when a and/or b + * had to be negated). + */ + r = zint_co_reduce(a, b, len, pa, pb, qa, qb); + pa -= (pa + pa) & -(int64_t)(r & 1); + pb -= (pb + pb) & -(int64_t)(r & 1); + qa -= (qa + qa) & -(int64_t)(r >> 1); + qb -= (qb + qb) & -(int64_t)(r >> 1); + zint_co_reduce_mod(u0, u1, y, len, y0i, pa, pb, qa, qb); + zint_co_reduce_mod(v0, v1, x, len, x0i, pa, pb, qa, qb); + } + + /* + * At that point, array a[] should contain the GCD, and the + * results (u,v) should already be set. We check that the GCD + * is indeed 1. We also check that the two operands x and y + * are odd. + */ + rc = a[0] ^ 1; + for (j = 1; j < len; j ++) { + rc |= a[j]; + } + return (int)((1 - ((rc | -rc) >> 31)) & x[0] & y[0]); +} + +/* + * Add k*y*2^sc to x. The result is assumed to fit in the array of + * size xlen (truncation is applied if necessary). + * Scale factor 'sc' is provided as sch and scl, such that: + * sch = sc / 31 + * scl = sc % 31 + * xlen MUST NOT be lower than ylen. + * + * x[] and y[] are both signed integers, using two's complement for + * negative values. + */ +static void +zint_add_scaled_mul_small(uint32_t *x, size_t xlen, + const uint32_t *y, size_t ylen, int32_t k, + uint32_t sch, uint32_t scl) { + size_t u; + uint32_t ysign, tw; + int32_t cc; + + if (ylen == 0) { + return; + } + + ysign = -(y[ylen - 1] >> 30) >> 1; + tw = 0; + cc = 0; + for (u = sch; u < xlen; u ++) { + size_t v; + uint32_t wy, wys, ccu; + uint64_t z; + + /* + * Get the next word of y (scaled). + */ + v = u - sch; + if (v < ylen) { + wy = y[v]; + } else { + wy = ysign; + } + wys = ((wy << scl) & 0x7FFFFFFF) | tw; + tw = wy >> (31 - scl); + + /* + * The expression below does not overflow. + */ + z = (uint64_t)((int64_t)wys * (int64_t)k + (int64_t)x[u] + cc); + x[u] = (uint32_t)z & 0x7FFFFFFF; + + /* + * Right-shifting the signed value z would yield + * implementation-defined results (arithmetic shift is + * not guaranteed). However, we can cast to unsigned, + * and get the next carry as an unsigned word. We can + * then convert it back to signed by using the guaranteed + * fact that 'int32_t' uses two's complement with no + * trap representation or padding bit, and with a layout + * compatible with that of 'uint32_t'. + */ + ccu = (uint32_t)(z >> 31); + cc = *(int32_t *)&ccu; + } +} + +/* + * Subtract y*2^sc from x. The result is assumed to fit in the array of + * size xlen (truncation is applied if necessary). + * Scale factor 'sc' is provided as sch and scl, such that: + * sch = sc / 31 + * scl = sc % 31 + * xlen MUST NOT be lower than ylen. + * + * x[] and y[] are both signed integers, using two's complement for + * negative values. + */ +static void +zint_sub_scaled(uint32_t *x, size_t xlen, + const uint32_t *y, size_t ylen, uint32_t sch, uint32_t scl) { + size_t u; + uint32_t ysign, tw; + uint32_t cc; + + if (ylen == 0) { + return; + } + + ysign = -(y[ylen - 1] >> 30) >> 1; + tw = 0; + cc = 0; + for (u = sch; u < xlen; u ++) { + size_t v; + uint32_t w, wy, wys; + + /* + * Get the next word of y (scaled). + */ + v = u - sch; + if (v < ylen) { + wy = y[v]; + } else { + wy = ysign; + } + wys = ((wy << scl) & 0x7FFFFFFF) | tw; + tw = wy >> (31 - scl); + + w = x[u] - wys - cc; + x[u] = w & 0x7FFFFFFF; + cc = w >> 31; + } +} + +/* + * Convert a one-word signed big integer into a signed value. + */ +static inline int32_t +zint_one_to_plain(const uint32_t *x) { + uint32_t w; + + w = x[0]; + w |= (w & 0x40000000) << 1; + return *(int32_t *)&w; +} + +/* ==================================================================== */ + +/* + * Convert a polynomial to floating-point values. + * + * Each coefficient has length flen words, and starts fstride words after + * the previous. + * + * IEEE-754 binary64 values can represent values in a finite range, + * roughly 2^(-1023) to 2^(+1023); thus, if coefficients are too large, + * they should be "trimmed" by pointing not to the lowest word of each, + * but upper. + */ +static void +poly_big_to_fp(fpr *d, const uint32_t *f, size_t flen, size_t fstride, + unsigned logn) { + size_t n, u; + + n = MKN(logn); + if (flen == 0) { + for (u = 0; u < n; u ++) { + d[u] = fpr_zero; + } + return; + } + for (u = 0; u < n; u ++, f += fstride) { + size_t v; + uint32_t neg, cc, xm; + fpr x, fsc; + + /* + * Get sign of the integer; if it is negative, then we + * will load its absolute value instead, and negate the + * result. + */ + neg = -(f[flen - 1] >> 30); + xm = neg >> 1; + cc = neg & 1; + x = fpr_zero; + fsc = fpr_one; + for (v = 0; v < flen; v ++, fsc = fpr_mul(fsc, fpr_ptwo31)) { + uint32_t w; + + w = (f[v] ^ xm) + cc; + cc = w >> 31; + w &= 0x7FFFFFFF; + w -= (w << 1) & neg; + x = fpr_add(x, fpr_mul(fpr_of(*(int32_t *)&w), fsc)); + } + d[u] = x; + } +} + +/* + * Convert a polynomial to small integers. Source values are supposed + * to be one-word integers, signed over 31 bits. Returned value is 0 + * if any of the coefficients exceeds the provided limit (in absolute + * value), or 1 on success. + * + * This is not constant-time; this is not a problem here, because on + * any failure, the NTRU-solving process will be deemed to have failed + * and the (f,g) polynomials will be discarded. + */ +static int +poly_big_to_small(int8_t *d, const uint32_t *s, int lim, unsigned logn) { + size_t n, u; + + n = MKN(logn); + for (u = 0; u < n; u ++) { + int32_t z; + + z = zint_one_to_plain(s + u); + if (z < -lim || z > lim) { + return 0; + } + d[u] = (int8_t)z; + } + return 1; +} + +/* + * Subtract k*f from F, where F, f and k are polynomials modulo X^N+1. + * Coefficients of polynomial k are small integers (signed values in the + * -2^31..2^31 range) scaled by 2^sc. Value sc is provided as sch = sc / 31 + * and scl = sc % 31. + * + * This function implements the basic quadratic multiplication algorithm, + * which is efficient in space (no extra buffer needed) but slow at + * high degree. + */ +static void +poly_sub_scaled(uint32_t *F, size_t Flen, size_t Fstride, + const uint32_t *f, size_t flen, size_t fstride, + const int32_t *k, uint32_t sch, uint32_t scl, unsigned logn) { + size_t n, u; + + n = MKN(logn); + for (u = 0; u < n; u ++) { + int32_t kf; + size_t v; + uint32_t *x; + const uint32_t *y; + + kf = -k[u]; + x = F + u * Fstride; + y = f; + for (v = 0; v < n; v ++) { + zint_add_scaled_mul_small( + x, Flen, y, flen, kf, sch, scl); + if (u + v == n - 1) { + x = F; + kf = -kf; + } else { + x += Fstride; + } + y += fstride; + } + } +} + +/* + * Subtract k*f from F. Coefficients of polynomial k are small integers + * (signed values in the -2^31..2^31 range) scaled by 2^sc. This function + * assumes that the degree is large, and integers relatively small. + * The value sc is provided as sch = sc / 31 and scl = sc % 31. + */ +static void +poly_sub_scaled_ntt(uint32_t *F, size_t Flen, size_t Fstride, + const uint32_t *f, size_t flen, size_t fstride, + const int32_t *k, uint32_t sch, uint32_t scl, unsigned logn, + uint32_t *tmp) { + uint32_t *gm, *igm, *fk, *t1, *x; + const uint32_t *y; + size_t n, u, tlen; + const small_prime *primes; + + n = MKN(logn); + tlen = flen + 1; + gm = tmp; + igm = gm + MKN(logn); + fk = igm + MKN(logn); + t1 = fk + n * tlen; + + primes = PRIMES; + + /* + * Compute k*f in fk[], in RNS notation. + */ + for (u = 0; u < tlen; u ++) { + uint32_t p, p0i, R2, Rx; + size_t v; + + p = primes[u].p; + p0i = modp_ninv31(p); + R2 = modp_R2(p, p0i); + Rx = modp_Rx((unsigned)flen, p, p0i, R2); + modp_mkgm2(gm, igm, logn, primes[u].g, p, p0i); + + for (v = 0; v < n; v ++) { + t1[v] = modp_set(k[v], p); + } + modp_NTT2(t1, gm, logn, p, p0i); + for (v = 0, y = f, x = fk + u; + v < n; v ++, y += fstride, x += tlen) { + *x = zint_mod_small_signed(y, flen, p, p0i, R2, Rx); + } + modp_NTT2_ext(fk + u, tlen, gm, logn, p, p0i); + for (v = 0, x = fk + u; v < n; v ++, x += tlen) { + *x = modp_montymul( + modp_montymul(t1[v], *x, p, p0i), R2, p, p0i); + } + modp_iNTT2_ext(fk + u, tlen, igm, logn, p, p0i); + } + + /* + * Rebuild k*f. + */ + zint_rebuild_CRT(fk, tlen, tlen, n, primes, 1, t1); + + /* + * Subtract k*f, scaled, from F. + */ + for (u = 0, x = F, y = fk; u < n; u ++, x += Fstride, y += tlen) { + zint_sub_scaled(x, Flen, y, tlen, sch, scl); + } +} + +/* ==================================================================== */ + + +#define RNG_CONTEXT inner_shake256_context + +/* + * Get a random 8-byte integer from a SHAKE-based RNG. This function + * ensures consistent interpretation of the SHAKE output so that + * the same values will be obtained over different platforms, in case + * a known seed is used. + */ +static inline uint64_t +get_rng_u64(inner_shake256_context *rng) { + /* + * We enforce little-endian representation. + */ + + uint8_t tmp[8]; + + inner_shake256_extract(rng, tmp, sizeof tmp); + return (uint64_t)tmp[0] + | ((uint64_t)tmp[1] << 8) + | ((uint64_t)tmp[2] << 16) + | ((uint64_t)tmp[3] << 24) + | ((uint64_t)tmp[4] << 32) + | ((uint64_t)tmp[5] << 40) + | ((uint64_t)tmp[6] << 48) + | ((uint64_t)tmp[7] << 56); +} + +/* + * Table below incarnates a discrete Gaussian distribution: + * D(x) = exp(-(x^2)/(2*sigma^2)) + * where sigma = 1.17*sqrt(q/(2*N)), q = 12289, and N = 1024. + * Element 0 of the table is P(x = 0). + * For k > 0, element k is P(x >= k+1 | x > 0). + * Probabilities are scaled up by 2^63. + */ +static const uint64_t gauss_1024_12289[] = { + 1283868770400643928u, 6416574995475331444u, 4078260278032692663u, + 2353523259288686585u, 1227179971273316331u, 575931623374121527u, + 242543240509105209u, 91437049221049666u, 30799446349977173u, + 9255276791179340u, 2478152334826140u, 590642893610164u, + 125206034929641u, 23590435911403u, 3948334035941u, + 586753615614u, 77391054539u, 9056793210u, + 940121950u, 86539696u, 7062824u, + 510971u, 32764u, 1862u, + 94u, 4u, 0u +}; + +/* + * Generate a random value with a Gaussian distribution centered on 0. + * The RNG must be ready for extraction (already flipped). + * + * Distribution has standard deviation 1.17*sqrt(q/(2*N)). The + * precomputed table is for N = 1024. Since the sum of two independent + * values of standard deviation sigma has standard deviation + * sigma*sqrt(2), then we can just generate more values and add them + * together for lower dimensions. + */ +static int +mkgauss(RNG_CONTEXT *rng, unsigned logn) { + unsigned u, g; + int val; + + g = 1U << (10 - logn); + val = 0; + for (u = 0; u < g; u ++) { + /* + * Each iteration generates one value with the + * Gaussian distribution for N = 1024. + * + * We use two random 64-bit values. First value + * decides on whether the generated value is 0, and, + * if not, the sign of the value. Second random 64-bit + * word is used to generate the non-zero value. + * + * For constant-time code we have to read the complete + * table. This has negligible cost, compared with the + * remainder of the keygen process (solving the NTRU + * equation). + */ + uint64_t r; + uint32_t f, v, k, neg; + + /* + * First value: + * - flag 'neg' is randomly selected to be 0 or 1. + * - flag 'f' is set to 1 if the generated value is zero, + * or set to 0 otherwise. + */ + r = get_rng_u64(rng); + neg = (uint32_t)(r >> 63); + r &= ~((uint64_t)1 << 63); + f = (uint32_t)((r - gauss_1024_12289[0]) >> 63); + + /* + * We produce a new random 63-bit integer r, and go over + * the array, starting at index 1. We store in v the + * index of the first array element which is not greater + * than r, unless the flag f was already 1. + */ + v = 0; + r = get_rng_u64(rng); + r &= ~((uint64_t)1 << 63); + for (k = 1; k < (uint32_t)((sizeof gauss_1024_12289) + / (sizeof gauss_1024_12289[0])); k ++) { + uint32_t t; + + t = (uint32_t)((r - gauss_1024_12289[k]) >> 63) ^ 1; + v |= k & -(t & (f ^ 1)); + f |= t; + } + + /* + * We apply the sign ('neg' flag). If the value is zero, + * the sign has no effect. + */ + v = (v ^ -neg) + neg; + + /* + * Generated value is added to val. + */ + val += *(int32_t *)&v; + } + return val; +} + +/* + * The MAX_BL_SMALL[] and MAX_BL_LARGE[] contain the lengths, in 31-bit + * words, of intermediate values in the computation: + * + * MAX_BL_SMALL[depth]: length for the input f and g at that depth + * MAX_BL_LARGE[depth]: length for the unreduced F and G at that depth + * + * Rules: + * + * - Within an array, values grow. + * + * - The 'SMALL' array must have an entry for maximum depth, corresponding + * to the size of values used in the binary GCD. There is no such value + * for the 'LARGE' array (the binary GCD yields already reduced + * coefficients). + * + * - MAX_BL_LARGE[depth] >= MAX_BL_SMALL[depth + 1]. + * + * - Values must be large enough to handle the common cases, with some + * margins. + * + * - Values must not be "too large" either because we will convert some + * integers into floating-point values by considering the top 10 words, + * i.e. 310 bits; hence, for values of length more than 10 words, we + * should take care to have the length centered on the expected size. + * + * The following average lengths, in bits, have been measured on thousands + * of random keys (fg = max length of the absolute value of coefficients + * of f and g at that depth; FG = idem for the unreduced F and G; for the + * maximum depth, F and G are the output of binary GCD, multiplied by q; + * for each value, the average and standard deviation are provided). + * + * Binary case: + * depth: 10 fg: 6307.52 (24.48) FG: 6319.66 (24.51) + * depth: 9 fg: 3138.35 (12.25) FG: 9403.29 (27.55) + * depth: 8 fg: 1576.87 ( 7.49) FG: 4703.30 (14.77) + * depth: 7 fg: 794.17 ( 4.98) FG: 2361.84 ( 9.31) + * depth: 6 fg: 400.67 ( 3.10) FG: 1188.68 ( 6.04) + * depth: 5 fg: 202.22 ( 1.87) FG: 599.81 ( 3.87) + * depth: 4 fg: 101.62 ( 1.02) FG: 303.49 ( 2.38) + * depth: 3 fg: 50.37 ( 0.53) FG: 153.65 ( 1.39) + * depth: 2 fg: 24.07 ( 0.25) FG: 78.20 ( 0.73) + * depth: 1 fg: 10.99 ( 0.08) FG: 39.82 ( 0.41) + * depth: 0 fg: 4.00 ( 0.00) FG: 19.61 ( 0.49) + * + * Integers are actually represented either in binary notation over + * 31-bit words (signed, using two's complement), or in RNS, modulo + * many small primes. These small primes are close to, but slightly + * lower than, 2^31. Use of RNS loses less than two bits, even for + * the largest values. + * + * IMPORTANT: if these values are modified, then the temporary buffer + * sizes (FALCON_KEYGEN_TEMP_*, in inner.h) must be recomputed + * accordingly. + */ + +static const size_t MAX_BL_SMALL[] = { + 1, 1, 2, 2, 4, 7, 14, 27, 53, 106, 209 +}; + +static const size_t MAX_BL_LARGE[] = { + 2, 2, 5, 7, 12, 21, 40, 78, 157, 308 +}; + +/* + * Average and standard deviation for the maximum size (in bits) of + * coefficients of (f,g), depending on depth. These values are used + * to compute bounds for Babai's reduction. + */ +static const struct { + int avg; + int std; +} BITLENGTH[] = { + { 4, 0 }, + { 11, 1 }, + { 24, 1 }, + { 50, 1 }, + { 102, 1 }, + { 202, 2 }, + { 401, 4 }, + { 794, 5 }, + { 1577, 8 }, + { 3138, 13 }, + { 6308, 25 } +}; + +/* + * Minimal recursion depth at which we rebuild intermediate values + * when reconstructing f and g. + */ +#define DEPTH_INT_FG 4 + +/* + * Compute squared norm of a short vector. Returned value is saturated to + * 2^32-1 if it is not lower than 2^31. + */ +static uint32_t +poly_small_sqnorm(const int8_t *f, unsigned logn) { + size_t n, u; + uint32_t s, ng; + + n = MKN(logn); + s = 0; + ng = 0; + for (u = 0; u < n; u ++) { + int32_t z; + + z = f[u]; + s += (uint32_t)(z * z); + ng |= s; + } + return s | -(ng >> 31); +} + +/* + * Align (upwards) the provided 'data' pointer with regards to 'base' + * so that the offset is a multiple of the size of 'fpr'. + */ +static fpr * +align_fpr(void *base, void *data) { + uint8_t *cb, *cd; + size_t k, km; + + cb = base; + cd = data; + k = (size_t)(cd - cb); + km = k % sizeof(fpr); + if (km) { + k += (sizeof(fpr)) - km; + } + return (fpr *)(cb + k); +} + +/* + * Align (upwards) the provided 'data' pointer with regards to 'base' + * so that the offset is a multiple of the size of 'uint32_t'. + */ +static uint32_t * +align_u32(void *base, void *data) { + uint8_t *cb, *cd; + size_t k, km; + + cb = base; + cd = data; + k = (size_t)(cd - cb); + km = k % sizeof(uint32_t); + if (km) { + k += (sizeof(uint32_t)) - km; + } + return (uint32_t *)(cb + k); +} + +/* + * Convert a small vector to floating point. + */ +static void +poly_small_to_fp(fpr *x, const int8_t *f, unsigned logn) { + size_t n, u; + + n = MKN(logn); + for (u = 0; u < n; u ++) { + x[u] = fpr_of(f[u]); + } +} + +/* + * Input: f,g of degree N = 2^logn; 'depth' is used only to get their + * individual length. + * + * Output: f',g' of degree N/2, with the length for 'depth+1'. + * + * Values are in RNS; input and/or output may also be in NTT. + */ +static void +make_fg_step(uint32_t *data, unsigned logn, unsigned depth, + int in_ntt, int out_ntt) { + size_t n, hn, u; + size_t slen, tlen; + uint32_t *fd, *gd, *fs, *gs, *gm, *igm, *t1; + const small_prime *primes; + + n = (size_t)1 << logn; + hn = n >> 1; + slen = MAX_BL_SMALL[depth]; + tlen = MAX_BL_SMALL[depth + 1]; + primes = PRIMES; + + /* + * Prepare room for the result. + */ + fd = data; + gd = fd + hn * tlen; + fs = gd + hn * tlen; + gs = fs + n * slen; + gm = gs + n * slen; + igm = gm + n; + t1 = igm + n; + memmove(fs, data, 2 * n * slen * sizeof * data); + + /* + * First slen words: we use the input values directly, and apply + * inverse NTT as we go. + */ + for (u = 0; u < slen; u ++) { + uint32_t p, p0i, R2; + size_t v; + uint32_t *x; + + p = primes[u].p; + p0i = modp_ninv31(p); + R2 = modp_R2(p, p0i); + modp_mkgm2(gm, igm, logn, primes[u].g, p, p0i); + + for (v = 0, x = fs + u; v < n; v ++, x += slen) { + t1[v] = *x; + } + if (!in_ntt) { + modp_NTT2(t1, gm, logn, p, p0i); + } + for (v = 0, x = fd + u; v < hn; v ++, x += tlen) { + uint32_t w0, w1; + + w0 = t1[(v << 1) + 0]; + w1 = t1[(v << 1) + 1]; + *x = modp_montymul( + modp_montymul(w0, w1, p, p0i), R2, p, p0i); + } + if (in_ntt) { + modp_iNTT2_ext(fs + u, slen, igm, logn, p, p0i); + } + + for (v = 0, x = gs + u; v < n; v ++, x += slen) { + t1[v] = *x; + } + if (!in_ntt) { + modp_NTT2(t1, gm, logn, p, p0i); + } + for (v = 0, x = gd + u; v < hn; v ++, x += tlen) { + uint32_t w0, w1; + + w0 = t1[(v << 1) + 0]; + w1 = t1[(v << 1) + 1]; + *x = modp_montymul( + modp_montymul(w0, w1, p, p0i), R2, p, p0i); + } + if (in_ntt) { + modp_iNTT2_ext(gs + u, slen, igm, logn, p, p0i); + } + + if (!out_ntt) { + modp_iNTT2_ext(fd + u, tlen, igm, logn - 1, p, p0i); + modp_iNTT2_ext(gd + u, tlen, igm, logn - 1, p, p0i); + } + } + + /* + * Since the fs and gs words have been de-NTTized, we can use the + * CRT to rebuild the values. + */ + zint_rebuild_CRT(fs, slen, slen, n, primes, 1, gm); + zint_rebuild_CRT(gs, slen, slen, n, primes, 1, gm); + + /* + * Remaining words: use modular reductions to extract the values. + */ + for (u = slen; u < tlen; u ++) { + uint32_t p, p0i, R2, Rx; + size_t v; + uint32_t *x; + + p = primes[u].p; + p0i = modp_ninv31(p); + R2 = modp_R2(p, p0i); + Rx = modp_Rx((unsigned)slen, p, p0i, R2); + modp_mkgm2(gm, igm, logn, primes[u].g, p, p0i); + for (v = 0, x = fs; v < n; v ++, x += slen) { + t1[v] = zint_mod_small_signed(x, slen, p, p0i, R2, Rx); + } + modp_NTT2(t1, gm, logn, p, p0i); + for (v = 0, x = fd + u; v < hn; v ++, x += tlen) { + uint32_t w0, w1; + + w0 = t1[(v << 1) + 0]; + w1 = t1[(v << 1) + 1]; + *x = modp_montymul( + modp_montymul(w0, w1, p, p0i), R2, p, p0i); + } + for (v = 0, x = gs; v < n; v ++, x += slen) { + t1[v] = zint_mod_small_signed(x, slen, p, p0i, R2, Rx); + } + modp_NTT2(t1, gm, logn, p, p0i); + for (v = 0, x = gd + u; v < hn; v ++, x += tlen) { + uint32_t w0, w1; + + w0 = t1[(v << 1) + 0]; + w1 = t1[(v << 1) + 1]; + *x = modp_montymul( + modp_montymul(w0, w1, p, p0i), R2, p, p0i); + } + + if (!out_ntt) { + modp_iNTT2_ext(fd + u, tlen, igm, logn - 1, p, p0i); + modp_iNTT2_ext(gd + u, tlen, igm, logn - 1, p, p0i); + } + } +} + +/* + * Compute f and g at a specific depth, in RNS notation. + * + * Returned values are stored in the data[] array, at slen words per integer. + * + * Conditions: + * 0 <= depth <= logn + * + * Space use in data[]: enough room for any two successive values (f', g', + * f and g). + */ +static void +make_fg(uint32_t *data, const int8_t *f, const int8_t *g, + unsigned logn, unsigned depth, int out_ntt) { + size_t n, u; + uint32_t *ft, *gt, p0; + unsigned d; + const small_prime *primes; + + n = MKN(logn); + ft = data; + gt = ft + n; + primes = PRIMES; + p0 = primes[0].p; + for (u = 0; u < n; u ++) { + ft[u] = modp_set(f[u], p0); + gt[u] = modp_set(g[u], p0); + } + + if (depth == 0 && out_ntt) { + uint32_t *gm, *igm; + uint32_t p, p0i; + + p = primes[0].p; + p0i = modp_ninv31(p); + gm = gt + n; + igm = gm + MKN(logn); + modp_mkgm2(gm, igm, logn, primes[0].g, p, p0i); + modp_NTT2(ft, gm, logn, p, p0i); + modp_NTT2(gt, gm, logn, p, p0i); + return; + } + + if (depth == 0) { + return; + } + if (depth == 1) { + make_fg_step(data, logn, 0, 0, out_ntt); + return; + } + make_fg_step(data, logn, 0, 0, 1); + for (d = 1; d + 1 < depth; d ++) { + make_fg_step(data, logn - d, d, 1, 1); + } + make_fg_step(data, logn - depth + 1, depth - 1, 1, out_ntt); +} + +/* + * Solving the NTRU equation, deepest level: compute the resultants of + * f and g with X^N+1, and use binary GCD. The F and G values are + * returned in tmp[]. + * + * Returned value: 1 on success, 0 on error. + */ +static int +solve_NTRU_deepest(unsigned logn_top, + const int8_t *f, const int8_t *g, uint32_t *tmp) { + size_t len; + uint32_t *Fp, *Gp, *fp, *gp, *t1, q; + const small_prime *primes; + + len = MAX_BL_SMALL[logn_top]; + primes = PRIMES; + + Fp = tmp; + Gp = Fp + len; + fp = Gp + len; + gp = fp + len; + t1 = gp + len; + + make_fg(fp, f, g, logn_top, logn_top, 0); + + /* + * We use the CRT to rebuild the resultants as big integers. + * There are two such big integers. The resultants are always + * nonnegative. + */ + zint_rebuild_CRT(fp, len, len, 2, primes, 0, t1); + + /* + * Apply the binary GCD. The zint_bezout() function works only + * if both inputs are odd. + * + * We can test on the result and return 0 because that would + * imply failure of the NTRU solving equation, and the (f,g) + * values will be abandoned in that case. + */ + if (!zint_bezout(Gp, Fp, fp, gp, len, t1)) { + return 0; + } + + /* + * Multiply the two values by the target value q. Values must + * fit in the destination arrays. + * We can again test on the returned words: a non-zero output + * of zint_mul_small() means that we exceeded our array + * capacity, and that implies failure and rejection of (f,g). + */ + q = 12289; + if (zint_mul_small(Fp, len, q) != 0 + || zint_mul_small(Gp, len, q) != 0) { + return 0; + } + + return 1; +} + +/* + * Solving the NTRU equation, intermediate level. Upon entry, the F and G + * from the previous level should be in the tmp[] array. + * This function MAY be invoked for the top-level (in which case depth = 0). + * + * Returned value: 1 on success, 0 on error. + */ +static int +solve_NTRU_intermediate(unsigned logn_top, + const int8_t *f, const int8_t *g, unsigned depth, uint32_t *tmp) { + /* + * In this function, 'logn' is the log2 of the degree for + * this step. If N = 2^logn, then: + * - the F and G values already in fk->tmp (from the deeper + * levels) have degree N/2; + * - this function should return F and G of degree N. + */ + unsigned logn; + size_t n, hn, slen, dlen, llen, rlen, FGlen, u; + uint32_t *Fd, *Gd, *Ft, *Gt, *ft, *gt, *t1; + fpr *rt1, *rt2, *rt3, *rt4, *rt5; + int scale_fg, minbl_fg, maxbl_fg, maxbl_FG, scale_k; + uint32_t *x, *y; + int32_t *k; + const small_prime *primes; + + logn = logn_top - depth; + n = (size_t)1 << logn; + hn = n >> 1; + + /* + * slen = size for our input f and g; also size of the reduced + * F and G we return (degree N) + * + * dlen = size of the F and G obtained from the deeper level + * (degree N/2 or N/3) + * + * llen = size for intermediary F and G before reduction (degree N) + * + * We build our non-reduced F and G as two independent halves each, + * of degree N/2 (F = F0 + X*F1, G = G0 + X*G1). + */ + slen = MAX_BL_SMALL[depth]; + dlen = MAX_BL_SMALL[depth + 1]; + llen = MAX_BL_LARGE[depth]; + primes = PRIMES; + + /* + * Fd and Gd are the F and G from the deeper level. + */ + Fd = tmp; + Gd = Fd + dlen * hn; + + /* + * Compute the input f and g for this level. Note that we get f + * and g in RNS + NTT representation. + */ + ft = Gd + dlen * hn; + make_fg(ft, f, g, logn_top, depth, 1); + + /* + * Move the newly computed f and g to make room for our candidate + * F and G (unreduced). + */ + Ft = tmp; + Gt = Ft + n * llen; + t1 = Gt + n * llen; + memmove(t1, ft, 2 * n * slen * sizeof * ft); + ft = t1; + gt = ft + slen * n; + t1 = gt + slen * n; + + /* + * Move Fd and Gd _after_ f and g. + */ + memmove(t1, Fd, 2 * hn * dlen * sizeof * Fd); + Fd = t1; + Gd = Fd + hn * dlen; + + /* + * We reduce Fd and Gd modulo all the small primes we will need, + * and store the values in Ft and Gt (only n/2 values in each). + */ + for (u = 0; u < llen; u ++) { + uint32_t p, p0i, R2, Rx; + size_t v; + uint32_t *xs, *ys, *xd, *yd; + + p = primes[u].p; + p0i = modp_ninv31(p); + R2 = modp_R2(p, p0i); + Rx = modp_Rx((unsigned)dlen, p, p0i, R2); + for (v = 0, xs = Fd, ys = Gd, xd = Ft + u, yd = Gt + u; + v < hn; + v ++, xs += dlen, ys += dlen, xd += llen, yd += llen) { + *xd = zint_mod_small_signed(xs, dlen, p, p0i, R2, Rx); + *yd = zint_mod_small_signed(ys, dlen, p, p0i, R2, Rx); + } + } + + /* + * We do not need Fd and Gd after that point. + */ + + /* + * Compute our F and G modulo sufficiently many small primes. + */ + for (u = 0; u < llen; u ++) { + uint32_t p, p0i, R2; + uint32_t *gm, *igm, *fx, *gx, *Fp, *Gp; + size_t v; + + /* + * All computations are done modulo p. + */ + p = primes[u].p; + p0i = modp_ninv31(p); + R2 = modp_R2(p, p0i); + + /* + * If we processed slen words, then f and g have been + * de-NTTized, and are in RNS; we can rebuild them. + */ + if (u == slen) { + zint_rebuild_CRT(ft, slen, slen, n, primes, 1, t1); + zint_rebuild_CRT(gt, slen, slen, n, primes, 1, t1); + } + + gm = t1; + igm = gm + n; + fx = igm + n; + gx = fx + n; + + modp_mkgm2(gm, igm, logn, primes[u].g, p, p0i); + + if (u < slen) { + for (v = 0, x = ft + u, y = gt + u; + v < n; v ++, x += slen, y += slen) { + fx[v] = *x; + gx[v] = *y; + } + modp_iNTT2_ext(ft + u, slen, igm, logn, p, p0i); + modp_iNTT2_ext(gt + u, slen, igm, logn, p, p0i); + } else { + uint32_t Rx; + + Rx = modp_Rx((unsigned)slen, p, p0i, R2); + for (v = 0, x = ft, y = gt; + v < n; v ++, x += slen, y += slen) { + fx[v] = zint_mod_small_signed(x, slen, + p, p0i, R2, Rx); + gx[v] = zint_mod_small_signed(y, slen, + p, p0i, R2, Rx); + } + modp_NTT2(fx, gm, logn, p, p0i); + modp_NTT2(gx, gm, logn, p, p0i); + } + + /* + * Get F' and G' modulo p and in NTT representation + * (they have degree n/2). These values were computed in + * a previous step, and stored in Ft and Gt. + */ + Fp = gx + n; + Gp = Fp + hn; + for (v = 0, x = Ft + u, y = Gt + u; + v < hn; v ++, x += llen, y += llen) { + Fp[v] = *x; + Gp[v] = *y; + } + modp_NTT2(Fp, gm, logn - 1, p, p0i); + modp_NTT2(Gp, gm, logn - 1, p, p0i); + + /* + * Compute our F and G modulo p. + * + * General case: + * + * we divide degree by d = 2 or 3 + * f'(x^d) = N(f)(x^d) = f * adj(f) + * g'(x^d) = N(g)(x^d) = g * adj(g) + * f'*G' - g'*F' = q + * F = F'(x^d) * adj(g) + * G = G'(x^d) * adj(f) + * + * We compute things in the NTT. We group roots of phi + * such that all roots x in a group share the same x^d. + * If the roots in a group are x_1, x_2... x_d, then: + * + * N(f)(x_1^d) = f(x_1)*f(x_2)*...*f(x_d) + * + * Thus, we have: + * + * G(x_1) = f(x_2)*f(x_3)*...*f(x_d)*G'(x_1^d) + * G(x_2) = f(x_1)*f(x_3)*...*f(x_d)*G'(x_1^d) + * ... + * G(x_d) = f(x_1)*f(x_2)*...*f(x_{d-1})*G'(x_1^d) + * + * In all cases, we can thus compute F and G in NTT + * representation by a few simple multiplications. + * Moreover, in our chosen NTT representation, roots + * from the same group are consecutive in RAM. + */ + for (v = 0, x = Ft + u, y = Gt + u; v < hn; + v ++, x += (llen << 1), y += (llen << 1)) { + uint32_t ftA, ftB, gtA, gtB; + uint32_t mFp, mGp; + + ftA = fx[(v << 1) + 0]; + ftB = fx[(v << 1) + 1]; + gtA = gx[(v << 1) + 0]; + gtB = gx[(v << 1) + 1]; + mFp = modp_montymul(Fp[v], R2, p, p0i); + mGp = modp_montymul(Gp[v], R2, p, p0i); + x[0] = modp_montymul(gtB, mFp, p, p0i); + x[llen] = modp_montymul(gtA, mFp, p, p0i); + y[0] = modp_montymul(ftB, mGp, p, p0i); + y[llen] = modp_montymul(ftA, mGp, p, p0i); + } + modp_iNTT2_ext(Ft + u, llen, igm, logn, p, p0i); + modp_iNTT2_ext(Gt + u, llen, igm, logn, p, p0i); + } + + /* + * Rebuild F and G with the CRT. + */ + zint_rebuild_CRT(Ft, llen, llen, n, primes, 1, t1); + zint_rebuild_CRT(Gt, llen, llen, n, primes, 1, t1); + + /* + * At that point, Ft, Gt, ft and gt are consecutive in RAM (in that + * order). + */ + + /* + * Apply Babai reduction to bring back F and G to size slen. + * + * We use the FFT to compute successive approximations of the + * reduction coefficient. We first isolate the top bits of + * the coefficients of f and g, and convert them to floating + * point; with the FFT, we compute adj(f), adj(g), and + * 1/(f*adj(f)+g*adj(g)). + * + * Then, we repeatedly apply the following: + * + * - Get the top bits of the coefficients of F and G into + * floating point, and use the FFT to compute: + * (F*adj(f)+G*adj(g))/(f*adj(f)+g*adj(g)) + * + * - Convert back that value into normal representation, and + * round it to the nearest integers, yielding a polynomial k. + * Proper scaling is applied to f, g, F and G so that the + * coefficients fit on 32 bits (signed). + * + * - Subtract k*f from F and k*g from G. + * + * Under normal conditions, this process reduces the size of F + * and G by some bits at each iteration. For constant-time + * operation, we do not want to measure the actual length of + * F and G; instead, we do the following: + * + * - f and g are converted to floating-point, with some scaling + * if necessary to keep values in the representable range. + * + * - For each iteration, we _assume_ a maximum size for F and G, + * and use the values at that size. If we overreach, then + * we get zeros, which is harmless: the resulting coefficients + * of k will be 0 and the value won't be reduced. + * + * - We conservatively assume that F and G will be reduced by + * at least 25 bits at each iteration. + * + * Even when reaching the bottom of the reduction, reduction + * coefficient will remain low. If it goes out-of-range, then + * something wrong occurred and the whole NTRU solving fails. + */ + + /* + * Memory layout: + * - We need to compute and keep adj(f), adj(g), and + * 1/(f*adj(f)+g*adj(g)) (sizes N, N and N/2 fp numbers, + * respectively). + * - At each iteration we need two extra fp buffer (N fp values), + * and produce a k (N 32-bit words). k will be shared with one + * of the fp buffers. + * - To compute k*f and k*g efficiently (with the NTT), we need + * some extra room; we reuse the space of the temporary buffers. + * + * Arrays of 'fpr' are obtained from the temporary array itself. + * We ensure that the base is at a properly aligned offset (the + * source array tmp[] is supposed to be already aligned). + */ + + rt3 = align_fpr(tmp, t1); + rt4 = rt3 + n; + rt5 = rt4 + n; + rt1 = rt5 + (n >> 1); + k = (int32_t *)align_u32(tmp, rt1); + rt2 = align_fpr(tmp, k + n); + if (rt2 < (rt1 + n)) { + rt2 = rt1 + n; + } + t1 = (uint32_t *)k + n; + + /* + * Get f and g into rt3 and rt4 as floating-point approximations. + * + * We need to "scale down" the floating-point representation of + * coefficients when they are too big. We want to keep the value + * below 2^310 or so. Thus, when values are larger than 10 words, + * we consider only the top 10 words. Array lengths have been + * computed so that average maximum length will fall in the + * middle or the upper half of these top 10 words. + */ + rlen = slen; + if (rlen > 10) { + rlen = 10; + } + poly_big_to_fp(rt3, ft + slen - rlen, rlen, slen, logn); + poly_big_to_fp(rt4, gt + slen - rlen, rlen, slen, logn); + + /* + * Values in rt3 and rt4 are downscaled by 2^(scale_fg). + */ + scale_fg = 31 * (int)(slen - rlen); + + /* + * Estimated boundaries for the maximum size (in bits) of the + * coefficients of (f,g). We use the measured average, and + * allow for a deviation of at most six times the standard + * deviation. + */ + minbl_fg = BITLENGTH[depth].avg - 6 * BITLENGTH[depth].std; + maxbl_fg = BITLENGTH[depth].avg + 6 * BITLENGTH[depth].std; + + /* + * Compute 1/(f*adj(f)+g*adj(g)) in rt5. We also keep adj(f) + * and adj(g) in rt3 and rt4, respectively. + */ + PQCLEAN_FALCON1024_CLEAN_FFT(rt3, logn); + PQCLEAN_FALCON1024_CLEAN_FFT(rt4, logn); + PQCLEAN_FALCON1024_CLEAN_poly_invnorm2_fft(rt5, rt3, rt4, logn); + PQCLEAN_FALCON1024_CLEAN_poly_adj_fft(rt3, logn); + PQCLEAN_FALCON1024_CLEAN_poly_adj_fft(rt4, logn); + + /* + * Reduce F and G repeatedly. + * + * The expected maximum bit length of coefficients of F and G + * is kept in maxbl_FG, with the corresponding word length in + * FGlen. + */ + FGlen = llen; + maxbl_FG = 31 * (int)llen; + + /* + * Each reduction operation computes the reduction polynomial + * "k". We need that polynomial to have coefficients that fit + * on 32-bit signed integers, with some scaling; thus, we use + * a descending sequence of scaling values, down to zero. + * + * The size of the coefficients of k is (roughly) the difference + * between the size of the coefficients of (F,G) and the size + * of the coefficients of (f,g). Thus, the maximum size of the + * coefficients of k is, at the start, maxbl_FG - minbl_fg; + * this is our starting scale value for k. + * + * We need to estimate the size of (F,G) during the execution of + * the algorithm; we are allowed some overestimation but not too + * much (poly_big_to_fp() uses a 310-bit window). Generally + * speaking, after applying a reduction with k scaled to + * scale_k, the size of (F,G) will be size(f,g) + scale_k + dd, + * where 'dd' is a few bits to account for the fact that the + * reduction is never perfect (intuitively, dd is on the order + * of sqrt(N), so at most 5 bits; we here allow for 10 extra + * bits). + * + * The size of (f,g) is not known exactly, but maxbl_fg is an + * upper bound. + */ + scale_k = maxbl_FG - minbl_fg; + + for (;;) { + int scale_FG, dc, new_maxbl_FG; + uint32_t scl, sch; + fpr pdc, pt; + + /* + * Convert current F and G into floating-point. We apply + * scaling if the current length is more than 10 words. + */ + rlen = FGlen; + if (rlen > 10) { + rlen = 10; + } + scale_FG = 31 * (int)(FGlen - rlen); + poly_big_to_fp(rt1, Ft + FGlen - rlen, rlen, llen, logn); + poly_big_to_fp(rt2, Gt + FGlen - rlen, rlen, llen, logn); + + /* + * Compute (F*adj(f)+G*adj(g))/(f*adj(f)+g*adj(g)) in rt2. + */ + PQCLEAN_FALCON1024_CLEAN_FFT(rt1, logn); + PQCLEAN_FALCON1024_CLEAN_FFT(rt2, logn); + PQCLEAN_FALCON1024_CLEAN_poly_mul_fft(rt1, rt3, logn); + PQCLEAN_FALCON1024_CLEAN_poly_mul_fft(rt2, rt4, logn); + PQCLEAN_FALCON1024_CLEAN_poly_add(rt2, rt1, logn); + PQCLEAN_FALCON1024_CLEAN_poly_mul_autoadj_fft(rt2, rt5, logn); + PQCLEAN_FALCON1024_CLEAN_iFFT(rt2, logn); + + /* + * (f,g) are scaled by 'scale_fg', meaning that the + * numbers in rt3/rt4 should be multiplied by 2^(scale_fg) + * to have their true mathematical value. + * + * (F,G) are similarly scaled by 'scale_FG'. Therefore, + * the value we computed in rt2 is scaled by + * 'scale_FG-scale_fg'. + * + * We want that value to be scaled by 'scale_k', hence we + * apply a corrective scaling. After scaling, the values + * should fit in -2^31-1..+2^31-1. + */ + dc = scale_k - scale_FG + scale_fg; + + /* + * We will need to multiply values by 2^(-dc). The value + * 'dc' is not secret, so we can compute 2^(-dc) with a + * non-constant-time process. + * (We could use ldexp(), but we prefer to avoid any + * dependency on libm. When using FP emulation, we could + * use our fpr_ldexp(), which is constant-time.) + */ + if (dc < 0) { + dc = -dc; + pt = fpr_two; + } else { + pt = fpr_onehalf; + } + pdc = fpr_one; + while (dc != 0) { + if ((dc & 1) != 0) { + pdc = fpr_mul(pdc, pt); + } + dc >>= 1; + pt = fpr_sqr(pt); + } + + for (u = 0; u < n; u ++) { + fpr xv; + + xv = fpr_mul(rt2[u], pdc); + + /* + * Sometimes the values can be out-of-bounds if + * the algorithm fails; we must not call + * fpr_rint() (and cast to int32_t) if the value + * is not in-bounds. Note that the test does not + * break constant-time discipline, since any + * failure here implies that we discard the current + * secret key (f,g). + */ + if (!fpr_lt(fpr_mtwo31m1, xv) + || !fpr_lt(xv, fpr_ptwo31m1)) { + return 0; + } + k[u] = (int32_t)fpr_rint(xv); + } + + /* + * Values in k[] are integers. They really are scaled + * down by maxbl_FG - minbl_fg bits. + * + * If we are at low depth, then we use the NTT to + * compute k*f and k*g. + */ + sch = (uint32_t)(scale_k / 31); + scl = (uint32_t)(scale_k % 31); + if (depth <= DEPTH_INT_FG) { + poly_sub_scaled_ntt(Ft, FGlen, llen, ft, slen, slen, + k, sch, scl, logn, t1); + poly_sub_scaled_ntt(Gt, FGlen, llen, gt, slen, slen, + k, sch, scl, logn, t1); + } else { + poly_sub_scaled(Ft, FGlen, llen, ft, slen, slen, + k, sch, scl, logn); + poly_sub_scaled(Gt, FGlen, llen, gt, slen, slen, + k, sch, scl, logn); + } + + /* + * We compute the new maximum size of (F,G), assuming that + * (f,g) has _maximal_ length (i.e. that reduction is + * "late" instead of "early". We also adjust FGlen + * accordingly. + */ + new_maxbl_FG = scale_k + maxbl_fg + 10; + if (new_maxbl_FG < maxbl_FG) { + maxbl_FG = new_maxbl_FG; + if ((int)FGlen * 31 >= maxbl_FG + 31) { + FGlen --; + } + } + + /* + * We suppose that scaling down achieves a reduction by + * at least 25 bits per iteration. We stop when we have + * done the loop with an unscaled k. + */ + if (scale_k <= 0) { + break; + } + scale_k -= 25; + if (scale_k < 0) { + scale_k = 0; + } + } + + /* + * If (F,G) length was lowered below 'slen', then we must take + * care to re-extend the sign. + */ + if (FGlen < slen) { + for (u = 0; u < n; u ++, Ft += llen, Gt += llen) { + size_t v; + uint32_t sw; + + sw = -(Ft[FGlen - 1] >> 30) >> 1; + for (v = FGlen; v < slen; v ++) { + Ft[v] = sw; + } + sw = -(Gt[FGlen - 1] >> 30) >> 1; + for (v = FGlen; v < slen; v ++) { + Gt[v] = sw; + } + } + } + + /* + * Compress encoding of all values to 'slen' words (this is the + * expected output format). + */ + for (u = 0, x = tmp, y = tmp; + u < (n << 1); u ++, x += slen, y += llen) { + memmove(x, y, slen * sizeof * y); + } + return 1; +} + +/* + * Solving the NTRU equation, binary case, depth = 1. Upon entry, the + * F and G from the previous level should be in the tmp[] array. + * + * Returned value: 1 on success, 0 on error. + */ +static int +solve_NTRU_binary_depth1(unsigned logn_top, + const int8_t *f, const int8_t *g, uint32_t *tmp) { + /* + * The first half of this function is a copy of the corresponding + * part in solve_NTRU_intermediate(), for the reconstruction of + * the unreduced F and G. The second half (Babai reduction) is + * done differently, because the unreduced F and G fit in 53 bits + * of precision, allowing a much simpler process with lower RAM + * usage. + */ + unsigned depth, logn; + size_t n_top, n, hn, slen, dlen, llen, u; + uint32_t *Fd, *Gd, *Ft, *Gt, *ft, *gt, *t1; + fpr *rt1, *rt2, *rt3, *rt4, *rt5, *rt6; + uint32_t *x, *y; + + depth = 1; + n_top = (size_t)1 << logn_top; + logn = logn_top - depth; + n = (size_t)1 << logn; + hn = n >> 1; + + /* + * Equations are: + * + * f' = f0^2 - X^2*f1^2 + * g' = g0^2 - X^2*g1^2 + * F' and G' are a solution to f'G' - g'F' = q (from deeper levels) + * F = F'*(g0 - X*g1) + * G = G'*(f0 - X*f1) + * + * f0, f1, g0, g1, f', g', F' and G' are all "compressed" to + * degree N/2 (their odd-indexed coefficients are all zero). + */ + + /* + * slen = size for our input f and g; also size of the reduced + * F and G we return (degree N) + * + * dlen = size of the F and G obtained from the deeper level + * (degree N/2) + * + * llen = size for intermediary F and G before reduction (degree N) + * + * We build our non-reduced F and G as two independent halves each, + * of degree N/2 (F = F0 + X*F1, G = G0 + X*G1). + */ + slen = MAX_BL_SMALL[depth]; + dlen = MAX_BL_SMALL[depth + 1]; + llen = MAX_BL_LARGE[depth]; + + /* + * Fd and Gd are the F and G from the deeper level. Ft and Gt + * are the destination arrays for the unreduced F and G. + */ + Fd = tmp; + Gd = Fd + dlen * hn; + Ft = Gd + dlen * hn; + Gt = Ft + llen * n; + + /* + * We reduce Fd and Gd modulo all the small primes we will need, + * and store the values in Ft and Gt. + */ + for (u = 0; u < llen; u ++) { + uint32_t p, p0i, R2, Rx; + size_t v; + uint32_t *xs, *ys, *xd, *yd; + + p = PRIMES[u].p; + p0i = modp_ninv31(p); + R2 = modp_R2(p, p0i); + Rx = modp_Rx((unsigned)dlen, p, p0i, R2); + for (v = 0, xs = Fd, ys = Gd, xd = Ft + u, yd = Gt + u; + v < hn; + v ++, xs += dlen, ys += dlen, xd += llen, yd += llen) { + *xd = zint_mod_small_signed(xs, dlen, p, p0i, R2, Rx); + *yd = zint_mod_small_signed(ys, dlen, p, p0i, R2, Rx); + } + } + + /* + * Now Fd and Gd are not needed anymore; we can squeeze them out. + */ + memmove(tmp, Ft, llen * n * sizeof(uint32_t)); + Ft = tmp; + memmove(Ft + llen * n, Gt, llen * n * sizeof(uint32_t)); + Gt = Ft + llen * n; + ft = Gt + llen * n; + gt = ft + slen * n; + + t1 = gt + slen * n; + + /* + * Compute our F and G modulo sufficiently many small primes. + */ + for (u = 0; u < llen; u ++) { + uint32_t p, p0i, R2; + uint32_t *gm, *igm, *fx, *gx, *Fp, *Gp; + unsigned e; + size_t v; + + /* + * All computations are done modulo p. + */ + p = PRIMES[u].p; + p0i = modp_ninv31(p); + R2 = modp_R2(p, p0i); + + /* + * We recompute things from the source f and g, of full + * degree. However, we will need only the n first elements + * of the inverse NTT table (igm); the call to modp_mkgm() + * below will fill n_top elements in igm[] (thus overflowing + * into fx[]) but later code will overwrite these extra + * elements. + */ + gm = t1; + igm = gm + n_top; + fx = igm + n; + gx = fx + n_top; + modp_mkgm2(gm, igm, logn_top, PRIMES[u].g, p, p0i); + + /* + * Set ft and gt to f and g modulo p, respectively. + */ + for (v = 0; v < n_top; v ++) { + fx[v] = modp_set(f[v], p); + gx[v] = modp_set(g[v], p); + } + + /* + * Convert to NTT and compute our f and g. + */ + modp_NTT2(fx, gm, logn_top, p, p0i); + modp_NTT2(gx, gm, logn_top, p, p0i); + for (e = logn_top; e > logn; e --) { + modp_poly_rec_res(fx, e, p, p0i, R2); + modp_poly_rec_res(gx, e, p, p0i, R2); + } + + /* + * From that point onward, we only need tables for + * degree n, so we can save some space. + */ + if (depth > 0) { /* always true */ + memmove(gm + n, igm, n * sizeof * igm); + igm = gm + n; + memmove(igm + n, fx, n * sizeof * ft); + fx = igm + n; + memmove(fx + n, gx, n * sizeof * gt); + gx = fx + n; + } + + /* + * Get F' and G' modulo p and in NTT representation + * (they have degree n/2). These values were computed + * in a previous step, and stored in Ft and Gt. + */ + Fp = gx + n; + Gp = Fp + hn; + for (v = 0, x = Ft + u, y = Gt + u; + v < hn; v ++, x += llen, y += llen) { + Fp[v] = *x; + Gp[v] = *y; + } + modp_NTT2(Fp, gm, logn - 1, p, p0i); + modp_NTT2(Gp, gm, logn - 1, p, p0i); + + /* + * Compute our F and G modulo p. + * + * Equations are: + * + * f'(x^2) = N(f)(x^2) = f * adj(f) + * g'(x^2) = N(g)(x^2) = g * adj(g) + * + * f'*G' - g'*F' = q + * + * F = F'(x^2) * adj(g) + * G = G'(x^2) * adj(f) + * + * The NTT representation of f is f(w) for all w which + * are roots of phi. In the binary case, as well as in + * the ternary case for all depth except the deepest, + * these roots can be grouped in pairs (w,-w), and we + * then have: + * + * f(w) = adj(f)(-w) + * f(-w) = adj(f)(w) + * + * and w^2 is then a root for phi at the half-degree. + * + * At the deepest level in the ternary case, this still + * holds, in the following sense: the roots of x^2-x+1 + * are (w,-w^2) (for w^3 = -1, and w != -1), and we + * have: + * + * f(w) = adj(f)(-w^2) + * f(-w^2) = adj(f)(w) + * + * In all case, we can thus compute F and G in NTT + * representation by a few simple multiplications. + * Moreover, the two roots for each pair are consecutive + * in our bit-reversal encoding. + */ + for (v = 0, x = Ft + u, y = Gt + u; + v < hn; v ++, x += (llen << 1), y += (llen << 1)) { + uint32_t ftA, ftB, gtA, gtB; + uint32_t mFp, mGp; + + ftA = fx[(v << 1) + 0]; + ftB = fx[(v << 1) + 1]; + gtA = gx[(v << 1) + 0]; + gtB = gx[(v << 1) + 1]; + mFp = modp_montymul(Fp[v], R2, p, p0i); + mGp = modp_montymul(Gp[v], R2, p, p0i); + x[0] = modp_montymul(gtB, mFp, p, p0i); + x[llen] = modp_montymul(gtA, mFp, p, p0i); + y[0] = modp_montymul(ftB, mGp, p, p0i); + y[llen] = modp_montymul(ftA, mGp, p, p0i); + } + modp_iNTT2_ext(Ft + u, llen, igm, logn, p, p0i); + modp_iNTT2_ext(Gt + u, llen, igm, logn, p, p0i); + + /* + * Also save ft and gt (only up to size slen). + */ + if (u < slen) { + modp_iNTT2(fx, igm, logn, p, p0i); + modp_iNTT2(gx, igm, logn, p, p0i); + for (v = 0, x = ft + u, y = gt + u; + v < n; v ++, x += slen, y += slen) { + *x = fx[v]; + *y = gx[v]; + } + } + } + + /* + * Rebuild f, g, F and G with the CRT. Note that the elements of F + * and G are consecutive, and thus can be rebuilt in a single + * loop; similarly, the elements of f and g are consecutive. + */ + zint_rebuild_CRT(Ft, llen, llen, n << 1, PRIMES, 1, t1); + zint_rebuild_CRT(ft, slen, slen, n << 1, PRIMES, 1, t1); + + /* + * Here starts the Babai reduction, specialized for depth = 1. + * + * Candidates F and G (from Ft and Gt), and base f and g (ft and gt), + * are converted to floating point. There is no scaling, and a + * single pass is sufficient. + */ + + /* + * Convert F and G into floating point (rt1 and rt2). + */ + rt1 = align_fpr(tmp, gt + slen * n); + rt2 = rt1 + n; + poly_big_to_fp(rt1, Ft, llen, llen, logn); + poly_big_to_fp(rt2, Gt, llen, llen, logn); + + /* + * Integer representation of F and G is no longer needed, we + * can remove it. + */ + memmove(tmp, ft, 2 * slen * n * sizeof * ft); + ft = tmp; + gt = ft + slen * n; + rt3 = align_fpr(tmp, gt + slen * n); + memmove(rt3, rt1, 2 * n * sizeof * rt1); + rt1 = rt3; + rt2 = rt1 + n; + rt3 = rt2 + n; + rt4 = rt3 + n; + + /* + * Convert f and g into floating point (rt3 and rt4). + */ + poly_big_to_fp(rt3, ft, slen, slen, logn); + poly_big_to_fp(rt4, gt, slen, slen, logn); + + /* + * Remove unneeded ft and gt. + */ + memmove(tmp, rt1, 4 * n * sizeof * rt1); + rt1 = (fpr *)tmp; + rt2 = rt1 + n; + rt3 = rt2 + n; + rt4 = rt3 + n; + + /* + * We now have: + * rt1 = F + * rt2 = G + * rt3 = f + * rt4 = g + * in that order in RAM. We convert all of them to FFT. + */ + PQCLEAN_FALCON1024_CLEAN_FFT(rt1, logn); + PQCLEAN_FALCON1024_CLEAN_FFT(rt2, logn); + PQCLEAN_FALCON1024_CLEAN_FFT(rt3, logn); + PQCLEAN_FALCON1024_CLEAN_FFT(rt4, logn); + + /* + * Compute: + * rt5 = F*adj(f) + G*adj(g) + * rt6 = 1 / (f*adj(f) + g*adj(g)) + * (Note that rt6 is half-length.) + */ + rt5 = rt4 + n; + rt6 = rt5 + n; + PQCLEAN_FALCON1024_CLEAN_poly_add_muladj_fft(rt5, rt1, rt2, rt3, rt4, logn); + PQCLEAN_FALCON1024_CLEAN_poly_invnorm2_fft(rt6, rt3, rt4, logn); + + /* + * Compute: + * rt5 = (F*adj(f)+G*adj(g)) / (f*adj(f)+g*adj(g)) + */ + PQCLEAN_FALCON1024_CLEAN_poly_mul_autoadj_fft(rt5, rt6, logn); + + /* + * Compute k as the rounded version of rt5. Check that none of + * the values is larger than 2^63-1 (in absolute value) + * because that would make the fpr_rint() do something undefined; + * note that any out-of-bounds value here implies a failure and + * (f,g) will be discarded, so we can make a simple test. + */ + PQCLEAN_FALCON1024_CLEAN_iFFT(rt5, logn); + for (u = 0; u < n; u ++) { + fpr z; + + z = rt5[u]; + if (!fpr_lt(z, fpr_ptwo63m1) || !fpr_lt(fpr_mtwo63m1, z)) { + return 0; + } + rt5[u] = fpr_of(fpr_rint(z)); + } + PQCLEAN_FALCON1024_CLEAN_FFT(rt5, logn); + + /* + * Subtract k*f from F, and k*g from G. + */ + PQCLEAN_FALCON1024_CLEAN_poly_mul_fft(rt3, rt5, logn); + PQCLEAN_FALCON1024_CLEAN_poly_mul_fft(rt4, rt5, logn); + PQCLEAN_FALCON1024_CLEAN_poly_sub(rt1, rt3, logn); + PQCLEAN_FALCON1024_CLEAN_poly_sub(rt2, rt4, logn); + PQCLEAN_FALCON1024_CLEAN_iFFT(rt1, logn); + PQCLEAN_FALCON1024_CLEAN_iFFT(rt2, logn); + + /* + * Convert back F and G to integers, and return. + */ + Ft = tmp; + Gt = Ft + n; + rt3 = align_fpr(tmp, Gt + n); + memmove(rt3, rt1, 2 * n * sizeof * rt1); + rt1 = rt3; + rt2 = rt1 + n; + for (u = 0; u < n; u ++) { + Ft[u] = (uint32_t)fpr_rint(rt1[u]); + Gt[u] = (uint32_t)fpr_rint(rt2[u]); + } + + return 1; +} + +/* + * Solving the NTRU equation, top level. Upon entry, the F and G + * from the previous level should be in the tmp[] array. + * + * Returned value: 1 on success, 0 on error. + */ +static int +solve_NTRU_binary_depth0(unsigned logn, + const int8_t *f, const int8_t *g, uint32_t *tmp) { + size_t n, hn, u; + uint32_t p, p0i, R2; + uint32_t *Fp, *Gp, *t1, *t2, *t3, *t4, *t5; + uint32_t *gm, *igm, *ft, *gt; + fpr *rt2, *rt3; + + n = (size_t)1 << logn; + hn = n >> 1; + + /* + * Equations are: + * + * f' = f0^2 - X^2*f1^2 + * g' = g0^2 - X^2*g1^2 + * F' and G' are a solution to f'G' - g'F' = q (from deeper levels) + * F = F'*(g0 - X*g1) + * G = G'*(f0 - X*f1) + * + * f0, f1, g0, g1, f', g', F' and G' are all "compressed" to + * degree N/2 (their odd-indexed coefficients are all zero). + * + * Everything should fit in 31-bit integers, hence we can just use + * the first small prime p = 2147473409. + */ + p = PRIMES[0].p; + p0i = modp_ninv31(p); + R2 = modp_R2(p, p0i); + + Fp = tmp; + Gp = Fp + hn; + ft = Gp + hn; + gt = ft + n; + gm = gt + n; + igm = gm + n; + + modp_mkgm2(gm, igm, logn, PRIMES[0].g, p, p0i); + + /* + * Convert F' anf G' in NTT representation. + */ + for (u = 0; u < hn; u ++) { + Fp[u] = modp_set(zint_one_to_plain(Fp + u), p); + Gp[u] = modp_set(zint_one_to_plain(Gp + u), p); + } + modp_NTT2(Fp, gm, logn - 1, p, p0i); + modp_NTT2(Gp, gm, logn - 1, p, p0i); + + /* + * Load f and g and convert them to NTT representation. + */ + for (u = 0; u < n; u ++) { + ft[u] = modp_set(f[u], p); + gt[u] = modp_set(g[u], p); + } + modp_NTT2(ft, gm, logn, p, p0i); + modp_NTT2(gt, gm, logn, p, p0i); + + /* + * Build the unreduced F,G in ft and gt. + */ + for (u = 0; u < n; u += 2) { + uint32_t ftA, ftB, gtA, gtB; + uint32_t mFp, mGp; + + ftA = ft[u + 0]; + ftB = ft[u + 1]; + gtA = gt[u + 0]; + gtB = gt[u + 1]; + mFp = modp_montymul(Fp[u >> 1], R2, p, p0i); + mGp = modp_montymul(Gp[u >> 1], R2, p, p0i); + ft[u + 0] = modp_montymul(gtB, mFp, p, p0i); + ft[u + 1] = modp_montymul(gtA, mFp, p, p0i); + gt[u + 0] = modp_montymul(ftB, mGp, p, p0i); + gt[u + 1] = modp_montymul(ftA, mGp, p, p0i); + } + modp_iNTT2(ft, igm, logn, p, p0i); + modp_iNTT2(gt, igm, logn, p, p0i); + + Gp = Fp + n; + t1 = Gp + n; + memmove(Fp, ft, 2 * n * sizeof * ft); + + /* + * We now need to apply the Babai reduction. At that point, + * we have F and G in two n-word arrays. + * + * We can compute F*adj(f)+G*adj(g) and f*adj(f)+g*adj(g) + * modulo p, using the NTT. We still move memory around in + * order to save RAM. + */ + t2 = t1 + n; + t3 = t2 + n; + t4 = t3 + n; + t5 = t4 + n; + + /* + * Compute the NTT tables in t1 and t2. We do not keep t2 + * (we'll recompute it later on). + */ + modp_mkgm2(t1, t2, logn, PRIMES[0].g, p, p0i); + + /* + * Convert F and G to NTT. + */ + modp_NTT2(Fp, t1, logn, p, p0i); + modp_NTT2(Gp, t1, logn, p, p0i); + + /* + * Load f and adj(f) in t4 and t5, and convert them to NTT + * representation. + */ + t4[0] = t5[0] = modp_set(f[0], p); + for (u = 1; u < n; u ++) { + t4[u] = modp_set(f[u], p); + t5[n - u] = modp_set(-f[u], p); + } + modp_NTT2(t4, t1, logn, p, p0i); + modp_NTT2(t5, t1, logn, p, p0i); + + /* + * Compute F*adj(f) in t2, and f*adj(f) in t3. + */ + for (u = 0; u < n; u ++) { + uint32_t w; + + w = modp_montymul(t5[u], R2, p, p0i); + t2[u] = modp_montymul(w, Fp[u], p, p0i); + t3[u] = modp_montymul(w, t4[u], p, p0i); + } + + /* + * Load g and adj(g) in t4 and t5, and convert them to NTT + * representation. + */ + t4[0] = t5[0] = modp_set(g[0], p); + for (u = 1; u < n; u ++) { + t4[u] = modp_set(g[u], p); + t5[n - u] = modp_set(-g[u], p); + } + modp_NTT2(t4, t1, logn, p, p0i); + modp_NTT2(t5, t1, logn, p, p0i); + + /* + * Add G*adj(g) to t2, and g*adj(g) to t3. + */ + for (u = 0; u < n; u ++) { + uint32_t w; + + w = modp_montymul(t5[u], R2, p, p0i); + t2[u] = modp_add(t2[u], + modp_montymul(w, Gp[u], p, p0i), p); + t3[u] = modp_add(t3[u], + modp_montymul(w, t4[u], p, p0i), p); + } + + /* + * Convert back t2 and t3 to normal representation (normalized + * around 0), and then + * move them to t1 and t2. We first need to recompute the + * inverse table for NTT. + */ + modp_mkgm2(t1, t4, logn, PRIMES[0].g, p, p0i); + modp_iNTT2(t2, t4, logn, p, p0i); + modp_iNTT2(t3, t4, logn, p, p0i); + for (u = 0; u < n; u ++) { + t1[u] = (uint32_t)modp_norm(t2[u], p); + t2[u] = (uint32_t)modp_norm(t3[u], p); + } + + /* + * At that point, array contents are: + * + * F (NTT representation) (Fp) + * G (NTT representation) (Gp) + * F*adj(f)+G*adj(g) (t1) + * f*adj(f)+g*adj(g) (t2) + * + * We want to divide t1 by t2. The result is not integral; it + * must be rounded. We thus need to use the FFT. + */ + + /* + * Get f*adj(f)+g*adj(g) in FFT representation. Since this + * polynomial is auto-adjoint, all its coordinates in FFT + * representation are actually real, so we can truncate off + * the imaginary parts. + */ + rt3 = align_fpr(tmp, t3); + for (u = 0; u < n; u ++) { + rt3[u] = fpr_of(((int32_t *)t2)[u]); + } + PQCLEAN_FALCON1024_CLEAN_FFT(rt3, logn); + rt2 = align_fpr(tmp, t2); + memmove(rt2, rt3, hn * sizeof * rt3); + + /* + * Convert F*adj(f)+G*adj(g) in FFT representation. + */ + rt3 = rt2 + hn; + for (u = 0; u < n; u ++) { + rt3[u] = fpr_of(((int32_t *)t1)[u]); + } + PQCLEAN_FALCON1024_CLEAN_FFT(rt3, logn); + + /* + * Compute (F*adj(f)+G*adj(g))/(f*adj(f)+g*adj(g)) and get + * its rounded normal representation in t1. + */ + PQCLEAN_FALCON1024_CLEAN_poly_div_autoadj_fft(rt3, rt2, logn); + PQCLEAN_FALCON1024_CLEAN_iFFT(rt3, logn); + for (u = 0; u < n; u ++) { + t1[u] = modp_set((int32_t)fpr_rint(rt3[u]), p); + } + + /* + * RAM contents are now: + * + * F (NTT representation) (Fp) + * G (NTT representation) (Gp) + * k (t1) + * + * We want to compute F-k*f, and G-k*g. + */ + t2 = t1 + n; + t3 = t2 + n; + t4 = t3 + n; + t5 = t4 + n; + modp_mkgm2(t2, t3, logn, PRIMES[0].g, p, p0i); + for (u = 0; u < n; u ++) { + t4[u] = modp_set(f[u], p); + t5[u] = modp_set(g[u], p); + } + modp_NTT2(t1, t2, logn, p, p0i); + modp_NTT2(t4, t2, logn, p, p0i); + modp_NTT2(t5, t2, logn, p, p0i); + for (u = 0; u < n; u ++) { + uint32_t kw; + + kw = modp_montymul(t1[u], R2, p, p0i); + Fp[u] = modp_sub(Fp[u], + modp_montymul(kw, t4[u], p, p0i), p); + Gp[u] = modp_sub(Gp[u], + modp_montymul(kw, t5[u], p, p0i), p); + } + modp_iNTT2(Fp, t3, logn, p, p0i); + modp_iNTT2(Gp, t3, logn, p, p0i); + for (u = 0; u < n; u ++) { + Fp[u] = (uint32_t)modp_norm(Fp[u], p); + Gp[u] = (uint32_t)modp_norm(Gp[u], p); + } + + return 1; +} + +/* + * Solve the NTRU equation. Returned value is 1 on success, 0 on error. + * G can be NULL, in which case that value is computed but not returned. + * If any of the coefficients of F and G exceeds lim (in absolute value), + * then 0 is returned. + */ +static int +solve_NTRU(unsigned logn, int8_t *F, int8_t *G, + const int8_t *f, const int8_t *g, int lim, uint32_t *tmp) { + size_t n, u; + uint32_t *ft, *gt, *Ft, *Gt, *gm; + uint32_t p, p0i, r; + const small_prime *primes; + + n = MKN(logn); + + if (!solve_NTRU_deepest(logn, f, g, tmp)) { + return 0; + } + + /* + * For logn <= 2, we need to use solve_NTRU_intermediate() + * directly, because coefficients are a bit too large and + * do not fit the hypotheses in solve_NTRU_binary_depth0(). + */ + if (logn <= 2) { + unsigned depth; + + depth = logn; + while (depth -- > 0) { + if (!solve_NTRU_intermediate(logn, f, g, depth, tmp)) { + return 0; + } + } + } else { + unsigned depth; + + depth = logn; + while (depth -- > 2) { + if (!solve_NTRU_intermediate(logn, f, g, depth, tmp)) { + return 0; + } + } + if (!solve_NTRU_binary_depth1(logn, f, g, tmp)) { + return 0; + } + if (!solve_NTRU_binary_depth0(logn, f, g, tmp)) { + return 0; + } + } + + /* + * If no buffer has been provided for G, use a temporary one. + */ + if (G == NULL) { + G = (int8_t *)(tmp + 2 * n); + } + + /* + * Final F and G are in fk->tmp, one word per coefficient + * (signed value over 31 bits). + */ + if (!poly_big_to_small(F, tmp, lim, logn) + || !poly_big_to_small(G, tmp + n, lim, logn)) { + return 0; + } + + /* + * Verify that the NTRU equation is fulfilled. Since all elements + * have short lengths, verifying modulo a small prime p works, and + * allows using the NTT. + * + * We put Gt[] first in tmp[], and process it first, so that it does + * not overlap with G[] in case we allocated it ourselves. + */ + Gt = tmp; + ft = Gt + n; + gt = ft + n; + Ft = gt + n; + gm = Ft + n; + + primes = PRIMES; + p = primes[0].p; + p0i = modp_ninv31(p); + modp_mkgm2(gm, tmp, logn, primes[0].g, p, p0i); + for (u = 0; u < n; u ++) { + Gt[u] = modp_set(G[u], p); + } + for (u = 0; u < n; u ++) { + ft[u] = modp_set(f[u], p); + gt[u] = modp_set(g[u], p); + Ft[u] = modp_set(F[u], p); + } + modp_NTT2(ft, gm, logn, p, p0i); + modp_NTT2(gt, gm, logn, p, p0i); + modp_NTT2(Ft, gm, logn, p, p0i); + modp_NTT2(Gt, gm, logn, p, p0i); + r = modp_montymul(12289, 1, p, p0i); + for (u = 0; u < n; u ++) { + uint32_t z; + + z = modp_sub(modp_montymul(ft[u], Gt[u], p, p0i), + modp_montymul(gt[u], Ft[u], p, p0i), p); + if (z != r) { + return 0; + } + } + + return 1; +} + +/* + * Generate a random polynomial with a Gaussian distribution. This function + * also makes sure that the resultant of the polynomial with phi is odd. + */ +static void +poly_small_mkgauss(RNG_CONTEXT *rng, int8_t *f, unsigned logn) { + size_t n, u; + unsigned mod2; + + n = MKN(logn); + mod2 = 0; + for (u = 0; u < n; u ++) { + int s; + +restart: + s = mkgauss(rng, logn); + + /* + * We need the coefficient to fit within -127..+127; + * realistically, this is always the case except for + * the very low degrees (N = 2 or 4), for which there + * is no real security anyway. + */ + if (s < -127 || s > 127) { + goto restart; + } + + /* + * We need the sum of all coefficients to be 1; otherwise, + * the resultant of the polynomial with X^N+1 will be even, + * and the binary GCD will fail. + */ + if (u == n - 1) { + if ((mod2 ^ (unsigned)(s & 1)) == 0) { + goto restart; + } + } else { + mod2 ^= (unsigned)(s & 1); + } + f[u] = (int8_t)s; + } +} + +/* see falcon.h */ +void +PQCLEAN_FALCON1024_CLEAN_keygen(inner_shake256_context *rng, + int8_t *f, int8_t *g, int8_t *F, int8_t *G, uint16_t *h, + unsigned logn, uint8_t *tmp) { + /* + * Algorithm is the following: + * + * - Generate f and g with the Gaussian distribution. + * + * - If either Res(f,phi) or Res(g,phi) is even, try again. + * + * - If ||(f,g)|| is too large, try again. + * + * - If ||B~_{f,g}|| is too large, try again. + * + * - If f is not invertible mod phi mod q, try again. + * + * - Compute h = g/f mod phi mod q. + * + * - Solve the NTRU equation fG - gF = q; if the solving fails, + * try again. Usual failure condition is when Res(f,phi) + * and Res(g,phi) are not prime to each other. + */ + size_t n, u; + uint16_t *h2, *tmp2; + RNG_CONTEXT *rc; + + n = MKN(logn); + rc = rng; + + /* + * We need to generate f and g randomly, until we find values + * such that the norm of (g,-f), and of the orthogonalized + * vector, are satisfying. The orthogonalized vector is: + * (q*adj(f)/(f*adj(f)+g*adj(g)), q*adj(g)/(f*adj(f)+g*adj(g))) + * (it is actually the (N+1)-th row of the Gram-Schmidt basis). + * + * In the binary case, coefficients of f and g are generated + * independently of each other, with a discrete Gaussian + * distribution of standard deviation 1.17*sqrt(q/(2*N)). Then, + * the two vectors have expected norm 1.17*sqrt(q), which is + * also our acceptance bound: we require both vectors to be no + * larger than that (this will be satisfied about 1/4th of the + * time, thus we expect sampling new (f,g) about 4 times for that + * step). + * + * We require that Res(f,phi) and Res(g,phi) are both odd (the + * NTRU equation solver requires it). + */ + for (;;) { + fpr *rt1, *rt2, *rt3; + fpr bnorm; + uint32_t normf, normg, norm; + int lim; + + /* + * The poly_small_mkgauss() function makes sure + * that the sum of coefficients is 1 modulo 2 + * (i.e. the resultant of the polynomial with phi + * will be odd). + */ + poly_small_mkgauss(rc, f, logn); + poly_small_mkgauss(rc, g, logn); + + /* + * Verify that all coefficients are within the bounds + * defined in max_fg_bits. This is the case with + * overwhelming probability; this guarantees that the + * key will be encodable with FALCON_COMP_TRIM. + */ + lim = 1 << (PQCLEAN_FALCON1024_CLEAN_max_fg_bits[logn] - 1); + for (u = 0; u < n; u ++) { + /* + * We can use non-CT tests since on any failure + * we will discard f and g. + */ + if (f[u] >= lim || f[u] <= -lim + || g[u] >= lim || g[u] <= -lim) { + lim = -1; + break; + } + } + if (lim < 0) { + continue; + } + + /* + * Bound is 1.17*sqrt(q). We compute the squared + * norms. With q = 12289, the squared bound is: + * (1.17^2)* 12289 = 16822.4121 + * Since f and g are integral, the squared norm + * of (g,-f) is an integer. + */ + normf = poly_small_sqnorm(f, logn); + normg = poly_small_sqnorm(g, logn); + norm = (normf + normg) | -((normf | normg) >> 31); + if (norm >= 16823) { + continue; + } + + /* + * We compute the orthogonalized vector norm. + */ + rt1 = (fpr *)tmp; + rt2 = rt1 + n; + rt3 = rt2 + n; + poly_small_to_fp(rt1, f, logn); + poly_small_to_fp(rt2, g, logn); + PQCLEAN_FALCON1024_CLEAN_FFT(rt1, logn); + PQCLEAN_FALCON1024_CLEAN_FFT(rt2, logn); + PQCLEAN_FALCON1024_CLEAN_poly_invnorm2_fft(rt3, rt1, rt2, logn); + PQCLEAN_FALCON1024_CLEAN_poly_adj_fft(rt1, logn); + PQCLEAN_FALCON1024_CLEAN_poly_adj_fft(rt2, logn); + PQCLEAN_FALCON1024_CLEAN_poly_mulconst(rt1, fpr_q, logn); + PQCLEAN_FALCON1024_CLEAN_poly_mulconst(rt2, fpr_q, logn); + PQCLEAN_FALCON1024_CLEAN_poly_mul_autoadj_fft(rt1, rt3, logn); + PQCLEAN_FALCON1024_CLEAN_poly_mul_autoadj_fft(rt2, rt3, logn); + PQCLEAN_FALCON1024_CLEAN_iFFT(rt1, logn); + PQCLEAN_FALCON1024_CLEAN_iFFT(rt2, logn); + bnorm = fpr_zero; + for (u = 0; u < n; u ++) { + bnorm = fpr_add(bnorm, fpr_sqr(rt1[u])); + bnorm = fpr_add(bnorm, fpr_sqr(rt2[u])); + } + if (!fpr_lt(bnorm, fpr_bnorm_max)) { + continue; + } + + /* + * Compute public key h = g/f mod X^N+1 mod q. If this + * fails, we must restart. + */ + if (h == NULL) { + h2 = (uint16_t *)tmp; + tmp2 = h2 + n; + } else { + h2 = h; + tmp2 = (uint16_t *)tmp; + } + if (!PQCLEAN_FALCON1024_CLEAN_compute_public(h2, f, g, logn, (uint8_t *)tmp2)) { + continue; + } + + /* + * Solve the NTRU equation to get F and G. + */ + lim = (1 << (PQCLEAN_FALCON1024_CLEAN_max_FG_bits[logn] - 1)) - 1; + if (!solve_NTRU(logn, F, G, f, g, lim, (uint32_t *)tmp)) { + continue; + } + + /* + * Key pair is generated. + */ + break; + } +} diff --git a/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/manifest.mn b/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/manifest.mn new file mode 100644 index 000000000..ed57e0aee --- /dev/null +++ b/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/manifest.mn @@ -0,0 +1,32 @@ +# DO NOT EDIT: generated from manifest.mn.subdirs.template +# +# This Source Code Form is subject to the terms of the Mozilla Public +# License, v. 2.0. If a copy of the MPL was not distributed with this +# file, You can obtain one at http://mozilla.org/MPL/2.0/. +CORE_DEPTH = ../../../../../.. + +MODULE = oqs + +LIBRARY_NAME = oqs_src_sig_falcon_pqclean_falcon-1024_clean +SHARED_LIBRARY = $(NULL) + +CSRCS = \ + codec.c \ + common.c \ + fft.c \ + fpr.c \ + inner.c \ + keygen.c \ + pqclean.c \ + rng.c \ + sign.c \ + vrfy.c \ + $(NULL) + +# only add module debugging in opt builds if DEBUG_PKCS11 is set +ifdef DEBUG_PKCS11 + DEFINES += -DDEBUG_MODULE +endif + +# This part of the code, including all sub-dirs, can be optimized for size +export ALLOW_OPT_CODE_SIZE = 1 diff --git a/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/pqclean.c b/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/pqclean.c new file mode 100644 index 000000000..292357a86 --- /dev/null +++ b/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/pqclean.c @@ -0,0 +1,386 @@ +#include "api.h" +#include "inner.h" +#include "randombytes.h" +#include <stddef.h> +#include <string.h> +/* + * Wrapper for implementing the PQClean API. + */ + + + +#define NONCELEN 40 +#define SEEDLEN 48 + +/* + * Encoding formats (nnnn = log of degree, 9 for Falcon-512, 10 for Falcon-1024) + * + * private key: + * header byte: 0101nnnn + * private f (6 or 5 bits by element, depending on degree) + * private g (6 or 5 bits by element, depending on degree) + * private F (8 bits by element) + * + * public key: + * header byte: 0000nnnn + * public h (14 bits by element) + * + * signature: + * header byte: 0011nnnn + * nonce 40 bytes + * value (12 bits by element) + * + * message + signature: + * signature length (2 bytes, big-endian) + * nonce 40 bytes + * message + * header byte: 0010nnnn + * value (12 bits by element) + * (signature length is 1+len(value), not counting the nonce) + */ + +/* see api.h */ +int +PQCLEAN_FALCON1024_CLEAN_crypto_sign_keypair(unsigned char *pk, unsigned char *sk) { + union { + uint8_t b[28 * 1024]; + uint64_t dummy_u64; + fpr dummy_fpr; + } tmp; + int8_t f[1024], g[1024], F[1024], G[1024]; + uint16_t h[1024]; + unsigned char seed[SEEDLEN]; + inner_shake256_context rng; + size_t u, v; + + + /* + * Generate key pair. + */ + randombytes(seed, sizeof seed); + inner_shake256_init(&rng); + inner_shake256_inject(&rng, seed, sizeof seed); + inner_shake256_flip(&rng); + PQCLEAN_FALCON1024_CLEAN_keygen(&rng, f, g, F, G, h, 10, tmp.b); + inner_shake256_ctx_release(&rng); + + /* + * Encode private key. + */ + sk[0] = 0x50 + 10; + u = 1; + v = PQCLEAN_FALCON1024_CLEAN_trim_i8_encode( + sk + u, PQCLEAN_FALCON1024_CLEAN_CRYPTO_SECRETKEYBYTES - u, + f, 10, PQCLEAN_FALCON1024_CLEAN_max_fg_bits[10]); + if (v == 0) { + return -1; + } + u += v; + v = PQCLEAN_FALCON1024_CLEAN_trim_i8_encode( + sk + u, PQCLEAN_FALCON1024_CLEAN_CRYPTO_SECRETKEYBYTES - u, + g, 10, PQCLEAN_FALCON1024_CLEAN_max_fg_bits[10]); + if (v == 0) { + return -1; + } + u += v; + v = PQCLEAN_FALCON1024_CLEAN_trim_i8_encode( + sk + u, PQCLEAN_FALCON1024_CLEAN_CRYPTO_SECRETKEYBYTES - u, + F, 10, PQCLEAN_FALCON1024_CLEAN_max_FG_bits[10]); + if (v == 0) { + return -1; + } + u += v; + if (u != PQCLEAN_FALCON1024_CLEAN_CRYPTO_SECRETKEYBYTES) { + return -1; + } + + /* + * Encode public key. + */ + pk[0] = 0x00 + 10; + v = PQCLEAN_FALCON1024_CLEAN_modq_encode( + pk + 1, PQCLEAN_FALCON1024_CLEAN_CRYPTO_PUBLICKEYBYTES - 1, + h, 10); + if (v != PQCLEAN_FALCON1024_CLEAN_CRYPTO_PUBLICKEYBYTES - 1) { + return -1; + } + + return 0; +} + +/* + * Compute the signature. nonce[] receives the nonce and must have length + * NONCELEN bytes. sigbuf[] receives the signature value (without nonce + * or header byte), with *sigbuflen providing the maximum value length and + * receiving the actual value length. + * + * If a signature could be computed but not encoded because it would + * exceed the output buffer size, then a new signature is computed. If + * the provided buffer size is too low, this could loop indefinitely, so + * the caller must provide a size that can accommodate signatures with a + * large enough probability. + * + * Return value: 0 on success, -1 on error. + */ +static int +do_sign(uint8_t *nonce, uint8_t *sigbuf, size_t *sigbuflen, + const uint8_t *m, size_t mlen, const uint8_t *sk) { + union { + uint8_t b[72 * 1024]; + uint64_t dummy_u64; + fpr dummy_fpr; + } tmp; + int8_t f[1024], g[1024], F[1024], G[1024]; + union { + int16_t sig[1024]; + uint16_t hm[1024]; + } r; + unsigned char seed[SEEDLEN]; + inner_shake256_context sc; + size_t u, v; + + /* + * Decode the private key. + */ + if (sk[0] != 0x50 + 10) { + return -1; + } + u = 1; + v = PQCLEAN_FALCON1024_CLEAN_trim_i8_decode( + f, 10, PQCLEAN_FALCON1024_CLEAN_max_fg_bits[10], + sk + u, PQCLEAN_FALCON1024_CLEAN_CRYPTO_SECRETKEYBYTES - u); + if (v == 0) { + return -1; + } + u += v; + v = PQCLEAN_FALCON1024_CLEAN_trim_i8_decode( + g, 10, PQCLEAN_FALCON1024_CLEAN_max_fg_bits[10], + sk + u, PQCLEAN_FALCON1024_CLEAN_CRYPTO_SECRETKEYBYTES - u); + if (v == 0) { + return -1; + } + u += v; + v = PQCLEAN_FALCON1024_CLEAN_trim_i8_decode( + F, 10, PQCLEAN_FALCON1024_CLEAN_max_FG_bits[10], + sk + u, PQCLEAN_FALCON1024_CLEAN_CRYPTO_SECRETKEYBYTES - u); + if (v == 0) { + return -1; + } + u += v; + if (u != PQCLEAN_FALCON1024_CLEAN_CRYPTO_SECRETKEYBYTES) { + return -1; + } + if (!PQCLEAN_FALCON1024_CLEAN_complete_private(G, f, g, F, 10, tmp.b)) { + return -1; + } + + + /* + * Create a random nonce (40 bytes). + */ + randombytes(nonce, NONCELEN); + + /* + * Hash message nonce + message into a vector. + */ + inner_shake256_init(&sc); + inner_shake256_inject(&sc, nonce, NONCELEN); + inner_shake256_inject(&sc, m, mlen); + inner_shake256_flip(&sc); + PQCLEAN_FALCON1024_CLEAN_hash_to_point_ct(&sc, r.hm, 10, tmp.b); + inner_shake256_ctx_release(&sc); + + /* + * Initialize a RNG. + */ + randombytes(seed, sizeof seed); + inner_shake256_init(&sc); + inner_shake256_inject(&sc, seed, sizeof seed); + inner_shake256_flip(&sc); + + /* + * Compute and return the signature. This loops until a signature + * value is found that fits in the provided buffer. + */ + for (;;) { + PQCLEAN_FALCON1024_CLEAN_sign_dyn(r.sig, &sc, f, g, F, G, r.hm, 10, tmp.b); + v = PQCLEAN_FALCON1024_CLEAN_comp_encode(sigbuf, *sigbuflen, r.sig, 10); + if (v != 0) { + inner_shake256_ctx_release(&sc); + *sigbuflen = v; + return 0; + } + } +} + +/* + * Verify a sigature. The nonce has size NONCELEN bytes. sigbuf[] + * (of size sigbuflen) contains the signature value, not including the + * header byte or nonce. Return value is 0 on success, -1 on error. + */ +static int +do_verify( + const uint8_t *nonce, const uint8_t *sigbuf, size_t sigbuflen, + const uint8_t *m, size_t mlen, const uint8_t *pk) { + union { + uint8_t b[2 * 1024]; + uint64_t dummy_u64; + fpr dummy_fpr; + } tmp; + uint16_t h[1024], hm[1024]; + int16_t sig[1024]; + inner_shake256_context sc; + + /* + * Decode public key. + */ + if (pk[0] != 0x00 + 10) { + return -1; + } + if (PQCLEAN_FALCON1024_CLEAN_modq_decode(h, 10, + pk + 1, PQCLEAN_FALCON1024_CLEAN_CRYPTO_PUBLICKEYBYTES - 1) + != PQCLEAN_FALCON1024_CLEAN_CRYPTO_PUBLICKEYBYTES - 1) { + return -1; + } + PQCLEAN_FALCON1024_CLEAN_to_ntt_monty(h, 10); + + /* + * Decode signature. + */ + if (sigbuflen == 0) { + return -1; + } + if (PQCLEAN_FALCON1024_CLEAN_comp_decode(sig, 10, sigbuf, sigbuflen) != sigbuflen) { + return -1; + } + + /* + * Hash nonce + message into a vector. + */ + inner_shake256_init(&sc); + inner_shake256_inject(&sc, nonce, NONCELEN); + inner_shake256_inject(&sc, m, mlen); + inner_shake256_flip(&sc); + PQCLEAN_FALCON1024_CLEAN_hash_to_point_ct(&sc, hm, 10, tmp.b); + inner_shake256_ctx_release(&sc); + + /* + * Verify signature. + */ + if (!PQCLEAN_FALCON1024_CLEAN_verify_raw(hm, sig, h, 10, tmp.b)) { + return -1; + } + return 0; +} + +/* see api.h */ +int +PQCLEAN_FALCON1024_CLEAN_crypto_sign_signature( + uint8_t *sig, size_t *siglen, + const uint8_t *m, size_t mlen, const uint8_t *sk) { + /* + * The PQCLEAN_FALCON1024_CLEAN_CRYPTO_BYTES constant is used for + * the signed message object (as produced by PQCLEAN_FALCON1024_CLEAN_crypto_sign()) + * and includes a two-byte length value, so we take care here + * to only generate signatures that are two bytes shorter than + * the maximum. This is done to ensure that PQCLEAN_FALCON1024_CLEAN_crypto_sign() + * and PQCLEAN_FALCON1024_CLEAN_crypto_sign_signature() produce the exact same signature + * value, if used on the same message, with the same private key, + * and using the same output from randombytes() (this is for + * reproducibility of tests). + */ + size_t vlen; + + vlen = PQCLEAN_FALCON1024_CLEAN_CRYPTO_BYTES - NONCELEN - 3; + if (do_sign(sig + 1, sig + 1 + NONCELEN, &vlen, m, mlen, sk) < 0) { + return -1; + } + sig[0] = 0x30 + 10; + *siglen = 1 + NONCELEN + vlen; + return 0; +} + +/* see api.h */ +int +PQCLEAN_FALCON1024_CLEAN_crypto_sign_verify( + const uint8_t *sig, size_t siglen, + const uint8_t *m, size_t mlen, const uint8_t *pk) { + if (siglen < 1 + NONCELEN) { + return -1; + } + if (sig[0] != 0x30 + 10) { + return -1; + } + return do_verify(sig + 1, + sig + 1 + NONCELEN, siglen - 1 - NONCELEN, m, mlen, pk); +} + +/* see api.h */ +int +PQCLEAN_FALCON1024_CLEAN_crypto_sign( + uint8_t *sm, size_t *smlen, + const uint8_t *m, size_t mlen, const uint8_t *sk) { + uint8_t *pm, *sigbuf; + size_t sigbuflen; + + /* + * Move the message to its final location; this is a memmove() so + * it handles overlaps properly. + */ + memmove(sm + 2 + NONCELEN, m, mlen); + pm = sm + 2 + NONCELEN; + sigbuf = pm + 1 + mlen; + sigbuflen = PQCLEAN_FALCON1024_CLEAN_CRYPTO_BYTES - NONCELEN - 3; + if (do_sign(sm + 2, sigbuf, &sigbuflen, pm, mlen, sk) < 0) { + return -1; + } + pm[mlen] = 0x20 + 10; + sigbuflen ++; + sm[0] = (uint8_t)(sigbuflen >> 8); + sm[1] = (uint8_t)sigbuflen; + *smlen = mlen + 2 + NONCELEN + sigbuflen; + return 0; +} + +/* see api.h */ +int +PQCLEAN_FALCON1024_CLEAN_crypto_sign_open( + uint8_t *m, size_t *mlen, + const uint8_t *sm, size_t smlen, const uint8_t *pk) { + const uint8_t *sigbuf; + size_t pmlen, sigbuflen; + + if (smlen < 3 + NONCELEN) { + return -1; + } + sigbuflen = ((size_t)sm[0] << 8) | (size_t)sm[1]; + if (sigbuflen < 2 || sigbuflen > (smlen - NONCELEN - 2)) { + return -1; + } + sigbuflen --; + pmlen = smlen - NONCELEN - 3 - sigbuflen; + if (sm[2 + NONCELEN + pmlen] != 0x20 + 10) { + return -1; + } + sigbuf = sm + 2 + NONCELEN + pmlen + 1; + + /* + * The 2-byte length header and the one-byte signature header + * have been verified. Nonce is at sm+2, followed by the message + * itself. Message length is in pmlen. sigbuf/sigbuflen point to + * the signature value (excluding the header byte). + */ + if (do_verify(sm + 2, sigbuf, sigbuflen, + sm + 2 + NONCELEN, pmlen, pk) < 0) { + return -1; + } + + /* + * Signature is correct, we just have to copy/move the message + * to its final destination. The memmove() properly handles + * overlaps. + */ + memmove(m, sm + 2 + NONCELEN, pmlen); + *mlen = pmlen; + return 0; +} diff --git a/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/pqclean_falcon-1024_clean.gyp b/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/pqclean_falcon-1024_clean.gyp new file mode 100644 index 000000000..5e06930d4 --- /dev/null +++ b/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/pqclean_falcon-1024_clean.gyp @@ -0,0 +1,48 @@ +# DO NOT EDIT: generated from subdir.gyp.template +# This Source Code Form is subject to the terms of the Mozilla Public +# License, v. 2.0. If a copy of the MPL was not distributed with this +# file, You can obtain one at http://mozilla.org/MPL/2.0/. +{ + 'includes': [ + '../../../../../../coreconf/config.gypi' + ], + 'targets': [ + { + 'target_name': 'oqs_src_sig_falcon_pqclean_falcon-1024_clean', + 'type': 'static_library', + 'sources': [ + 'codec.c', + 'common.c', + 'fft.c', + 'fpr.c', + 'inner.c', + 'keygen.c', + 'pqclean.c', + 'rng.c', + 'sign.c', + 'vrfy.c', + ], + 'dependencies': [ + '<(DEPTH)/exports.gyp:nss_exports' + ] + } + ], + 'target_defaults': { + 'defines': [ + ], + 'include_dirs': [ + '<(DEPTH)/lib/liboqs/src/common/pqclean_shims', + '<(DEPTH)/lib/liboqs/src/common/sha3/xkcp_low/KeccakP-1600/plain-64bits', + ], + [ 'OS=="mac"', { + 'defines': [ + 'OQS_HAVE_POSIX_MEMALIGN', + 'OQS_HAVE_ALIGNED_ALLOC', + 'OQS_HAVE_MEMALIGN' + ] + }] + }, + 'variables': { + 'module': 'oqs' + } +} diff --git a/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/rng.c b/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/rng.c new file mode 100644 index 000000000..f5739a8f4 --- /dev/null +++ b/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/rng.c @@ -0,0 +1,201 @@ +#include "inner.h" +#include <assert.h> +/* + * PRNG and interface to the system RNG. + * + * ==========================(LICENSE BEGIN)============================ + * + * Copyright (c) 2017-2019 Falcon Project + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the + * "Software"), to deal in the Software without restriction, including + * without limitation the rights to use, copy, modify, merge, publish, + * distribute, sublicense, and/or sell copies of the Software, and to + * permit persons to whom the Software is furnished to do so, subject to + * the following conditions: + * + * The above copyright notice and this permission notice shall be + * included in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, + * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF + * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. + * IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY + * CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, + * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE + * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. + * + * ===========================(LICENSE END)============================= + * + * @author Thomas Pornin <thomas.pornin@nccgroup.com> + */ + + + +/* + * Include relevant system header files. For Win32, this will also need + * linking with advapi32.dll, which we trigger with an appropriate #pragma. + */ + +/* see inner.h */ +int +PQCLEAN_FALCON1024_CLEAN_get_seed(void *seed, size_t len) { + (void)seed; + if (len == 0) { + return 1; + } + return 0; +} + +/* see inner.h */ +void +PQCLEAN_FALCON1024_CLEAN_prng_init(prng *p, inner_shake256_context *src) { + /* + * To ensure reproducibility for a given seed, we + * must enforce little-endian interpretation of + * the state words. + */ + uint8_t tmp[56]; + uint64_t th, tl; + int i; + + inner_shake256_extract(src, tmp, 56); + for (i = 0; i < 14; i ++) { + uint32_t w; + + w = (uint32_t)tmp[(i << 2) + 0] + | ((uint32_t)tmp[(i << 2) + 1] << 8) + | ((uint32_t)tmp[(i << 2) + 2] << 16) + | ((uint32_t)tmp[(i << 2) + 3] << 24); + *(uint32_t *)(p->state.d + (i << 2)) = w; + } + tl = *(uint32_t *)(p->state.d + 48); + th = *(uint32_t *)(p->state.d + 52); + *(uint64_t *)(p->state.d + 48) = tl + (th << 32); + PQCLEAN_FALCON1024_CLEAN_prng_refill(p); +} + +/* + * PRNG based on ChaCha20. + * + * State consists in key (32 bytes) then IV (16 bytes) and block counter + * (8 bytes). Normally, we should not care about local endianness (this + * is for a PRNG), but for the NIST competition we need reproducible KAT + * vectors that work across architectures, so we enforce little-endian + * interpretation where applicable. Moreover, output words are "spread + * out" over the output buffer with the interleaving pattern that is + * naturally obtained from the AVX2 implementation that runs eight + * ChaCha20 instances in parallel. + * + * The block counter is XORed into the first 8 bytes of the IV. + */ +void +PQCLEAN_FALCON1024_CLEAN_prng_refill(prng *p) { + + static const uint32_t CW[] = { + 0x61707865, 0x3320646e, 0x79622d32, 0x6b206574 + }; + + uint64_t cc; + size_t u; + + /* + * State uses local endianness. Only the output bytes must be + * converted to little endian (if used on a big-endian machine). + */ + cc = *(uint64_t *)(p->state.d + 48); + for (u = 0; u < 8; u ++) { + uint32_t state[16]; + size_t v; + int i; + + memcpy(&state[0], CW, sizeof CW); + memcpy(&state[4], p->state.d, 48); + state[14] ^= (uint32_t)cc; + state[15] ^= (uint32_t)(cc >> 32); + for (i = 0; i < 10; i ++) { + +#define QROUND(a, b, c, d) do { \ + state[a] += state[b]; \ + state[d] ^= state[a]; \ + state[d] = (state[d] << 16) | (state[d] >> 16); \ + state[c] += state[d]; \ + state[b] ^= state[c]; \ + state[b] = (state[b] << 12) | (state[b] >> 20); \ + state[a] += state[b]; \ + state[d] ^= state[a]; \ + state[d] = (state[d] << 8) | (state[d] >> 24); \ + state[c] += state[d]; \ + state[b] ^= state[c]; \ + state[b] = (state[b] << 7) | (state[b] >> 25); \ + } while (0) + + QROUND( 0, 4, 8, 12); + QROUND( 1, 5, 9, 13); + QROUND( 2, 6, 10, 14); + QROUND( 3, 7, 11, 15); + QROUND( 0, 5, 10, 15); + QROUND( 1, 6, 11, 12); + QROUND( 2, 7, 8, 13); + QROUND( 3, 4, 9, 14); + +#undef QROUND + + } + + for (v = 0; v < 4; v ++) { + state[v] += CW[v]; + } + for (v = 4; v < 14; v ++) { + state[v] += ((uint32_t *)p->state.d)[v - 4]; + } + state[14] += ((uint32_t *)p->state.d)[10] + ^ (uint32_t)cc; + state[15] += ((uint32_t *)p->state.d)[11] + ^ (uint32_t)(cc >> 32); + cc ++; + + /* + * We mimic the interleaving that is used in the AVX2 + * implementation. + */ + for (v = 0; v < 16; v ++) { + p->buf.d[(u << 2) + (v << 5) + 0] = + (uint8_t)state[v]; + p->buf.d[(u << 2) + (v << 5) + 1] = + (uint8_t)(state[v] >> 8); + p->buf.d[(u << 2) + (v << 5) + 2] = + (uint8_t)(state[v] >> 16); + p->buf.d[(u << 2) + (v << 5) + 3] = + (uint8_t)(state[v] >> 24); + } + } + *(uint64_t *)(p->state.d + 48) = cc; + + + p->ptr = 0; +} + +/* see inner.h */ +void +PQCLEAN_FALCON1024_CLEAN_prng_get_bytes(prng *p, void *dst, size_t len) { + uint8_t *buf; + + buf = dst; + while (len > 0) { + size_t clen; + + clen = (sizeof p->buf.d) - p->ptr; + if (clen > len) { + clen = len; + } + memcpy(buf, p->buf.d, clen); + buf += clen; + len -= clen; + p->ptr += clen; + if (p->ptr == sizeof p->buf.d) { + PQCLEAN_FALCON1024_CLEAN_prng_refill(p); + } + } +} diff --git a/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/sign.c b/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/sign.c new file mode 100644 index 000000000..0baa9148e --- /dev/null +++ b/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/sign.c @@ -0,0 +1,1254 @@ +#include "inner.h" + +/* + * Falcon signature generation. + * + * ==========================(LICENSE BEGIN)============================ + * + * Copyright (c) 2017-2019 Falcon Project + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the + * "Software"), to deal in the Software without restriction, including + * without limitation the rights to use, copy, modify, merge, publish, + * distribute, sublicense, and/or sell copies of the Software, and to + * permit persons to whom the Software is furnished to do so, subject to + * the following conditions: + * + * The above copyright notice and this permission notice shall be + * included in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, + * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF + * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. + * IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY + * CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, + * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE + * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. + * + * ===========================(LICENSE END)============================= + * + * @author Thomas Pornin <thomas.pornin@nccgroup.com> + */ + + +/* =================================================================== */ + +/* + * Compute degree N from logarithm 'logn'. + */ +#define MKN(logn) ((size_t)1 << (logn)) + +/* =================================================================== */ +/* + * Binary case: + * N = 2^logn + * phi = X^N+1 + */ + +/* + * Get the size of the LDL tree for an input with polynomials of size + * 2^logn. The size is expressed in the number of elements. + */ +static inline unsigned +ffLDL_treesize(unsigned logn) { + /* + * For logn = 0 (polynomials are constant), the "tree" is a + * single element. Otherwise, the tree node has size 2^logn, and + * has two child trees for size logn-1 each. Thus, treesize s() + * must fulfill these two relations: + * + * s(0) = 1 + * s(logn) = (2^logn) + 2*s(logn-1) + */ + return (logn + 1) << logn; +} + +/* + * Inner function for ffLDL_fft(). It expects the matrix to be both + * auto-adjoint and quasicyclic; also, it uses the source operands + * as modifiable temporaries. + * + * tmp[] must have room for at least one polynomial. + */ +static void +ffLDL_fft_inner(fpr *tree, + fpr *g0, fpr *g1, unsigned logn, fpr *tmp) { + size_t n, hn; + + n = MKN(logn); + if (n == 1) { + tree[0] = g0[0]; + return; + } + hn = n >> 1; + + /* + * The LDL decomposition yields L (which is written in the tree) + * and the diagonal of D. Since d00 = g0, we just write d11 + * into tmp. + */ + PQCLEAN_FALCON1024_CLEAN_poly_LDLmv_fft(tmp, tree, g0, g1, g0, logn); + + /* + * Split d00 (currently in g0) and d11 (currently in tmp). We + * reuse g0 and g1 as temporary storage spaces: + * d00 splits into g1, g1+hn + * d11 splits into g0, g0+hn + */ + PQCLEAN_FALCON1024_CLEAN_poly_split_fft(g1, g1 + hn, g0, logn); + PQCLEAN_FALCON1024_CLEAN_poly_split_fft(g0, g0 + hn, tmp, logn); + + /* + * Each split result is the first row of a new auto-adjoint + * quasicyclic matrix for the next recursive step. + */ + ffLDL_fft_inner(tree + n, + g1, g1 + hn, logn - 1, tmp); + ffLDL_fft_inner(tree + n + ffLDL_treesize(logn - 1), + g0, g0 + hn, logn - 1, tmp); +} + +/* + * Compute the ffLDL tree of an auto-adjoint matrix G. The matrix + * is provided as three polynomials (FFT representation). + * + * The "tree" array is filled with the computed tree, of size + * (logn+1)*(2^logn) elements (see ffLDL_treesize()). + * + * Input arrays MUST NOT overlap, except possibly the three unmodified + * arrays g00, g01 and g11. tmp[] should have room for at least three + * polynomials of 2^logn elements each. + */ +static void +ffLDL_fft(fpr *tree, const fpr *g00, + const fpr *g01, const fpr *g11, + unsigned logn, fpr *tmp) { + size_t n, hn; + fpr *d00, *d11; + + n = MKN(logn); + if (n == 1) { + tree[0] = g00[0]; + return; + } + hn = n >> 1; + d00 = tmp; + d11 = tmp + n; + tmp += n << 1; + + memcpy(d00, g00, n * sizeof * g00); + PQCLEAN_FALCON1024_CLEAN_poly_LDLmv_fft(d11, tree, g00, g01, g11, logn); + + PQCLEAN_FALCON1024_CLEAN_poly_split_fft(tmp, tmp + hn, d00, logn); + PQCLEAN_FALCON1024_CLEAN_poly_split_fft(d00, d00 + hn, d11, logn); + memcpy(d11, tmp, n * sizeof * tmp); + ffLDL_fft_inner(tree + n, + d11, d11 + hn, logn - 1, tmp); + ffLDL_fft_inner(tree + n + ffLDL_treesize(logn - 1), + d00, d00 + hn, logn - 1, tmp); +} + +/* + * Normalize an ffLDL tree: each leaf of value x is replaced with + * sigma / sqrt(x). + */ +static void +ffLDL_binary_normalize(fpr *tree, unsigned logn) { + /* + * TODO: make an iterative version. + */ + size_t n; + + n = MKN(logn); + if (n == 1) { + /* + * We actually store in the tree leaf the inverse of + * the value mandated by the specification: this + * saves a division both here and in the sampler. + */ + tree[0] = fpr_mul(fpr_sqrt(tree[0]), fpr_inv_sigma); + } else { + ffLDL_binary_normalize(tree + n, logn - 1); + ffLDL_binary_normalize(tree + n + ffLDL_treesize(logn - 1), + logn - 1); + } +} + +/* =================================================================== */ + +/* + * Convert an integer polynomial (with small values) into the + * representation with complex numbers. + */ +static void +smallints_to_fpr(fpr *r, const int8_t *t, unsigned logn) { + size_t n, u; + + n = MKN(logn); + for (u = 0; u < n; u ++) { + r[u] = fpr_of(t[u]); + } +} + +/* + * The expanded private key contains: + * - The B0 matrix (four elements) + * - The ffLDL tree + */ + +static inline size_t +skoff_b00(unsigned logn) { + (void)logn; + return 0; +} + +static inline size_t +skoff_b01(unsigned logn) { + return MKN(logn); +} + +static inline size_t +skoff_b10(unsigned logn) { + return 2 * MKN(logn); +} + +static inline size_t +skoff_b11(unsigned logn) { + return 3 * MKN(logn); +} + +static inline size_t +skoff_tree(unsigned logn) { + return 4 * MKN(logn); +} + +/* see inner.h */ +void +PQCLEAN_FALCON1024_CLEAN_expand_privkey(fpr *expanded_key, + const int8_t *f, const int8_t *g, + const int8_t *F, const int8_t *G, + unsigned logn, uint8_t *tmp) { + size_t n; + fpr *rf, *rg, *rF, *rG; + fpr *b00, *b01, *b10, *b11; + fpr *g00, *g01, *g11, *gxx; + fpr *tree; + + n = MKN(logn); + b00 = expanded_key + skoff_b00(logn); + b01 = expanded_key + skoff_b01(logn); + b10 = expanded_key + skoff_b10(logn); + b11 = expanded_key + skoff_b11(logn); + tree = expanded_key + skoff_tree(logn); + + /* + * We load the private key elements directly into the B0 matrix, + * since B0 = [[g, -f], [G, -F]]. + */ + rf = b01; + rg = b00; + rF = b11; + rG = b10; + + smallints_to_fpr(rf, f, logn); + smallints_to_fpr(rg, g, logn); + smallints_to_fpr(rF, F, logn); + smallints_to_fpr(rG, G, logn); + + /* + * Compute the FFT for the key elements, and negate f and F. + */ + PQCLEAN_FALCON1024_CLEAN_FFT(rf, logn); + PQCLEAN_FALCON1024_CLEAN_FFT(rg, logn); + PQCLEAN_FALCON1024_CLEAN_FFT(rF, logn); + PQCLEAN_FALCON1024_CLEAN_FFT(rG, logn); + PQCLEAN_FALCON1024_CLEAN_poly_neg(rf, logn); + PQCLEAN_FALCON1024_CLEAN_poly_neg(rF, logn); + + /* + * The Gram matrix is G = B x B*. Formulas are: + * g00 = b00*adj(b00) + b01*adj(b01) + * g01 = b00*adj(b10) + b01*adj(b11) + * g10 = b10*adj(b00) + b11*adj(b01) + * g11 = b10*adj(b10) + b11*adj(b11) + * + * For historical reasons, this implementation uses + * g00, g01 and g11 (upper triangle). + */ + g00 = (fpr *)tmp; + g01 = g00 + n; + g11 = g01 + n; + gxx = g11 + n; + + memcpy(g00, b00, n * sizeof * b00); + PQCLEAN_FALCON1024_CLEAN_poly_mulselfadj_fft(g00, logn); + memcpy(gxx, b01, n * sizeof * b01); + PQCLEAN_FALCON1024_CLEAN_poly_mulselfadj_fft(gxx, logn); + PQCLEAN_FALCON1024_CLEAN_poly_add(g00, gxx, logn); + + memcpy(g01, b00, n * sizeof * b00); + PQCLEAN_FALCON1024_CLEAN_poly_muladj_fft(g01, b10, logn); + memcpy(gxx, b01, n * sizeof * b01); + PQCLEAN_FALCON1024_CLEAN_poly_muladj_fft(gxx, b11, logn); + PQCLEAN_FALCON1024_CLEAN_poly_add(g01, gxx, logn); + + memcpy(g11, b10, n * sizeof * b10); + PQCLEAN_FALCON1024_CLEAN_poly_mulselfadj_fft(g11, logn); + memcpy(gxx, b11, n * sizeof * b11); + PQCLEAN_FALCON1024_CLEAN_poly_mulselfadj_fft(gxx, logn); + PQCLEAN_FALCON1024_CLEAN_poly_add(g11, gxx, logn); + + /* + * Compute the Falcon tree. + */ + ffLDL_fft(tree, g00, g01, g11, logn, gxx); + + /* + * Normalize tree. + */ + ffLDL_binary_normalize(tree, logn); +} + +typedef int (*samplerZ)(void *ctx, fpr mu, fpr sigma); + +/* + * Perform Fast Fourier Sampling for target vector t. The Gram matrix + * is provided (G = [[g00, g01], [adj(g01), g11]]). The sampled vector + * is written over (t0,t1). The Gram matrix is modified as well. The + * tmp[] buffer must have room for four polynomials. + */ +static void +ffSampling_fft_dyntree(samplerZ samp, void *samp_ctx, + fpr *t0, fpr *t1, + fpr *g00, fpr *g01, fpr *g11, + unsigned logn, fpr *tmp) { + size_t n, hn; + fpr *z0, *z1; + + /* + * Deepest level: the LDL tree leaf value is just g00 (the + * array has length only 1 at this point); we normalize it + * with regards to sigma, then use it for sampling. + */ + if (logn == 0) { + fpr leaf; + + leaf = g00[0]; + leaf = fpr_mul(fpr_sqrt(leaf), fpr_inv_sigma); + t0[0] = fpr_of(samp(samp_ctx, t0[0], leaf)); + t1[0] = fpr_of(samp(samp_ctx, t1[0], leaf)); + return; + } + + n = (size_t)1 << logn; + hn = n >> 1; + + /* + * Decompose G into LDL. We only need d00 (identical to g00), + * d11, and l10; we do that in place. + */ + PQCLEAN_FALCON1024_CLEAN_poly_LDL_fft(g00, g01, g11, logn); + + /* + * Split d00 and d11 and expand them into half-size quasi-cyclic + * Gram matrices. We also save l10 in tmp[]. + */ + PQCLEAN_FALCON1024_CLEAN_poly_split_fft(tmp, tmp + hn, g00, logn); + memcpy(g00, tmp, n * sizeof * tmp); + PQCLEAN_FALCON1024_CLEAN_poly_split_fft(tmp, tmp + hn, g11, logn); + memcpy(g11, tmp, n * sizeof * tmp); + memcpy(tmp, g01, n * sizeof * g01); + memcpy(g01, g00, hn * sizeof * g00); + memcpy(g01 + hn, g11, hn * sizeof * g00); + + /* + * The half-size Gram matrices for the recursive LDL tree + * building are now: + * - left sub-tree: g00, g00+hn, g01 + * - right sub-tree: g11, g11+hn, g01+hn + * l10 is in tmp[]. + */ + + /* + * We split t1 and use the first recursive call on the two + * halves, using the right sub-tree. The result is merged + * back into tmp + 2*n. + */ + z1 = tmp + n; + PQCLEAN_FALCON1024_CLEAN_poly_split_fft(z1, z1 + hn, t1, logn); + ffSampling_fft_dyntree(samp, samp_ctx, z1, z1 + hn, + g11, g11 + hn, g01 + hn, logn - 1, z1 + n); + PQCLEAN_FALCON1024_CLEAN_poly_merge_fft(tmp + (n << 1), z1, z1 + hn, logn); + + /* + * Compute tb0 = t0 + (t1 - z1) * l10. + * At that point, l10 is in tmp, t1 is unmodified, and z1 is + * in tmp + (n << 1). The buffer in z1 is free. + * + * In the end, z1 is written over t1, and tb0 is in t0. + */ + memcpy(z1, t1, n * sizeof * t1); + PQCLEAN_FALCON1024_CLEAN_poly_sub(z1, tmp + (n << 1), logn); + memcpy(t1, tmp + (n << 1), n * sizeof * tmp); + PQCLEAN_FALCON1024_CLEAN_poly_mul_fft(tmp, z1, logn); + PQCLEAN_FALCON1024_CLEAN_poly_add(t0, tmp, logn); + + /* + * Second recursive invocation, on the split tb0 (currently in t0) + * and the left sub-tree. + */ + z0 = tmp; + PQCLEAN_FALCON1024_CLEAN_poly_split_fft(z0, z0 + hn, t0, logn); + ffSampling_fft_dyntree(samp, samp_ctx, z0, z0 + hn, + g00, g00 + hn, g01, logn - 1, z0 + n); + PQCLEAN_FALCON1024_CLEAN_poly_merge_fft(t0, z0, z0 + hn, logn); +} + +/* + * Perform Fast Fourier Sampling for target vector t and LDL tree T. + * tmp[] must have size for at least two polynomials of size 2^logn. + */ +static void +ffSampling_fft(samplerZ samp, void *samp_ctx, + fpr *z0, fpr *z1, + const fpr *tree, + const fpr *t0, const fpr *t1, unsigned logn, + fpr *tmp) { + size_t n, hn; + const fpr *tree0, *tree1; + + /* + * When logn == 2, we inline the last two recursion levels. + */ + if (logn == 2) { + fpr x0, x1, y0, y1, w0, w1, w2, w3, sigma; + fpr a_re, a_im, b_re, b_im, c_re, c_im; + + tree0 = tree + 4; + tree1 = tree + 8; + + /* + * We split t1 into w*, then do the recursive invocation, + * with output in w*. We finally merge back into z1. + */ + a_re = t1[0]; + a_im = t1[2]; + b_re = t1[1]; + b_im = t1[3]; + c_re = fpr_add(a_re, b_re); + c_im = fpr_add(a_im, b_im); + w0 = fpr_half(c_re); + w1 = fpr_half(c_im); + c_re = fpr_sub(a_re, b_re); + c_im = fpr_sub(a_im, b_im); + w2 = fpr_mul(fpr_add(c_re, c_im), fpr_invsqrt8); + w3 = fpr_mul(fpr_sub(c_im, c_re), fpr_invsqrt8); + + x0 = w2; + x1 = w3; + sigma = tree1[3]; + w2 = fpr_of(samp(samp_ctx, x0, sigma)); + w3 = fpr_of(samp(samp_ctx, x1, sigma)); + a_re = fpr_sub(x0, w2); + a_im = fpr_sub(x1, w3); + b_re = tree1[0]; + b_im = tree1[1]; + c_re = fpr_sub(fpr_mul(a_re, b_re), fpr_mul(a_im, b_im)); + c_im = fpr_add(fpr_mul(a_re, b_im), fpr_mul(a_im, b_re)); + x0 = fpr_add(c_re, w0); + x1 = fpr_add(c_im, w1); + sigma = tree1[2]; + w0 = fpr_of(samp(samp_ctx, x0, sigma)); + w1 = fpr_of(samp(samp_ctx, x1, sigma)); + + a_re = w0; + a_im = w1; + b_re = w2; + b_im = w3; + c_re = fpr_mul(fpr_sub(b_re, b_im), fpr_invsqrt2); + c_im = fpr_mul(fpr_add(b_re, b_im), fpr_invsqrt2); + z1[0] = w0 = fpr_add(a_re, c_re); + z1[2] = w2 = fpr_add(a_im, c_im); + z1[1] = w1 = fpr_sub(a_re, c_re); + z1[3] = w3 = fpr_sub(a_im, c_im); + + /* + * Compute tb0 = t0 + (t1 - z1) * L. Value tb0 ends up in w*. + */ + w0 = fpr_sub(t1[0], w0); + w1 = fpr_sub(t1[1], w1); + w2 = fpr_sub(t1[2], w2); + w3 = fpr_sub(t1[3], w3); + + a_re = w0; + a_im = w2; + b_re = tree[0]; + b_im = tree[2]; + w0 = fpr_sub(fpr_mul(a_re, b_re), fpr_mul(a_im, b_im)); + w2 = fpr_add(fpr_mul(a_re, b_im), fpr_mul(a_im, b_re)); + a_re = w1; + a_im = w3; + b_re = tree[1]; + b_im = tree[3]; + w1 = fpr_sub(fpr_mul(a_re, b_re), fpr_mul(a_im, b_im)); + w3 = fpr_add(fpr_mul(a_re, b_im), fpr_mul(a_im, b_re)); + + w0 = fpr_add(w0, t0[0]); + w1 = fpr_add(w1, t0[1]); + w2 = fpr_add(w2, t0[2]); + w3 = fpr_add(w3, t0[3]); + + /* + * Second recursive invocation. + */ + a_re = w0; + a_im = w2; + b_re = w1; + b_im = w3; + c_re = fpr_add(a_re, b_re); + c_im = fpr_add(a_im, b_im); + w0 = fpr_half(c_re); + w1 = fpr_half(c_im); + c_re = fpr_sub(a_re, b_re); + c_im = fpr_sub(a_im, b_im); + w2 = fpr_mul(fpr_add(c_re, c_im), fpr_invsqrt8); + w3 = fpr_mul(fpr_sub(c_im, c_re), fpr_invsqrt8); + + x0 = w2; + x1 = w3; + sigma = tree0[3]; + w2 = y0 = fpr_of(samp(samp_ctx, x0, sigma)); + w3 = y1 = fpr_of(samp(samp_ctx, x1, sigma)); + a_re = fpr_sub(x0, y0); + a_im = fpr_sub(x1, y1); + b_re = tree0[0]; + b_im = tree0[1]; + c_re = fpr_sub(fpr_mul(a_re, b_re), fpr_mul(a_im, b_im)); + c_im = fpr_add(fpr_mul(a_re, b_im), fpr_mul(a_im, b_re)); + x0 = fpr_add(c_re, w0); + x1 = fpr_add(c_im, w1); + sigma = tree0[2]; + w0 = fpr_of(samp(samp_ctx, x0, sigma)); + w1 = fpr_of(samp(samp_ctx, x1, sigma)); + + a_re = w0; + a_im = w1; + b_re = w2; + b_im = w3; + c_re = fpr_mul(fpr_sub(b_re, b_im), fpr_invsqrt2); + c_im = fpr_mul(fpr_add(b_re, b_im), fpr_invsqrt2); + z0[0] = fpr_add(a_re, c_re); + z0[2] = fpr_add(a_im, c_im); + z0[1] = fpr_sub(a_re, c_re); + z0[3] = fpr_sub(a_im, c_im); + + return; + } + + /* + * Case logn == 1 is reachable only when using Falcon-2 (the + * smallest size for which Falcon is mathematically defined, but + * of course way too insecure to be of any use). + */ + if (logn == 1) { + fpr x0, x1, y0, y1, sigma; + fpr a_re, a_im, b_re, b_im, c_re, c_im; + + x0 = t1[0]; + x1 = t1[1]; + sigma = tree[3]; + z1[0] = y0 = fpr_of(samp(samp_ctx, x0, sigma)); + z1[1] = y1 = fpr_of(samp(samp_ctx, x1, sigma)); + a_re = fpr_sub(x0, y0); + a_im = fpr_sub(x1, y1); + b_re = tree[0]; + b_im = tree[1]; + c_re = fpr_sub(fpr_mul(a_re, b_re), fpr_mul(a_im, b_im)); + c_im = fpr_add(fpr_mul(a_re, b_im), fpr_mul(a_im, b_re)); + x0 = fpr_add(c_re, t0[0]); + x1 = fpr_add(c_im, t0[1]); + sigma = tree[2]; + z0[0] = fpr_of(samp(samp_ctx, x0, sigma)); + z0[1] = fpr_of(samp(samp_ctx, x1, sigma)); + + return; + } + + /* + * Normal end of recursion is for logn == 0. Since the last + * steps of the recursions were inlined in the blocks above + * (when logn == 1 or 2), this case is not reachable, and is + * retained here only for documentation purposes. + + if (logn == 0) { + fpr x0, x1, sigma; + + x0 = t0[0]; + x1 = t1[0]; + sigma = tree[0]; + z0[0] = fpr_of(samp(samp_ctx, x0, sigma)); + z1[0] = fpr_of(samp(samp_ctx, x1, sigma)); + return; + } + + */ + + /* + * General recursive case (logn >= 3). + */ + + n = (size_t)1 << logn; + hn = n >> 1; + tree0 = tree + n; + tree1 = tree + n + ffLDL_treesize(logn - 1); + + /* + * We split t1 into z1 (reused as temporary storage), then do + * the recursive invocation, with output in tmp. We finally + * merge back into z1. + */ + PQCLEAN_FALCON1024_CLEAN_poly_split_fft(z1, z1 + hn, t1, logn); + ffSampling_fft(samp, samp_ctx, tmp, tmp + hn, + tree1, z1, z1 + hn, logn - 1, tmp + n); + PQCLEAN_FALCON1024_CLEAN_poly_merge_fft(z1, tmp, tmp + hn, logn); + + /* + * Compute tb0 = t0 + (t1 - z1) * L. Value tb0 ends up in tmp[]. + */ + memcpy(tmp, t1, n * sizeof * t1); + PQCLEAN_FALCON1024_CLEAN_poly_sub(tmp, z1, logn); + PQCLEAN_FALCON1024_CLEAN_poly_mul_fft(tmp, tree, logn); + PQCLEAN_FALCON1024_CLEAN_poly_add(tmp, t0, logn); + + /* + * Second recursive invocation. + */ + PQCLEAN_FALCON1024_CLEAN_poly_split_fft(z0, z0 + hn, tmp, logn); + ffSampling_fft(samp, samp_ctx, tmp, tmp + hn, + tree0, z0, z0 + hn, logn - 1, tmp + n); + PQCLEAN_FALCON1024_CLEAN_poly_merge_fft(z0, tmp, tmp + hn, logn); +} + +/* + * Compute a signature: the signature contains two vectors, s1 and s2. + * The s1 vector is not returned. The squared norm of (s1,s2) is + * computed, and if it is short enough, then s2 is returned into the + * s2[] buffer, and 1 is returned; otherwise, s2[] is untouched and 0 is + * returned; the caller should then try again. This function uses an + * expanded key. + * + * tmp[] must have room for at least six polynomials. + */ +static int +do_sign_tree(samplerZ samp, void *samp_ctx, int16_t *s2, + const fpr *expanded_key, + const uint16_t *hm, + unsigned logn, fpr *tmp) { + size_t n, u; + fpr *t0, *t1, *tx, *ty; + const fpr *b00, *b01, *b10, *b11, *tree; + fpr ni; + uint32_t sqn, ng; + int16_t *s1tmp, *s2tmp; + + n = MKN(logn); + t0 = tmp; + t1 = t0 + n; + b00 = expanded_key + skoff_b00(logn); + b01 = expanded_key + skoff_b01(logn); + b10 = expanded_key + skoff_b10(logn); + b11 = expanded_key + skoff_b11(logn); + tree = expanded_key + skoff_tree(logn); + + /* + * Set the target vector to [hm, 0] (hm is the hashed message). + */ + for (u = 0; u < n; u ++) { + t0[u] = fpr_of(hm[u]); + /* This is implicit. + t1[u] = fpr_zero; + */ + } + + /* + * Apply the lattice basis to obtain the real target + * vector (after normalization with regards to modulus). + */ + PQCLEAN_FALCON1024_CLEAN_FFT(t0, logn); + ni = fpr_inverse_of_q; + memcpy(t1, t0, n * sizeof * t0); + PQCLEAN_FALCON1024_CLEAN_poly_mul_fft(t1, b01, logn); + PQCLEAN_FALCON1024_CLEAN_poly_mulconst(t1, fpr_neg(ni), logn); + PQCLEAN_FALCON1024_CLEAN_poly_mul_fft(t0, b11, logn); + PQCLEAN_FALCON1024_CLEAN_poly_mulconst(t0, ni, logn); + + tx = t1 + n; + ty = tx + n; + + /* + * Apply sampling. Output is written back in [tx, ty]. + */ + ffSampling_fft(samp, samp_ctx, tx, ty, tree, t0, t1, logn, ty + n); + + /* + * Get the lattice point corresponding to that tiny vector. + */ + memcpy(t0, tx, n * sizeof * tx); + memcpy(t1, ty, n * sizeof * ty); + PQCLEAN_FALCON1024_CLEAN_poly_mul_fft(tx, b00, logn); + PQCLEAN_FALCON1024_CLEAN_poly_mul_fft(ty, b10, logn); + PQCLEAN_FALCON1024_CLEAN_poly_add(tx, ty, logn); + memcpy(ty, t0, n * sizeof * t0); + PQCLEAN_FALCON1024_CLEAN_poly_mul_fft(ty, b01, logn); + + memcpy(t0, tx, n * sizeof * tx); + PQCLEAN_FALCON1024_CLEAN_poly_mul_fft(t1, b11, logn); + PQCLEAN_FALCON1024_CLEAN_poly_add(t1, ty, logn); + + PQCLEAN_FALCON1024_CLEAN_iFFT(t0, logn); + PQCLEAN_FALCON1024_CLEAN_iFFT(t1, logn); + + /* + * Compute the signature. + */ + s1tmp = (int16_t *)tx; + sqn = 0; + ng = 0; + for (u = 0; u < n; u ++) { + int32_t z; + + z = (int32_t)hm[u] - (int32_t)fpr_rint(t0[u]); + sqn += (uint32_t)(z * z); + ng |= sqn; + s1tmp[u] = (int16_t)z; + } + sqn |= -(ng >> 31); + + /* + * With "normal" degrees (e.g. 512 or 1024), it is very + * improbable that the computed vector is not short enough; + * however, it may happen in practice for the very reduced + * versions (e.g. degree 16 or below). In that case, the caller + * will loop, and we must not write anything into s2[] because + * s2[] may overlap with the hashed message hm[] and we need + * hm[] for the next iteration. + */ + s2tmp = (int16_t *)tmp; + for (u = 0; u < n; u ++) { + s2tmp[u] = (int16_t) - fpr_rint(t1[u]); + } + if (PQCLEAN_FALCON1024_CLEAN_is_short_half(sqn, s2tmp, logn)) { + memcpy(s2, s2tmp, n * sizeof * s2); + memcpy(tmp, s1tmp, n * sizeof * s1tmp); + return 1; + } + return 0; +} + +/* + * Compute a signature: the signature contains two vectors, s1 and s2. + * The s1 vector is not returned. The squared norm of (s1,s2) is + * computed, and if it is short enough, then s2 is returned into the + * s2[] buffer, and 1 is returned; otherwise, s2[] is untouched and 0 is + * returned; the caller should then try again. + * + * tmp[] must have room for at least nine polynomials. + */ +static int +do_sign_dyn(samplerZ samp, void *samp_ctx, int16_t *s2, + const int8_t *f, const int8_t *g, + const int8_t *F, const int8_t *G, + const uint16_t *hm, unsigned logn, fpr *tmp) { + size_t n, u; + fpr *t0, *t1, *tx, *ty; + fpr *b00, *b01, *b10, *b11, *g00, *g01, *g11; + fpr ni; + uint32_t sqn, ng; + int16_t *s1tmp, *s2tmp; + + n = MKN(logn); + + /* + * Lattice basis is B = [[g, -f], [G, -F]]. We convert it to FFT. + */ + b00 = tmp; + b01 = b00 + n; + b10 = b01 + n; + b11 = b10 + n; + smallints_to_fpr(b01, f, logn); + smallints_to_fpr(b00, g, logn); + smallints_to_fpr(b11, F, logn); + smallints_to_fpr(b10, G, logn); + PQCLEAN_FALCON1024_CLEAN_FFT(b01, logn); + PQCLEAN_FALCON1024_CLEAN_FFT(b00, logn); + PQCLEAN_FALCON1024_CLEAN_FFT(b11, logn); + PQCLEAN_FALCON1024_CLEAN_FFT(b10, logn); + PQCLEAN_FALCON1024_CLEAN_poly_neg(b01, logn); + PQCLEAN_FALCON1024_CLEAN_poly_neg(b11, logn); + + /* + * Compute the Gram matrix G = B x B*. Formulas are: + * g00 = b00*adj(b00) + b01*adj(b01) + * g01 = b00*adj(b10) + b01*adj(b11) + * g10 = b10*adj(b00) + b11*adj(b01) + * g11 = b10*adj(b10) + b11*adj(b11) + * + * For historical reasons, this implementation uses + * g00, g01 and g11 (upper triangle). g10 is not kept + * since it is equal to adj(g01). + * + * We _replace_ the matrix B with the Gram matrix, but we + * must keep b01 and b11 for computing the target vector. + */ + t0 = b11 + n; + t1 = t0 + n; + + memcpy(t0, b01, n * sizeof * b01); + PQCLEAN_FALCON1024_CLEAN_poly_mulselfadj_fft(t0, logn); // t0 <- b01*adj(b01) + + memcpy(t1, b00, n * sizeof * b00); + PQCLEAN_FALCON1024_CLEAN_poly_muladj_fft(t1, b10, logn); // t1 <- b00*adj(b10) + PQCLEAN_FALCON1024_CLEAN_poly_mulselfadj_fft(b00, logn); // b00 <- b00*adj(b00) + PQCLEAN_FALCON1024_CLEAN_poly_add(b00, t0, logn); // b00 <- g00 + memcpy(t0, b01, n * sizeof * b01); + PQCLEAN_FALCON1024_CLEAN_poly_muladj_fft(b01, b11, logn); // b01 <- b01*adj(b11) + PQCLEAN_FALCON1024_CLEAN_poly_add(b01, t1, logn); // b01 <- g01 + + PQCLEAN_FALCON1024_CLEAN_poly_mulselfadj_fft(b10, logn); // b10 <- b10*adj(b10) + memcpy(t1, b11, n * sizeof * b11); + PQCLEAN_FALCON1024_CLEAN_poly_mulselfadj_fft(t1, logn); // t1 <- b11*adj(b11) + PQCLEAN_FALCON1024_CLEAN_poly_add(b10, t1, logn); // b10 <- g11 + + /* + * We rename variables to make things clearer. The three elements + * of the Gram matrix uses the first 3*n slots of tmp[], followed + * by b11 and b01 (in that order). + */ + g00 = b00; + g01 = b01; + g11 = b10; + b01 = t0; + t0 = b01 + n; + t1 = t0 + n; + + /* + * Memory layout at that point: + * g00 g01 g11 b11 b01 t0 t1 + */ + + /* + * Set the target vector to [hm, 0] (hm is the hashed message). + */ + for (u = 0; u < n; u ++) { + t0[u] = fpr_of(hm[u]); + /* This is implicit. + t1[u] = fpr_zero; + */ + } + + /* + * Apply the lattice basis to obtain the real target + * vector (after normalization with regards to modulus). + */ + PQCLEAN_FALCON1024_CLEAN_FFT(t0, logn); + ni = fpr_inverse_of_q; + memcpy(t1, t0, n * sizeof * t0); + PQCLEAN_FALCON1024_CLEAN_poly_mul_fft(t1, b01, logn); + PQCLEAN_FALCON1024_CLEAN_poly_mulconst(t1, fpr_neg(ni), logn); + PQCLEAN_FALCON1024_CLEAN_poly_mul_fft(t0, b11, logn); + PQCLEAN_FALCON1024_CLEAN_poly_mulconst(t0, ni, logn); + + /* + * b01 and b11 can be discarded, so we move back (t0,t1). + * Memory layout is now: + * g00 g01 g11 t0 t1 + */ + memcpy(b11, t0, n * 2 * sizeof * t0); + t0 = g11 + n; + t1 = t0 + n; + + /* + * Apply sampling; result is written over (t0,t1). + */ + ffSampling_fft_dyntree(samp, samp_ctx, + t0, t1, g00, g01, g11, logn, t1 + n); + + /* + * We arrange the layout back to: + * b00 b01 b10 b11 t0 t1 + * + * We did not conserve the matrix basis, so we must recompute + * it now. + */ + b00 = tmp; + b01 = b00 + n; + b10 = b01 + n; + b11 = b10 + n; + memmove(b11 + n, t0, n * 2 * sizeof * t0); + t0 = b11 + n; + t1 = t0 + n; + smallints_to_fpr(b01, f, logn); + smallints_to_fpr(b00, g, logn); + smallints_to_fpr(b11, F, logn); + smallints_to_fpr(b10, G, logn); + PQCLEAN_FALCON1024_CLEAN_FFT(b01, logn); + PQCLEAN_FALCON1024_CLEAN_FFT(b00, logn); + PQCLEAN_FALCON1024_CLEAN_FFT(b11, logn); + PQCLEAN_FALCON1024_CLEAN_FFT(b10, logn); + PQCLEAN_FALCON1024_CLEAN_poly_neg(b01, logn); + PQCLEAN_FALCON1024_CLEAN_poly_neg(b11, logn); + tx = t1 + n; + ty = tx + n; + + /* + * Get the lattice point corresponding to that tiny vector. + */ + memcpy(tx, t0, n * sizeof * t0); + memcpy(ty, t1, n * sizeof * t1); + PQCLEAN_FALCON1024_CLEAN_poly_mul_fft(tx, b00, logn); + PQCLEAN_FALCON1024_CLEAN_poly_mul_fft(ty, b10, logn); + PQCLEAN_FALCON1024_CLEAN_poly_add(tx, ty, logn); + memcpy(ty, t0, n * sizeof * t0); + PQCLEAN_FALCON1024_CLEAN_poly_mul_fft(ty, b01, logn); + + memcpy(t0, tx, n * sizeof * tx); + PQCLEAN_FALCON1024_CLEAN_poly_mul_fft(t1, b11, logn); + PQCLEAN_FALCON1024_CLEAN_poly_add(t1, ty, logn); + PQCLEAN_FALCON1024_CLEAN_iFFT(t0, logn); + PQCLEAN_FALCON1024_CLEAN_iFFT(t1, logn); + + s1tmp = (int16_t *)tx; + sqn = 0; + ng = 0; + for (u = 0; u < n; u ++) { + int32_t z; + + z = (int32_t)hm[u] - (int32_t)fpr_rint(t0[u]); + sqn += (uint32_t)(z * z); + ng |= sqn; + s1tmp[u] = (int16_t)z; + } + sqn |= -(ng >> 31); + + /* + * With "normal" degrees (e.g. 512 or 1024), it is very + * improbable that the computed vector is not short enough; + * however, it may happen in practice for the very reduced + * versions (e.g. degree 16 or below). In that case, the caller + * will loop, and we must not write anything into s2[] because + * s2[] may overlap with the hashed message hm[] and we need + * hm[] for the next iteration. + */ + s2tmp = (int16_t *)tmp; + for (u = 0; u < n; u ++) { + s2tmp[u] = (int16_t) - fpr_rint(t1[u]); + } + if (PQCLEAN_FALCON1024_CLEAN_is_short_half(sqn, s2tmp, logn)) { + memcpy(s2, s2tmp, n * sizeof * s2); + memcpy(tmp, s1tmp, n * sizeof * s1tmp); + return 1; + } + return 0; +} + +/* + * Sample an integer value along a half-gaussian distribution centered + * on zero and standard deviation 1.8205, with a precision of 72 bits. + */ +int +PQCLEAN_FALCON1024_CLEAN_gaussian0_sampler(prng *p) { + + static const uint32_t dist[] = { + 10745844u, 3068844u, 3741698u, + 5559083u, 1580863u, 8248194u, + 2260429u, 13669192u, 2736639u, + 708981u, 4421575u, 10046180u, + 169348u, 7122675u, 4136815u, + 30538u, 13063405u, 7650655u, + 4132u, 14505003u, 7826148u, + 417u, 16768101u, 11363290u, + 31u, 8444042u, 8086568u, + 1u, 12844466u, 265321u, + 0u, 1232676u, 13644283u, + 0u, 38047u, 9111839u, + 0u, 870u, 6138264u, + 0u, 14u, 12545723u, + 0u, 0u, 3104126u, + 0u, 0u, 28824u, + 0u, 0u, 198u, + 0u, 0u, 1u + }; + + uint32_t v0, v1, v2, hi; + uint64_t lo; + size_t u; + int z; + + /* + * Get a random 72-bit value, into three 24-bit limbs v0..v2. + */ + lo = prng_get_u64(p); + hi = prng_get_u8(p); + v0 = (uint32_t)lo & 0xFFFFFF; + v1 = (uint32_t)(lo >> 24) & 0xFFFFFF; + v2 = (uint32_t)(lo >> 48) | (hi << 16); + + /* + * Sampled value is z, such that v0..v2 is lower than the first + * z elements of the table. + */ + z = 0; + for (u = 0; u < (sizeof dist) / sizeof(dist[0]); u += 3) { + uint32_t w0, w1, w2, cc; + + w0 = dist[u + 2]; + w1 = dist[u + 1]; + w2 = dist[u + 0]; + cc = (v0 - w0) >> 31; + cc = (v1 - w1 - cc) >> 31; + cc = (v2 - w2 - cc) >> 31; + z += (int)cc; + } + return z; + +} + +/* + * Sample a bit with probability exp(-x) for some x >= 0. + */ +static int +BerExp(prng *p, fpr x, fpr ccs) { + int s, i; + fpr r; + uint32_t sw, w; + uint64_t z; + + /* + * Reduce x modulo log(2): x = s*log(2) + r, with s an integer, + * and 0 <= r < log(2). Since x >= 0, we can use fpr_trunc(). + */ + s = (int)fpr_trunc(fpr_mul(x, fpr_inv_log2)); + r = fpr_sub(x, fpr_mul(fpr_of(s), fpr_log2)); + + /* + * It may happen (quite rarely) that s >= 64; if sigma = 1.2 + * (the minimum value for sigma), r = 0 and b = 1, then we get + * s >= 64 if the half-Gaussian produced a z >= 13, which happens + * with probability about 0.000000000230383991, which is + * approximatively equal to 2^(-32). In any case, if s >= 64, + * then BerExp will be non-zero with probability less than + * 2^(-64), so we can simply saturate s at 63. + */ + sw = (uint32_t)s; + sw ^= (sw ^ 63) & -((63 - sw) >> 31); + s = (int)sw; + + /* + * Compute exp(-r); we know that 0 <= r < log(2) at this point, so + * we can use fpr_expm_p63(), which yields a result scaled to 2^63. + * We scale it up to 2^64, then right-shift it by s bits because + * we really want exp(-x) = 2^(-s)*exp(-r). + * + * The "-1" operation makes sure that the value fits on 64 bits + * (i.e. if r = 0, we may get 2^64, and we prefer 2^64-1 in that + * case). The bias is negligible since fpr_expm_p63() only computes + * with 51 bits of precision or so. + */ + z = ((fpr_expm_p63(r, ccs) << 1) - 1) >> s; + + /* + * Sample a bit with probability exp(-x). Since x = s*log(2) + r, + * exp(-x) = 2^-s * exp(-r), we compare lazily exp(-x) with the + * PRNG output to limit its consumption, the sign of the difference + * yields the expected result. + */ + i = 64; + do { + i -= 8; + w = prng_get_u8(p) - ((uint32_t)(z >> i) & 0xFF); + } while (!w && i > 0); + return (int)(w >> 31); +} + +/* + * The sampler produces a random integer that follows a discrete Gaussian + * distribution, centered on mu, and with standard deviation sigma. The + * provided parameter isigma is equal to 1/sigma. + * + * The value of sigma MUST lie between 1 and 2 (i.e. isigma lies between + * 0.5 and 1); in Falcon, sigma should always be between 1.2 and 1.9. + */ +int +PQCLEAN_FALCON1024_CLEAN_sampler(void *ctx, fpr mu, fpr isigma) { + sampler_context *spc; + int s, z0, z, b; + fpr r, dss, ccs, x; + + spc = ctx; + + /* + * Center is mu. We compute mu = s + r where s is an integer + * and 0 <= r < 1. + */ + s = (int)fpr_floor(mu); + r = fpr_sub(mu, fpr_of(s)); + + /* + * dss = 1/(2*sigma^2) = 0.5*(isigma^2). + */ + dss = fpr_half(fpr_sqr(isigma)); + + /* + * ccs = sigma_min / sigma = sigma_min * isigma. + */ + ccs = fpr_mul(isigma, spc->sigma_min); + + /* + * We now need to sample on center r. + */ + for (;;) { + /* + * Sample z for a Gaussian distribution. Then get a + * random bit b to turn the sampling into a bimodal + * distribution: if b = 1, we use z+1, otherwise we + * use -z. We thus have two situations: + * + * - b = 1: z >= 1 and sampled against a Gaussian + * centered on 1. + * - b = 0: z <= 0 and sampled against a Gaussian + * centered on 0. + */ + z0 = PQCLEAN_FALCON1024_CLEAN_gaussian0_sampler(&spc->p); + b = (int)prng_get_u8(&spc->p) & 1; + z = b + ((b << 1) - 1) * z0; + + /* + * Rejection sampling. We want a Gaussian centered on r; + * but we sampled against a Gaussian centered on b (0 or + * 1). But we know that z is always in the range where + * our sampling distribution is greater than the Gaussian + * distribution, so rejection works. + * + * We got z with distribution: + * G(z) = exp(-((z-b)^2)/(2*sigma0^2)) + * We target distribution: + * S(z) = exp(-((z-r)^2)/(2*sigma^2)) + * Rejection sampling works by keeping the value z with + * probability S(z)/G(z), and starting again otherwise. + * This requires S(z) <= G(z), which is the case here. + * Thus, we simply need to keep our z with probability: + * P = exp(-x) + * where: + * x = ((z-r)^2)/(2*sigma^2) - ((z-b)^2)/(2*sigma0^2) + * + * Here, we scale up the Bernouilli distribution, which + * makes rejection more probable, but makes rejection + * rate sufficiently decorrelated from the Gaussian + * center and standard deviation that the whole sampler + * can be said to be constant-time. + */ + x = fpr_mul(fpr_sqr(fpr_sub(fpr_of(z), r)), dss); + x = fpr_sub(x, fpr_mul(fpr_of(z0 * z0), fpr_inv_2sqrsigma0)); + if (BerExp(&spc->p, x, ccs)) { + /* + * Rejection sampling was centered on r, but the + * actual center is mu = s + r. + */ + return s + z; + } + } +} + +/* see inner.h */ +void +PQCLEAN_FALCON1024_CLEAN_sign_tree(int16_t *sig, inner_shake256_context *rng, + const fpr *expanded_key, + const uint16_t *hm, unsigned logn, uint8_t *tmp) { + fpr *ftmp; + + ftmp = (fpr *)tmp; + for (;;) { + /* + * Signature produces short vectors s1 and s2. The + * signature is acceptable only if the aggregate vector + * s1,s2 is short; we must use the same bound as the + * verifier. + * + * If the signature is acceptable, then we return only s2 + * (the verifier recomputes s1 from s2, the hashed message, + * and the public key). + */ + sampler_context spc; + samplerZ samp; + void *samp_ctx; + + /* + * Normal sampling. We use a fast PRNG seeded from our + * SHAKE context ('rng'). + */ + if (logn == 10) { + spc.sigma_min = fpr_sigma_min_10; + } else { + spc.sigma_min = fpr_sigma_min_9; + } + PQCLEAN_FALCON1024_CLEAN_prng_init(&spc.p, rng); + samp = PQCLEAN_FALCON1024_CLEAN_sampler; + samp_ctx = &spc; + + /* + * Do the actual signature. + */ + if (do_sign_tree(samp, samp_ctx, sig, + expanded_key, hm, logn, ftmp)) { + break; + } + } +} + +/* see inner.h */ +void +PQCLEAN_FALCON1024_CLEAN_sign_dyn(int16_t *sig, inner_shake256_context *rng, + const int8_t *f, const int8_t *g, + const int8_t *F, const int8_t *G, + const uint16_t *hm, unsigned logn, uint8_t *tmp) { + fpr *ftmp; + + ftmp = (fpr *)tmp; + for (;;) { + /* + * Signature produces short vectors s1 and s2. The + * signature is acceptable only if the aggregate vector + * s1,s2 is short; we must use the same bound as the + * verifier. + * + * If the signature is acceptable, then we return only s2 + * (the verifier recomputes s1 from s2, the hashed message, + * and the public key). + */ + sampler_context spc; + samplerZ samp; + void *samp_ctx; + + /* + * Normal sampling. We use a fast PRNG seeded from our + * SHAKE context ('rng'). + */ + if (logn == 10) { + spc.sigma_min = fpr_sigma_min_10; + } else { + spc.sigma_min = fpr_sigma_min_9; + } + PQCLEAN_FALCON1024_CLEAN_prng_init(&spc.p, rng); + samp = PQCLEAN_FALCON1024_CLEAN_sampler; + samp_ctx = &spc; + + /* + * Do the actual signature. + */ + if (do_sign_dyn(samp, samp_ctx, sig, + f, g, F, G, hm, logn, ftmp)) { + break; + } + } +} diff --git a/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/vrfy.c b/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/vrfy.c new file mode 100644 index 000000000..93f2d526b --- /dev/null +++ b/lib/liboqs/src/sig/falcon/pqclean_falcon-1024_clean/vrfy.c @@ -0,0 +1,853 @@ +#include "inner.h" + +/* + * Falcon signature verification. + * + * ==========================(LICENSE BEGIN)============================ + * + * Copyright (c) 2017-2019 Falcon Project + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the + * "Software"), to deal in the Software without restriction, including + * without limitation the rights to use, copy, modify, merge, publish, + * distribute, sublicense, and/or sell copies of the Software, and to + * permit persons to whom the Software is furnished to do so, subject to + * the following conditions: + * + * The above copyright notice and this permission notice shall be + * included in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, + * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF + * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. + * IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY + * CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, + * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE + * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. + * + * ===========================(LICENSE END)============================= + * + * @author Thomas Pornin <thomas.pornin@nccgroup.com> + */ + + +/* ===================================================================== */ +/* + * Constants for NTT. + * + * n = 2^logn (2 <= n <= 1024) + * phi = X^n + 1 + * q = 12289 + * q0i = -1/q mod 2^16 + * R = 2^16 mod q + * R2 = 2^32 mod q + */ + +#define Q 12289 +#define Q0I 12287 +#define R 4091 +#define R2 10952 + +/* + * Table for NTT, binary case: + * GMb[x] = R*(g^rev(x)) mod q + * where g = 7 (it is a 2048-th primitive root of 1 modulo q) + * and rev() is the bit-reversal function over 10 bits. + */ +static const uint16_t GMb[] = { + 4091, 7888, 11060, 11208, 6960, 4342, 6275, 9759, + 1591, 6399, 9477, 5266, 586, 5825, 7538, 9710, + 1134, 6407, 1711, 965, 7099, 7674, 3743, 6442, + 10414, 8100, 1885, 1688, 1364, 10329, 10164, 9180, + 12210, 6240, 997, 117, 4783, 4407, 1549, 7072, + 2829, 6458, 4431, 8877, 7144, 2564, 5664, 4042, + 12189, 432, 10751, 1237, 7610, 1534, 3983, 7863, + 2181, 6308, 8720, 6570, 4843, 1690, 14, 3872, + 5569, 9368, 12163, 2019, 7543, 2315, 4673, 7340, + 1553, 1156, 8401, 11389, 1020, 2967, 10772, 7045, + 3316, 11236, 5285, 11578, 10637, 10086, 9493, 6180, + 9277, 6130, 3323, 883, 10469, 489, 1502, 2851, + 11061, 9729, 2742, 12241, 4970, 10481, 10078, 1195, + 730, 1762, 3854, 2030, 5892, 10922, 9020, 5274, + 9179, 3604, 3782, 10206, 3180, 3467, 4668, 2446, + 7613, 9386, 834, 7703, 6836, 3403, 5351, 12276, + 3580, 1739, 10820, 9787, 10209, 4070, 12250, 8525, + 10401, 2749, 7338, 10574, 6040, 943, 9330, 1477, + 6865, 9668, 3585, 6633, 12145, 4063, 3684, 7680, + 8188, 6902, 3533, 9807, 6090, 727, 10099, 7003, + 6945, 1949, 9731, 10559, 6057, 378, 7871, 8763, + 8901, 9229, 8846, 4551, 9589, 11664, 7630, 8821, + 5680, 4956, 6251, 8388, 10156, 8723, 2341, 3159, + 1467, 5460, 8553, 7783, 2649, 2320, 9036, 6188, + 737, 3698, 4699, 5753, 9046, 3687, 16, 914, + 5186, 10531, 4552, 1964, 3509, 8436, 7516, 5381, + 10733, 3281, 7037, 1060, 2895, 7156, 8887, 5357, + 6409, 8197, 2962, 6375, 5064, 6634, 5625, 278, + 932, 10229, 8927, 7642, 351, 9298, 237, 5858, + 7692, 3146, 12126, 7586, 2053, 11285, 3802, 5204, + 4602, 1748, 11300, 340, 3711, 4614, 300, 10993, + 5070, 10049, 11616, 12247, 7421, 10707, 5746, 5654, + 3835, 5553, 1224, 8476, 9237, 3845, 250, 11209, + 4225, 6326, 9680, 12254, 4136, 2778, 692, 8808, + 6410, 6718, 10105, 10418, 3759, 7356, 11361, 8433, + 6437, 3652, 6342, 8978, 5391, 2272, 6476, 7416, + 8418, 10824, 11986, 5733, 876, 7030, 2167, 2436, + 3442, 9217, 8206, 4858, 5964, 2746, 7178, 1434, + 7389, 8879, 10661, 11457, 4220, 1432, 10832, 4328, + 8557, 1867, 9454, 2416, 3816, 9076, 686, 5393, + 2523, 4339, 6115, 619, 937, 2834, 7775, 3279, + 2363, 7488, 6112, 5056, 824, 10204, 11690, 1113, + 2727, 9848, 896, 2028, 5075, 2654, 10464, 7884, + 12169, 5434, 3070, 6400, 9132, 11672, 12153, 4520, + 1273, 9739, 11468, 9937, 10039, 9720, 2262, 9399, + 11192, 315, 4511, 1158, 6061, 6751, 11865, 357, + 7367, 4550, 983, 8534, 8352, 10126, 7530, 9253, + 4367, 5221, 3999, 8777, 3161, 6990, 4130, 11652, + 3374, 11477, 1753, 292, 8681, 2806, 10378, 12188, + 5800, 11811, 3181, 1988, 1024, 9340, 2477, 10928, + 4582, 6750, 3619, 5503, 5233, 2463, 8470, 7650, + 7964, 6395, 1071, 1272, 3474, 11045, 3291, 11344, + 8502, 9478, 9837, 1253, 1857, 6233, 4720, 11561, + 6034, 9817, 3339, 1797, 2879, 6242, 5200, 2114, + 7962, 9353, 11363, 5475, 6084, 9601, 4108, 7323, + 10438, 9471, 1271, 408, 6911, 3079, 360, 8276, + 11535, 9156, 9049, 11539, 850, 8617, 784, 7919, + 8334, 12170, 1846, 10213, 12184, 7827, 11903, 5600, + 9779, 1012, 721, 2784, 6676, 6552, 5348, 4424, + 6816, 8405, 9959, 5150, 2356, 5552, 5267, 1333, + 8801, 9661, 7308, 5788, 4910, 909, 11613, 4395, + 8238, 6686, 4302, 3044, 2285, 12249, 1963, 9216, + 4296, 11918, 695, 4371, 9793, 4884, 2411, 10230, + 2650, 841, 3890, 10231, 7248, 8505, 11196, 6688, + 4059, 6060, 3686, 4722, 11853, 5816, 7058, 6868, + 11137, 7926, 4894, 12284, 4102, 3908, 3610, 6525, + 7938, 7982, 11977, 6755, 537, 4562, 1623, 8227, + 11453, 7544, 906, 11816, 9548, 10858, 9703, 2815, + 11736, 6813, 6979, 819, 8903, 6271, 10843, 348, + 7514, 8339, 6439, 694, 852, 5659, 2781, 3716, + 11589, 3024, 1523, 8659, 4114, 10738, 3303, 5885, + 2978, 7289, 11884, 9123, 9323, 11830, 98, 2526, + 2116, 4131, 11407, 1844, 3645, 3916, 8133, 2224, + 10871, 8092, 9651, 5989, 7140, 8480, 1670, 159, + 10923, 4918, 128, 7312, 725, 9157, 5006, 6393, + 3494, 6043, 10972, 6181, 11838, 3423, 10514, 7668, + 3693, 6658, 6905, 11953, 10212, 11922, 9101, 8365, + 5110, 45, 2400, 1921, 4377, 2720, 1695, 51, + 2808, 650, 1896, 9997, 9971, 11980, 8098, 4833, + 4135, 4257, 5838, 4765, 10985, 11532, 590, 12198, + 482, 12173, 2006, 7064, 10018, 3912, 12016, 10519, + 11362, 6954, 2210, 284, 5413, 6601, 3865, 10339, + 11188, 6231, 517, 9564, 11281, 3863, 1210, 4604, + 8160, 11447, 153, 7204, 5763, 5089, 9248, 12154, + 11748, 1354, 6672, 179, 5532, 2646, 5941, 12185, + 862, 3158, 477, 7279, 5678, 7914, 4254, 302, + 2893, 10114, 6890, 9560, 9647, 11905, 4098, 9824, + 10269, 1353, 10715, 5325, 6254, 3951, 1807, 6449, + 5159, 1308, 8315, 3404, 1877, 1231, 112, 6398, + 11724, 12272, 7286, 1459, 12274, 9896, 3456, 800, + 1397, 10678, 103, 7420, 7976, 936, 764, 632, + 7996, 8223, 8445, 7758, 10870, 9571, 2508, 1946, + 6524, 10158, 1044, 4338, 2457, 3641, 1659, 4139, + 4688, 9733, 11148, 3946, 2082, 5261, 2036, 11850, + 7636, 12236, 5366, 2380, 1399, 7720, 2100, 3217, + 10912, 8898, 7578, 11995, 2791, 1215, 3355, 2711, + 2267, 2004, 8568, 10176, 3214, 2337, 1750, 4729, + 4997, 7415, 6315, 12044, 4374, 7157, 4844, 211, + 8003, 10159, 9290, 11481, 1735, 2336, 5793, 9875, + 8192, 986, 7527, 1401, 870, 3615, 8465, 2756, + 9770, 2034, 10168, 3264, 6132, 54, 2880, 4763, + 11805, 3074, 8286, 9428, 4881, 6933, 1090, 10038, + 2567, 708, 893, 6465, 4962, 10024, 2090, 5718, + 10743, 780, 4733, 4623, 2134, 2087, 4802, 884, + 5372, 5795, 5938, 4333, 6559, 7549, 5269, 10664, + 4252, 3260, 5917, 10814, 5768, 9983, 8096, 7791, + 6800, 7491, 6272, 1907, 10947, 6289, 11803, 6032, + 11449, 1171, 9201, 7933, 2479, 7970, 11337, 7062, + 8911, 6728, 6542, 8114, 8828, 6595, 3545, 4348, + 4610, 2205, 6999, 8106, 5560, 10390, 9321, 2499, + 2413, 7272, 6881, 10582, 9308, 9437, 3554, 3326, + 5991, 11969, 3415, 12283, 9838, 12063, 4332, 7830, + 11329, 6605, 12271, 2044, 11611, 7353, 11201, 11582, + 3733, 8943, 9978, 1627, 7168, 3935, 5050, 2762, + 7496, 10383, 755, 1654, 12053, 4952, 10134, 4394, + 6592, 7898, 7497, 8904, 12029, 3581, 10748, 5674, + 10358, 4901, 7414, 8771, 710, 6764, 8462, 7193, + 5371, 7274, 11084, 290, 7864, 6827, 11822, 2509, + 6578, 4026, 5807, 1458, 5721, 5762, 4178, 2105, + 11621, 4852, 8897, 2856, 11510, 9264, 2520, 8776, + 7011, 2647, 1898, 7039, 5950, 11163, 5488, 6277, + 9182, 11456, 633, 10046, 11554, 5633, 9587, 2333, + 7008, 7084, 5047, 7199, 9865, 8997, 569, 6390, + 10845, 9679, 8268, 11472, 4203, 1997, 2, 9331, + 162, 6182, 2000, 3649, 9792, 6363, 7557, 6187, + 8510, 9935, 5536, 9019, 3706, 12009, 1452, 3067, + 5494, 9692, 4865, 6019, 7106, 9610, 4588, 10165, + 6261, 5887, 2652, 10172, 1580, 10379, 4638, 9949 +}; + +/* + * Table for inverse NTT, binary case: + * iGMb[x] = R*((1/g)^rev(x)) mod q + * Since g = 7, 1/g = 8778 mod 12289. + */ +static const uint16_t iGMb[] = { + 4091, 4401, 1081, 1229, 2530, 6014, 7947, 5329, + 2579, 4751, 6464, 11703, 7023, 2812, 5890, 10698, + 3109, 2125, 1960, 10925, 10601, 10404, 4189, 1875, + 5847, 8546, 4615, 5190, 11324, 10578, 5882, 11155, + 8417, 12275, 10599, 7446, 5719, 3569, 5981, 10108, + 4426, 8306, 10755, 4679, 11052, 1538, 11857, 100, + 8247, 6625, 9725, 5145, 3412, 7858, 5831, 9460, + 5217, 10740, 7882, 7506, 12172, 11292, 6049, 79, + 13, 6938, 8886, 5453, 4586, 11455, 2903, 4676, + 9843, 7621, 8822, 9109, 2083, 8507, 8685, 3110, + 7015, 3269, 1367, 6397, 10259, 8435, 10527, 11559, + 11094, 2211, 1808, 7319, 48, 9547, 2560, 1228, + 9438, 10787, 11800, 1820, 11406, 8966, 6159, 3012, + 6109, 2796, 2203, 1652, 711, 7004, 1053, 8973, + 5244, 1517, 9322, 11269, 900, 3888, 11133, 10736, + 4949, 7616, 9974, 4746, 10270, 126, 2921, 6720, + 6635, 6543, 1582, 4868, 42, 673, 2240, 7219, + 1296, 11989, 7675, 8578, 11949, 989, 10541, 7687, + 7085, 8487, 1004, 10236, 4703, 163, 9143, 4597, + 6431, 12052, 2991, 11938, 4647, 3362, 2060, 11357, + 12011, 6664, 5655, 7225, 5914, 9327, 4092, 5880, + 6932, 3402, 5133, 9394, 11229, 5252, 9008, 1556, + 6908, 4773, 3853, 8780, 10325, 7737, 1758, 7103, + 11375, 12273, 8602, 3243, 6536, 7590, 8591, 11552, + 6101, 3253, 9969, 9640, 4506, 3736, 6829, 10822, + 9130, 9948, 3566, 2133, 3901, 6038, 7333, 6609, + 3468, 4659, 625, 2700, 7738, 3443, 3060, 3388, + 3526, 4418, 11911, 6232, 1730, 2558, 10340, 5344, + 5286, 2190, 11562, 6199, 2482, 8756, 5387, 4101, + 4609, 8605, 8226, 144, 5656, 8704, 2621, 5424, + 10812, 2959, 11346, 6249, 1715, 4951, 9540, 1888, + 3764, 39, 8219, 2080, 2502, 1469, 10550, 8709, + 5601, 1093, 3784, 5041, 2058, 8399, 11448, 9639, + 2059, 9878, 7405, 2496, 7918, 11594, 371, 7993, + 3073, 10326, 40, 10004, 9245, 7987, 5603, 4051, + 7894, 676, 11380, 7379, 6501, 4981, 2628, 3488, + 10956, 7022, 6737, 9933, 7139, 2330, 3884, 5473, + 7865, 6941, 5737, 5613, 9505, 11568, 11277, 2510, + 6689, 386, 4462, 105, 2076, 10443, 119, 3955, + 4370, 11505, 3672, 11439, 750, 3240, 3133, 754, + 4013, 11929, 9210, 5378, 11881, 11018, 2818, 1851, + 4966, 8181, 2688, 6205, 6814, 926, 2936, 4327, + 10175, 7089, 6047, 9410, 10492, 8950, 2472, 6255, + 728, 7569, 6056, 10432, 11036, 2452, 2811, 3787, + 945, 8998, 1244, 8815, 11017, 11218, 5894, 4325, + 4639, 3819, 9826, 7056, 6786, 8670, 5539, 7707, + 1361, 9812, 2949, 11265, 10301, 9108, 478, 6489, + 101, 1911, 9483, 3608, 11997, 10536, 812, 8915, + 637, 8159, 5299, 9128, 3512, 8290, 7068, 7922, + 3036, 4759, 2163, 3937, 3755, 11306, 7739, 4922, + 11932, 424, 5538, 6228, 11131, 7778, 11974, 1097, + 2890, 10027, 2569, 2250, 2352, 821, 2550, 11016, + 7769, 136, 617, 3157, 5889, 9219, 6855, 120, + 4405, 1825, 9635, 7214, 10261, 11393, 2441, 9562, + 11176, 599, 2085, 11465, 7233, 6177, 4801, 9926, + 9010, 4514, 9455, 11352, 11670, 6174, 7950, 9766, + 6896, 11603, 3213, 8473, 9873, 2835, 10422, 3732, + 7961, 1457, 10857, 8069, 832, 1628, 3410, 4900, + 10855, 5111, 9543, 6325, 7431, 4083, 3072, 8847, + 9853, 10122, 5259, 11413, 6556, 303, 1465, 3871, + 4873, 5813, 10017, 6898, 3311, 5947, 8637, 5852, + 3856, 928, 4933, 8530, 1871, 2184, 5571, 5879, + 3481, 11597, 9511, 8153, 35, 2609, 5963, 8064, + 1080, 12039, 8444, 3052, 3813, 11065, 6736, 8454, + 2340, 7651, 1910, 10709, 2117, 9637, 6402, 6028, + 2124, 7701, 2679, 5183, 6270, 7424, 2597, 6795, + 9222, 10837, 280, 8583, 3270, 6753, 2354, 3779, + 6102, 4732, 5926, 2497, 8640, 10289, 6107, 12127, + 2958, 12287, 10292, 8086, 817, 4021, 2610, 1444, + 5899, 11720, 3292, 2424, 5090, 7242, 5205, 5281, + 9956, 2702, 6656, 735, 2243, 11656, 833, 3107, + 6012, 6801, 1126, 6339, 5250, 10391, 9642, 5278, + 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5225, 10283, 116, 11807, + 91, 11699, 757, 1304, 7524, 6451, 8032, 8154, + 7456, 4191, 309, 2318, 2292, 10393, 11639, 9481, + 12238, 10594, 9569, 7912, 10368, 9889, 12244, 7179, + 3924, 3188, 367, 2077, 336, 5384, 5631, 8596, + 4621, 1775, 8866, 451, 6108, 1317, 6246, 8795, + 5896, 7283, 3132, 11564, 4977, 12161, 7371, 1366, + 12130, 10619, 3809, 5149, 6300, 2638, 4197, 1418, + 10065, 4156, 8373, 8644, 10445, 882, 8158, 10173, + 9763, 12191, 459, 2966, 3166, 405, 5000, 9311, + 6404, 8986, 1551, 8175, 3630, 10766, 9265, 700, + 8573, 9508, 6630, 11437, 11595, 5850, 3950, 4775, + 11941, 1446, 6018, 3386, 11470, 5310, 5476, 553, + 9474, 2586, 1431, 2741, 473, 11383, 4745, 836, + 4062, 10666, 7727, 11752, 5534, 312, 4307, 4351, + 5764, 8679, 8381, 8187, 5, 7395, 4363, 1152, + 5421, 5231, 6473, 436, 7567, 8603, 6229, 8230 +}; + +/* + * Reduce a small signed integer modulo q. The source integer MUST + * be between -q/2 and +q/2. + */ +static inline uint32_t +mq_conv_small(int x) { + /* + * If x < 0, the cast to uint32_t will set the high bit to 1. + */ + uint32_t y; + + y = (uint32_t)x; + y += Q & -(y >> 31); + return y; +} + +/* + * Addition modulo q. Operands must be in the 0..q-1 range. + */ +static inline uint32_t +mq_add(uint32_t x, uint32_t y) { + /* + * We compute x + y - q. If the result is negative, then the + * high bit will be set, and 'd >> 31' will be equal to 1; + * thus '-(d >> 31)' will be an all-one pattern. Otherwise, + * it will be an all-zero pattern. In other words, this + * implements a conditional addition of q. + */ + uint32_t d; + + d = x + y - Q; + d += Q & -(d >> 31); + return d; +} + +/* + * Subtraction modulo q. Operands must be in the 0..q-1 range. + */ +static inline uint32_t +mq_sub(uint32_t x, uint32_t y) { + /* + * As in mq_add(), we use a conditional addition to ensure the + * result is in the 0..q-1 range. + */ + uint32_t d; + + d = x - y; + d += Q & -(d >> 31); + return d; +} + +/* + * Division by 2 modulo q. Operand must be in the 0..q-1 range. + */ +static inline uint32_t +mq_rshift1(uint32_t x) { + x += Q & -(x & 1); + return (x >> 1); +} + +/* + * Montgomery multiplication modulo q. If we set R = 2^16 mod q, then + * this function computes: x * y / R mod q + * Operands must be in the 0..q-1 range. + */ +static inline uint32_t +mq_montymul(uint32_t x, uint32_t y) { + uint32_t z, w; + + /* + * We compute x*y + k*q with a value of k chosen so that the 16 + * low bits of the result are 0. We can then shift the value. + * After the shift, result may still be larger than q, but it + * will be lower than 2*q, so a conditional subtraction works. + */ + + z = x * y; + w = ((z * Q0I) & 0xFFFF) * Q; + + /* + * When adding z and w, the result will have its low 16 bits + * equal to 0. Since x, y and z are lower than q, the sum will + * be no more than (2^15 - 1) * q + (q - 1)^2, which will + * fit on 29 bits. + */ + z = (z + w) >> 16; + + /* + * After the shift, analysis shows that the value will be less + * than 2q. We do a subtraction then conditional subtraction to + * ensure the result is in the expected range. + */ + z -= Q; + z += Q & -(z >> 31); + return z; +} + +/* + * Montgomery squaring (computes (x^2)/R). + */ +static inline uint32_t +mq_montysqr(uint32_t x) { + return mq_montymul(x, x); +} + +/* + * Divide x by y modulo q = 12289. + */ +static inline uint32_t +mq_div_12289(uint32_t x, uint32_t y) { + /* + * We invert y by computing y^(q-2) mod q. + * + * We use the following addition chain for exponent e = 12287: + * + * e0 = 1 + * e1 = 2 * e0 = 2 + * e2 = e1 + e0 = 3 + * e3 = e2 + e1 = 5 + * e4 = 2 * e3 = 10 + * e5 = 2 * e4 = 20 + * e6 = 2 * e5 = 40 + * e7 = 2 * e6 = 80 + * e8 = 2 * e7 = 160 + * e9 = e8 + e2 = 163 + * e10 = e9 + e8 = 323 + * e11 = 2 * e10 = 646 + * e12 = 2 * e11 = 1292 + * e13 = e12 + e9 = 1455 + * e14 = 2 * e13 = 2910 + * e15 = 2 * e14 = 5820 + * e16 = e15 + e10 = 6143 + * e17 = 2 * e16 = 12286 + * e18 = e17 + e0 = 12287 + * + * Additions on exponents are converted to Montgomery + * multiplications. We define all intermediate results as so + * many local variables, and let the C compiler work out which + * must be kept around. + */ + uint32_t y0, y1, y2, y3, y4, y5, y6, y7, y8, y9; + uint32_t y10, y11, y12, y13, y14, y15, y16, y17, y18; + + y0 = mq_montymul(y, R2); + y1 = mq_montysqr(y0); + y2 = mq_montymul(y1, y0); + y3 = mq_montymul(y2, y1); + y4 = mq_montysqr(y3); + y5 = mq_montysqr(y4); + y6 = mq_montysqr(y5); + y7 = mq_montysqr(y6); + y8 = mq_montysqr(y7); + y9 = mq_montymul(y8, y2); + y10 = mq_montymul(y9, y8); + y11 = mq_montysqr(y10); + y12 = mq_montysqr(y11); + y13 = mq_montymul(y12, y9); + y14 = mq_montysqr(y13); + y15 = mq_montysqr(y14); + y16 = mq_montymul(y15, y10); + y17 = mq_montysqr(y16); + y18 = mq_montymul(y17, y0); + + /* + * Final multiplication with x, which is not in Montgomery + * representation, computes the correct division result. + */ + return mq_montymul(y18, x); +} + +/* + * Compute NTT on a ring element. + */ +static void +mq_NTT(uint16_t *a, unsigned logn) { + size_t n, t, m; + + n = (size_t)1 << logn; + t = n; + for (m = 1; m < n; m <<= 1) { + size_t ht, i, j1; + + ht = t >> 1; + for (i = 0, j1 = 0; i < m; i ++, j1 += t) { + size_t j, j2; + uint32_t s; + + s = GMb[m + i]; + j2 = j1 + ht; + for (j = j1; j < j2; j ++) { + uint32_t u, v; + + u = a[j]; + v = mq_montymul(a[j + ht], s); + a[j] = (uint16_t)mq_add(u, v); + a[j + ht] = (uint16_t)mq_sub(u, v); + } + } + t = ht; + } +} + +/* + * Compute the inverse NTT on a ring element, binary case. + */ +static void +mq_iNTT(uint16_t *a, unsigned logn) { + size_t n, t, m; + uint32_t ni; + + n = (size_t)1 << logn; + t = 1; + m = n; + while (m > 1) { + size_t hm, dt, i, j1; + + hm = m >> 1; + dt = t << 1; + for (i = 0, j1 = 0; i < hm; i ++, j1 += dt) { + size_t j, j2; + uint32_t s; + + j2 = j1 + t; + s = iGMb[hm + i]; + for (j = j1; j < j2; j ++) { + uint32_t u, v, w; + + u = a[j]; + v = a[j + t]; + a[j] = (uint16_t)mq_add(u, v); + w = mq_sub(u, v); + a[j + t] = (uint16_t) + mq_montymul(w, s); + } + } + t = dt; + m = hm; + } + + /* + * To complete the inverse NTT, we must now divide all values by + * n (the vector size). We thus need the inverse of n, i.e. we + * need to divide 1 by 2 logn times. But we also want it in + * Montgomery representation, i.e. we also want to multiply it + * by R = 2^16. In the common case, this should be a simple right + * shift. The loop below is generic and works also in corner cases; + * its computation time is negligible. + */ + ni = R; + for (m = n; m > 1; m >>= 1) { + ni = mq_rshift1(ni); + } + for (m = 0; m < n; m ++) { + a[m] = (uint16_t)mq_montymul(a[m], ni); + } +} + +/* + * Convert a polynomial (mod q) to Montgomery representation. + */ +static void +mq_poly_tomonty(uint16_t *f, unsigned logn) { + size_t u, n; + + n = (size_t)1 << logn; + for (u = 0; u < n; u ++) { + f[u] = (uint16_t)mq_montymul(f[u], R2); + } +} + +/* + * Multiply two polynomials together (NTT representation, and using + * a Montgomery multiplication). Result f*g is written over f. + */ +static void +mq_poly_montymul_ntt(uint16_t *f, const uint16_t *g, unsigned logn) { + size_t u, n; + + n = (size_t)1 << logn; + for (u = 0; u < n; u ++) { + f[u] = (uint16_t)mq_montymul(f[u], g[u]); + } +} + +/* + * Subtract polynomial g from polynomial f. + */ +static void +mq_poly_sub(uint16_t *f, const uint16_t *g, unsigned logn) { + size_t u, n; + + n = (size_t)1 << logn; + for (u = 0; u < n; u ++) { + f[u] = (uint16_t)mq_sub(f[u], g[u]); + } +} + +/* ===================================================================== */ + +/* see inner.h */ +void +PQCLEAN_FALCON1024_CLEAN_to_ntt_monty(uint16_t *h, unsigned logn) { + mq_NTT(h, logn); + mq_poly_tomonty(h, logn); +} + +/* see inner.h */ +int +PQCLEAN_FALCON1024_CLEAN_verify_raw(const uint16_t *c0, const int16_t *s2, + const uint16_t *h, unsigned logn, uint8_t *tmp) { + size_t u, n; + uint16_t *tt; + + n = (size_t)1 << logn; + tt = (uint16_t *)tmp; + + /* + * Reduce s2 elements modulo q ([0..q-1] range). + */ + for (u = 0; u < n; u ++) { + uint32_t w; + + w = (uint32_t)s2[u]; + w += Q & -(w >> 31); + tt[u] = (uint16_t)w; + } + + /* + * Compute -s1 = s2*h - c0 mod phi mod q (in tt[]). + */ + mq_NTT(tt, logn); + mq_poly_montymul_ntt(tt, h, logn); + mq_iNTT(tt, logn); + mq_poly_sub(tt, c0, logn); + + /* + * Normalize -s1 elements into the [-q/2..q/2] range. + */ + for (u = 0; u < n; u ++) { + int32_t w; + + w = (int32_t)tt[u]; + w -= (int32_t)(Q & -(((Q >> 1) - (uint32_t)w) >> 31)); + ((int16_t *)tt)[u] = (int16_t)w; + } + + /* + * Signature is valid if and only if the aggregate (-s1,s2) vector + * is short enough. + */ + return PQCLEAN_FALCON1024_CLEAN_is_short((int16_t *)tt, s2, logn); +} + +/* see inner.h */ +int +PQCLEAN_FALCON1024_CLEAN_compute_public(uint16_t *h, + const int8_t *f, const int8_t *g, unsigned logn, uint8_t *tmp) { + size_t u, n; + uint16_t *tt; + + n = (size_t)1 << logn; + tt = (uint16_t *)tmp; + for (u = 0; u < n; u ++) { + tt[u] = (uint16_t)mq_conv_small(f[u]); + h[u] = (uint16_t)mq_conv_small(g[u]); + } + mq_NTT(h, logn); + mq_NTT(tt, logn); + for (u = 0; u < n; u ++) { + if (tt[u] == 0) { + return 0; + } + h[u] = (uint16_t)mq_div_12289(h[u], tt[u]); + } + mq_iNTT(h, logn); + return 1; +} + +/* see inner.h */ +int +PQCLEAN_FALCON1024_CLEAN_complete_private(int8_t *G, + const int8_t *f, const int8_t *g, const int8_t *F, + unsigned logn, uint8_t *tmp) { + size_t u, n; + uint16_t *t1, *t2; + + n = (size_t)1 << logn; + t1 = (uint16_t *)tmp; + t2 = t1 + n; + for (u = 0; u < n; u ++) { + t1[u] = (uint16_t)mq_conv_small(g[u]); + t2[u] = (uint16_t)mq_conv_small(F[u]); + } + mq_NTT(t1, logn); + mq_NTT(t2, logn); + mq_poly_tomonty(t1, logn); + mq_poly_montymul_ntt(t1, t2, logn); + for (u = 0; u < n; u ++) { + t2[u] = (uint16_t)mq_conv_small(f[u]); + } + mq_NTT(t2, logn); + for (u = 0; u < n; u ++) { + if (t2[u] == 0) { + return 0; + } + t1[u] = (uint16_t)mq_div_12289(t1[u], t2[u]); + } + mq_iNTT(t1, logn); + for (u = 0; u < n; u ++) { + uint32_t w; + int32_t gi; + + w = t1[u]; + w -= (Q & ~ -((w - (Q >> 1)) >> 31)); + gi = *(int32_t *)&w; + if (gi < -127 || gi > +127) { + return 0; + } + G[u] = (int8_t)gi; + } + return 1; +} + +/* see inner.h */ +int +PQCLEAN_FALCON1024_CLEAN_is_invertible( + const int16_t *s2, unsigned logn, uint8_t *tmp) { + size_t u, n; + uint16_t *tt; + uint32_t r; + + n = (size_t)1 << logn; + tt = (uint16_t *)tmp; + for (u = 0; u < n; u ++) { + uint32_t w; + + w = (uint32_t)s2[u]; + w += Q & -(w >> 31); + tt[u] = (uint16_t)w; + } + mq_NTT(tt, logn); + r = 0; + for (u = 0; u < n; u ++) { + r |= (uint32_t)(tt[u] - 1); + } + return (int)(1u - (r >> 31)); +} + +/* see inner.h */ +int +PQCLEAN_FALCON1024_CLEAN_verify_recover(uint16_t *h, + const uint16_t *c0, const int16_t *s1, const int16_t *s2, + unsigned logn, uint8_t *tmp) { + size_t u, n; + uint16_t *tt; + uint32_t r; + + n = (size_t)1 << logn; + + /* + * Reduce elements of s1 and s2 modulo q; then write s2 into tt[] + * and c0 - s1 into h[]. + */ + tt = (uint16_t *)tmp; + for (u = 0; u < n; u ++) { + uint32_t w; + + w = (uint32_t)s2[u]; + w += Q & -(w >> 31); + tt[u] = (uint16_t)w; + + w = (uint32_t)s1[u]; + w += Q & -(w >> 31); + w = mq_sub(c0[u], w); + h[u] = (uint16_t)w; + } + + /* + * Compute h = (c0 - s1) / s2. If one of the coefficients of s2 + * is zero (in NTT representation) then the operation fails. We + * keep that information into a flag so that we do not deviate + * from strict constant-time processing; if all coefficients of + * s2 are non-zero, then the high bit of r will be zero. + */ + mq_NTT(tt, logn); + mq_NTT(h, logn); + r = 0; + for (u = 0; u < n; u ++) { + r |= (uint32_t)(tt[u] - 1); + h[u] = (uint16_t)mq_div_12289(h[u], tt[u]); + } + mq_iNTT(h, logn); + + /* + * Signature is acceptable if and only if it is short enough, + * and s2 was invertible mod phi mod q. The caller must still + * check that the rebuilt public key matches the expected + * value (e.g. through a hash). + */ + r = ~r & (uint32_t) - PQCLEAN_FALCON1024_CLEAN_is_short(s1, s2, logn); + return (int)(r >> 31); +} + +/* see inner.h */ +int +PQCLEAN_FALCON1024_CLEAN_count_nttzero(const int16_t *sig, unsigned logn, uint8_t *tmp) { + uint16_t *s2; + size_t u, n; + uint32_t r; + + n = (size_t)1 << logn; + s2 = (uint16_t *)tmp; + for (u = 0; u < n; u ++) { + uint32_t w; + + w = (uint32_t)sig[u]; + w += Q & -(w >> 31); + s2[u] = (uint16_t)w; + } + mq_NTT(s2, logn); + r = 0; + for (u = 0; u < n; u ++) { + uint32_t w; + + w = (uint32_t)s2[u] - 1u; + r += (w >> 31); + } + return (int)r; +} diff --git a/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/Makefile b/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/Makefile new file mode 100644 index 000000000..fe090f3ff --- /dev/null +++ b/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/Makefile @@ -0,0 +1,49 @@ +#! gmake +# +# This Source Code Form is subject to the terms of the Mozilla Public +# License, v. 2.0. If a copy of the MPL was not distributed with this +# file, You can obtain one at http://mozilla.org/MPL/2.0/. + +####################################################################### +# (1) Include initial platform-independent assignments (MANDATORY). # +####################################################################### + +include manifest.mn + +####################################################################### +# (2) Include "global" configuration information. (OPTIONAL) # +####################################################################### + +USE_GCOV = +include $(CORE_DEPTH)/coreconf/config.mk + +####################################################################### +# (3) Include "component" configuration information. (OPTIONAL) # +####################################################################### + + + +####################################################################### +# (4) Include "local" platform-dependent assignments (OPTIONAL). # +####################################################################### + +include config.mk + +####################################################################### +# (5) Execute "global" rules. (OPTIONAL) # +####################################################################### + +include $(CORE_DEPTH)/coreconf/rules.mk + +####################################################################### +# (6) Execute "component" rules. (OPTIONAL) # +####################################################################### + + + +####################################################################### +# (7) Execute "local" rules. (OPTIONAL). # +####################################################################### + +WARNING_CFLAGS = $(NULL) + diff --git a/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/api.h b/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/api.h new file mode 100644 index 000000000..a2e5e1d50 --- /dev/null +++ b/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/api.h @@ -0,0 +1,80 @@ +#ifndef PQCLEAN_FALCON512_CLEAN_API_H +#define PQCLEAN_FALCON512_CLEAN_API_H + +#include <stddef.h> +#include <stdint.h> + +#define PQCLEAN_FALCON512_CLEAN_CRYPTO_SECRETKEYBYTES 1281 +#define PQCLEAN_FALCON512_CLEAN_CRYPTO_PUBLICKEYBYTES 897 +#define PQCLEAN_FALCON512_CLEAN_CRYPTO_BYTES 690 + +#define PQCLEAN_FALCON512_CLEAN_CRYPTO_ALGNAME "Falcon-512" + +/* + * Generate a new key pair. Public key goes into pk[], private key in sk[]. + * Key sizes are exact (in bytes): + * public (pk): PQCLEAN_FALCON512_CLEAN_CRYPTO_PUBLICKEYBYTES + * private (sk): PQCLEAN_FALCON512_CLEAN_CRYPTO_SECRETKEYBYTES + * + * Return value: 0 on success, -1 on error. + */ +int PQCLEAN_FALCON512_CLEAN_crypto_sign_keypair( + uint8_t *pk, uint8_t *sk); + +/* + * Compute a signature on a provided message (m, mlen), with a given + * private key (sk). Signature is written in sig[], with length written + * into *siglen. Signature length is variable; maximum signature length + * (in bytes) is PQCLEAN_FALCON512_CLEAN_CRYPTO_BYTES. + * + * sig[], m[] and sk[] may overlap each other arbitrarily. + * + * Return value: 0 on success, -1 on error. + */ +int PQCLEAN_FALCON512_CLEAN_crypto_sign_signature( + uint8_t *sig, size_t *siglen, + const uint8_t *m, size_t mlen, const uint8_t *sk); + +/* + * Verify a signature (sig, siglen) on a message (m, mlen) with a given + * public key (pk). + * + * sig[], m[] and pk[] may overlap each other arbitrarily. + * + * Return value: 0 on success, -1 on error. + */ +int PQCLEAN_FALCON512_CLEAN_crypto_sign_verify( + const uint8_t *sig, size_t siglen, + const uint8_t *m, size_t mlen, const uint8_t *pk); + +/* + * Compute a signature on a message and pack the signature and message + * into a single object, written into sm[]. The length of that output is + * written in *smlen; that length may be larger than the message length + * (mlen) by up to PQCLEAN_FALCON512_CLEAN_CRYPTO_BYTES. + * + * sm[] and m[] may overlap each other arbitrarily; however, sm[] shall + * not overlap with sk[]. + * + * Return value: 0 on success, -1 on error. + */ +int PQCLEAN_FALCON512_CLEAN_crypto_sign( + uint8_t *sm, size_t *smlen, + const uint8_t *m, size_t mlen, const uint8_t *sk); + +/* + * Open a signed message object (sm, smlen) and verify the signature; + * on success, the message itself is written into m[] and its length + * into *mlen. The message is shorter than the signed message object, + * but the size difference depends on the signature value; the difference + * may range up to PQCLEAN_FALCON512_CLEAN_CRYPTO_BYTES. + * + * m[], sm[] and pk[] may overlap each other arbitrarily. + * + * Return value: 0 on success, -1 on error. + */ +int PQCLEAN_FALCON512_CLEAN_crypto_sign_open( + uint8_t *m, size_t *mlen, + const uint8_t *sm, size_t smlen, const uint8_t *pk); + +#endif diff --git a/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/codec.c b/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/codec.c new file mode 100644 index 000000000..76709bc9d --- /dev/null +++ b/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/codec.c @@ -0,0 +1,555 @@ +#include "inner.h" + +/* + * Encoding/decoding of keys and signatures. + * + * ==========================(LICENSE BEGIN)============================ + * + * Copyright (c) 2017-2019 Falcon Project + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the + * "Software"), to deal in the Software without restriction, including + * without limitation the rights to use, copy, modify, merge, publish, + * distribute, sublicense, and/or sell copies of the Software, and to + * permit persons to whom the Software is furnished to do so, subject to + * the following conditions: + * + * The above copyright notice and this permission notice shall be + * included in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, + * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF + * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. + * IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY + * CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, + * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE + * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. + * + * ===========================(LICENSE END)============================= + * + * @author Thomas Pornin <thomas.pornin@nccgroup.com> + */ + + +/* see inner.h */ +size_t +PQCLEAN_FALCON512_CLEAN_modq_encode( + void *out, size_t max_out_len, + const uint16_t *x, unsigned logn) { + size_t n, out_len, u; + uint8_t *buf; + uint32_t acc; + int acc_len; + + n = (size_t)1 << logn; + for (u = 0; u < n; u ++) { + if (x[u] >= 12289) { + return 0; + } + } + out_len = ((n * 14) + 7) >> 3; + if (out == NULL) { + return out_len; + } + if (out_len > max_out_len) { + return 0; + } + buf = out; + acc = 0; + acc_len = 0; + for (u = 0; u < n; u ++) { + acc = (acc << 14) | x[u]; + acc_len += 14; + while (acc_len >= 8) { + acc_len -= 8; + *buf ++ = (uint8_t)(acc >> acc_len); + } + } + if (acc_len > 0) { + *buf = (uint8_t)(acc << (8 - acc_len)); + } + return out_len; +} + +/* see inner.h */ +size_t +PQCLEAN_FALCON512_CLEAN_modq_decode( + uint16_t *x, unsigned logn, + const void *in, size_t max_in_len) { + size_t n, in_len, u; + const uint8_t *buf; + uint32_t acc; + int acc_len; + + n = (size_t)1 << logn; + in_len = ((n * 14) + 7) >> 3; + if (in_len > max_in_len) { + return 0; + } + buf = in; + acc = 0; + acc_len = 0; + u = 0; + while (u < n) { + acc = (acc << 8) | (*buf ++); + acc_len += 8; + if (acc_len >= 14) { + unsigned w; + + acc_len -= 14; + w = (acc >> acc_len) & 0x3FFF; + if (w >= 12289) { + return 0; + } + x[u ++] = (uint16_t)w; + } + } + if ((acc & (((uint32_t)1 << acc_len) - 1)) != 0) { + return 0; + } + return in_len; +} + +/* see inner.h */ +size_t +PQCLEAN_FALCON512_CLEAN_trim_i16_encode( + void *out, size_t max_out_len, + const int16_t *x, unsigned logn, unsigned bits) { + size_t n, u, out_len; + int minv, maxv; + uint8_t *buf; + uint32_t acc, mask; + unsigned acc_len; + + n = (size_t)1 << logn; + maxv = (1 << (bits - 1)) - 1; + minv = -maxv; + for (u = 0; u < n; u ++) { + if (x[u] < minv || x[u] > maxv) { + return 0; + } + } + out_len = ((n * bits) + 7) >> 3; + if (out == NULL) { + return out_len; + } + if (out_len > max_out_len) { + return 0; + } + buf = out; + acc = 0; + acc_len = 0; + mask = ((uint32_t)1 << bits) - 1; + for (u = 0; u < n; u ++) { + acc = (acc << bits) | ((uint16_t)x[u] & mask); + acc_len += bits; + while (acc_len >= 8) { + acc_len -= 8; + *buf ++ = (uint8_t)(acc >> acc_len); + } + } + if (acc_len > 0) { + *buf ++ = (uint8_t)(acc << (8 - acc_len)); + } + return out_len; +} + +/* see inner.h */ +size_t +PQCLEAN_FALCON512_CLEAN_trim_i16_decode( + int16_t *x, unsigned logn, unsigned bits, + const void *in, size_t max_in_len) { + size_t n, in_len; + const uint8_t *buf; + size_t u; + uint32_t acc, mask1, mask2; + unsigned acc_len; + + n = (size_t)1 << logn; + in_len = ((n * bits) + 7) >> 3; + if (in_len > max_in_len) { + return 0; + } + buf = in; + u = 0; + acc = 0; + acc_len = 0; + mask1 = ((uint32_t)1 << bits) - 1; + mask2 = (uint32_t)1 << (bits - 1); + while (u < n) { + acc = (acc << 8) | *buf ++; + acc_len += 8; + while (acc_len >= bits && u < n) { + uint32_t w; + + acc_len -= bits; + w = (acc >> acc_len) & mask1; + w |= -(w & mask2); + if (w == -mask2) { + /* + * The -2^(bits-1) value is forbidden. + */ + return 0; + } + w |= -(w & mask2); + x[u ++] = (int16_t) * (int32_t *)&w; + } + } + if ((acc & (((uint32_t)1 << acc_len) - 1)) != 0) { + /* + * Extra bits in the last byte must be zero. + */ + return 0; + } + return in_len; +} + +/* see inner.h */ +size_t +PQCLEAN_FALCON512_CLEAN_trim_i8_encode( + void *out, size_t max_out_len, + const int8_t *x, unsigned logn, unsigned bits) { + size_t n, u, out_len; + int minv, maxv; + uint8_t *buf; + uint32_t acc, mask; + unsigned acc_len; + + n = (size_t)1 << logn; + maxv = (1 << (bits - 1)) - 1; + minv = -maxv; + for (u = 0; u < n; u ++) { + if (x[u] < minv || x[u] > maxv) { + return 0; + } + } + out_len = ((n * bits) + 7) >> 3; + if (out == NULL) { + return out_len; + } + if (out_len > max_out_len) { + return 0; + } + buf = out; + acc = 0; + acc_len = 0; + mask = ((uint32_t)1 << bits) - 1; + for (u = 0; u < n; u ++) { + acc = (acc << bits) | ((uint8_t)x[u] & mask); + acc_len += bits; + while (acc_len >= 8) { + acc_len -= 8; + *buf ++ = (uint8_t)(acc >> acc_len); + } + } + if (acc_len > 0) { + *buf ++ = (uint8_t)(acc << (8 - acc_len)); + } + return out_len; +} + +/* see inner.h */ +size_t +PQCLEAN_FALCON512_CLEAN_trim_i8_decode( + int8_t *x, unsigned logn, unsigned bits, + const void *in, size_t max_in_len) { + size_t n, in_len; + const uint8_t *buf; + size_t u; + uint32_t acc, mask1, mask2; + unsigned acc_len; + + n = (size_t)1 << logn; + in_len = ((n * bits) + 7) >> 3; + if (in_len > max_in_len) { + return 0; + } + buf = in; + u = 0; + acc = 0; + acc_len = 0; + mask1 = ((uint32_t)1 << bits) - 1; + mask2 = (uint32_t)1 << (bits - 1); + while (u < n) { + acc = (acc << 8) | *buf ++; + acc_len += 8; + while (acc_len >= bits && u < n) { + uint32_t w; + + acc_len -= bits; + w = (acc >> acc_len) & mask1; + w |= -(w & mask2); + if (w == -mask2) { + /* + * The -2^(bits-1) value is forbidden. + */ + return 0; + } + x[u ++] = (int8_t) * (int32_t *)&w; + } + } + if ((acc & (((uint32_t)1 << acc_len) - 1)) != 0) { + /* + * Extra bits in the last byte must be zero. + */ + return 0; + } + return in_len; +} + +/* see inner.h */ +size_t +PQCLEAN_FALCON512_CLEAN_comp_encode( + void *out, size_t max_out_len, + const int16_t *x, unsigned logn) { + uint8_t *buf; + size_t n, u, v; + uint32_t acc; + unsigned acc_len; + + n = (size_t)1 << logn; + buf = out; + + /* + * Make sure that all values are within the -2047..+2047 range. + */ + for (u = 0; u < n; u ++) { + if (x[u] < -2047 || x[u] > +2047) { + return 0; + } + } + + acc = 0; + acc_len = 0; + v = 0; + for (u = 0; u < n; u ++) { + int t; + unsigned w; + + /* + * Get sign and absolute value of next integer; push the + * sign bit. + */ + acc <<= 1; + t = x[u]; + if (t < 0) { + t = -t; + acc |= 1; + } + w = (unsigned)t; + + /* + * Push the low 7 bits of the absolute value. + */ + acc <<= 7; + acc |= w & 127u; + w >>= 7; + + /* + * We pushed exactly 8 bits. + */ + acc_len += 8; + + /* + * Push as many zeros as necessary, then a one. Since the + * absolute value is at most 2047, w can only range up to + * 15 at this point, thus we will add at most 16 bits + * here. With the 8 bits above and possibly up to 7 bits + * from previous iterations, we may go up to 31 bits, which + * will fit in the accumulator, which is an uint32_t. + */ + acc <<= (w + 1); + acc |= 1; + acc_len += w + 1; + + /* + * Produce all full bytes. + */ + while (acc_len >= 8) { + acc_len -= 8; + if (buf != NULL) { + if (v >= max_out_len) { + return 0; + } + buf[v] = (uint8_t)(acc >> acc_len); + } + v ++; + } + } + + /* + * Flush remaining bits (if any). + */ + if (acc_len > 0) { + if (buf != NULL) { + if (v >= max_out_len) { + return 0; + } + buf[v] = (uint8_t)(acc << (8 - acc_len)); + } + v ++; + } + + return v; +} + +/* see inner.h */ +size_t +PQCLEAN_FALCON512_CLEAN_comp_decode( + int16_t *x, unsigned logn, + const void *in, size_t max_in_len) { + const uint8_t *buf; + size_t n, u, v; + uint32_t acc; + unsigned acc_len; + + n = (size_t)1 << logn; + buf = in; + acc = 0; + acc_len = 0; + v = 0; + for (u = 0; u < n; u ++) { + unsigned b, s, m; + + /* + * Get next eight bits: sign and low seven bits of the + * absolute value. + */ + if (v >= max_in_len) { + return 0; + } + acc = (acc << 8) | (uint32_t)buf[v ++]; + b = acc >> acc_len; + s = b & 128; + m = b & 127; + + /* + * Get next bits until a 1 is reached. + */ + for (;;) { + if (acc_len == 0) { + if (v >= max_in_len) { + return 0; + } + acc = (acc << 8) | (uint32_t)buf[v ++]; + acc_len = 8; + } + acc_len --; + if (((acc >> acc_len) & 1) != 0) { + break; + } + m += 128; + if (m > 2047) { + return 0; + } + } + x[u] = (int16_t) m; + if (s) { + x[u] = (int16_t) - x[u]; + } + } + return v; +} + +/* + * Key elements and signatures are polynomials with small integer + * coefficients. Here are some statistics gathered over many + * generated key pairs (10000 or more for each degree): + * + * log(n) n max(f,g) std(f,g) max(F,G) std(F,G) + * 1 2 129 56.31 143 60.02 + * 2 4 123 40.93 160 46.52 + * 3 8 97 28.97 159 38.01 + * 4 16 100 21.48 154 32.50 + * 5 32 71 15.41 151 29.36 + * 6 64 59 11.07 138 27.77 + * 7 128 39 7.91 144 27.00 + * 8 256 32 5.63 148 26.61 + * 9 512 22 4.00 137 26.46 + * 10 1024 15 2.84 146 26.41 + * + * We want a compact storage format for private key, and, as part of + * key generation, we are allowed to reject some keys which would + * otherwise be fine (this does not induce any noticeable vulnerability + * as long as we reject only a small proportion of possible keys). + * Hence, we enforce at key generation time maximum values for the + * elements of f, g, F and G, so that their encoding can be expressed + * in fixed-width values. Limits have been chosen so that generated + * keys are almost always within bounds, thus not impacting neither + * security or performance. + * + * IMPORTANT: the code assumes that all coefficients of f, g, F and G + * ultimately fit in the -127..+127 range. Thus, none of the elements + * of max_fg_bits[] and max_FG_bits[] shall be greater than 8. + */ + +const uint8_t PQCLEAN_FALCON512_CLEAN_max_fg_bits[] = { + 0, /* unused */ + 8, + 8, + 8, + 8, + 8, + 7, + 7, + 6, + 6, + 5 +}; + +const uint8_t PQCLEAN_FALCON512_CLEAN_max_FG_bits[] = { + 0, /* unused */ + 8, + 8, + 8, + 8, + 8, + 8, + 8, + 8, + 8, + 8 +}; + +/* + * When generating a new key pair, we can always reject keys which + * feature an abnormally large coefficient. This can also be done for + * signatures, albeit with some care: in case the signature process is + * used in a derandomized setup (explicitly seeded with the message and + * private key), we have to follow the specification faithfully, and the + * specification only enforces a limit on the L2 norm of the signature + * vector. The limit on the L2 norm implies that the absolute value of + * a coefficient of the signature cannot be more than the following: + * + * log(n) n max sig coeff (theoretical) + * 1 2 412 + * 2 4 583 + * 3 8 824 + * 4 16 1166 + * 5 32 1649 + * 6 64 2332 + * 7 128 3299 + * 8 256 4665 + * 9 512 6598 + * 10 1024 9331 + * + * However, the largest observed signature coefficients during our + * experiments was 1077 (in absolute value), hence we can assume that, + * with overwhelming probability, signature coefficients will fit + * in -2047..2047, i.e. 12 bits. + */ + +const uint8_t PQCLEAN_FALCON512_CLEAN_max_sig_bits[] = { + 0, /* unused */ + 10, + 11, + 11, + 12, + 12, + 12, + 12, + 12, + 12, + 12 +}; diff --git a/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/common.c b/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/common.c new file mode 100644 index 000000000..dea433f6c --- /dev/null +++ b/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/common.c @@ -0,0 +1,294 @@ +#include "inner.h" + +/* + * Support functions for signatures (hash-to-point, norm). + * + * ==========================(LICENSE BEGIN)============================ + * + * Copyright (c) 2017-2019 Falcon Project + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the + * "Software"), to deal in the Software without restriction, including + * without limitation the rights to use, copy, modify, merge, publish, + * distribute, sublicense, and/or sell copies of the Software, and to + * permit persons to whom the Software is furnished to do so, subject to + * the following conditions: + * + * The above copyright notice and this permission notice shall be + * included in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, + * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF + * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. + * IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY + * CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, + * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE + * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. + * + * ===========================(LICENSE END)============================= + * + * @author Thomas Pornin <thomas.pornin@nccgroup.com> + */ + + +/* see inner.h */ +void +PQCLEAN_FALCON512_CLEAN_hash_to_point_vartime( + inner_shake256_context *sc, + uint16_t *x, unsigned logn) { + /* + * This is the straightforward per-the-spec implementation. It + * is not constant-time, thus it might reveal information on the + * plaintext (at least, enough to check the plaintext against a + * list of potential plaintexts) in a scenario where the + * attacker does not have access to the signature value or to + * the public key, but knows the nonce (without knowledge of the + * nonce, the hashed output cannot be matched against potential + * plaintexts). + */ + size_t n; + + n = (size_t)1 << logn; + while (n > 0) { + uint8_t buf[2]; + uint32_t w; + + inner_shake256_extract(sc, (void *)buf, sizeof buf); + w = ((unsigned)buf[0] << 8) | (unsigned)buf[1]; + if (w < 61445) { + while (w >= 12289) { + w -= 12289; + } + *x ++ = (uint16_t)w; + n --; + } + } +} + +/* see inner.h */ +void +PQCLEAN_FALCON512_CLEAN_hash_to_point_ct( + inner_shake256_context *sc, + uint16_t *x, unsigned logn, uint8_t *tmp) { + /* + * Each 16-bit sample is a value in 0..65535. The value is + * kept if it falls in 0..61444 (because 61445 = 5*12289) + * and rejected otherwise; thus, each sample has probability + * about 0.93758 of being selected. + * + * We want to oversample enough to be sure that we will + * have enough values with probability at least 1 - 2^(-256). + * Depending on degree N, this leads to the following + * required oversampling: + * + * logn n oversampling + * 1 2 65 + * 2 4 67 + * 3 8 71 + * 4 16 77 + * 5 32 86 + * 6 64 100 + * 7 128 122 + * 8 256 154 + * 9 512 205 + * 10 1024 287 + * + * If logn >= 7, then the provided temporary buffer is large + * enough. Otherwise, we use a stack buffer of 63 entries + * (i.e. 126 bytes) for the values that do not fit in tmp[]. + */ + + static const uint16_t overtab[] = { + 0, /* unused */ + 65, + 67, + 71, + 77, + 86, + 100, + 122, + 154, + 205, + 287 + }; + + unsigned n, n2, u, m, p, over; + uint16_t *tt1, tt2[63]; + + /* + * We first generate m 16-bit value. Values 0..n-1 go to x[]. + * Values n..2*n-1 go to tt1[]. Values 2*n and later go to tt2[]. + * We also reduce modulo q the values; rejected values are set + * to 0xFFFF. + */ + n = 1U << logn; + n2 = n << 1; + over = overtab[logn]; + m = n + over; + tt1 = (uint16_t *)tmp; + for (u = 0; u < m; u ++) { + uint8_t buf[2]; + uint32_t w, wr; + + inner_shake256_extract(sc, buf, sizeof buf); + w = ((uint32_t)buf[0] << 8) | (uint32_t)buf[1]; + wr = w - ((uint32_t)24578 & (((w - 24578) >> 31) - 1)); + wr = wr - ((uint32_t)24578 & (((wr - 24578) >> 31) - 1)); + wr = wr - ((uint32_t)12289 & (((wr - 12289) >> 31) - 1)); + wr |= ((w - 61445) >> 31) - 1; + if (u < n) { + x[u] = (uint16_t)wr; + } else if (u < n2) { + tt1[u - n] = (uint16_t)wr; + } else { + tt2[u - n2] = (uint16_t)wr; + } + } + + /* + * Now we must "squeeze out" the invalid values. We do this in + * a logarithmic sequence of passes; each pass computes where a + * value should go, and moves it down by 'p' slots if necessary, + * where 'p' uses an increasing powers-of-two scale. It can be + * shown that in all cases where the loop decides that a value + * has to be moved down by p slots, the destination slot is + * "free" (i.e. contains an invalid value). + */ + for (p = 1; p <= over; p <<= 1) { + unsigned v; + + /* + * In the loop below: + * + * - v contains the index of the final destination of + * the value; it is recomputed dynamically based on + * whether values are valid or not. + * + * - u is the index of the value we consider ("source"); + * its address is s. + * + * - The loop may swap the value with the one at index + * u-p. The address of the swap destination is d. + */ + v = 0; + for (u = 0; u < m; u ++) { + uint16_t *s, *d; + unsigned j, sv, dv, mk; + + if (u < n) { + s = &x[u]; + } else if (u < n2) { + s = &tt1[u - n]; + } else { + s = &tt2[u - n2]; + } + sv = *s; + + /* + * The value in sv should ultimately go to + * address v, i.e. jump back by u-v slots. + */ + j = u - v; + + /* + * We increment v for the next iteration, but + * only if the source value is valid. The mask + * 'mk' is -1 if the value is valid, 0 otherwise, + * so we _subtract_ mk. + */ + mk = (sv >> 15) - 1U; + v -= mk; + + /* + * In this loop we consider jumps by p slots; if + * u < p then there is nothing more to do. + */ + if (u < p) { + continue; + } + + /* + * Destination for the swap: value at address u-p. + */ + if ((u - p) < n) { + d = &x[u - p]; + } else if ((u - p) < n2) { + d = &tt1[(u - p) - n]; + } else { + d = &tt2[(u - p) - n2]; + } + dv = *d; + + /* + * The swap should be performed only if the source + * is valid AND the jump j has its 'p' bit set. + */ + mk &= -(((j & p) + 0x1FF) >> 9); + + *s = (uint16_t)(sv ^ (mk & (sv ^ dv))); + *d = (uint16_t)(dv ^ (mk & (sv ^ dv))); + } + } +} + +/* see inner.h */ +int +PQCLEAN_FALCON512_CLEAN_is_short( + const int16_t *s1, const int16_t *s2, unsigned logn) { + /* + * We use the l2-norm. Code below uses only 32-bit operations to + * compute the square of the norm with saturation to 2^32-1 if + * the value exceeds 2^31-1. + */ + size_t n, u; + uint32_t s, ng; + + n = (size_t)1 << logn; + s = 0; + ng = 0; + for (u = 0; u < n; u ++) { + int32_t z; + + z = s1[u]; + s += (uint32_t)(z * z); + ng |= s; + z = s2[u]; + s += (uint32_t)(z * z); + ng |= s; + } + s |= -(ng >> 31); + + /* + * Acceptance bound on the l2-norm is: + * 1.2*1.55*sqrt(q)*sqrt(2*N) + * Value 7085 is floor((1.2^2)*(1.55^2)*2*1024). + */ + return s < (((uint32_t)7085 * (uint32_t)12289) >> (10 - logn)); +} + +/* see inner.h */ +int +PQCLEAN_FALCON512_CLEAN_is_short_half( + uint32_t sqn, const int16_t *s2, unsigned logn) { + size_t n, u; + uint32_t ng; + + n = (size_t)1 << logn; + ng = -(sqn >> 31); + for (u = 0; u < n; u ++) { + int32_t z; + + z = s2[u]; + sqn += (uint32_t)(z * z); + ng |= sqn; + } + sqn |= -(ng >> 31); + + /* + * Acceptance bound on the l2-norm is: + * 1.2*1.55*sqrt(q)*sqrt(2*N) + * Value 7085 is floor((1.2^2)*(1.55^2)*2*1024). + */ + return sqn < (((uint32_t)7085 * (uint32_t)12289) >> (10 - logn)); +} diff --git a/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/config.mk b/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/config.mk new file mode 100644 index 000000000..b28c9ce64 --- /dev/null +++ b/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/config.mk @@ -0,0 +1,17 @@ +# DO NOT EDIT: generated from config.mk.subdirs.template +# +# This Source Code Form is subject to the terms of the Mozilla Public +# License, v. 2.0. If a copy of the MPL was not distributed with this +# file, You can obtain one at http://mozilla.org/MPL/2.0/. + +# add fixes for platform integration issues here. +# +# liboqs programs expect the public include files to be in oqs/xxxx, +# So we put liboqs in it's own module, oqs, and point to the dist files +INCLUDES += -I$(CORE_DEPTH)/lib/liboqs/src/common/pqclean_shims -I$(CORE_DEPTH)/lib/liboqs/src/common/sha3/xkcp_low/KeccakP-1600/plain-64bits +DEFINES += + +ifeq ($(OS_ARCH), Darwin) +DEFINES += -DOQS_HAVE_ALIGNED_ALLOC -DOQS_HAVE_MEMALIGN -DOQS_HAVE_POSIX_MEMALIGN +endif + diff --git a/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/fft.c b/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/fft.c new file mode 100644 index 000000000..a7d9bdad0 --- /dev/null +++ b/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/fft.c @@ -0,0 +1,700 @@ +#include "inner.h" + +/* + * FFT code. + * + * ==========================(LICENSE BEGIN)============================ + * + * Copyright (c) 2017-2019 Falcon Project + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the + * "Software"), to deal in the Software without restriction, including + * without limitation the rights to use, copy, modify, merge, publish, + * distribute, sublicense, and/or sell copies of the Software, and to + * permit persons to whom the Software is furnished to do so, subject to + * the following conditions: + * + * The above copyright notice and this permission notice shall be + * included in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, + * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF + * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. + * IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY + * CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, + * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE + * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. + * + * ===========================(LICENSE END)============================= + * + * @author Thomas Pornin <thomas.pornin@nccgroup.com> + */ + + +/* + * Rules for complex number macros: + * -------------------------------- + * + * Operand order is: destination, source1, source2... + * + * Each operand is a real and an imaginary part. + * + * All overlaps are allowed. + */ + +/* + * Addition of two complex numbers (d = a + b). + */ +#define FPC_ADD(d_re, d_im, a_re, a_im, b_re, b_im) do { \ + fpr fpct_re, fpct_im; \ + fpct_re = fpr_add(a_re, b_re); \ + fpct_im = fpr_add(a_im, b_im); \ + (d_re) = fpct_re; \ + (d_im) = fpct_im; \ + } while (0) + +/* + * Subtraction of two complex numbers (d = a - b). + */ +#define FPC_SUB(d_re, d_im, a_re, a_im, b_re, b_im) do { \ + fpr fpct_re, fpct_im; \ + fpct_re = fpr_sub(a_re, b_re); \ + fpct_im = fpr_sub(a_im, b_im); \ + (d_re) = fpct_re; \ + (d_im) = fpct_im; \ + } while (0) + +/* + * Multplication of two complex numbers (d = a * b). + */ +#define FPC_MUL(d_re, d_im, a_re, a_im, b_re, b_im) do { \ + fpr fpct_a_re, fpct_a_im; \ + fpr fpct_b_re, fpct_b_im; \ + fpr fpct_d_re, fpct_d_im; \ + fpct_a_re = (a_re); \ + fpct_a_im = (a_im); \ + fpct_b_re = (b_re); \ + fpct_b_im = (b_im); \ + fpct_d_re = fpr_sub( \ + fpr_mul(fpct_a_re, fpct_b_re), \ + fpr_mul(fpct_a_im, fpct_b_im)); \ + fpct_d_im = fpr_add( \ + fpr_mul(fpct_a_re, fpct_b_im), \ + fpr_mul(fpct_a_im, fpct_b_re)); \ + (d_re) = fpct_d_re; \ + (d_im) = fpct_d_im; \ + } while (0) + +/* + * Squaring of a complex number (d = a * a). + */ +#define FPC_SQR(d_re, d_im, a_re, a_im) do { \ + fpr fpct_a_re, fpct_a_im; \ + fpr fpct_d_re, fpct_d_im; \ + fpct_a_re = (a_re); \ + fpct_a_im = (a_im); \ + fpct_d_re = fpr_sub(fpr_sqr(fpct_a_re), fpr_sqr(fpct_a_im)); \ + fpct_d_im = fpr_double(fpr_mul(fpct_a_re, fpct_a_im)); \ + (d_re) = fpct_d_re; \ + (d_im) = fpct_d_im; \ + } while (0) + +/* + * Inversion of a complex number (d = 1 / a). + */ +#define FPC_INV(d_re, d_im, a_re, a_im) do { \ + fpr fpct_a_re, fpct_a_im; \ + fpr fpct_d_re, fpct_d_im; \ + fpr fpct_m; \ + fpct_a_re = (a_re); \ + fpct_a_im = (a_im); \ + fpct_m = fpr_add(fpr_sqr(fpct_a_re), fpr_sqr(fpct_a_im)); \ + fpct_m = fpr_inv(fpct_m); \ + fpct_d_re = fpr_mul(fpct_a_re, fpct_m); \ + fpct_d_im = fpr_mul(fpr_neg(fpct_a_im), fpct_m); \ + (d_re) = fpct_d_re; \ + (d_im) = fpct_d_im; \ + } while (0) + +/* + * Division of complex numbers (d = a / b). + */ +#define FPC_DIV(d_re, d_im, a_re, a_im, b_re, b_im) do { \ + fpr fpct_a_re, fpct_a_im; \ + fpr fpct_b_re, fpct_b_im; \ + fpr fpct_d_re, fpct_d_im; \ + fpr fpct_m; \ + fpct_a_re = (a_re); \ + fpct_a_im = (a_im); \ + fpct_b_re = (b_re); \ + fpct_b_im = (b_im); \ + fpct_m = fpr_add(fpr_sqr(fpct_b_re), fpr_sqr(fpct_b_im)); \ + fpct_m = fpr_inv(fpct_m); \ + fpct_b_re = fpr_mul(fpct_b_re, fpct_m); \ + fpct_b_im = fpr_mul(fpr_neg(fpct_b_im), fpct_m); \ + fpct_d_re = fpr_sub( \ + fpr_mul(fpct_a_re, fpct_b_re), \ + fpr_mul(fpct_a_im, fpct_b_im)); \ + fpct_d_im = fpr_add( \ + fpr_mul(fpct_a_re, fpct_b_im), \ + fpr_mul(fpct_a_im, fpct_b_re)); \ + (d_re) = fpct_d_re; \ + (d_im) = fpct_d_im; \ + } while (0) + +/* + * Let w = exp(i*pi/N); w is a primitive 2N-th root of 1. We define the + * values w_j = w^(2j+1) for all j from 0 to N-1: these are the roots + * of X^N+1 in the field of complex numbers. A crucial property is that + * w_{N-1-j} = conj(w_j) = 1/w_j for all j. + * + * FFT representation of a polynomial f (taken modulo X^N+1) is the + * set of values f(w_j). Since f is real, conj(f(w_j)) = f(conj(w_j)), + * thus f(w_{N-1-j}) = conj(f(w_j)). We thus store only half the values, + * for j = 0 to N/2-1; the other half can be recomputed easily when (if) + * needed. A consequence is that FFT representation has the same size + * as normal representation: N/2 complex numbers use N real numbers (each + * complex number is the combination of a real and an imaginary part). + * + * We use a specific ordering which makes computations easier. Let rev() + * be the bit-reversal function over log(N) bits. For j in 0..N/2-1, we + * store the real and imaginary parts of f(w_j) in slots: + * + * Re(f(w_j)) -> slot rev(j)/2 + * Im(f(w_j)) -> slot rev(j)/2+N/2 + * + * (Note that rev(j) is even for j < N/2.) + */ + +/* see inner.h */ +void +PQCLEAN_FALCON512_CLEAN_FFT(fpr *f, unsigned logn) { + /* + * FFT algorithm in bit-reversal order uses the following + * iterative algorithm: + * + * t = N + * for m = 1; m < N; m *= 2: + * ht = t/2 + * for i1 = 0; i1 < m; i1 ++: + * j1 = i1 * t + * s = GM[m + i1] + * for j = j1; j < (j1 + ht); j ++: + * x = f[j] + * y = s * f[j + ht] + * f[j] = x + y + * f[j + ht] = x - y + * t = ht + * + * GM[k] contains w^rev(k) for primitive root w = exp(i*pi/N). + * + * In the description above, f[] is supposed to contain complex + * numbers. In our in-memory representation, the real and + * imaginary parts of f[k] are in array slots k and k+N/2. + * + * We only keep the first half of the complex numbers. We can + * see that after the first iteration, the first and second halves + * of the array of complex numbers have separate lives, so we + * simply ignore the second part. + */ + + unsigned u; + size_t t, n, hn, m; + + /* + * First iteration: compute f[j] + i * f[j+N/2] for all j < N/2 + * (because GM[1] = w^rev(1) = w^(N/2) = i). + * In our chosen representation, this is a no-op: everything is + * already where it should be. + */ + + /* + * Subsequent iterations are truncated to use only the first + * half of values. + */ + n = (size_t)1 << logn; + hn = n >> 1; + t = hn; + for (u = 1, m = 2; u < logn; u ++, m <<= 1) { + size_t ht, hm, i1, j1; + + ht = t >> 1; + hm = m >> 1; + for (i1 = 0, j1 = 0; i1 < hm; i1 ++, j1 += t) { + size_t j, j2; + + j2 = j1 + ht; + fpr s_re, s_im; + + s_re = fpr_gm_tab[((m + i1) << 1) + 0]; + s_im = fpr_gm_tab[((m + i1) << 1) + 1]; + for (j = j1; j < j2; j ++) { + fpr x_re, x_im, y_re, y_im; + + x_re = f[j]; + x_im = f[j + hn]; + y_re = f[j + ht]; + y_im = f[j + ht + hn]; + FPC_MUL(y_re, y_im, y_re, y_im, s_re, s_im); + FPC_ADD(f[j], f[j + hn], + x_re, x_im, y_re, y_im); + FPC_SUB(f[j + ht], f[j + ht + hn], + x_re, x_im, y_re, y_im); + } + } + t = ht; + } +} + +/* see inner.h */ +void +PQCLEAN_FALCON512_CLEAN_iFFT(fpr *f, unsigned logn) { + /* + * Inverse FFT algorithm in bit-reversal order uses the following + * iterative algorithm: + * + * t = 1 + * for m = N; m > 1; m /= 2: + * hm = m/2 + * dt = t*2 + * for i1 = 0; i1 < hm; i1 ++: + * j1 = i1 * dt + * s = iGM[hm + i1] + * for j = j1; j < (j1 + t); j ++: + * x = f[j] + * y = f[j + t] + * f[j] = x + y + * f[j + t] = s * (x - y) + * t = dt + * for i1 = 0; i1 < N; i1 ++: + * f[i1] = f[i1] / N + * + * iGM[k] contains (1/w)^rev(k) for primitive root w = exp(i*pi/N) + * (actually, iGM[k] = 1/GM[k] = conj(GM[k])). + * + * In the main loop (not counting the final division loop), in + * all iterations except the last, the first and second half of f[] + * (as an array of complex numbers) are separate. In our chosen + * representation, we do not keep the second half. + * + * The last iteration recombines the recomputed half with the + * implicit half, and should yield only real numbers since the + * target polynomial is real; moreover, s = i at that step. + * Thus, when considering x and y: + * y = conj(x) since the final f[j] must be real + * Therefore, f[j] is filled with 2*Re(x), and f[j + t] is + * filled with 2*Im(x). + * But we already have Re(x) and Im(x) in array slots j and j+t + * in our chosen representation. That last iteration is thus a + * simple doubling of the values in all the array. + * + * We make the last iteration a no-op by tweaking the final + * division into a division by N/2, not N. + */ + size_t u, n, hn, t, m; + + n = (size_t)1 << logn; + t = 1; + m = n; + hn = n >> 1; + for (u = logn; u > 1; u --) { + size_t hm, dt, i1, j1; + + hm = m >> 1; + dt = t << 1; + for (i1 = 0, j1 = 0; j1 < hn; i1 ++, j1 += dt) { + size_t j, j2; + + j2 = j1 + t; + fpr s_re, s_im; + + s_re = fpr_gm_tab[((hm + i1) << 1) + 0]; + s_im = fpr_neg(fpr_gm_tab[((hm + i1) << 1) + 1]); + for (j = j1; j < j2; j ++) { + fpr x_re, x_im, y_re, y_im; + + x_re = f[j]; + x_im = f[j + hn]; + y_re = f[j + t]; + y_im = f[j + t + hn]; + FPC_ADD(f[j], f[j + hn], + x_re, x_im, y_re, y_im); + FPC_SUB(x_re, x_im, x_re, x_im, y_re, y_im); + FPC_MUL(f[j + t], f[j + t + hn], + x_re, x_im, s_re, s_im); + } + } + t = dt; + m = hm; + } + + /* + * Last iteration is a no-op, provided that we divide by N/2 + * instead of N. We need to make a special case for logn = 0. + */ + if (logn > 0) { + fpr ni; + + ni = fpr_p2_tab[logn]; + for (u = 0; u < n; u ++) { + f[u] = fpr_mul(f[u], ni); + } + } +} + +/* see inner.h */ +void +PQCLEAN_FALCON512_CLEAN_poly_add( + fpr *a, const fpr *b, unsigned logn) { + size_t n, u; + + n = (size_t)1 << logn; + for (u = 0; u < n; u ++) { + a[u] = fpr_add(a[u], b[u]); + } +} + +/* see inner.h */ +void +PQCLEAN_FALCON512_CLEAN_poly_sub( + fpr *a, const fpr *b, unsigned logn) { + size_t n, u; + + n = (size_t)1 << logn; + for (u = 0; u < n; u ++) { + a[u] = fpr_sub(a[u], b[u]); + } +} + +/* see inner.h */ +void +PQCLEAN_FALCON512_CLEAN_poly_neg(fpr *a, unsigned logn) { + size_t n, u; + + n = (size_t)1 << logn; + for (u = 0; u < n; u ++) { + a[u] = fpr_neg(a[u]); + } +} + +/* see inner.h */ +void +PQCLEAN_FALCON512_CLEAN_poly_adj_fft(fpr *a, unsigned logn) { + size_t n, u; + + n = (size_t)1 << logn; + for (u = (n >> 1); u < n; u ++) { + a[u] = fpr_neg(a[u]); + } +} + +/* see inner.h */ +void +PQCLEAN_FALCON512_CLEAN_poly_mul_fft( + fpr *a, const fpr *b, unsigned logn) { + size_t n, hn, u; + + n = (size_t)1 << logn; + hn = n >> 1; + for (u = 0; u < hn; u ++) { + fpr a_re, a_im, b_re, b_im; + + a_re = a[u]; + a_im = a[u + hn]; + b_re = b[u]; + b_im = b[u + hn]; + FPC_MUL(a[u], a[u + hn], a_re, a_im, b_re, b_im); + } +} + +/* see inner.h */ +void +PQCLEAN_FALCON512_CLEAN_poly_muladj_fft( + fpr *a, const fpr *b, unsigned logn) { + size_t n, hn, u; + + n = (size_t)1 << logn; + hn = n >> 1; + for (u = 0; u < hn; u ++) { + fpr a_re, a_im, b_re, b_im; + + a_re = a[u]; + a_im = a[u + hn]; + b_re = b[u]; + b_im = fpr_neg(b[u + hn]); + FPC_MUL(a[u], a[u + hn], a_re, a_im, b_re, b_im); + } +} + +/* see inner.h */ +void +PQCLEAN_FALCON512_CLEAN_poly_mulselfadj_fft(fpr *a, unsigned logn) { + /* + * Since each coefficient is multiplied with its own conjugate, + * the result contains only real values. + */ + size_t n, hn, u; + + n = (size_t)1 << logn; + hn = n >> 1; + for (u = 0; u < hn; u ++) { + fpr a_re, a_im; + + a_re = a[u]; + a_im = a[u + hn]; + a[u] = fpr_add(fpr_sqr(a_re), fpr_sqr(a_im)); + a[u + hn] = fpr_zero; + } +} + +/* see inner.h */ +void +PQCLEAN_FALCON512_CLEAN_poly_mulconst(fpr *a, fpr x, unsigned logn) { + size_t n, u; + + n = (size_t)1 << logn; + for (u = 0; u < n; u ++) { + a[u] = fpr_mul(a[u], x); + } +} + +/* see inner.h */ +void +PQCLEAN_FALCON512_CLEAN_poly_div_fft( + fpr *a, const fpr *b, unsigned logn) { + size_t n, hn, u; + + n = (size_t)1 << logn; + hn = n >> 1; + for (u = 0; u < hn; u ++) { + fpr a_re, a_im, b_re, b_im; + + a_re = a[u]; + a_im = a[u + hn]; + b_re = b[u]; + b_im = b[u + hn]; + FPC_DIV(a[u], a[u + hn], a_re, a_im, b_re, b_im); + } +} + +/* see inner.h */ +void +PQCLEAN_FALCON512_CLEAN_poly_invnorm2_fft(fpr *d, + const fpr *a, const fpr *b, unsigned logn) { + size_t n, hn, u; + + n = (size_t)1 << logn; + hn = n >> 1; + for (u = 0; u < hn; u ++) { + fpr a_re, a_im; + fpr b_re, b_im; + + a_re = a[u]; + a_im = a[u + hn]; + b_re = b[u]; + b_im = b[u + hn]; + d[u] = fpr_inv(fpr_add( + fpr_add(fpr_sqr(a_re), fpr_sqr(a_im)), + fpr_add(fpr_sqr(b_re), fpr_sqr(b_im)))); + } +} + +/* see inner.h */ +void +PQCLEAN_FALCON512_CLEAN_poly_add_muladj_fft(fpr *d, + const fpr *F, const fpr *G, + const fpr *f, const fpr *g, unsigned logn) { + size_t n, hn, u; + + n = (size_t)1 << logn; + hn = n >> 1; + for (u = 0; u < hn; u ++) { + fpr F_re, F_im, G_re, G_im; + fpr f_re, f_im, g_re, g_im; + fpr a_re, a_im, b_re, b_im; + + F_re = F[u]; + F_im = F[u + hn]; + G_re = G[u]; + G_im = G[u + hn]; + f_re = f[u]; + f_im = f[u + hn]; + g_re = g[u]; + g_im = g[u + hn]; + + FPC_MUL(a_re, a_im, F_re, F_im, f_re, fpr_neg(f_im)); + FPC_MUL(b_re, b_im, G_re, G_im, g_re, fpr_neg(g_im)); + d[u] = fpr_add(a_re, b_re); + d[u + hn] = fpr_add(a_im, b_im); + } +} + +/* see inner.h */ +void +PQCLEAN_FALCON512_CLEAN_poly_mul_autoadj_fft( + fpr *a, const fpr *b, unsigned logn) { + size_t n, hn, u; + + n = (size_t)1 << logn; + hn = n >> 1; + for (u = 0; u < hn; u ++) { + a[u] = fpr_mul(a[u], b[u]); + a[u + hn] = fpr_mul(a[u + hn], b[u]); + } +} + +/* see inner.h */ +void +PQCLEAN_FALCON512_CLEAN_poly_div_autoadj_fft( + fpr *a, const fpr *b, unsigned logn) { + size_t n, hn, u; + + n = (size_t)1 << logn; + hn = n >> 1; + for (u = 0; u < hn; u ++) { + fpr ib; + + ib = fpr_inv(b[u]); + a[u] = fpr_mul(a[u], ib); + a[u + hn] = fpr_mul(a[u + hn], ib); + } +} + +/* see inner.h */ +void +PQCLEAN_FALCON512_CLEAN_poly_LDL_fft( + const fpr *g00, + fpr *g01, fpr *g11, unsigned logn) { + size_t n, hn, u; + + n = (size_t)1 << logn; + hn = n >> 1; + for (u = 0; u < hn; u ++) { + fpr g00_re, g00_im, g01_re, g01_im, g11_re, g11_im; + fpr mu_re, mu_im; + + g00_re = g00[u]; + g00_im = g00[u + hn]; + g01_re = g01[u]; + g01_im = g01[u + hn]; + g11_re = g11[u]; + g11_im = g11[u + hn]; + FPC_DIV(mu_re, mu_im, g01_re, g01_im, g00_re, g00_im); + FPC_MUL(g01_re, g01_im, mu_re, mu_im, g01_re, fpr_neg(g01_im)); + FPC_SUB(g11[u], g11[u + hn], g11_re, g11_im, g01_re, g01_im); + g01[u] = mu_re; + g01[u + hn] = fpr_neg(mu_im); + } +} + +/* see inner.h */ +void +PQCLEAN_FALCON512_CLEAN_poly_LDLmv_fft( + fpr *d11, fpr *l10, + const fpr *g00, const fpr *g01, + const fpr *g11, unsigned logn) { + size_t n, hn, u; + + n = (size_t)1 << logn; + hn = n >> 1; + for (u = 0; u < hn; u ++) { + fpr g00_re, g00_im, g01_re, g01_im, g11_re, g11_im; + fpr mu_re, mu_im; + + g00_re = g00[u]; + g00_im = g00[u + hn]; + g01_re = g01[u]; + g01_im = g01[u + hn]; + g11_re = g11[u]; + g11_im = g11[u + hn]; + FPC_DIV(mu_re, mu_im, g01_re, g01_im, g00_re, g00_im); + FPC_MUL(g01_re, g01_im, mu_re, mu_im, g01_re, fpr_neg(g01_im)); + FPC_SUB(d11[u], d11[u + hn], g11_re, g11_im, g01_re, g01_im); + l10[u] = mu_re; + l10[u + hn] = fpr_neg(mu_im); + } +} + +/* see inner.h */ +void +PQCLEAN_FALCON512_CLEAN_poly_split_fft( + fpr *f0, fpr *f1, + const fpr *f, unsigned logn) { + /* + * The FFT representation we use is in bit-reversed order + * (element i contains f(w^(rev(i))), where rev() is the + * bit-reversal function over the ring degree. This changes + * indexes with regards to the Falcon specification. + */ + size_t n, hn, qn, u; + + n = (size_t)1 << logn; + hn = n >> 1; + qn = hn >> 1; + + /* + * We process complex values by pairs. For logn = 1, there is only + * one complex value (the other one is the implicit conjugate), + * so we add the two lines below because the loop will be + * skipped. + */ + f0[0] = f[0]; + f1[0] = f[hn]; + + for (u = 0; u < qn; u ++) { + fpr a_re, a_im, b_re, b_im; + fpr t_re, t_im; + + a_re = f[(u << 1) + 0]; + a_im = f[(u << 1) + 0 + hn]; + b_re = f[(u << 1) + 1]; + b_im = f[(u << 1) + 1 + hn]; + + FPC_ADD(t_re, t_im, a_re, a_im, b_re, b_im); + f0[u] = fpr_half(t_re); + f0[u + qn] = fpr_half(t_im); + + FPC_SUB(t_re, t_im, a_re, a_im, b_re, b_im); + FPC_MUL(t_re, t_im, t_re, t_im, + fpr_gm_tab[((u + hn) << 1) + 0], + fpr_neg(fpr_gm_tab[((u + hn) << 1) + 1])); + f1[u] = fpr_half(t_re); + f1[u + qn] = fpr_half(t_im); + } +} + +/* see inner.h */ +void +PQCLEAN_FALCON512_CLEAN_poly_merge_fft( + fpr *f, + const fpr *f0, const fpr *f1, unsigned logn) { + size_t n, hn, qn, u; + + n = (size_t)1 << logn; + hn = n >> 1; + qn = hn >> 1; + + /* + * An extra copy to handle the special case logn = 1. + */ + f[0] = f0[0]; + f[hn] = f1[0]; + + for (u = 0; u < qn; u ++) { + fpr a_re, a_im, b_re, b_im; + fpr t_re, t_im; + + a_re = f0[u]; + a_im = f0[u + qn]; + FPC_MUL(b_re, b_im, f1[u], f1[u + qn], + fpr_gm_tab[((u + hn) << 1) + 0], + fpr_gm_tab[((u + hn) << 1) + 1]); + FPC_ADD(t_re, t_im, a_re, a_im, b_re, b_im); + f[(u << 1) + 0] = t_re; + f[(u << 1) + 0 + hn] = t_im; + FPC_SUB(t_re, t_im, a_re, a_im, b_re, b_im); + f[(u << 1) + 1] = t_re; + f[(u << 1) + 1 + hn] = t_im; + } +} diff --git a/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/fpr.c b/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/fpr.c new file mode 100644 index 000000000..669c825ee --- /dev/null +++ b/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/fpr.c @@ -0,0 +1,1890 @@ +#include "inner.h" + +/* + * Floating-point operations. + * + * This file implements the non-inline functions declared in + * fpr.h, as well as the constants for FFT / iFFT. + * + * ==========================(LICENSE BEGIN)============================ + * + * Copyright (c) 2017-2019 Falcon Project + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the + * "Software"), to deal in the Software without restriction, including + * without limitation the rights to use, copy, modify, merge, publish, + * distribute, sublicense, and/or sell copies of the Software, and to + * permit persons to whom the Software is furnished to do so, subject to + * the following conditions: + * + * The above copyright notice and this permission notice shall be + * included in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, + * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF + * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. + * IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY + * CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, + * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE + * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. + * + * ===========================(LICENSE END)============================= + * + * @author Thomas Pornin <thomas.pornin@nccgroup.com> + */ + + + +/* + * Normalize a provided unsigned integer to the 2^63..2^64-1 range by + * left-shifting it if necessary. The exponent e is adjusted accordingly + * (i.e. if the value was left-shifted by n bits, then n is subtracted + * from e). If source m is 0, then it remains 0, but e is altered. + * Both m and e must be simple variables (no expressions allowed). + */ +#define FPR_NORM64(m, e) do { \ + uint32_t nt; \ + \ + (e) -= 63; \ + \ + nt = (uint32_t)((m) >> 32); \ + nt = (nt | -nt) >> 31; \ + (m) ^= ((m) ^ ((m) << 32)) & ((uint64_t)nt - 1); \ + (e) += (int)(nt << 5); \ + \ + nt = (uint32_t)((m) >> 48); \ + nt = (nt | -nt) >> 31; \ + (m) ^= ((m) ^ ((m) << 16)) & ((uint64_t)nt - 1); \ + (e) += (int)(nt << 4); \ + \ + nt = (uint32_t)((m) >> 56); \ + nt = (nt | -nt) >> 31; \ + (m) ^= ((m) ^ ((m) << 8)) & ((uint64_t)nt - 1); \ + (e) += (int)(nt << 3); \ + \ + nt = (uint32_t)((m) >> 60); \ + nt = (nt | -nt) >> 31; \ + (m) ^= ((m) ^ ((m) << 4)) & ((uint64_t)nt - 1); \ + (e) += (int)(nt << 2); \ + \ + nt = (uint32_t)((m) >> 62); \ + nt = (nt | -nt) >> 31; \ + (m) ^= ((m) ^ ((m) << 2)) & ((uint64_t)nt - 1); \ + (e) += (int)(nt << 1); \ + \ + nt = (uint32_t)((m) >> 63); \ + (m) ^= ((m) ^ ((m) << 1)) & ((uint64_t)nt - 1); \ + (e) += (int)(nt); \ + } while (0) + +uint64_t +fpr_ursh(uint64_t x, int n) { + x ^= (x ^ (x >> 32)) & -(uint64_t)(n >> 5); + return x >> (n & 31); +} + +int64_t +fpr_irsh(int64_t x, int n) { + x ^= (x ^ (x >> 32)) & -(int64_t)(n >> 5); + return x >> (n & 31); +} + +uint64_t +fpr_ulsh(uint64_t x, int n) { + x ^= (x ^ (x << 32)) & -(uint64_t)(n >> 5); + return x << (n & 31); +} + +fpr +FPR(int s, int e, uint64_t m) { + fpr x; + uint32_t t; + unsigned f; + + /* + * If e >= -1076, then the value is "normal"; otherwise, it + * should be a subnormal, which we clamp down to zero. + */ + e += 1076; + t = (uint32_t)e >> 31; + m &= (uint64_t)t - 1; + + /* + * If m = 0 then we want a zero; make e = 0 too, but conserve + * the sign. + */ + t = (uint32_t)(m >> 54); + e &= -(int)t; + + /* + * The 52 mantissa bits come from m. Value m has its top bit set + * (unless it is a zero); we leave it "as is": the top bit will + * increment the exponent by 1, except when m = 0, which is + * exactly what we want. + */ + x = (((uint64_t)s << 63) | (m >> 2)) + ((uint64_t)(uint32_t)e << 52); + + /* + * Rounding: if the low three bits of m are 011, 110 or 111, + * then the value should be incremented to get the next + * representable value. This implements the usual + * round-to-nearest rule (with preference to even values in case + * of a tie). Note that the increment may make a carry spill + * into the exponent field, which is again exactly what we want + * in that case. + */ + f = (unsigned)m & 7U; + x += (0xC8U >> f) & 1; + return x; +} + +fpr +fpr_scaled(int64_t i, int sc) { + /* + * To convert from int to float, we have to do the following: + * 1. Get the absolute value of the input, and its sign + * 2. Shift right or left the value as appropriate + * 3. Pack the result + * + * We can assume that the source integer is not -2^63. + */ + int s, e; + uint32_t t; + uint64_t m; + + /* + * Extract sign bit. + * We have: -i = 1 + ~i + */ + s = (int)((uint64_t)i >> 63); + i ^= -(int64_t)s; + i += s; + + /* + * For now we suppose that i != 0. + * Otherwise, we set m to i and left-shift it as much as needed + * to get a 1 in the top bit. We can do that in a logarithmic + * number of conditional shifts. + */ + m = (uint64_t)i; + e = 9 + sc; + FPR_NORM64(m, e); + + /* + * Now m is in the 2^63..2^64-1 range. We must divide it by 512; + * if one of the dropped bits is a 1, this should go into the + * "sticky bit". + */ + m |= ((uint32_t)m & 0x1FF) + 0x1FF; + m >>= 9; + + /* + * Corrective action: if i = 0 then all of the above was + * incorrect, and we clamp e and m down to zero. + */ + t = (uint32_t)((uint64_t)(i | -i) >> 63); + m &= -(uint64_t)t; + e &= -(int)t; + + /* + * Assemble back everything. The FPR() function will handle cases + * where e is too low. + */ + return FPR(s, e, m); +} + +fpr +fpr_of(int64_t i) { + return fpr_scaled(i, 0); +} + +int64_t +fpr_rint(fpr x) { + uint64_t m, d; + int e; + uint32_t s, dd, f; + + /* + * We assume that the value fits in -(2^63-1)..+(2^63-1). We can + * thus extract the mantissa as a 63-bit integer, then right-shift + * it as needed. + */ + m = ((x << 10) | ((uint64_t)1 << 62)) & (((uint64_t)1 << 63) - 1); + e = 1085 - ((int)(x >> 52) & 0x7FF); + + /* + * If a shift of more than 63 bits is needed, then simply set m + * to zero. This also covers the case of an input operand equal + * to zero. + */ + m &= -(uint64_t)((uint32_t)(e - 64) >> 31); + e &= 63; + + /* + * Right-shift m as needed. Shift count is e. Proper rounding + * mandates that: + * - If the highest dropped bit is zero, then round low. + * - If the highest dropped bit is one, and at least one of the + * other dropped bits is one, then round up. + * - If the highest dropped bit is one, and all other dropped + * bits are zero, then round up if the lowest kept bit is 1, + * or low otherwise (i.e. ties are broken by "rounding to even"). + * + * We thus first extract a word consisting of all the dropped bit + * AND the lowest kept bit; then we shrink it down to three bits, + * the lowest being "sticky". + */ + d = fpr_ulsh(m, 63 - e); + dd = (uint32_t)d | ((uint32_t)(d >> 32) & 0x1FFFFFFF); + f = (uint32_t)(d >> 61) | ((dd | -dd) >> 31); + m = fpr_ursh(m, e) + (uint64_t)((0xC8U >> f) & 1U); + + /* + * Apply the sign bit. + */ + s = (uint32_t)(x >> 63); + return ((int64_t)m ^ -(int64_t)s) + (int64_t)s; +} + +int64_t +fpr_floor(fpr x) { + uint64_t t; + int64_t xi; + int e, cc; + + /* + * We extract the integer as a _signed_ 64-bit integer with + * a scaling factor. Since we assume that the value fits + * in the -(2^63-1)..+(2^63-1) range, we can left-shift the + * absolute value to make it in the 2^62..2^63-1 range: we + * will only need a right-shift afterwards. + */ + e = (int)(x >> 52) & 0x7FF; + t = x >> 63; + xi = (int64_t)(((x << 10) | ((uint64_t)1 << 62)) + & (((uint64_t)1 << 63) - 1)); + xi = (xi ^ -(int64_t)t) + (int64_t)t; + cc = 1085 - e; + + /* + * We perform an arithmetic right-shift on the value. This + * applies floor() semantics on both positive and negative values + * (rounding toward minus infinity). + */ + xi = fpr_irsh(xi, cc & 63); + + /* + * If the true shift count was 64 or more, then we should instead + * replace xi with 0 (if nonnegative) or -1 (if negative). Edge + * case: -0 will be floored to -1, not 0 (whether this is correct + * is debatable; in any case, the other functions normalize zero + * to +0). + * + * For an input of zero, the non-shifted xi was incorrect (we used + * a top implicit bit of value 1, not 0), but this does not matter + * since this operation will clamp it down. + */ + xi ^= (xi ^ -(int64_t)t) & -(int64_t)((uint32_t)(63 - cc) >> 31); + return xi; +} + +int64_t +fpr_trunc(fpr x) { + uint64_t t, xu; + int e, cc; + + /* + * Extract the absolute value. Since we assume that the value + * fits in the -(2^63-1)..+(2^63-1) range, we can left-shift + * the absolute value into the 2^62..2^63-1 range, and then + * do a right shift afterwards. + */ + e = (int)(x >> 52) & 0x7FF; + xu = ((x << 10) | ((uint64_t)1 << 62)) & (((uint64_t)1 << 63) - 1); + cc = 1085 - e; + xu = fpr_ursh(xu, cc & 63); + + /* + * If the exponent is too low (cc > 63), then the shift was wrong + * and we must clamp the value to 0. This also covers the case + * of an input equal to zero. + */ + xu &= -(uint64_t)((uint32_t)(cc - 64) >> 31); + + /* + * Apply back the sign, if the source value is negative. + */ + t = x >> 63; + xu = (xu ^ -t) + t; + return *(int64_t *)&xu; +} + +fpr +fpr_add(fpr x, fpr y) { + uint64_t m, xu, yu, za; + uint32_t cs; + int ex, ey, sx, sy, cc; + + /* + * Make sure that the first operand (x) has the larger absolute + * value. This guarantees that the exponent of y is less than + * or equal to the exponent of x, and, if they are equal, then + * the mantissa of y will not be greater than the mantissa of x. + * + * After this swap, the result will have the sign x, except in + * the following edge case: abs(x) = abs(y), and x and y have + * opposite sign bits; in that case, the result shall be +0 + * even if the sign bit of x is 1. To handle this case properly, + * we do the swap is abs(x) = abs(y) AND the sign of x is 1. + */ + m = ((uint64_t)1 << 63) - 1; + za = (x & m) - (y & m); + cs = (uint32_t)(za >> 63) + | ((1U - (uint32_t)(-za >> 63)) & (uint32_t)(x >> 63)); + m = (x ^ y) & -(uint64_t)cs; + x ^= m; + y ^= m; + + /* + * Extract sign bits, exponents and mantissas. The mantissas are + * scaled up to 2^55..2^56-1, and the exponent is unbiased. If + * an operand is zero, its mantissa is set to 0 at this step, and + * its exponent will be -1078. + */ + ex = (int)(x >> 52); + sx = ex >> 11; + ex &= 0x7FF; + m = (uint64_t)(uint32_t)((ex + 0x7FF) >> 11) << 52; + xu = ((x & (((uint64_t)1 << 52) - 1)) | m) << 3; + ex -= 1078; + ey = (int)(y >> 52); + sy = ey >> 11; + ey &= 0x7FF; + m = (uint64_t)(uint32_t)((ey + 0x7FF) >> 11) << 52; + yu = ((y & (((uint64_t)1 << 52) - 1)) | m) << 3; + ey -= 1078; + + /* + * x has the larger exponent; hence, we only need to right-shift y. + * If the shift count is larger than 59 bits then we clamp the + * value to zero. + */ + cc = ex - ey; + yu &= -(uint64_t)((uint32_t)(cc - 60) >> 31); + cc &= 63; + + /* + * The lowest bit of yu is "sticky". + */ + m = fpr_ulsh(1, cc) - 1; + yu |= (yu & m) + m; + yu = fpr_ursh(yu, cc); + + /* + * If the operands have the same sign, then we add the mantissas; + * otherwise, we subtract the mantissas. + */ + xu += yu - ((yu << 1) & -(uint64_t)(sx ^ sy)); + + /* + * The result may be smaller, or slightly larger. We normalize + * it to the 2^63..2^64-1 range (if xu is zero, then it stays + * at zero). + */ + FPR_NORM64(xu, ex); + + /* + * Scale down the value to 2^54..s^55-1, handling the last bit + * as sticky. + */ + xu |= ((uint32_t)xu & 0x1FF) + 0x1FF; + xu >>= 9; + ex += 9; + + /* + * In general, the result has the sign of x. However, if the + * result is exactly zero, then the following situations may + * be encountered: + * x > 0, y = -x -> result should be +0 + * x < 0, y = -x -> result should be +0 + * x = +0, y = +0 -> result should be +0 + * x = -0, y = +0 -> result should be +0 + * x = +0, y = -0 -> result should be +0 + * x = -0, y = -0 -> result should be -0 + * + * But at the conditional swap step at the start of the + * function, we ensured that if abs(x) = abs(y) and the + * sign of x was 1, then x and y were swapped. Thus, the + * two following cases cannot actually happen: + * x < 0, y = -x + * x = -0, y = +0 + * In all other cases, the sign bit of x is conserved, which + * is what the FPR() function does. The FPR() function also + * properly clamps values to zero when the exponent is too + * low, but does not alter the sign in that case. + */ + return FPR(sx, ex, xu); +} + +fpr +fpr_sub(fpr x, fpr y) { + y ^= (uint64_t)1 << 63; + return fpr_add(x, y); +} + +fpr +fpr_neg(fpr x) { + x ^= (uint64_t)1 << 63; + return x; +} + +fpr +fpr_half(fpr x) { + /* + * To divide a value by 2, we just have to subtract 1 from its + * exponent, but we have to take care of zero. + */ + uint32_t t; + + x -= (uint64_t)1 << 52; + t = (((uint32_t)(x >> 52) & 0x7FF) + 1) >> 11; + x &= (uint64_t)t - 1; + return x; +} + +fpr +fpr_double(fpr x) { + /* + * To double a value, we just increment by one the exponent. We + * don't care about infinites or NaNs; however, 0 is a + * special case. + */ + x += (uint64_t)((((unsigned)(x >> 52) & 0x7FFU) + 0x7FFU) >> 11) << 52; + return x; +} + +fpr +fpr_mul(fpr x, fpr y) { + uint64_t xu, yu, w, zu, zv; + uint32_t x0, x1, y0, y1, z0, z1, z2; + int ex, ey, d, e, s; + + /* + * Extract absolute values as scaled unsigned integers. We + * don't extract exponents yet. + */ + xu = (x & (((uint64_t)1 << 52) - 1)) | ((uint64_t)1 << 52); + yu = (y & (((uint64_t)1 << 52) - 1)) | ((uint64_t)1 << 52); + + /* + * We have two 53-bit integers to multiply; we need to split + * each into a lower half and a upper half. Moreover, we + * prefer to have lower halves to be of 25 bits each, for + * reasons explained later on. + */ + x0 = (uint32_t)xu & 0x01FFFFFF; + x1 = (uint32_t)(xu >> 25); + y0 = (uint32_t)yu & 0x01FFFFFF; + y1 = (uint32_t)(yu >> 25); + w = (uint64_t)x0 * (uint64_t)y0; + z0 = (uint32_t)w & 0x01FFFFFF; + z1 = (uint32_t)(w >> 25); + w = (uint64_t)x0 * (uint64_t)y1; + z1 += (uint32_t)w & 0x01FFFFFF; + z2 = (uint32_t)(w >> 25); + w = (uint64_t)x1 * (uint64_t)y0; + z1 += (uint32_t)w & 0x01FFFFFF; + z2 += (uint32_t)(w >> 25); + zu = (uint64_t)x1 * (uint64_t)y1; + z2 += (z1 >> 25); + z1 &= 0x01FFFFFF; + zu += z2; + + /* + * Since xu and yu are both in the 2^52..2^53-1 range, the + * product is in the 2^104..2^106-1 range. We first reassemble + * it and round it into the 2^54..2^56-1 range; the bottom bit + * is made "sticky". Since the low limbs z0 and z1 are 25 bits + * each, we just take the upper part (zu), and consider z0 and + * z1 only for purposes of stickiness. + * (This is the reason why we chose 25-bit limbs above.) + */ + zu |= ((z0 | z1) + 0x01FFFFFF) >> 25; + + /* + * We normalize zu to the 2^54..s^55-1 range: it could be one + * bit too large at this point. This is done with a conditional + * right-shift that takes into account the sticky bit. + */ + zv = (zu >> 1) | (zu & 1); + w = zu >> 55; + zu ^= (zu ^ zv) & -w; + + /* + * Get the aggregate scaling factor: + * + * - Each exponent is biased by 1023. + * + * - Integral mantissas are scaled by 2^52, hence an + * extra 52 bias for each exponent. + * + * - However, we right-shifted z by 50 bits, and then + * by 0 or 1 extra bit (depending on the value of w). + * + * In total, we must add the exponents, then subtract + * 2 * (1023 + 52), then add 50 + w. + */ + ex = (int)((x >> 52) & 0x7FF); + ey = (int)((y >> 52) & 0x7FF); + e = ex + ey - 2100 + (int)w; + + /* + * Sign bit is the XOR of the operand sign bits. + */ + s = (int)((x ^ y) >> 63); + + /* + * Corrective actions for zeros: if either of the operands is + * zero, then the computations above were wrong. Test for zero + * is whether ex or ey is zero. We just have to set the mantissa + * (zu) to zero, the FPR() function will normalize e. + */ + d = ((ex + 0x7FF) & (ey + 0x7FF)) >> 11; + zu &= -(uint64_t)d; + + /* + * FPR() packs the result and applies proper rounding. + */ + return FPR(s, e, zu); +} + +fpr +fpr_sqr(fpr x) { + return fpr_mul(x, x); +} + +fpr +fpr_div(fpr x, fpr y) { + uint64_t xu, yu, q, q2, w; + int i, ex, ey, e, d, s; + + /* + * Extract mantissas of x and y (unsigned). + */ + xu = (x & (((uint64_t)1 << 52) - 1)) | ((uint64_t)1 << 52); + yu = (y & (((uint64_t)1 << 52) - 1)) | ((uint64_t)1 << 52); + + /* + * Perform bit-by-bit division of xu by yu. We run it for 55 bits. + */ + q = 0; + for (i = 0; i < 55; i ++) { + /* + * If yu is less than or equal xu, then subtract it and + * push a 1 in the quotient; otherwise, leave xu unchanged + * and push a 0. + */ + uint64_t b; + + b = ((xu - yu) >> 63) - 1; + xu -= b & yu; + q |= b & 1; + xu <<= 1; + q <<= 1; + } + + /* + * We got 55 bits in the quotient, followed by an extra zero. We + * want that 56th bit to be "sticky": it should be a 1 if and + * only if the remainder (xu) is non-zero. + */ + q |= (xu | -xu) >> 63; + + /* + * Quotient is at most 2^56-1. Its top bit may be zero, but in + * that case the next-to-top bit will be a one, since the + * initial xu and yu were both in the 2^52..2^53-1 range. + * We perform a conditional shift to normalize q to the + * 2^54..2^55-1 range (with the bottom bit being sticky). + */ + q2 = (q >> 1) | (q & 1); + w = q >> 55; + q ^= (q ^ q2) & -w; + + /* + * Extract exponents to compute the scaling factor: + * + * - Each exponent is biased and we scaled them up by + * 52 bits; but these biases will cancel out. + * + * - The division loop produced a 55-bit shifted result, + * so we must scale it down by 55 bits. + * + * - If w = 1, we right-shifted the integer by 1 bit, + * hence we must add 1 to the scaling. + */ + ex = (int)((x >> 52) & 0x7FF); + ey = (int)((y >> 52) & 0x7FF); + e = ex - ey - 55 + (int)w; + + /* + * Sign is the XOR of the signs of the operands. + */ + s = (int)((x ^ y) >> 63); + + /* + * Corrective actions for zeros: if x = 0, then the computation + * is wrong, and we must clamp e and q to 0. We do not care + * about the case y = 0 (as per assumptions in this module, + * the caller does not perform divisions by zero). + */ + d = (ex + 0x7FF) >> 11; + s &= d; + e &= -d; + q &= -(uint64_t)d; + + /* + * FPR() packs the result and applies proper rounding. + */ + return FPR(s, e, q); +} + +fpr +fpr_inv(fpr x) { + return fpr_div(4607182418800017408u, x); +} + +fpr +fpr_sqrt(fpr x) { + uint64_t xu, q, s, r; + int ex, e; + + /* + * Extract the mantissa and the exponent. We don't care about + * the sign: by assumption, the operand is nonnegative. + * We want the "true" exponent corresponding to a mantissa + * in the 1..2 range. + */ + xu = (x & (((uint64_t)1 << 52) - 1)) | ((uint64_t)1 << 52); + ex = (int)((x >> 52) & 0x7FF); + e = ex - 1023; + + /* + * If the exponent is odd, double the mantissa and decrement + * the exponent. The exponent is then halved to account for + * the square root. + */ + xu += xu & -(uint64_t)(e & 1); + e >>= 1; + + /* + * Double the mantissa. + */ + xu <<= 1; + + /* + * We now have a mantissa in the 2^53..2^55-1 range. It + * represents a value between 1 (inclusive) and 4 (exclusive) + * in fixed point notation (with 53 fractional bits). We + * compute the square root bit by bit. + */ + q = 0; + s = 0; + r = (uint64_t)1 << 53; + for (int i = 0; i < 54; i ++) { + uint64_t t, b; + + t = s + r; + b = ((xu - t) >> 63) - 1; + s += (r << 1) & b; + xu -= t & b; + q += r & b; + xu <<= 1; + r >>= 1; + } + + /* + * Now, q is a rounded-low 54-bit value, with a leading 1, + * 52 fractional digits, and an additional guard bit. We add + * an extra sticky bit to account for what remains of the operand. + */ + q <<= 1; + q |= (xu | -xu) >> 63; + + /* + * Result q is in the 2^54..2^55-1 range; we bias the exponent + * by 54 bits (the value e at that point contains the "true" + * exponent, but q is now considered an integer, i.e. scaled + * up. + */ + e -= 54; + + /* + * Corrective action for an operand of value zero. + */ + q &= -(uint64_t)((ex + 0x7FF) >> 11); + + /* + * Apply rounding and back result. + */ + return FPR(0, e, q); +} + +int +fpr_lt(fpr x, fpr y) { + /* + * If both x and y are positive, then a signed comparison yields + * the proper result: + * - For positive values, the order is preserved. + * - The sign bit is at the same place as in integers, so + * sign is preserved. + * Moreover, we can compute [x < y] as sgn(x-y) and the computation + * of x-y will not overflow. + * + * If the signs differ, then sgn(x) gives the proper result. + * + * If both x and y are negative, then the order is reversed. + * Hence [x < y] = sgn(y-x). We must compute this separately from + * sgn(x-y); simply inverting sgn(x-y) would not handle the edge + * case x = y properly. + */ + int cc0, cc1; + int64_t sx; + int64_t sy; + + sx = *(int64_t *)&x; + sy = *(int64_t *)&y; + sy &= ~((sx ^ sy) >> 63); /* set sy=0 if signs differ */ + + cc0 = (int)((sx - sy) >> 63) & 1; /* Neither subtraction overflows when */ + cc1 = (int)((sy - sx) >> 63) & 1; /* the signs are the same. */ + + return cc0 ^ ((cc0 ^ cc1) & (int)((x & y) >> 63)); +} + +uint64_t +fpr_expm_p63(fpr x, fpr ccs) { + /* + * Polynomial approximation of exp(-x) is taken from FACCT: + * https://eprint.iacr.org/2018/1234 + * Specifically, values are extracted from the implementation + * referenced from the FACCT article, and available at: + * https://github.com/raykzhao/gaussian + * Here, the coefficients have been scaled up by 2^63 and + * converted to integers. + * + * Tests over more than 24 billions of random inputs in the + * 0..log(2) range have never shown a deviation larger than + * 2^(-50) from the true mathematical value. + */ + static const uint64_t C[] = { + 0x00000004741183A3u, + 0x00000036548CFC06u, + 0x0000024FDCBF140Au, + 0x0000171D939DE045u, + 0x0000D00CF58F6F84u, + 0x000680681CF796E3u, + 0x002D82D8305B0FEAu, + 0x011111110E066FD0u, + 0x0555555555070F00u, + 0x155555555581FF00u, + 0x400000000002B400u, + 0x7FFFFFFFFFFF4800u, + 0x8000000000000000u + }; + + uint64_t z, y; + size_t u; + uint32_t z0, z1, y0, y1; + uint64_t a, b; + + y = C[0]; + z = (uint64_t)fpr_trunc(fpr_mul(x, fpr_ptwo63)) << 1; + for (u = 1; u < (sizeof C) / sizeof(C[0]); u ++) { + /* + * Compute product z * y over 128 bits, but keep only + * the top 64 bits. + * + * TODO: On some architectures/compilers we could use + * some intrinsics (__umulh() on MSVC) or other compiler + * extensions (unsigned __int128 on GCC / Clang) for + * improved speed; however, most 64-bit architectures + * also have appropriate IEEE754 floating-point support, + * which is better. + */ + uint64_t c; + + z0 = (uint32_t)z; + z1 = (uint32_t)(z >> 32); + y0 = (uint32_t)y; + y1 = (uint32_t)(y >> 32); + a = ((uint64_t)z0 * (uint64_t)y1) + + (((uint64_t)z0 * (uint64_t)y0) >> 32); + b = ((uint64_t)z1 * (uint64_t)y0); + c = (a >> 32) + (b >> 32); + c += (((uint64_t)(uint32_t)a + (uint64_t)(uint32_t)b) >> 32); + c += (uint64_t)z1 * (uint64_t)y1; + y = C[u] - c; + } + + /* + * The scaling factor must be applied at the end. Since y is now + * in fixed-point notation, we have to convert the factor to the + * same format, and do an extra integer multiplication. + */ + z = (uint64_t)fpr_trunc(fpr_mul(ccs, fpr_ptwo63)) << 1; + z0 = (uint32_t)z; + z1 = (uint32_t)(z >> 32); + y0 = (uint32_t)y; + y1 = (uint32_t)(y >> 32); + a = ((uint64_t)z0 * (uint64_t)y1) + + (((uint64_t)z0 * (uint64_t)y0) >> 32); + b = ((uint64_t)z1 * (uint64_t)y0); + y = (a >> 32) + (b >> 32); + y += (((uint64_t)(uint32_t)a + (uint64_t)(uint32_t)b) >> 32); + y += (uint64_t)z1 * (uint64_t)y1; + + return y; +} + +const fpr fpr_gm_tab[] = { + 0, 0, + 9223372036854775808U, 4607182418800017408U, + 4604544271217802189U, 4604544271217802189U, + 13827916308072577997U, 4604544271217802189U, + 4606496786581982534U, 4600565431771507043U, + 13823937468626282851U, 4606496786581982534U, + 4600565431771507043U, 4606496786581982534U, + 13829868823436758342U, 4600565431771507043U, + 4607009347991985328U, 4596196889902818827U, + 13819568926757594635U, 4607009347991985328U, + 4603179351334086856U, 4605664432017547683U, + 13829036468872323491U, 4603179351334086856U, + 4605664432017547683U, 4603179351334086856U, + 13826551388188862664U, 4605664432017547683U, + 4596196889902818827U, 4607009347991985328U, + 13830381384846761136U, 4596196889902818827U, + 4607139046673687846U, 4591727299969791020U, + 13815099336824566828U, 4607139046673687846U, + 4603889326261607894U, 4605137878724712257U, + 13828509915579488065U, 4603889326261607894U, + 4606118860100255153U, 4602163548591158843U, + 13825535585445934651U, 4606118860100255153U, + 4598900923775164166U, 4606794571824115162U, + 13830166608678890970U, 4598900923775164166U, + 4606794571824115162U, 4598900923775164166U, + 13822272960629939974U, 4606794571824115162U, + 4602163548591158843U, 4606118860100255153U, + 13829490896955030961U, 4602163548591158843U, + 4605137878724712257U, 4603889326261607894U, + 13827261363116383702U, 4605137878724712257U, + 4591727299969791020U, 4607139046673687846U, + 13830511083528463654U, 4591727299969791020U, + 4607171569234046334U, 4587232218149935124U, + 13810604255004710932U, 4607171569234046334U, + 4604224084862889120U, 4604849113969373103U, + 13828221150824148911U, 4604224084862889120U, + 4606317631232591731U, 4601373767755717824U, + 13824745804610493632U, 4606317631232591731U, + 4599740487990714333U, 4606655894547498725U, + 13830027931402274533U, 4599740487990714333U, + 4606912484326125783U, 4597922303871901467U, + 13821294340726677275U, 4606912484326125783U, + 4602805845399633902U, 4605900952042040894U, + 13829272988896816702U, 4602805845399633902U, + 4605409869824231233U, 4603540801876750389U, + 13826912838731526197U, 4605409869824231233U, + 4594454542771183930U, 4607084929468638487U, + 13830456966323414295U, 4594454542771183930U, + 4607084929468638487U, 4594454542771183930U, + 13817826579625959738U, 4607084929468638487U, + 4603540801876750389U, 4605409869824231233U, + 13828781906679007041U, 4603540801876750389U, + 4605900952042040894U, 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4604563781218984604U, 4604524701268679793U, + 13827896738123455601U, 4604563781218984604U, + 4569220649180767418U, 4607182376410422530U, + 13830554413265198338U, 4569220649180767418U +}; + +const fpr fpr_p2_tab[] = { + 4611686018427387904U, + 4607182418800017408U, + 4602678819172646912U, + 4598175219545276416U, + 4593671619917905920U, + 4589168020290535424U, + 4584664420663164928U, + 4580160821035794432U, + 4575657221408423936U, + 4571153621781053440U, + 4566650022153682944U +}; diff --git a/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/fpr.h b/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/fpr.h new file mode 100644 index 000000000..fb6830e71 --- /dev/null +++ b/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/fpr.h @@ -0,0 +1,253 @@ +#ifndef PQCLEAN_FALCON512_CLEAN_FPR_H +#define PQCLEAN_FALCON512_CLEAN_FPR_H + +/* + * Floating-point operations. + * + * ==========================(LICENSE BEGIN)============================ + * + * Copyright (c) 2017-2019 Falcon Project + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the + * "Software"), to deal in the Software without restriction, including + * without limitation the rights to use, copy, modify, merge, publish, + * distribute, sublicense, and/or sell copies of the Software, and to + * permit persons to whom the Software is furnished to do so, subject to + * the following conditions: + * + * The above copyright notice and this permission notice shall be + * included in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, + * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF + * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. + * IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY + * CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, + * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE + * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. + * + * ===========================(LICENSE END)============================= + * + * @author Thomas Pornin <thomas.pornin@nccgroup.com> + */ + + +/* ====================================================================== */ +/* + * Custom floating-point implementation with integer arithmetics. We + * use IEEE-754 "binary64" format, with some simplifications: + * + * - Top bit is s = 1 for negative, 0 for positive. + * + * - Exponent e uses the next 11 bits (bits 52 to 62, inclusive). + * + * - Mantissa m uses the 52 low bits. + * + * Encoded value is, in general: (-1)^s * 2^(e-1023) * (1 + m*2^(-52)) + * i.e. the mantissa really is a 53-bit number (less than 2.0, but not + * less than 1.0), but the top bit (equal to 1 by definition) is omitted + * in the encoding. + * + * In IEEE-754, there are some special values: + * + * - If e = 2047, then the value is either an infinite (m = 0) or + * a NaN (m != 0). + * + * - If e = 0, then the value is either a zero (m = 0) or a subnormal, + * aka "denormalized number" (m != 0). + * + * Of these, we only need the zeros. The caller is responsible for not + * providing operands that would lead to infinites, NaNs or subnormals. + * If inputs are such that values go out of range, then indeterminate + * values are returned (it would still be deterministic, but no specific + * value may be relied upon). + * + * At the C level, the three parts are stored in a 64-bit unsigned + * word. + * + * One may note that a property of the IEEE-754 format is that order + * is preserved for positive values: if two positive floating-point + * values x and y are such that x < y, then their respective encodings + * as _signed_ 64-bit integers i64(x) and i64(y) will be such that + * i64(x) < i64(y). For negative values, order is reversed: if x < 0, + * y < 0, and x < y, then ia64(x) > ia64(y). + * + * IMPORTANT ASSUMPTIONS: + * ====================== + * + * For proper computations, and constant-time behaviour, we assume the + * following: + * + * - 32x32->64 multiplication (unsigned) has an execution time that + * is independent of its operands. This is true of most modern + * x86 and ARM cores. Notable exceptions are the ARM Cortex M0, M0+ + * and M3 (in the M0 and M0+, this is done in software, so it depends + * on that routine), and the PowerPC cores from the G3/G4 lines. + * For more info, see: https://www.bearssl.org/ctmul.html + * + * - Left-shifts and right-shifts of 32-bit values have an execution + * time which does not depend on the shifted value nor on the + * shift count. An historical exception is the Pentium IV, but most + * modern CPU have barrel shifters. Some small microcontrollers + * might have varying-time shifts (not the ARM Cortex M*, though). + * + * - Right-shift of a signed negative value performs a sign extension. + * As per the C standard, this operation returns an + * implementation-defined result (this is NOT an "undefined + * behaviour"). On most/all systems, an arithmetic shift is + * performed, because this is what makes most sense. + */ + +/* + * Normally we should declare the 'fpr' type to be a struct or union + * around the internal 64-bit value; however, we want to use the + * direct 64-bit integer type to enable a lighter call convention on + * ARM platforms. This means that direct (invalid) use of operators + * such as '*' or '+' will not be caught by the compiler. We rely on + * the "normal" (non-emulated) code to detect such instances. + */ +typedef uint64_t fpr; + +/* + * For computations, we split values into an integral mantissa in the + * 2^54..2^55 range, and an (adjusted) exponent. The lowest bit is + * "sticky" (it is set to 1 if any of the bits below it is 1); when + * re-encoding, the low two bits are dropped, but may induce an + * increment in the value for proper rounding. + */ + +/* + * Right-shift a 64-bit unsigned value by a possibly secret shift count. + * We assumed that the underlying architecture had a barrel shifter for + * 32-bit shifts, but for 64-bit shifts on a 32-bit system, this will + * typically invoke a software routine that is not necessarily + * constant-time; hence the function below. + * + * Shift count n MUST be in the 0..63 range. + */ +#define fpr_ursh PQCLEAN_FALCON512_CLEAN_fpr_ursh +uint64_t fpr_ursh(uint64_t x, int n); + +/* + * Right-shift a 64-bit signed value by a possibly secret shift count + * (see fpr_ursh() for the rationale). + * + * Shift count n MUST be in the 0..63 range. + */ +#define fpr_irsh PQCLEAN_FALCON512_CLEAN_fpr_irsh +int64_t fpr_irsh(int64_t x, int n); + +/* + * Left-shift a 64-bit unsigned value by a possibly secret shift count + * (see fpr_ursh() for the rationale). + * + * Shift count n MUST be in the 0..63 range. + */ +#define fpr_ulsh PQCLEAN_FALCON512_CLEAN_fpr_ulsh +uint64_t fpr_ulsh(uint64_t x, int n); + +/* + * Expectations: + * s = 0 or 1 + * exponent e is "arbitrary" and unbiased + * 2^54 <= m < 2^55 + * Numerical value is (-1)^2 * m * 2^e + * + * Exponents which are too low lead to value zero. If the exponent is + * too large, the returned value is indeterminate. + * + * If m = 0, then a zero is returned (using the provided sign). + * If e < -1076, then a zero is returned (regardless of the value of m). + * If e >= -1076 and e != 0, m must be within the expected range + * (2^54 to 2^55-1). + */ +#define FPR PQCLEAN_FALCON512_CLEAN_FPR +fpr FPR(int s, int e, uint64_t m); + + +#define fpr_scaled PQCLEAN_FALCON512_CLEAN_fpr_scaled +fpr fpr_scaled(int64_t i, int sc); + +#define fpr_of PQCLEAN_FALCON512_CLEAN_fpr_of +fpr fpr_of(int64_t i); + +static const fpr fpr_q = 4667981563525332992; +static const fpr fpr_inverse_of_q = 4545632735260551042; +static const fpr fpr_inv_2sqrsigma0 = 4594603506513722306; +static const fpr fpr_inv_sigma = 4573359825155195350; +static const fpr fpr_sigma_min_9 = 4608495221497168882; +static const fpr fpr_sigma_min_10 = 4608586345619182117; +static const fpr fpr_log2 = 4604418534313441775; +static const fpr fpr_inv_log2 = 4609176140021203710; +static const fpr fpr_bnorm_max = 4670353323383631276; +static const fpr fpr_zero = 0; +static const fpr fpr_one = 4607182418800017408; +static const fpr fpr_two = 4611686018427387904; +static const fpr fpr_onehalf = 4602678819172646912; +static const fpr fpr_invsqrt2 = 4604544271217802189; +static const fpr fpr_invsqrt8 = 4600040671590431693; +static const fpr fpr_ptwo31 = 4746794007248502784; +static const fpr fpr_ptwo31m1 = 4746794007244308480; +static const fpr fpr_mtwo31m1 = 13970166044099084288U; +static const fpr fpr_ptwo63m1 = 4890909195324358656; +static const fpr fpr_mtwo63m1 = 14114281232179134464U; +static const fpr fpr_ptwo63 = 4890909195324358656; + +#define fpr_rint PQCLEAN_FALCON512_CLEAN_fpr_rint +int64_t fpr_rint(fpr x); + +#define fpr_floor PQCLEAN_FALCON512_CLEAN_fpr_floor +int64_t fpr_floor(fpr x); + +#define fpr_trunc PQCLEAN_FALCON512_CLEAN_fpr_trunc +int64_t fpr_trunc(fpr x); + +#define fpr_add PQCLEAN_FALCON512_CLEAN_fpr_add +fpr fpr_add(fpr x, fpr y); + +#define fpr_sub PQCLEAN_FALCON512_CLEAN_fpr_sub +fpr fpr_sub(fpr x, fpr y); + +#define fpr_neg PQCLEAN_FALCON512_CLEAN_fpr_neg +fpr fpr_neg(fpr x); + +#define fpr_half PQCLEAN_FALCON512_CLEAN_fpr_half +fpr fpr_half(fpr x); + +#define fpr_double PQCLEAN_FALCON512_CLEAN_fpr_double +fpr fpr_double(fpr x); + +#define fpr_mul PQCLEAN_FALCON512_CLEAN_fpr_mul +fpr fpr_mul(fpr x, fpr y); + +#define fpr_sqr PQCLEAN_FALCON512_CLEAN_fpr_sqr +fpr fpr_sqr(fpr x); + +#define fpr_div PQCLEAN_FALCON512_CLEAN_fpr_div +fpr fpr_div(fpr x, fpr y); + +#define fpr_inv PQCLEAN_FALCON512_CLEAN_fpr_inv +fpr fpr_inv(fpr x); + +#define fpr_sqrt PQCLEAN_FALCON512_CLEAN_fpr_sqrt +fpr fpr_sqrt(fpr x); + +#define fpr_lt PQCLEAN_FALCON512_CLEAN_fpr_lt +int fpr_lt(fpr x, fpr y); + +/* + * Compute exp(x) for x such that |x| <= ln 2. We want a precision of 50 + * bits or so. + */ +#define fpr_expm_p63 PQCLEAN_FALCON512_CLEAN_fpr_expm_p63 +uint64_t fpr_expm_p63(fpr x, fpr ccs); + +#define fpr_gm_tab PQCLEAN_FALCON512_CLEAN_fpr_gm_tab +extern const fpr fpr_gm_tab[]; + +#define fpr_p2_tab PQCLEAN_FALCON512_CLEAN_fpr_p2_tab +extern const fpr fpr_p2_tab[]; + +/* ====================================================================== */ +#endif diff --git a/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/inner.c b/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/inner.c new file mode 100755 index 000000000..dd90bd57e --- /dev/null +++ b/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/inner.c @@ -0,0 +1,70 @@ +#include "inner.h" + +/* + * ==========================(LICENSE BEGIN)============================ + * + * Copyright (c) 2017-2019 Falcon Project + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the + * "Software"), to deal in the Software without restriction, including + * without limitation the rights to use, copy, modify, merge, publish, + * distribute, sublicense, and/or sell copies of the Software, and to + * permit persons to whom the Software is furnished to do so, subject to + * the following conditions: + * + * The above copyright notice and this permission notice shall be + * included in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, + * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF + * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. + * IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY + * CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, + * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE + * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. + * + * ===========================(LICENSE END)============================= + */ + +unsigned set_fpu_cw(unsigned x) { + return x; +} + + +uint64_t prng_get_u64(prng *p) { + size_t u; + + /* + * If there are less than 9 bytes in the buffer, we refill it. + * This means that we may drop the last few bytes, but this allows + * for faster extraction code. Also, it means that we never leave + * an empty buffer. + */ + u = p->ptr; + if (u >= (sizeof p->buf.d) - 9) { + PQCLEAN_FALCON512_CLEAN_prng_refill(p); + u = 0; + } + p->ptr = u + 8; + + return (uint64_t)p->buf.d[u + 0] + | ((uint64_t)p->buf.d[u + 1] << 8) + | ((uint64_t)p->buf.d[u + 2] << 16) + | ((uint64_t)p->buf.d[u + 3] << 24) + | ((uint64_t)p->buf.d[u + 4] << 32) + | ((uint64_t)p->buf.d[u + 5] << 40) + | ((uint64_t)p->buf.d[u + 6] << 48) + | ((uint64_t)p->buf.d[u + 7] << 56); +} + + +unsigned prng_get_u8(prng *p) { + unsigned v; + + v = p->buf.d[p->ptr ++]; + if (p->ptr == sizeof p->buf.d) { + PQCLEAN_FALCON512_CLEAN_prng_refill(p); + } + return v; +} diff --git a/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/inner.h b/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/inner.h new file mode 100644 index 000000000..d469c9237 --- /dev/null +++ b/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/inner.h @@ -0,0 +1,793 @@ +#ifndef PQCLEAN_FALCON512_CLEAN_INNER_H +#define PQCLEAN_FALCON512_CLEAN_INNER_H + + +/* + * Internal functions for Falcon. This is not the API intended to be + * used by applications; instead, this internal API provides all the + * primitives on which wrappers build to provide external APIs. + * + * ==========================(LICENSE BEGIN)============================ + * + * Copyright (c) 2017-2019 Falcon Project + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the + * "Software"), to deal in the Software without restriction, including + * without limitation the rights to use, copy, modify, merge, publish, + * distribute, sublicense, and/or sell copies of the Software, and to + * permit persons to whom the Software is furnished to do so, subject to + * the following conditions: + * + * The above copyright notice and this permission notice shall be + * included in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, + * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF + * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. + * IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY + * CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, + * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE + * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. + * + * ===========================(LICENSE END)============================= + * + * @author Thomas Pornin <thomas.pornin@nccgroup.com> + */ + +/* + * IMPORTANT API RULES + * ------------------- + * + * This API has some non-trivial usage rules: + * + * + * - All public functions (i.e. the non-static ones) must be referenced + * with the PQCLEAN_FALCON512_CLEAN_ macro (e.g. PQCLEAN_FALCON512_CLEAN_verify_raw for the verify_raw() + * function). That macro adds a prefix to the name, which is + * configurable with the FALCON_PREFIX macro. This allows compiling + * the code into a specific "namespace" and potentially including + * several versions of this code into a single application (e.g. to + * have an AVX2 and a non-AVX2 variants and select the one to use at + * runtime based on availability of AVX2 opcodes). + * + * - Functions that need temporary buffers expects them as a final + * tmp[] array of type uint8_t*, with a size which is documented for + * each function. However, most have some alignment requirements, + * because they will use the array to store 16-bit, 32-bit or 64-bit + * values (e.g. uint64_t or double). The caller must ensure proper + * alignment. What happens on unaligned access depends on the + * underlying architecture, ranging from a slight time penalty + * to immediate termination of the process. + * + * - Some functions rely on specific rounding rules and precision for + * floating-point numbers. On some systems (in particular 32-bit x86 + * with the 387 FPU), this requires setting an hardware control + * word. The caller MUST use set_fpu_cw() to ensure proper precision: + * + * oldcw = set_fpu_cw(2); + * PQCLEAN_FALCON512_CLEAN_sign_dyn(...); + * set_fpu_cw(oldcw); + * + * On systems where the native floating-point precision is already + * proper, or integer-based emulation is used, the set_fpu_cw() + * function does nothing, so it can be called systematically. + */ +#include "fips202.h" +#include "fpr.h" +#include <stdint.h> +#include <stdlib.h> +#include <string.h> + + + + + +/* + * Some computations with floating-point elements, in particular + * rounding to the nearest integer, rely on operations using _exactly_ + * the precision of IEEE-754 binary64 type (i.e. 52 bits). On 32-bit + * x86, the 387 FPU may be used (depending on the target OS) and, in + * that case, may use more precision bits (i.e. 64 bits, for an 80-bit + * total type length); to prevent miscomputations, we define an explicit + * function that modifies the precision in the FPU control word. + * + * set_fpu_cw() sets the precision to the provided value, and returns + * the previously set precision; callers are supposed to restore the + * previous precision on exit. The correct (52-bit) precision is + * configured with the value "2". On unsupported compilers, or on + * targets other than 32-bit x86, or when the native 'double' type is + * not used, the set_fpu_cw() function does nothing at all. + */ +#define set_fpu_cw PQCLEAN_FALCON512_CLEAN_set_fpu_cw +unsigned set_fpu_cw(unsigned x); + +/* ==================================================================== */ +/* + * SHAKE256 implementation (shake.c). + * + * API is defined to be easily replaced with the fips202.h API defined + * as part of PQClean. + */ + + + +#define inner_shake256_context shake256incctx +#define inner_shake256_init(sc) shake256_inc_init(sc) +#define inner_shake256_inject(sc, in, len) shake256_inc_absorb(sc, in, len) +#define inner_shake256_flip(sc) shake256_inc_finalize(sc) +#define inner_shake256_extract(sc, out, len) shake256_inc_squeeze(out, len, sc) +#define inner_shake256_ctx_release(sc) shake256_inc_ctx_release(sc) + + +/* ==================================================================== */ +/* + * Encoding/decoding functions (codec.c). + * + * Encoding functions take as parameters an output buffer (out) with + * a given maximum length (max_out_len); returned value is the actual + * number of bytes which have been written. If the output buffer is + * not large enough, then 0 is returned (some bytes may have been + * written to the buffer). If 'out' is NULL, then 'max_out_len' is + * ignored; instead, the function computes and returns the actual + * required output length (in bytes). + * + * Decoding functions take as parameters an input buffer (in) with + * its maximum length (max_in_len); returned value is the actual number + * of bytes that have been read from the buffer. If the provided length + * is too short, then 0 is returned. + * + * Values to encode or decode are vectors of integers, with N = 2^logn + * elements. + * + * Three encoding formats are defined: + * + * - modq: sequence of values modulo 12289, each encoded over exactly + * 14 bits. The encoder and decoder verify that integers are within + * the valid range (0..12288). Values are arrays of uint16. + * + * - trim: sequence of signed integers, a specified number of bits + * each. The number of bits is provided as parameter and includes + * the sign bit. Each integer x must be such that |x| < 2^(bits-1) + * (which means that the -2^(bits-1) value is forbidden); encode and + * decode functions check that property. Values are arrays of + * int16_t or int8_t, corresponding to names 'trim_i16' and + * 'trim_i8', respectively. + * + * - comp: variable-length encoding for signed integers; each integer + * uses a minimum of 9 bits, possibly more. This is normally used + * only for signatures. + * + */ + +size_t PQCLEAN_FALCON512_CLEAN_modq_encode(void *out, size_t max_out_len, + const uint16_t *x, unsigned logn); +size_t PQCLEAN_FALCON512_CLEAN_trim_i16_encode(void *out, size_t max_out_len, + const int16_t *x, unsigned logn, unsigned bits); +size_t PQCLEAN_FALCON512_CLEAN_trim_i8_encode(void *out, size_t max_out_len, + const int8_t *x, unsigned logn, unsigned bits); +size_t PQCLEAN_FALCON512_CLEAN_comp_encode(void *out, size_t max_out_len, + const int16_t *x, unsigned logn); + +size_t PQCLEAN_FALCON512_CLEAN_modq_decode(uint16_t *x, unsigned logn, + const void *in, size_t max_in_len); +size_t PQCLEAN_FALCON512_CLEAN_trim_i16_decode(int16_t *x, unsigned logn, unsigned bits, + const void *in, size_t max_in_len); +size_t PQCLEAN_FALCON512_CLEAN_trim_i8_decode(int8_t *x, unsigned logn, unsigned bits, + const void *in, size_t max_in_len); +size_t PQCLEAN_FALCON512_CLEAN_comp_decode(int16_t *x, unsigned logn, + const void *in, size_t max_in_len); + +/* + * Number of bits for key elements, indexed by logn (1 to 10). This + * is at most 8 bits for all degrees, but some degrees may have shorter + * elements. + */ +extern const uint8_t PQCLEAN_FALCON512_CLEAN_max_fg_bits[]; +extern const uint8_t PQCLEAN_FALCON512_CLEAN_max_FG_bits[]; + +/* + * Maximum size, in bits, of elements in a signature, indexed by logn + * (1 to 10). The size includes the sign bit. + */ +extern const uint8_t PQCLEAN_FALCON512_CLEAN_max_sig_bits[]; + +/* ==================================================================== */ +/* + * Support functions used for both signature generation and signature + * verification (common.c). + */ + +/* + * From a SHAKE256 context (must be already flipped), produce a new + * point. This is the non-constant-time version, which may leak enough + * information to serve as a stop condition on a brute force attack on + * the hashed message (provided that the nonce value is known). + */ +void PQCLEAN_FALCON512_CLEAN_hash_to_point_vartime(inner_shake256_context *sc, + uint16_t *x, unsigned logn); + +/* + * From a SHAKE256 context (must be already flipped), produce a new + * point. The temporary buffer (tmp) must have room for 2*2^logn bytes. + * This function is constant-time but is typically more expensive than + * PQCLEAN_FALCON512_CLEAN_hash_to_point_vartime(). + * + * tmp[] must have 16-bit alignment. + */ +void PQCLEAN_FALCON512_CLEAN_hash_to_point_ct(inner_shake256_context *sc, + uint16_t *x, unsigned logn, uint8_t *tmp); + +/* + * Tell whether a given vector (2N coordinates, in two halves) is + * acceptable as a signature. This compares the appropriate norm of the + * vector with the acceptance bound. Returned value is 1 on success + * (vector is short enough to be acceptable), 0 otherwise. + */ +int PQCLEAN_FALCON512_CLEAN_is_short(const int16_t *s1, const int16_t *s2, unsigned logn); + +/* + * Tell whether a given vector (2N coordinates, in two halves) is + * acceptable as a signature. Instead of the first half s1, this + * function receives the "saturated squared norm" of s1, i.e. the + * sum of the squares of the coordinates of s1 (saturated at 2^32-1 + * if the sum exceeds 2^31-1). + * + * Returned value is 1 on success (vector is short enough to be + * acceptable), 0 otherwise. + */ +int PQCLEAN_FALCON512_CLEAN_is_short_half(uint32_t sqn, const int16_t *s2, unsigned logn); + +/* ==================================================================== */ +/* + * Signature verification functions (vrfy.c). + */ + +/* + * Convert a public key to NTT + Montgomery format. Conversion is done + * in place. + */ +void PQCLEAN_FALCON512_CLEAN_to_ntt_monty(uint16_t *h, unsigned logn); + +/* + * Internal signature verification code: + * c0[] contains the hashed nonce+message + * s2[] is the decoded signature + * h[] contains the public key, in NTT + Montgomery format + * logn is the degree log + * tmp[] temporary, must have at least 2*2^logn bytes + * Returned value is 1 on success, 0 on error. + * + * tmp[] must have 16-bit alignment. + */ +int PQCLEAN_FALCON512_CLEAN_verify_raw(const uint16_t *c0, const int16_t *s2, + const uint16_t *h, unsigned logn, uint8_t *tmp); + +/* + * Compute the public key h[], given the private key elements f[] and + * g[]. This computes h = g/f mod phi mod q, where phi is the polynomial + * modulus. This function returns 1 on success, 0 on error (an error is + * reported if f is not invertible mod phi mod q). + * + * The tmp[] array must have room for at least 2*2^logn elements. + * tmp[] must have 16-bit alignment. + */ +int PQCLEAN_FALCON512_CLEAN_compute_public(uint16_t *h, + const int8_t *f, const int8_t *g, unsigned logn, uint8_t *tmp); + +/* + * Recompute the fourth private key element. Private key consists in + * four polynomials with small coefficients f, g, F and G, which are + * such that fG - gF = q mod phi; furthermore, f is invertible modulo + * phi and modulo q. This function recomputes G from f, g and F. + * + * The tmp[] array must have room for at least 4*2^logn bytes. + * + * Returned value is 1 in success, 0 on error (f not invertible). + * tmp[] must have 16-bit alignment. + */ +int PQCLEAN_FALCON512_CLEAN_complete_private(int8_t *G, + const int8_t *f, const int8_t *g, const int8_t *F, + unsigned logn, uint8_t *tmp); + +/* + * Test whether a given polynomial is invertible modulo phi and q. + * Polynomial coefficients are small integers. + * + * tmp[] must have 16-bit alignment. + */ +int PQCLEAN_FALCON512_CLEAN_is_invertible( + const int16_t *s2, unsigned logn, uint8_t *tmp); + +/* + * Count the number of elements of value zero in the NTT representation + * of the given polynomial: this is the number of primitive 2n-th roots + * of unity (modulo q = 12289) that are roots of the provided polynomial + * (taken modulo q). + * + * tmp[] must have 16-bit alignment. + */ +int PQCLEAN_FALCON512_CLEAN_count_nttzero(const int16_t *sig, unsigned logn, uint8_t *tmp); + +/* + * Internal signature verification with public key recovery: + * h[] receives the public key (NOT in NTT/Montgomery format) + * c0[] contains the hashed nonce+message + * s1[] is the first signature half + * s2[] is the second signature half + * logn is the degree log + * tmp[] temporary, must have at least 2*2^logn bytes + * Returned value is 1 on success, 0 on error. Success is returned if + * the signature is a short enough vector; in that case, the public + * key has been written to h[]. However, the caller must still + * verify that h[] is the correct value (e.g. with regards to a known + * hash of the public key). + * + * h[] may not overlap with any of the other arrays. + * + * tmp[] must have 16-bit alignment. + */ +int PQCLEAN_FALCON512_CLEAN_verify_recover(uint16_t *h, + const uint16_t *c0, const int16_t *s1, const int16_t *s2, + unsigned logn, uint8_t *tmp); + +/* ==================================================================== */ +/* + * Implementation of floating-point real numbers (fpr.h, fpr.c). + */ + +/* + * Real numbers are implemented by an extra header file, included below. + * This is meant to support pluggable implementations. The default + * implementation relies on the C type 'double'. + * + * The included file must define the following types, functions and + * constants: + * + * fpr + * type for a real number + * + * fpr fpr_of(int64_t i) + * cast an integer into a real number; source must be in the + * -(2^63-1)..+(2^63-1) range + * + * fpr fpr_scaled(int64_t i, int sc) + * compute i*2^sc as a real number; source 'i' must be in the + * -(2^63-1)..+(2^63-1) range + * + * fpr fpr_ldexp(fpr x, int e) + * compute x*2^e + * + * int64_t fpr_rint(fpr x) + * round x to the nearest integer; x must be in the -(2^63-1) + * to +(2^63-1) range + * + * int64_t fpr_trunc(fpr x) + * round to an integer; this rounds towards zero; value must + * be in the -(2^63-1) to +(2^63-1) range + * + * fpr fpr_add(fpr x, fpr y) + * compute x + y + * + * fpr fpr_sub(fpr x, fpr y) + * compute x - y + * + * fpr fpr_neg(fpr x) + * compute -x + * + * fpr fpr_half(fpr x) + * compute x/2 + * + * fpr fpr_double(fpr x) + * compute x*2 + * + * fpr fpr_mul(fpr x, fpr y) + * compute x * y + * + * fpr fpr_sqr(fpr x) + * compute x * x + * + * fpr fpr_inv(fpr x) + * compute 1/x + * + * fpr fpr_div(fpr x, fpr y) + * compute x/y + * + * fpr fpr_sqrt(fpr x) + * compute the square root of x + * + * int fpr_lt(fpr x, fpr y) + * return 1 if x < y, 0 otherwise + * + * uint64_t fpr_expm_p63(fpr x) + * return exp(x), assuming that 0 <= x < log(2). Returned value + * is scaled to 63 bits (i.e. it really returns 2^63*exp(-x), + * rounded to the nearest integer). Computation should have a + * precision of at least 45 bits. + * + * const fpr fpr_gm_tab[] + * array of constants for FFT / iFFT + * + * const fpr fpr_p2_tab[] + * precomputed powers of 2 (by index, 0 to 10) + * + * Constants of type 'fpr': + * + * fpr fpr_q 12289 + * fpr fpr_inverse_of_q 1/12289 + * fpr fpr_inv_2sqrsigma0 1/(2*(1.8205^2)) + * fpr fpr_inv_sigma 1/(1.55*sqrt(12289)) + * fpr fpr_sigma_min_9 1.291500756233514568549480827642 + * fpr fpr_sigma_min_10 1.311734375905083682667395805765 + * fpr fpr_log2 log(2) + * fpr fpr_inv_log2 1/log(2) + * fpr fpr_bnorm_max 16822.4121 + * fpr fpr_zero 0 + * fpr fpr_one 1 + * fpr fpr_two 2 + * fpr fpr_onehalf 0.5 + * fpr fpr_ptwo31 2^31 + * fpr fpr_ptwo31m1 2^31-1 + * fpr fpr_mtwo31m1 -(2^31-1) + * fpr fpr_ptwo63m1 2^63-1 + * fpr fpr_mtwo63m1 -(2^63-1) + * fpr fpr_ptwo63 2^63 + */ + +/* ==================================================================== */ +/* + * RNG (rng.c). + * + * A PRNG based on ChaCha20 is implemented; it is seeded from a SHAKE256 + * context (flipped) and is used for bulk pseudorandom generation. + * A system-dependent seed generator is also provided. + */ + +/* + * Obtain a random seed from the system RNG. + * + * Returned value is 1 on success, 0 on error. + */ +int PQCLEAN_FALCON512_CLEAN_get_seed(void *seed, size_t seed_len); + +/* + * Structure for a PRNG. This includes a large buffer so that values + * get generated in advance. The 'state' is used to keep the current + * PRNG algorithm state (contents depend on the selected algorithm). + * + * The unions with 'dummy_u64' are there to ensure proper alignment for + * 64-bit direct access. + */ +typedef struct { + union { + uint8_t d[512]; /* MUST be 512, exactly */ + uint64_t dummy_u64; + } buf; + size_t ptr; + union { + uint8_t d[256]; + uint64_t dummy_u64; + } state; + int type; +} prng; + +/* + * Instantiate a PRNG. That PRNG will feed over the provided SHAKE256 + * context (in "flipped" state) to obtain its initial state. + */ +void PQCLEAN_FALCON512_CLEAN_prng_init(prng *p, inner_shake256_context *src); + +/* + * Refill the PRNG buffer. This is normally invoked automatically, and + * is declared here only so that prng_get_u64() may be inlined. + */ +void PQCLEAN_FALCON512_CLEAN_prng_refill(prng *p); + +/* + * Get some bytes from a PRNG. + */ +void PQCLEAN_FALCON512_CLEAN_prng_get_bytes(prng *p, void *dst, size_t len); + +/* + * Get a 64-bit random value from a PRNG. + */ +#define prng_get_u64 PQCLEAN_FALCON512_CLEAN_prng_get_u64 +uint64_t prng_get_u64(prng *p); + +/* + * Get an 8-bit random value from a PRNG. + */ +#define prng_get_u8 PQCLEAN_FALCON512_CLEAN_prng_get_u8 +unsigned prng_get_u8(prng *p); + +/* ==================================================================== */ +/* + * FFT (falcon-fft.c). + * + * A real polynomial is represented as an array of N 'fpr' elements. + * The FFT representation of a real polynomial contains N/2 complex + * elements; each is stored as two real numbers, for the real and + * imaginary parts, respectively. See falcon-fft.c for details on the + * internal representation. + */ + +/* + * Compute FFT in-place: the source array should contain a real + * polynomial (N coefficients); its storage area is reused to store + * the FFT representation of that polynomial (N/2 complex numbers). + * + * 'logn' MUST lie between 1 and 10 (inclusive). + */ +void PQCLEAN_FALCON512_CLEAN_FFT(fpr *f, unsigned logn); + +/* + * Compute the inverse FFT in-place: the source array should contain the + * FFT representation of a real polynomial (N/2 elements); the resulting + * real polynomial (N coefficients of type 'fpr') is written over the + * array. + * + * 'logn' MUST lie between 1 and 10 (inclusive). + */ +void PQCLEAN_FALCON512_CLEAN_iFFT(fpr *f, unsigned logn); + +/* + * Add polynomial b to polynomial a. a and b MUST NOT overlap. This + * function works in both normal and FFT representations. + */ +void PQCLEAN_FALCON512_CLEAN_poly_add(fpr *a, const fpr *b, unsigned logn); + +/* + * Subtract polynomial b from polynomial a. a and b MUST NOT overlap. This + * function works in both normal and FFT representations. + */ +void PQCLEAN_FALCON512_CLEAN_poly_sub(fpr *a, const fpr *b, unsigned logn); + +/* + * Negate polynomial a. This function works in both normal and FFT + * representations. + */ +void PQCLEAN_FALCON512_CLEAN_poly_neg(fpr *a, unsigned logn); + +/* + * Compute adjoint of polynomial a. This function works only in FFT + * representation. + */ +void PQCLEAN_FALCON512_CLEAN_poly_adj_fft(fpr *a, unsigned logn); + +/* + * Multiply polynomial a with polynomial b. a and b MUST NOT overlap. + * This function works only in FFT representation. + */ +void PQCLEAN_FALCON512_CLEAN_poly_mul_fft(fpr *a, const fpr *b, unsigned logn); + +/* + * Multiply polynomial a with the adjoint of polynomial b. a and b MUST NOT + * overlap. This function works only in FFT representation. + */ +void PQCLEAN_FALCON512_CLEAN_poly_muladj_fft(fpr *a, const fpr *b, unsigned logn); + +/* + * Multiply polynomial with its own adjoint. This function works only in FFT + * representation. + */ +void PQCLEAN_FALCON512_CLEAN_poly_mulselfadj_fft(fpr *a, unsigned logn); + +/* + * Multiply polynomial with a real constant. This function works in both + * normal and FFT representations. + */ +void PQCLEAN_FALCON512_CLEAN_poly_mulconst(fpr *a, fpr x, unsigned logn); + +/* + * Divide polynomial a by polynomial b, modulo X^N+1 (FFT representation). + * a and b MUST NOT overlap. + */ +void PQCLEAN_FALCON512_CLEAN_poly_div_fft(fpr *a, const fpr *b, unsigned logn); + +/* + * Given f and g (in FFT representation), compute 1/(f*adj(f)+g*adj(g)) + * (also in FFT representation). Since the result is auto-adjoint, all its + * coordinates in FFT representation are real; as such, only the first N/2 + * values of d[] are filled (the imaginary parts are skipped). + * + * Array d MUST NOT overlap with either a or b. + */ +void PQCLEAN_FALCON512_CLEAN_poly_invnorm2_fft(fpr *d, + const fpr *a, const fpr *b, unsigned logn); + +/* + * Given F, G, f and g (in FFT representation), compute F*adj(f)+G*adj(g) + * (also in FFT representation). Destination d MUST NOT overlap with + * any of the source arrays. + */ +void PQCLEAN_FALCON512_CLEAN_poly_add_muladj_fft(fpr *d, + const fpr *F, const fpr *G, + const fpr *f, const fpr *g, unsigned logn); + +/* + * Multiply polynomial a by polynomial b, where b is autoadjoint. Both + * a and b are in FFT representation. Since b is autoadjoint, all its + * FFT coefficients are real, and the array b contains only N/2 elements. + * a and b MUST NOT overlap. + */ +void PQCLEAN_FALCON512_CLEAN_poly_mul_autoadj_fft(fpr *a, + const fpr *b, unsigned logn); + +/* + * Divide polynomial a by polynomial b, where b is autoadjoint. Both + * a and b are in FFT representation. Since b is autoadjoint, all its + * FFT coefficients are real, and the array b contains only N/2 elements. + * a and b MUST NOT overlap. + */ +void PQCLEAN_FALCON512_CLEAN_poly_div_autoadj_fft(fpr *a, + const fpr *b, unsigned logn); + +/* + * Perform an LDL decomposition of an auto-adjoint matrix G, in FFT + * representation. On input, g00, g01 and g11 are provided (where the + * matrix G = [[g00, g01], [adj(g01), g11]]). On output, the d00, l10 + * and d11 values are written in g00, g01 and g11, respectively + * (with D = [[d00, 0], [0, d11]] and L = [[1, 0], [l10, 1]]). + * (In fact, d00 = g00, so the g00 operand is left unmodified.) + */ +void PQCLEAN_FALCON512_CLEAN_poly_LDL_fft(const fpr *g00, + fpr *g01, fpr *g11, unsigned logn); + +/* + * Perform an LDL decomposition of an auto-adjoint matrix G, in FFT + * representation. This is identical to poly_LDL_fft() except that + * g00, g01 and g11 are unmodified; the outputs d11 and l10 are written + * in two other separate buffers provided as extra parameters. + */ +void PQCLEAN_FALCON512_CLEAN_poly_LDLmv_fft(fpr *d11, fpr *l10, + const fpr *g00, const fpr *g01, + const fpr *g11, unsigned logn); + +/* + * Apply "split" operation on a polynomial in FFT representation: + * f = f0(x^2) + x*f1(x^2), for half-size polynomials f0 and f1 + * (polynomials modulo X^(N/2)+1). f0, f1 and f MUST NOT overlap. + */ +void PQCLEAN_FALCON512_CLEAN_poly_split_fft(fpr *f0, fpr *f1, + const fpr *f, unsigned logn); + +/* + * Apply "merge" operation on two polynomials in FFT representation: + * given f0 and f1, polynomials moduo X^(N/2)+1, this function computes + * f = f0(x^2) + x*f1(x^2), in FFT representation modulo X^N+1. + * f MUST NOT overlap with either f0 or f1. + */ +void PQCLEAN_FALCON512_CLEAN_poly_merge_fft(fpr *f, + const fpr *f0, const fpr *f1, unsigned logn); + +/* ==================================================================== */ +/* + * Key pair generation. + */ + +/* + * Required sizes of the temporary buffer (in bytes). + * + * This size is 28*2^logn bytes, except for degrees 2 and 4 (logn = 1 + * or 2) where it is slightly greater. + */ +#define FALCON_KEYGEN_TEMP_1 136 +#define FALCON_KEYGEN_TEMP_2 272 +#define FALCON_KEYGEN_TEMP_3 224 +#define FALCON_KEYGEN_TEMP_4 448 +#define FALCON_KEYGEN_TEMP_5 896 +#define FALCON_KEYGEN_TEMP_6 1792 +#define FALCON_KEYGEN_TEMP_7 3584 +#define FALCON_KEYGEN_TEMP_8 7168 +#define FALCON_KEYGEN_TEMP_9 14336 +#define FALCON_KEYGEN_TEMP_10 28672 + +/* + * Generate a new key pair. Randomness is extracted from the provided + * SHAKE256 context, which must have already been seeded and flipped. + * The tmp[] array must have suitable size (see FALCON_KEYGEN_TEMP_* + * macros) and be aligned for the uint32_t, uint64_t and fpr types. + * + * The private key elements are written in f, g, F and G, and the + * public key is written in h. Either or both of G and h may be NULL, + * in which case the corresponding element is not returned (they can + * be recomputed from f, g and F). + * + * tmp[] must have 64-bit alignment. + * This function uses floating-point rounding (see set_fpu_cw()). + */ +void PQCLEAN_FALCON512_CLEAN_keygen(inner_shake256_context *rng, + int8_t *f, int8_t *g, int8_t *F, int8_t *G, uint16_t *h, + unsigned logn, uint8_t *tmp); + +/* ==================================================================== */ +/* + * Signature generation. + */ + +/* + * Expand a private key into the B0 matrix in FFT representation and + * the LDL tree. All the values are written in 'expanded_key', for + * a total of (8*logn+40)*2^logn bytes. + * + * The tmp[] array must have room for at least 48*2^logn bytes. + * + * tmp[] must have 64-bit alignment. + * This function uses floating-point rounding (see set_fpu_cw()). + */ +void PQCLEAN_FALCON512_CLEAN_expand_privkey(fpr *expanded_key, + const int8_t *f, const int8_t *g, const int8_t *F, const int8_t *G, + unsigned logn, uint8_t *tmp); + +/* + * Compute a signature over the provided hashed message (hm); the + * signature value is one short vector. This function uses an + * expanded key (as generated by PQCLEAN_FALCON512_CLEAN_expand_privkey()). + * + * The sig[] and hm[] buffers may overlap. + * + * On successful output, the start of the tmp[] buffer contains the s1 + * vector (as int16_t elements). + * + * The minimal size (in bytes) of tmp[] is 48*2^logn bytes. + * + * tmp[] must have 64-bit alignment. + * This function uses floating-point rounding (see set_fpu_cw()). + */ +void PQCLEAN_FALCON512_CLEAN_sign_tree(int16_t *sig, inner_shake256_context *rng, + const fpr *expanded_key, + const uint16_t *hm, unsigned logn, uint8_t *tmp); + +/* + * Compute a signature over the provided hashed message (hm); the + * signature value is one short vector. This function uses a raw + * key and dynamically recompute the B0 matrix and LDL tree; this + * saves RAM since there is no needed for an expanded key, but + * increases the signature cost. + * + * The sig[] and hm[] buffers may overlap. + * + * On successful output, the start of the tmp[] buffer contains the s1 + * vector (as int16_t elements). + * + * The minimal size (in bytes) of tmp[] is 72*2^logn bytes. + * + * tmp[] must have 64-bit alignment. + * This function uses floating-point rounding (see set_fpu_cw()). + */ +void PQCLEAN_FALCON512_CLEAN_sign_dyn(int16_t *sig, inner_shake256_context *rng, + const int8_t *f, const int8_t *g, + const int8_t *F, const int8_t *G, + const uint16_t *hm, unsigned logn, uint8_t *tmp); + +/* + * Internal sampler engine. Exported for tests. + * + * sampler_context wraps around a source of random numbers (PRNG) and + * the sigma_min value (nominally dependent on the degree). + * + * sampler() takes as parameters: + * ctx pointer to the sampler_context structure + * mu center for the distribution + * isigma inverse of the distribution standard deviation + * It returns an integer sampled along the Gaussian distribution centered + * on mu and of standard deviation sigma = 1/isigma. + * + * gaussian0_sampler() takes as parameter a pointer to a PRNG, and + * returns an integer sampled along a half-Gaussian with standard + * deviation sigma0 = 1.8205 (center is 0, returned value is + * nonnegative). + */ + +typedef struct { + prng p; + fpr sigma_min; +} sampler_context; + +int PQCLEAN_FALCON512_CLEAN_sampler(void *ctx, fpr mu, fpr isigma); + +int PQCLEAN_FALCON512_CLEAN_gaussian0_sampler(prng *p); + +/* ==================================================================== */ + +#endif diff --git a/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/keygen.c b/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/keygen.c new file mode 100644 index 000000000..f72ecd991 --- /dev/null +++ b/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/keygen.c @@ -0,0 +1,4231 @@ +#include "inner.h" + +/* + * Falcon key pair generation. + * + * ==========================(LICENSE BEGIN)============================ + * + * Copyright (c) 2017-2019 Falcon Project + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the + * "Software"), to deal in the Software without restriction, including + * without limitation the rights to use, copy, modify, merge, publish, + * distribute, sublicense, and/or sell copies of the Software, and to + * permit persons to whom the Software is furnished to do so, subject to + * the following conditions: + * + * The above copyright notice and this permission notice shall be + * included in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, + * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF + * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. + * IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY + * CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, + * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE + * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. + * + * ===========================(LICENSE END)============================= + * + * @author Thomas Pornin <thomas.pornin@nccgroup.com> + */ + + +#define MKN(logn) ((size_t)1 << (logn)) + +/* ==================================================================== */ +/* + * Modular arithmetics. + * + * We implement a few functions for computing modulo a small integer p. + * + * All functions require that 2^30 < p < 2^31. Moreover, operands must + * be in the 0..p-1 range. + * + * Modular addition and subtraction work for all such p. + * + * Montgomery multiplication requires that p is odd, and must be provided + * with an additional value p0i = -1/p mod 2^31. See below for some basics + * on Montgomery multiplication. + * + * Division computes an inverse modulo p by an exponentiation (with + * exponent p-2): this works only if p is prime. Multiplication + * requirements also apply, i.e. p must be odd and p0i must be provided. + * + * The NTT and inverse NTT need all of the above, and also that + * p = 1 mod 2048. + * + * ----------------------------------------------------------------------- + * + * We use Montgomery representation with 31-bit values: + * + * Let R = 2^31 mod p. When 2^30 < p < 2^31, R = 2^31 - p. + * Montgomery representation of an integer x modulo p is x*R mod p. + * + * Montgomery multiplication computes (x*y)/R mod p for + * operands x and y. Therefore: + * + * - if operands are x*R and y*R (Montgomery representations of x and + * y), then Montgomery multiplication computes (x*R*y*R)/R = (x*y)*R + * mod p, which is the Montgomery representation of the product x*y; + * + * - if operands are x*R and y (or x and y*R), then Montgomery + * multiplication returns x*y mod p: mixed-representation + * multiplications yield results in normal representation. + * + * To convert to Montgomery representation, we multiply by R, which is done + * by Montgomery-multiplying by R^2. Stand-alone conversion back from + * Montgomery representation is Montgomery-multiplication by 1. + */ + +/* + * Precomputed small primes. Each element contains the following: + * + * p The prime itself. + * + * g A primitive root of phi = X^N+1 (in field Z_p). + * + * s The inverse of the product of all previous primes in the array, + * computed modulo p and in Montgomery representation. + * + * All primes are such that p = 1 mod 2048, and are lower than 2^31. They + * are listed in decreasing order. + */ + +typedef struct { + uint32_t p; + uint32_t g; + uint32_t s; +} small_prime; + +static const small_prime PRIMES[] = { + { 2147473409, 383167813, 10239 }, + { 2147389441, 211808905, 471403745 }, + { 2147387393, 37672282, 1329335065 }, + { 2147377153, 1977035326, 968223422 }, + { 2147358721, 1067163706, 132460015 }, + { 2147352577, 1606082042, 598693809 }, + { 2147346433, 2033915641, 1056257184 }, + { 2147338241, 1653770625, 421286710 }, + { 2147309569, 631200819, 1111201074 }, + { 2147297281, 2038364663, 1042003613 }, + { 2147295233, 1962540515, 19440033 }, + { 2147239937, 2100082663, 353296760 }, + { 2147235841, 1991153006, 1703918027 }, + { 2147217409, 516405114, 1258919613 }, + { 2147205121, 409347988, 1089726929 }, + { 2147196929, 927788991, 1946238668 }, + { 2147178497, 1136922411, 1347028164 }, + { 2147100673, 868626236, 701164723 }, + { 2147082241, 1897279176, 617820870 }, + { 2147074049, 1888819123, 158382189 }, + { 2147051521, 25006327, 522758543 }, + { 2147043329, 327546255, 37227845 }, + { 2147039233, 766324424, 1133356428 }, + { 2146988033, 1862817362, 73861329 }, + { 2146963457, 404622040, 653019435 }, + { 2146959361, 1936581214, 995143093 }, + { 2146938881, 1559770096, 634921513 }, + { 2146908161, 422623708, 1985060172 }, + { 2146885633, 1751189170, 298238186 }, + { 2146871297, 578919515, 291810829 }, + { 2146846721, 1114060353, 915902322 }, + { 2146834433, 2069565474, 47859524 }, + { 2146818049, 1552824584, 646281055 }, + { 2146775041, 1906267847, 1597832891 }, + { 2146756609, 1847414714, 1228090888 }, + { 2146744321, 1818792070, 1176377637 }, + { 2146738177, 1118066398, 1054971214 }, + { 2146736129, 52057278, 933422153 }, + { 2146713601, 592259376, 1406621510 }, + { 2146695169, 263161877, 1514178701 }, + { 2146656257, 685363115, 384505091 }, + { 2146650113, 927727032, 537575289 }, + { 2146646017, 52575506, 1799464037 }, + { 2146643969, 1276803876, 1348954416 }, + { 2146603009, 814028633, 1521547704 }, 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2136242177, 358688773, 1640007994 }, + { 2136229889, 512677188, 75585225 }, + { 2136219649, 2095003250, 1970086149 }, + { 2136207361, 1909650722, 537760675 }, + { 2136176641, 1334616195, 1533487619 }, + { 2136158209, 2096285632, 1793285210 }, + { 2136143873, 1897347517, 293843959 }, + { 2136133633, 923586222, 1022655978 }, + { 2136096769, 1464868191, 1515074410 }, + { 2136094721, 2020679520, 2061636104 }, + { 2136076289, 290798503, 1814726809 }, + { 2136041473, 156415894, 1250757633 }, + { 2135996417, 297459940, 1132158924 }, + { 2135955457, 538755304, 1688831340 }, + { 0, 0, 0 } +}; + +/* + * Reduce a small signed integer modulo a small prime. The source + * value x MUST be such that -p < x < p. + */ +static inline uint32_t +modp_set(int32_t x, uint32_t p) { + uint32_t w; + + w = (uint32_t)x; + w += p & -(w >> 31); + return w; +} + +/* + * Normalize a modular integer around 0. + */ +static inline int32_t +modp_norm(uint32_t x, uint32_t p) { + return (int32_t)(x - (p & (((x - ((p + 1) >> 1)) >> 31) - 1))); +} + +/* + * Compute -1/p mod 2^31. This works for all odd integers p that fit + * on 31 bits. + */ +static uint32_t +modp_ninv31(uint32_t p) { + uint32_t y; + + y = 2 - p; + y *= 2 - p * y; + y *= 2 - p * y; + y *= 2 - p * y; + y *= 2 - p * y; + return (uint32_t)0x7FFFFFFF & -y; +} + +/* + * Compute R = 2^31 mod p. + */ +static inline uint32_t +modp_R(uint32_t p) { + /* + * Since 2^30 < p < 2^31, we know that 2^31 mod p is simply + * 2^31 - p. + */ + return ((uint32_t)1 << 31) - p; +} + +/* + * Addition modulo p. + */ +static inline uint32_t +modp_add(uint32_t a, uint32_t b, uint32_t p) { + uint32_t d; + + d = a + b - p; + d += p & -(d >> 31); + return d; +} + +/* + * Subtraction modulo p. + */ +static inline uint32_t +modp_sub(uint32_t a, uint32_t b, uint32_t p) { + uint32_t d; + + d = a - b; + d += p & -(d >> 31); + return d; +} + +/* + * Halving modulo p. + */ +/* unused +static inline uint32_t +modp_half(uint32_t a, uint32_t p) +{ + a += p & -(a & 1); + return a >> 1; +} +*/ + +/* + * Montgomery multiplication modulo p. The 'p0i' value is -1/p mod 2^31. + * It is required that p is an odd integer. + */ +static inline uint32_t +modp_montymul(uint32_t a, uint32_t b, uint32_t p, uint32_t p0i) { + uint64_t z, w; + uint32_t d; + + z = (uint64_t)a * (uint64_t)b; + w = ((z * p0i) & (uint64_t)0x7FFFFFFF) * p; + d = (uint32_t)((z + w) >> 31) - p; + d += p & -(d >> 31); + return d; +} + +/* + * Compute R2 = 2^62 mod p. + */ +static uint32_t +modp_R2(uint32_t p, uint32_t p0i) { + uint32_t z; + + /* + * Compute z = 2^31 mod p (this is the value 1 in Montgomery + * representation), then double it with an addition. + */ + z = modp_R(p); + z = modp_add(z, z, p); + + /* + * Square it five times to obtain 2^32 in Montgomery representation + * (i.e. 2^63 mod p). + */ + z = modp_montymul(z, z, p, p0i); + z = modp_montymul(z, z, p, p0i); + z = modp_montymul(z, z, p, p0i); + z = modp_montymul(z, z, p, p0i); + z = modp_montymul(z, z, p, p0i); + + /* + * Halve the value mod p to get 2^62. + */ + z = (z + (p & -(z & 1))) >> 1; + return z; +} + +/* + * Compute 2^(31*x) modulo p. This works for integers x up to 2^11. + * p must be prime such that 2^30 < p < 2^31; p0i must be equal to + * -1/p mod 2^31; R2 must be equal to 2^62 mod p. + */ +static inline uint32_t +modp_Rx(unsigned x, uint32_t p, uint32_t p0i, uint32_t R2) { + int i; + uint32_t r, z; + + /* + * 2^(31*x) = (2^31)*(2^(31*(x-1))); i.e. we want the Montgomery + * representation of (2^31)^e mod p, where e = x-1. + * R2 is 2^31 in Montgomery representation. + */ + x --; + r = R2; + z = modp_R(p); + for (i = 0; (1U << i) <= x; i ++) { + if ((x & (1U << i)) != 0) { + z = modp_montymul(z, r, p, p0i); + } + r = modp_montymul(r, r, p, p0i); + } + return z; +} + +/* + * Division modulo p. If the divisor (b) is 0, then 0 is returned. + * This function computes proper results only when p is prime. + * Parameters: + * a dividend + * b divisor + * p odd prime modulus + * p0i -1/p mod 2^31 + * R 2^31 mod R + */ +static uint32_t +modp_div(uint32_t a, uint32_t b, uint32_t p, uint32_t p0i, uint32_t R) { + uint32_t z, e; + int i; + + e = p - 2; + z = R; + for (i = 30; i >= 0; i --) { + uint32_t z2; + + z = modp_montymul(z, z, p, p0i); + z2 = modp_montymul(z, b, p, p0i); + z ^= (z ^ z2) & -(uint32_t)((e >> i) & 1); + } + + /* + * The loop above just assumed that b was in Montgomery + * representation, i.e. really contained b*R; under that + * assumption, it returns 1/b in Montgomery representation, + * which is R/b. But we gave it b in normal representation, + * so the loop really returned R/(b/R) = R^2/b. + * + * We want a/b, so we need one Montgomery multiplication with a, + * which also remove one of the R factors, and another such + * multiplication to remove the second R factor. + */ + z = modp_montymul(z, 1, p, p0i); + return modp_montymul(a, z, p, p0i); +} + +/* + * Bit-reversal index table. + */ +static const uint16_t REV10[] = { + 0, 512, 256, 768, 128, 640, 384, 896, 64, 576, 320, 832, + 192, 704, 448, 960, 32, 544, 288, 800, 160, 672, 416, 928, + 96, 608, 352, 864, 224, 736, 480, 992, 16, 528, 272, 784, + 144, 656, 400, 912, 80, 592, 336, 848, 208, 720, 464, 976, + 48, 560, 304, 816, 176, 688, 432, 944, 112, 624, 368, 880, + 240, 752, 496, 1008, 8, 520, 264, 776, 136, 648, 392, 904, + 72, 584, 328, 840, 200, 712, 456, 968, 40, 552, 296, 808, + 168, 680, 424, 936, 104, 616, 360, 872, 232, 744, 488, 1000, + 24, 536, 280, 792, 152, 664, 408, 920, 88, 600, 344, 856, + 216, 728, 472, 984, 56, 568, 312, 824, 184, 696, 440, 952, + 120, 632, 376, 888, 248, 760, 504, 1016, 4, 516, 260, 772, + 132, 644, 388, 900, 68, 580, 324, 836, 196, 708, 452, 964, + 36, 548, 292, 804, 164, 676, 420, 932, 100, 612, 356, 868, + 228, 740, 484, 996, 20, 532, 276, 788, 148, 660, 404, 916, + 84, 596, 340, 852, 212, 724, 468, 980, 52, 564, 308, 820, + 180, 692, 436, 948, 116, 628, 372, 884, 244, 756, 500, 1012, + 12, 524, 268, 780, 140, 652, 396, 908, 76, 588, 332, 844, + 204, 716, 460, 972, 44, 556, 300, 812, 172, 684, 428, 940, + 108, 620, 364, 876, 236, 748, 492, 1004, 28, 540, 284, 796, + 156, 668, 412, 924, 92, 604, 348, 860, 220, 732, 476, 988, + 60, 572, 316, 828, 188, 700, 444, 956, 124, 636, 380, 892, + 252, 764, 508, 1020, 2, 514, 258, 770, 130, 642, 386, 898, + 66, 578, 322, 834, 194, 706, 450, 962, 34, 546, 290, 802, + 162, 674, 418, 930, 98, 610, 354, 866, 226, 738, 482, 994, + 18, 530, 274, 786, 146, 658, 402, 914, 82, 594, 338, 850, + 210, 722, 466, 978, 50, 562, 306, 818, 178, 690, 434, 946, + 114, 626, 370, 882, 242, 754, 498, 1010, 10, 522, 266, 778, + 138, 650, 394, 906, 74, 586, 330, 842, 202, 714, 458, 970, + 42, 554, 298, 810, 170, 682, 426, 938, 106, 618, 362, 874, + 234, 746, 490, 1002, 26, 538, 282, 794, 154, 666, 410, 922, + 90, 602, 346, 858, 218, 730, 474, 986, 58, 570, 314, 826, + 186, 698, 442, 954, 122, 634, 378, 890, 250, 762, 506, 1018, + 6, 518, 262, 774, 134, 646, 390, 902, 70, 582, 326, 838, + 198, 710, 454, 966, 38, 550, 294, 806, 166, 678, 422, 934, + 102, 614, 358, 870, 230, 742, 486, 998, 22, 534, 278, 790, + 150, 662, 406, 918, 86, 598, 342, 854, 214, 726, 470, 982, + 54, 566, 310, 822, 182, 694, 438, 950, 118, 630, 374, 886, + 246, 758, 502, 1014, 14, 526, 270, 782, 142, 654, 398, 910, + 78, 590, 334, 846, 206, 718, 462, 974, 46, 558, 302, 814, + 174, 686, 430, 942, 110, 622, 366, 878, 238, 750, 494, 1006, + 30, 542, 286, 798, 158, 670, 414, 926, 94, 606, 350, 862, + 222, 734, 478, 990, 62, 574, 318, 830, 190, 702, 446, 958, + 126, 638, 382, 894, 254, 766, 510, 1022, 1, 513, 257, 769, + 129, 641, 385, 897, 65, 577, 321, 833, 193, 705, 449, 961, + 33, 545, 289, 801, 161, 673, 417, 929, 97, 609, 353, 865, + 225, 737, 481, 993, 17, 529, 273, 785, 145, 657, 401, 913, + 81, 593, 337, 849, 209, 721, 465, 977, 49, 561, 305, 817, + 177, 689, 433, 945, 113, 625, 369, 881, 241, 753, 497, 1009, + 9, 521, 265, 777, 137, 649, 393, 905, 73, 585, 329, 841, + 201, 713, 457, 969, 41, 553, 297, 809, 169, 681, 425, 937, + 105, 617, 361, 873, 233, 745, 489, 1001, 25, 537, 281, 793, + 153, 665, 409, 921, 89, 601, 345, 857, 217, 729, 473, 985, + 57, 569, 313, 825, 185, 697, 441, 953, 121, 633, 377, 889, + 249, 761, 505, 1017, 5, 517, 261, 773, 133, 645, 389, 901, + 69, 581, 325, 837, 197, 709, 453, 965, 37, 549, 293, 805, + 165, 677, 421, 933, 101, 613, 357, 869, 229, 741, 485, 997, + 21, 533, 277, 789, 149, 661, 405, 917, 85, 597, 341, 853, + 213, 725, 469, 981, 53, 565, 309, 821, 181, 693, 437, 949, + 117, 629, 373, 885, 245, 757, 501, 1013, 13, 525, 269, 781, + 141, 653, 397, 909, 77, 589, 333, 845, 205, 717, 461, 973, + 45, 557, 301, 813, 173, 685, 429, 941, 109, 621, 365, 877, + 237, 749, 493, 1005, 29, 541, 285, 797, 157, 669, 413, 925, + 93, 605, 349, 861, 221, 733, 477, 989, 61, 573, 317, 829, + 189, 701, 445, 957, 125, 637, 381, 893, 253, 765, 509, 1021, + 3, 515, 259, 771, 131, 643, 387, 899, 67, 579, 323, 835, + 195, 707, 451, 963, 35, 547, 291, 803, 163, 675, 419, 931, + 99, 611, 355, 867, 227, 739, 483, 995, 19, 531, 275, 787, + 147, 659, 403, 915, 83, 595, 339, 851, 211, 723, 467, 979, + 51, 563, 307, 819, 179, 691, 435, 947, 115, 627, 371, 883, + 243, 755, 499, 1011, 11, 523, 267, 779, 139, 651, 395, 907, + 75, 587, 331, 843, 203, 715, 459, 971, 43, 555, 299, 811, + 171, 683, 427, 939, 107, 619, 363, 875, 235, 747, 491, 1003, + 27, 539, 283, 795, 155, 667, 411, 923, 91, 603, 347, 859, + 219, 731, 475, 987, 59, 571, 315, 827, 187, 699, 443, 955, + 123, 635, 379, 891, 251, 763, 507, 1019, 7, 519, 263, 775, + 135, 647, 391, 903, 71, 583, 327, 839, 199, 711, 455, 967, + 39, 551, 295, 807, 167, 679, 423, 935, 103, 615, 359, 871, + 231, 743, 487, 999, 23, 535, 279, 791, 151, 663, 407, 919, + 87, 599, 343, 855, 215, 727, 471, 983, 55, 567, 311, 823, + 183, 695, 439, 951, 119, 631, 375, 887, 247, 759, 503, 1015, + 15, 527, 271, 783, 143, 655, 399, 911, 79, 591, 335, 847, + 207, 719, 463, 975, 47, 559, 303, 815, 175, 687, 431, 943, + 111, 623, 367, 879, 239, 751, 495, 1007, 31, 543, 287, 799, + 159, 671, 415, 927, 95, 607, 351, 863, 223, 735, 479, 991, + 63, 575, 319, 831, 191, 703, 447, 959, 127, 639, 383, 895, + 255, 767, 511, 1023 +}; + +/* + * Compute the roots for NTT and inverse NTT (binary case). Input + * parameter g is a primitive 2048-th root of 1 modulo p (i.e. g^1024 = + * -1 mod p). This fills gm[] and igm[] with powers of g and 1/g: + * gm[rev(i)] = g^i mod p + * igm[rev(i)] = (1/g)^i mod p + * where rev() is the "bit reversal" function over 10 bits. It fills + * the arrays only up to N = 2^logn values. + * + * The values stored in gm[] and igm[] are in Montgomery representation. + * + * p must be a prime such that p = 1 mod 2048. + */ +static void +modp_mkgm2(uint32_t *gm, uint32_t *igm, unsigned logn, + uint32_t g, uint32_t p, uint32_t p0i) { + size_t u, n; + unsigned k; + uint32_t ig, x1, x2, R2; + + n = (size_t)1 << logn; + + /* + * We want g such that g^(2N) = 1 mod p, but the provided + * generator has order 2048. We must square it a few times. + */ + R2 = modp_R2(p, p0i); + g = modp_montymul(g, R2, p, p0i); + for (k = logn; k < 10; k ++) { + g = modp_montymul(g, g, p, p0i); + } + + ig = modp_div(R2, g, p, p0i, modp_R(p)); + k = 10 - logn; + x1 = x2 = modp_R(p); + for (u = 0; u < n; u ++) { + size_t v; + + v = REV10[u << k]; + gm[v] = x1; + igm[v] = x2; + x1 = modp_montymul(x1, g, p, p0i); + x2 = modp_montymul(x2, ig, p, p0i); + } +} + +/* + * Compute the NTT over a polynomial (binary case). Polynomial elements + * are a[0], a[stride], a[2 * stride]... + */ +static void +modp_NTT2_ext(uint32_t *a, size_t stride, const uint32_t *gm, unsigned logn, + uint32_t p, uint32_t p0i) { + size_t t, m, n; + + if (logn == 0) { + return; + } + n = (size_t)1 << logn; + t = n; + for (m = 1; m < n; m <<= 1) { + size_t ht, u, v1; + + ht = t >> 1; + for (u = 0, v1 = 0; u < m; u ++, v1 += t) { + uint32_t s; + size_t v; + uint32_t *r1, *r2; + + s = gm[m + u]; + r1 = a + v1 * stride; + r2 = r1 + ht * stride; + for (v = 0; v < ht; v ++, r1 += stride, r2 += stride) { + uint32_t x, y; + + x = *r1; + y = modp_montymul(*r2, s, p, p0i); + *r1 = modp_add(x, y, p); + *r2 = modp_sub(x, y, p); + } + } + t = ht; + } +} + +/* + * Compute the inverse NTT over a polynomial (binary case). + */ +static void +modp_iNTT2_ext(uint32_t *a, size_t stride, const uint32_t *igm, unsigned logn, + uint32_t p, uint32_t p0i) { + size_t t, m, n, k; + uint32_t ni; + uint32_t *r; + + if (logn == 0) { + return; + } + n = (size_t)1 << logn; + t = 1; + for (m = n; m > 1; m >>= 1) { + size_t hm, dt, u, v1; + + hm = m >> 1; + dt = t << 1; + for (u = 0, v1 = 0; u < hm; u ++, v1 += dt) { + uint32_t s; + size_t v; + uint32_t *r1, *r2; + + s = igm[hm + u]; + r1 = a + v1 * stride; + r2 = r1 + t * stride; + for (v = 0; v < t; v ++, r1 += stride, r2 += stride) { + uint32_t x, y; + + x = *r1; + y = *r2; + *r1 = modp_add(x, y, p); + *r2 = modp_montymul( + modp_sub(x, y, p), s, p, p0i);; + } + } + t = dt; + } + + /* + * We need 1/n in Montgomery representation, i.e. R/n. Since + * 1 <= logn <= 10, R/n is an integer; morever, R/n <= 2^30 < p, + * thus a simple shift will do. + */ + ni = (uint32_t)1 << (31 - logn); + for (k = 0, r = a; k < n; k ++, r += stride) { + *r = modp_montymul(*r, ni, p, p0i); + } +} + +/* + * Simplified macros for NTT and iNTT (binary case) when the elements + * are consecutive in RAM. + */ +#define modp_NTT2(a, gm, logn, p, p0i) modp_NTT2_ext(a, 1, gm, logn, p, p0i) +#define modp_iNTT2(a, igm, logn, p, p0i) modp_iNTT2_ext(a, 1, igm, logn, p, p0i) + +/* + * Given polynomial f in NTT representation modulo p, compute f' of degree + * less than N/2 such that f' = f0^2 - X*f1^2, where f0 and f1 are + * polynomials of degree less than N/2 such that f = f0(X^2) + X*f1(X^2). + * + * The new polynomial is written "in place" over the first N/2 elements + * of f. + * + * If applied logn times successively on a given polynomial, the resulting + * degree-0 polynomial is the resultant of f and X^N+1 modulo p. + * + * This function applies only to the binary case; it is invoked from + * solve_NTRU_binary_depth1(). + */ +static void +modp_poly_rec_res(uint32_t *f, unsigned logn, + uint32_t p, uint32_t p0i, uint32_t R2) { + size_t hn, u; + + hn = (size_t)1 << (logn - 1); + for (u = 0; u < hn; u ++) { + uint32_t w0, w1; + + w0 = f[(u << 1) + 0]; + w1 = f[(u << 1) + 1]; + f[u] = modp_montymul(modp_montymul(w0, w1, p, p0i), R2, p, p0i); + } +} + +/* ==================================================================== */ +/* + * Custom bignum implementation. + * + * This is a very reduced set of functionalities. We need to do the + * following operations: + * + * - Rebuild the resultant and the polynomial coefficients from their + * values modulo small primes (of length 31 bits each). + * + * - Compute an extended GCD between the two computed resultants. + * + * - Extract top bits and add scaled values during the successive steps + * of Babai rounding. + * + * When rebuilding values using CRT, we must also recompute the product + * of the small prime factors. We always do it one small factor at a + * time, so the "complicated" operations can be done modulo the small + * prime with the modp_* functions. CRT coefficients (inverses) are + * precomputed. + * + * All values are positive until the last step: when the polynomial + * coefficients have been rebuilt, we normalize them around 0. But then, + * only additions and subtractions on the upper few bits are needed + * afterwards. + * + * We keep big integers as arrays of 31-bit words (in uint32_t values); + * the top bit of each uint32_t is kept equal to 0. Using 31-bit words + * makes it easier to keep track of carries. When negative values are + * used, two's complement is used. + */ + +/* + * Subtract integer b from integer a. Both integers are supposed to have + * the same size. The carry (0 or 1) is returned. Source arrays a and b + * MUST be distinct. + * + * The operation is performed as described above if ctr = 1. If + * ctl = 0, the value a[] is unmodified, but all memory accesses are + * still performed, and the carry is computed and returned. + */ +static uint32_t +zint_sub(uint32_t *a, const uint32_t *b, size_t len, + uint32_t ctl) { + size_t u; + uint32_t cc, m; + + cc = 0; + m = -ctl; + for (u = 0; u < len; u ++) { + uint32_t aw, w; + + aw = a[u]; + w = aw - b[u] - cc; + cc = w >> 31; + aw ^= ((w & 0x7FFFFFFF) ^ aw) & m; + a[u] = aw; + } + return cc; +} + +/* + * Mutiply the provided big integer m with a small value x. + * This function assumes that x < 2^31. The carry word is returned. + */ +static uint32_t +zint_mul_small(uint32_t *m, size_t mlen, uint32_t x) { + size_t u; + uint32_t cc; + + cc = 0; + for (u = 0; u < mlen; u ++) { + uint64_t z; + + z = (uint64_t)m[u] * (uint64_t)x + cc; + m[u] = (uint32_t)z & 0x7FFFFFFF; + cc = (uint32_t)(z >> 31); + } + return cc; +} + +/* + * Reduce a big integer d modulo a small integer p. + * Rules: + * d is unsigned + * p is prime + * 2^30 < p < 2^31 + * p0i = -(1/p) mod 2^31 + * R2 = 2^62 mod p + */ +static uint32_t +zint_mod_small_unsigned(const uint32_t *d, size_t dlen, + uint32_t p, uint32_t p0i, uint32_t R2) { + uint32_t x; + size_t u; + + /* + * Algorithm: we inject words one by one, starting with the high + * word. Each step is: + * - multiply x by 2^31 + * - add new word + */ + x = 0; + u = dlen; + while (u -- > 0) { + uint32_t w; + + x = modp_montymul(x, R2, p, p0i); + w = d[u] - p; + w += p & -(w >> 31); + x = modp_add(x, w, p); + } + return x; +} + +/* + * Similar to zint_mod_small_unsigned(), except that d may be signed. + * Extra parameter is Rx = 2^(31*dlen) mod p. + */ +static uint32_t +zint_mod_small_signed(const uint32_t *d, size_t dlen, + uint32_t p, uint32_t p0i, uint32_t R2, uint32_t Rx) { + uint32_t z; + + if (dlen == 0) { + return 0; + } + z = zint_mod_small_unsigned(d, dlen, p, p0i, R2); + z = modp_sub(z, Rx & -(d[dlen - 1] >> 30), p); + return z; +} + +/* + * Add y*s to x. x and y initially have length 'len' words; the new x + * has length 'len+1' words. 's' must fit on 31 bits. x[] and y[] must + * not overlap. + */ +static void +zint_add_mul_small(uint32_t *x, + const uint32_t *y, size_t len, uint32_t s) { + size_t u; + uint32_t cc; + + cc = 0; + for (u = 0; u < len; u ++) { + uint32_t xw, yw; + uint64_t z; + + xw = x[u]; + yw = y[u]; + z = (uint64_t)yw * (uint64_t)s + (uint64_t)xw + (uint64_t)cc; + x[u] = (uint32_t)z & 0x7FFFFFFF; + cc = (uint32_t)(z >> 31); + } + x[len] = cc; +} + +/* + * Normalize a modular integer around 0: if x > p/2, then x is replaced + * with x - p (signed encoding with two's complement); otherwise, x is + * untouched. The two integers x and p are encoded over the same length. + */ +static void +zint_norm_zero(uint32_t *x, const uint32_t *p, size_t len) { + size_t u; + uint32_t r, bb; + + /* + * Compare x with p/2. We use the shifted version of p, and p + * is odd, so we really compare with (p-1)/2; we want to perform + * the subtraction if and only if x > (p-1)/2. + */ + r = 0; + bb = 0; + u = len; + while (u -- > 0) { + uint32_t wx, wp, cc; + + /* + * Get the two words to compare in wx and wp (both over + * 31 bits exactly). + */ + wx = x[u]; + wp = (p[u] >> 1) | (bb << 30); + bb = p[u] & 1; + + /* + * We set cc to -1, 0 or 1, depending on whether wp is + * lower than, equal to, or greater than wx. + */ + cc = wp - wx; + cc = ((-cc) >> 31) | -(cc >> 31); + + /* + * If r != 0 then it is either 1 or -1, and we keep its + * value. Otherwise, if r = 0, then we replace it with cc. + */ + r |= cc & ((r & 1) - 1); + } + + /* + * At this point, r = -1, 0 or 1, depending on whether (p-1)/2 + * is lower than, equal to, or greater than x. We thus want to + * do the subtraction only if r = -1. + */ + zint_sub(x, p, len, r >> 31); +} + +/* + * Rebuild integers from their RNS representation. There are 'num' + * integers, and each consists in 'xlen' words. 'xx' points at that + * first word of the first integer; subsequent integers are accessed + * by adding 'xstride' repeatedly. + * + * The words of an integer are the RNS representation of that integer, + * using the provided 'primes' are moduli. This function replaces + * each integer with its multi-word value (little-endian order). + * + * If "normalize_signed" is non-zero, then the returned value is + * normalized to the -m/2..m/2 interval (where m is the product of all + * small prime moduli); two's complement is used for negative values. + */ +static void +zint_rebuild_CRT(uint32_t *xx, size_t xlen, size_t xstride, + size_t num, const small_prime *primes, int normalize_signed, + uint32_t *tmp) { + size_t u; + uint32_t *x; + + tmp[0] = primes[0].p; + for (u = 1; u < xlen; u ++) { + /* + * At the entry of each loop iteration: + * - the first u words of each array have been + * reassembled; + * - the first u words of tmp[] contains the + * product of the prime moduli processed so far. + * + * We call 'q' the product of all previous primes. + */ + uint32_t p, p0i, s, R2; + size_t v; + + p = primes[u].p; + s = primes[u].s; + p0i = modp_ninv31(p); + R2 = modp_R2(p, p0i); + + for (v = 0, x = xx; v < num; v ++, x += xstride) { + uint32_t xp, xq, xr; + /* + * xp = the integer x modulo the prime p for this + * iteration + * xq = (x mod q) mod p + */ + xp = x[u]; + xq = zint_mod_small_unsigned(x, u, p, p0i, R2); + + /* + * New value is (x mod q) + q * (s * (xp - xq) mod p) + */ + xr = modp_montymul(s, modp_sub(xp, xq, p), p, p0i); + zint_add_mul_small(x, tmp, u, xr); + } + + /* + * Update product of primes in tmp[]. + */ + tmp[u] = zint_mul_small(tmp, u, p); + } + + /* + * Normalize the reconstructed values around 0. + */ + if (normalize_signed) { + for (u = 0, x = xx; u < num; u ++, x += xstride) { + zint_norm_zero(x, tmp, xlen); + } + } +} + +/* + * Negate a big integer conditionally: value a is replaced with -a if + * and only if ctl = 1. Control value ctl must be 0 or 1. + */ +static void +zint_negate(uint32_t *a, size_t len, uint32_t ctl) { + size_t u; + uint32_t cc, m; + + /* + * If ctl = 1 then we flip the bits of a by XORing with + * 0x7FFFFFFF, and we add 1 to the value. If ctl = 0 then we XOR + * with 0 and add 0, which leaves the value unchanged. + */ + cc = ctl; + m = -ctl >> 1; + for (u = 0; u < len; u ++) { + uint32_t aw; + + aw = a[u]; + aw = (aw ^ m) + cc; + a[u] = aw & 0x7FFFFFFF; + cc = aw >> 31; + } +} + +/* + * Replace a with (a*xa+b*xb)/(2^31) and b with (a*ya+b*yb)/(2^31). + * The low bits are dropped (the caller should compute the coefficients + * such that these dropped bits are all zeros). If either or both + * yields a negative value, then the value is negated. + * + * Returned value is: + * 0 both values were positive + * 1 new a had to be negated + * 2 new b had to be negated + * 3 both new a and new b had to be negated + * + * Coefficients xa, xb, ya and yb may use the full signed 32-bit range. + */ +static uint32_t +zint_co_reduce(uint32_t *a, uint32_t *b, size_t len, + int64_t xa, int64_t xb, int64_t ya, int64_t yb) { + size_t u; + int64_t cca, ccb; + uint32_t nega, negb; + + cca = 0; + ccb = 0; + for (u = 0; u < len; u ++) { + uint32_t wa, wb; + uint64_t za, zb; + + wa = a[u]; + wb = b[u]; + za = wa * (uint64_t)xa + wb * (uint64_t)xb + (uint64_t)cca; + zb = wa * (uint64_t)ya + wb * (uint64_t)yb + (uint64_t)ccb; + if (u > 0) { + a[u - 1] = (uint32_t)za & 0x7FFFFFFF; + b[u - 1] = (uint32_t)zb & 0x7FFFFFFF; + } + cca = *(int64_t *)&za >> 31; + ccb = *(int64_t *)&zb >> 31; + } + a[len - 1] = (uint32_t)cca; + b[len - 1] = (uint32_t)ccb; + + nega = (uint32_t)((uint64_t)cca >> 63); + negb = (uint32_t)((uint64_t)ccb >> 63); + zint_negate(a, len, nega); + zint_negate(b, len, negb); + return nega | (negb << 1); +} + +/* + * Finish modular reduction. Rules on input parameters: + * + * if neg = 1, then -m <= a < 0 + * if neg = 0, then 0 <= a < 2*m + * + * If neg = 0, then the top word of a[] is allowed to use 32 bits. + * + * Modulus m must be odd. + */ +static void +zint_finish_mod(uint32_t *a, size_t len, const uint32_t *m, uint32_t neg) { + size_t u; + uint32_t cc, xm, ym; + + /* + * First pass: compare a (assumed nonnegative) with m. Note that + * if the top word uses 32 bits, subtracting m must yield a + * value less than 2^31 since a < 2*m. + */ + cc = 0; + for (u = 0; u < len; u ++) { + cc = (a[u] - m[u] - cc) >> 31; + } + + /* + * If neg = 1 then we must add m (regardless of cc) + * If neg = 0 and cc = 0 then we must subtract m + * If neg = 0 and cc = 1 then we must do nothing + * + * In the loop below, we conditionally subtract either m or -m + * from a. Word xm is a word of m (if neg = 0) or -m (if neg = 1); + * but if neg = 0 and cc = 1, then ym = 0 and it forces mw to 0. + */ + xm = -neg >> 1; + ym = -(neg | (1 - cc)); + cc = neg; + for (u = 0; u < len; u ++) { + uint32_t aw, mw; + + aw = a[u]; + mw = (m[u] ^ xm) & ym; + aw = aw - mw - cc; + a[u] = aw & 0x7FFFFFFF; + cc = aw >> 31; + } +} + +/* + * Replace a with (a*xa+b*xb)/(2^31) mod m, and b with + * (a*ya+b*yb)/(2^31) mod m. Modulus m must be odd; m0i = -1/m[0] mod 2^31. + */ +static void +zint_co_reduce_mod(uint32_t *a, uint32_t *b, const uint32_t *m, size_t len, + uint32_t m0i, int64_t xa, int64_t xb, int64_t ya, int64_t yb) { + size_t u; + int64_t cca, ccb; + uint32_t fa, fb; + + /* + * These are actually four combined Montgomery multiplications. + */ + cca = 0; + ccb = 0; + fa = ((a[0] * (uint32_t)xa + b[0] * (uint32_t)xb) * m0i) & 0x7FFFFFFF; + fb = ((a[0] * (uint32_t)ya + b[0] * (uint32_t)yb) * m0i) & 0x7FFFFFFF; + for (u = 0; u < len; u ++) { + uint32_t wa, wb; + uint64_t za, zb; + + wa = a[u]; + wb = b[u]; + za = wa * (uint64_t)xa + wb * (uint64_t)xb + + m[u] * (uint64_t)fa + (uint64_t)cca; + zb = wa * (uint64_t)ya + wb * (uint64_t)yb + + m[u] * (uint64_t)fb + (uint64_t)ccb; + if (u > 0) { + a[u - 1] = (uint32_t)za & 0x7FFFFFFF; + b[u - 1] = (uint32_t)zb & 0x7FFFFFFF; + } + cca = *(int64_t *)&za >> 31; + ccb = *(int64_t *)&zb >> 31; + } + a[len - 1] = (uint32_t)cca; + b[len - 1] = (uint32_t)ccb; + + /* + * At this point: + * -m <= a < 2*m + * -m <= b < 2*m + * (this is a case of Montgomery reduction) + * The top words of 'a' and 'b' may have a 32-th bit set. + * We want to add or subtract the modulus, as required. + */ + zint_finish_mod(a, len, m, (uint32_t)((uint64_t)cca >> 63)); + zint_finish_mod(b, len, m, (uint32_t)((uint64_t)ccb >> 63)); +} + +/* + * Compute a GCD between two positive big integers x and y. The two + * integers must be odd. Returned value is 1 if the GCD is 1, 0 + * otherwise. When 1 is returned, arrays u and v are filled with values + * such that: + * 0 <= u <= y + * 0 <= v <= x + * x*u - y*v = 1 + * x[] and y[] are unmodified. Both input values must have the same + * encoded length. Temporary array must be large enough to accommodate 4 + * extra values of that length. Arrays u, v and tmp may not overlap with + * each other, or with either x or y. + */ +static int +zint_bezout(uint32_t *u, uint32_t *v, + const uint32_t *x, const uint32_t *y, + size_t len, uint32_t *tmp) { + /* + * Algorithm is an extended binary GCD. We maintain 6 values + * a, b, u0, u1, v0 and v1 with the following invariants: + * + * a = x*u0 - y*v0 + * b = x*u1 - y*v1 + * 0 <= a <= x + * 0 <= b <= y + * 0 <= u0 < y + * 0 <= v0 < x + * 0 <= u1 <= y + * 0 <= v1 < x + * + * Initial values are: + * + * a = x u0 = 1 v0 = 0 + * b = y u1 = y v1 = x-1 + * + * Each iteration reduces either a or b, and maintains the + * invariants. Algorithm stops when a = b, at which point their + * common value is GCD(a,b) and (u0,v0) (or (u1,v1)) contains + * the values (u,v) we want to return. + * + * The formal definition of the algorithm is a sequence of steps: + * + * - If a is even, then: + * a <- a/2 + * u0 <- u0/2 mod y + * v0 <- v0/2 mod x + * + * - Otherwise, if b is even, then: + * b <- b/2 + * u1 <- u1/2 mod y + * v1 <- v1/2 mod x + * + * - Otherwise, if a > b, then: + * a <- (a-b)/2 + * u0 <- (u0-u1)/2 mod y + * v0 <- (v0-v1)/2 mod x + * + * - Otherwise: + * b <- (b-a)/2 + * u1 <- (u1-u0)/2 mod y + * v1 <- (v1-v0)/2 mod y + * + * We can show that the operations above preserve the invariants: + * + * - If a is even, then u0 and v0 are either both even or both + * odd (since a = x*u0 - y*v0, and x and y are both odd). + * If u0 and v0 are both even, then (u0,v0) <- (u0/2,v0/2). + * Otherwise, (u0,v0) <- ((u0+y)/2,(v0+x)/2). Either way, + * the a = x*u0 - y*v0 invariant is preserved. + * + * - The same holds for the case where b is even. + * + * - If a and b are odd, and a > b, then: + * + * a-b = x*(u0-u1) - y*(v0-v1) + * + * In that situation, if u0 < u1, then x*(u0-u1) < 0, but + * a-b > 0; therefore, it must be that v0 < v1, and the + * first part of the update is: (u0,v0) <- (u0-u1+y,v0-v1+x), + * which preserves the invariants. Otherwise, if u0 > u1, + * then u0-u1 >= 1, thus x*(u0-u1) >= x. But a <= x and + * b >= 0, hence a-b <= x. It follows that, in that case, + * v0-v1 >= 0. The first part of the update is then: + * (u0,v0) <- (u0-u1,v0-v1), which again preserves the + * invariants. + * + * Either way, once the subtraction is done, the new value of + * a, which is the difference of two odd values, is even, + * and the remaining of this step is a subcase of the + * first algorithm case (i.e. when a is even). + * + * - If a and b are odd, and b > a, then the a similar + * argument holds. + * + * The values a and b start at x and y, respectively. Since x + * and y are odd, their GCD is odd, and it is easily seen that + * all steps conserve the GCD (GCD(a-b,b) = GCD(a, b); + * GCD(a/2,b) = GCD(a,b) if GCD(a,b) is odd). Moreover, either a + * or b is reduced by at least one bit at each iteration, so + * the algorithm necessarily converges on the case a = b, at + * which point the common value is the GCD. + * + * In the algorithm expressed above, when a = b, the fourth case + * applies, and sets b = 0. Since a contains the GCD of x and y, + * which are both odd, a must be odd, and subsequent iterations + * (if any) will simply divide b by 2 repeatedly, which has no + * consequence. Thus, the algorithm can run for more iterations + * than necessary; the final GCD will be in a, and the (u,v) + * coefficients will be (u0,v0). + * + * + * The presentation above is bit-by-bit. It can be sped up by + * noticing that all decisions are taken based on the low bits + * and high bits of a and b. We can extract the two top words + * and low word of each of a and b, and compute reduction + * parameters pa, pb, qa and qb such that the new values for + * a and b are: + * a' = (a*pa + b*pb) / (2^31) + * b' = (a*qa + b*qb) / (2^31) + * the two divisions being exact. The coefficients are obtained + * just from the extracted words, and may be slightly off, requiring + * an optional correction: if a' < 0, then we replace pa with -pa + * and pb with -pb. Each such step will reduce the total length + * (sum of lengths of a and b) by at least 30 bits at each + * iteration. + */ + uint32_t *u0, *u1, *v0, *v1, *a, *b; + uint32_t x0i, y0i; + uint32_t num, rc; + size_t j; + + if (len == 0) { + return 0; + } + + /* + * u0 and v0 are the u and v result buffers; the four other + * values (u1, v1, a and b) are taken from tmp[]. + */ + u0 = u; + v0 = v; + u1 = tmp; + v1 = u1 + len; + a = v1 + len; + b = a + len; + + /* + * We'll need the Montgomery reduction coefficients. + */ + x0i = modp_ninv31(x[0]); + y0i = modp_ninv31(y[0]); + + /* + * Initialize a, b, u0, u1, v0 and v1. + * a = x u0 = 1 v0 = 0 + * b = y u1 = y v1 = x-1 + * Note that x is odd, so computing x-1 is easy. + */ + memcpy(a, x, len * sizeof * x); + memcpy(b, y, len * sizeof * y); + u0[0] = 1; + memset(u0 + 1, 0, (len - 1) * sizeof * u0); + memset(v0, 0, len * sizeof * v0); + memcpy(u1, y, len * sizeof * u1); + memcpy(v1, x, len * sizeof * v1); + v1[0] --; + + /* + * Each input operand may be as large as 31*len bits, and we + * reduce the total length by at least 30 bits at each iteration. + */ + for (num = 62 * (uint32_t)len + 30; num >= 30; num -= 30) { + uint32_t c0, c1; + uint32_t a0, a1, b0, b1; + uint64_t a_hi, b_hi; + uint32_t a_lo, b_lo; + int64_t pa, pb, qa, qb; + int i; + uint32_t r; + + /* + * Extract the top words of a and b. If j is the highest + * index >= 1 such that a[j] != 0 or b[j] != 0, then we + * want (a[j] << 31) + a[j-1] and (b[j] << 31) + b[j-1]. + * If a and b are down to one word each, then we use + * a[0] and b[0]. + */ + c0 = (uint32_t) -1; + c1 = (uint32_t) -1; + a0 = 0; + a1 = 0; + b0 = 0; + b1 = 0; + j = len; + while (j -- > 0) { + uint32_t aw, bw; + + aw = a[j]; + bw = b[j]; + a0 ^= (a0 ^ aw) & c0; + a1 ^= (a1 ^ aw) & c1; + b0 ^= (b0 ^ bw) & c0; + b1 ^= (b1 ^ bw) & c1; + c1 = c0; + c0 &= (((aw | bw) + 0x7FFFFFFF) >> 31) - (uint32_t)1; + } + + /* + * If c1 = 0, then we grabbed two words for a and b. + * If c1 != 0 but c0 = 0, then we grabbed one word. It + * is not possible that c1 != 0 and c0 != 0, because that + * would mean that both integers are zero. + */ + a1 |= a0 & c1; + a0 &= ~c1; + b1 |= b0 & c1; + b0 &= ~c1; + a_hi = ((uint64_t)a0 << 31) + a1; + b_hi = ((uint64_t)b0 << 31) + b1; + a_lo = a[0]; + b_lo = b[0]; + + /* + * Compute reduction factors: + * + * a' = a*pa + b*pb + * b' = a*qa + b*qb + * + * such that a' and b' are both multiple of 2^31, but are + * only marginally larger than a and b. + */ + pa = 1; + pb = 0; + qa = 0; + qb = 1; + for (i = 0; i < 31; i ++) { + /* + * At each iteration: + * + * a <- (a-b)/2 if: a is odd, b is odd, a_hi > b_hi + * b <- (b-a)/2 if: a is odd, b is odd, a_hi <= b_hi + * a <- a/2 if: a is even + * b <- b/2 if: a is odd, b is even + * + * We multiply a_lo and b_lo by 2 at each + * iteration, thus a division by 2 really is a + * non-multiplication by 2. + */ + uint32_t rt, oa, ob, cAB, cBA, cA; + uint64_t rz; + + /* + * rt = 1 if a_hi > b_hi, 0 otherwise. + */ + rz = b_hi - a_hi; + rt = (uint32_t)((rz ^ ((a_hi ^ b_hi) + & (a_hi ^ rz))) >> 63); + + /* + * cAB = 1 if b must be subtracted from a + * cBA = 1 if a must be subtracted from b + * cA = 1 if a must be divided by 2 + * + * Rules: + * + * cAB and cBA cannot both be 1. + * If a is not divided by 2, b is. + */ + oa = (a_lo >> i) & 1; + ob = (b_lo >> i) & 1; + cAB = oa & ob & rt; + cBA = oa & ob & ~rt; + cA = cAB | (oa ^ 1); + + /* + * Conditional subtractions. + */ + a_lo -= b_lo & -cAB; + a_hi -= b_hi & -(uint64_t)cAB; + pa -= qa & -(int64_t)cAB; + pb -= qb & -(int64_t)cAB; + b_lo -= a_lo & -cBA; + b_hi -= a_hi & -(uint64_t)cBA; + qa -= pa & -(int64_t)cBA; + qb -= pb & -(int64_t)cBA; + + /* + * Shifting. + */ + a_lo += a_lo & (cA - 1); + pa += pa & ((int64_t)cA - 1); + pb += pb & ((int64_t)cA - 1); + a_hi ^= (a_hi ^ (a_hi >> 1)) & -(uint64_t)cA; + b_lo += b_lo & -cA; + qa += qa & -(int64_t)cA; + qb += qb & -(int64_t)cA; + b_hi ^= (b_hi ^ (b_hi >> 1)) & ((uint64_t)cA - 1); + } + + /* + * Apply the computed parameters to our values. We + * may have to correct pa and pb depending on the + * returned value of zint_co_reduce() (when a and/or b + * had to be negated). + */ + r = zint_co_reduce(a, b, len, pa, pb, qa, qb); + pa -= (pa + pa) & -(int64_t)(r & 1); + pb -= (pb + pb) & -(int64_t)(r & 1); + qa -= (qa + qa) & -(int64_t)(r >> 1); + qb -= (qb + qb) & -(int64_t)(r >> 1); + zint_co_reduce_mod(u0, u1, y, len, y0i, pa, pb, qa, qb); + zint_co_reduce_mod(v0, v1, x, len, x0i, pa, pb, qa, qb); + } + + /* + * At that point, array a[] should contain the GCD, and the + * results (u,v) should already be set. We check that the GCD + * is indeed 1. We also check that the two operands x and y + * are odd. + */ + rc = a[0] ^ 1; + for (j = 1; j < len; j ++) { + rc |= a[j]; + } + return (int)((1 - ((rc | -rc) >> 31)) & x[0] & y[0]); +} + +/* + * Add k*y*2^sc to x. The result is assumed to fit in the array of + * size xlen (truncation is applied if necessary). + * Scale factor 'sc' is provided as sch and scl, such that: + * sch = sc / 31 + * scl = sc % 31 + * xlen MUST NOT be lower than ylen. + * + * x[] and y[] are both signed integers, using two's complement for + * negative values. + */ +static void +zint_add_scaled_mul_small(uint32_t *x, size_t xlen, + const uint32_t *y, size_t ylen, int32_t k, + uint32_t sch, uint32_t scl) { + size_t u; + uint32_t ysign, tw; + int32_t cc; + + if (ylen == 0) { + return; + } + + ysign = -(y[ylen - 1] >> 30) >> 1; + tw = 0; + cc = 0; + for (u = sch; u < xlen; u ++) { + size_t v; + uint32_t wy, wys, ccu; + uint64_t z; + + /* + * Get the next word of y (scaled). + */ + v = u - sch; + if (v < ylen) { + wy = y[v]; + } else { + wy = ysign; + } + wys = ((wy << scl) & 0x7FFFFFFF) | tw; + tw = wy >> (31 - scl); + + /* + * The expression below does not overflow. + */ + z = (uint64_t)((int64_t)wys * (int64_t)k + (int64_t)x[u] + cc); + x[u] = (uint32_t)z & 0x7FFFFFFF; + + /* + * Right-shifting the signed value z would yield + * implementation-defined results (arithmetic shift is + * not guaranteed). However, we can cast to unsigned, + * and get the next carry as an unsigned word. We can + * then convert it back to signed by using the guaranteed + * fact that 'int32_t' uses two's complement with no + * trap representation or padding bit, and with a layout + * compatible with that of 'uint32_t'. + */ + ccu = (uint32_t)(z >> 31); + cc = *(int32_t *)&ccu; + } +} + +/* + * Subtract y*2^sc from x. The result is assumed to fit in the array of + * size xlen (truncation is applied if necessary). + * Scale factor 'sc' is provided as sch and scl, such that: + * sch = sc / 31 + * scl = sc % 31 + * xlen MUST NOT be lower than ylen. + * + * x[] and y[] are both signed integers, using two's complement for + * negative values. + */ +static void +zint_sub_scaled(uint32_t *x, size_t xlen, + const uint32_t *y, size_t ylen, uint32_t sch, uint32_t scl) { + size_t u; + uint32_t ysign, tw; + uint32_t cc; + + if (ylen == 0) { + return; + } + + ysign = -(y[ylen - 1] >> 30) >> 1; + tw = 0; + cc = 0; + for (u = sch; u < xlen; u ++) { + size_t v; + uint32_t w, wy, wys; + + /* + * Get the next word of y (scaled). + */ + v = u - sch; + if (v < ylen) { + wy = y[v]; + } else { + wy = ysign; + } + wys = ((wy << scl) & 0x7FFFFFFF) | tw; + tw = wy >> (31 - scl); + + w = x[u] - wys - cc; + x[u] = w & 0x7FFFFFFF; + cc = w >> 31; + } +} + +/* + * Convert a one-word signed big integer into a signed value. + */ +static inline int32_t +zint_one_to_plain(const uint32_t *x) { + uint32_t w; + + w = x[0]; + w |= (w & 0x40000000) << 1; + return *(int32_t *)&w; +} + +/* ==================================================================== */ + +/* + * Convert a polynomial to floating-point values. + * + * Each coefficient has length flen words, and starts fstride words after + * the previous. + * + * IEEE-754 binary64 values can represent values in a finite range, + * roughly 2^(-1023) to 2^(+1023); thus, if coefficients are too large, + * they should be "trimmed" by pointing not to the lowest word of each, + * but upper. + */ +static void +poly_big_to_fp(fpr *d, const uint32_t *f, size_t flen, size_t fstride, + unsigned logn) { + size_t n, u; + + n = MKN(logn); + if (flen == 0) { + for (u = 0; u < n; u ++) { + d[u] = fpr_zero; + } + return; + } + for (u = 0; u < n; u ++, f += fstride) { + size_t v; + uint32_t neg, cc, xm; + fpr x, fsc; + + /* + * Get sign of the integer; if it is negative, then we + * will load its absolute value instead, and negate the + * result. + */ + neg = -(f[flen - 1] >> 30); + xm = neg >> 1; + cc = neg & 1; + x = fpr_zero; + fsc = fpr_one; + for (v = 0; v < flen; v ++, fsc = fpr_mul(fsc, fpr_ptwo31)) { + uint32_t w; + + w = (f[v] ^ xm) + cc; + cc = w >> 31; + w &= 0x7FFFFFFF; + w -= (w << 1) & neg; + x = fpr_add(x, fpr_mul(fpr_of(*(int32_t *)&w), fsc)); + } + d[u] = x; + } +} + +/* + * Convert a polynomial to small integers. Source values are supposed + * to be one-word integers, signed over 31 bits. Returned value is 0 + * if any of the coefficients exceeds the provided limit (in absolute + * value), or 1 on success. + * + * This is not constant-time; this is not a problem here, because on + * any failure, the NTRU-solving process will be deemed to have failed + * and the (f,g) polynomials will be discarded. + */ +static int +poly_big_to_small(int8_t *d, const uint32_t *s, int lim, unsigned logn) { + size_t n, u; + + n = MKN(logn); + for (u = 0; u < n; u ++) { + int32_t z; + + z = zint_one_to_plain(s + u); + if (z < -lim || z > lim) { + return 0; + } + d[u] = (int8_t)z; + } + return 1; +} + +/* + * Subtract k*f from F, where F, f and k are polynomials modulo X^N+1. + * Coefficients of polynomial k are small integers (signed values in the + * -2^31..2^31 range) scaled by 2^sc. Value sc is provided as sch = sc / 31 + * and scl = sc % 31. + * + * This function implements the basic quadratic multiplication algorithm, + * which is efficient in space (no extra buffer needed) but slow at + * high degree. + */ +static void +poly_sub_scaled(uint32_t *F, size_t Flen, size_t Fstride, + const uint32_t *f, size_t flen, size_t fstride, + const int32_t *k, uint32_t sch, uint32_t scl, unsigned logn) { + size_t n, u; + + n = MKN(logn); + for (u = 0; u < n; u ++) { + int32_t kf; + size_t v; + uint32_t *x; + const uint32_t *y; + + kf = -k[u]; + x = F + u * Fstride; + y = f; + for (v = 0; v < n; v ++) { + zint_add_scaled_mul_small( + x, Flen, y, flen, kf, sch, scl); + if (u + v == n - 1) { + x = F; + kf = -kf; + } else { + x += Fstride; + } + y += fstride; + } + } +} + +/* + * Subtract k*f from F. Coefficients of polynomial k are small integers + * (signed values in the -2^31..2^31 range) scaled by 2^sc. This function + * assumes that the degree is large, and integers relatively small. + * The value sc is provided as sch = sc / 31 and scl = sc % 31. + */ +static void +poly_sub_scaled_ntt(uint32_t *F, size_t Flen, size_t Fstride, + const uint32_t *f, size_t flen, size_t fstride, + const int32_t *k, uint32_t sch, uint32_t scl, unsigned logn, + uint32_t *tmp) { + uint32_t *gm, *igm, *fk, *t1, *x; + const uint32_t *y; + size_t n, u, tlen; + const small_prime *primes; + + n = MKN(logn); + tlen = flen + 1; + gm = tmp; + igm = gm + MKN(logn); + fk = igm + MKN(logn); + t1 = fk + n * tlen; + + primes = PRIMES; + + /* + * Compute k*f in fk[], in RNS notation. + */ + for (u = 0; u < tlen; u ++) { + uint32_t p, p0i, R2, Rx; + size_t v; + + p = primes[u].p; + p0i = modp_ninv31(p); + R2 = modp_R2(p, p0i); + Rx = modp_Rx((unsigned)flen, p, p0i, R2); + modp_mkgm2(gm, igm, logn, primes[u].g, p, p0i); + + for (v = 0; v < n; v ++) { + t1[v] = modp_set(k[v], p); + } + modp_NTT2(t1, gm, logn, p, p0i); + for (v = 0, y = f, x = fk + u; + v < n; v ++, y += fstride, x += tlen) { + *x = zint_mod_small_signed(y, flen, p, p0i, R2, Rx); + } + modp_NTT2_ext(fk + u, tlen, gm, logn, p, p0i); + for (v = 0, x = fk + u; v < n; v ++, x += tlen) { + *x = modp_montymul( + modp_montymul(t1[v], *x, p, p0i), R2, p, p0i); + } + modp_iNTT2_ext(fk + u, tlen, igm, logn, p, p0i); + } + + /* + * Rebuild k*f. + */ + zint_rebuild_CRT(fk, tlen, tlen, n, primes, 1, t1); + + /* + * Subtract k*f, scaled, from F. + */ + for (u = 0, x = F, y = fk; u < n; u ++, x += Fstride, y += tlen) { + zint_sub_scaled(x, Flen, y, tlen, sch, scl); + } +} + +/* ==================================================================== */ + + +#define RNG_CONTEXT inner_shake256_context + +/* + * Get a random 8-byte integer from a SHAKE-based RNG. This function + * ensures consistent interpretation of the SHAKE output so that + * the same values will be obtained over different platforms, in case + * a known seed is used. + */ +static inline uint64_t +get_rng_u64(inner_shake256_context *rng) { + /* + * We enforce little-endian representation. + */ + + uint8_t tmp[8]; + + inner_shake256_extract(rng, tmp, sizeof tmp); + return (uint64_t)tmp[0] + | ((uint64_t)tmp[1] << 8) + | ((uint64_t)tmp[2] << 16) + | ((uint64_t)tmp[3] << 24) + | ((uint64_t)tmp[4] << 32) + | ((uint64_t)tmp[5] << 40) + | ((uint64_t)tmp[6] << 48) + | ((uint64_t)tmp[7] << 56); +} + +/* + * Table below incarnates a discrete Gaussian distribution: + * D(x) = exp(-(x^2)/(2*sigma^2)) + * where sigma = 1.17*sqrt(q/(2*N)), q = 12289, and N = 1024. + * Element 0 of the table is P(x = 0). + * For k > 0, element k is P(x >= k+1 | x > 0). + * Probabilities are scaled up by 2^63. + */ +static const uint64_t gauss_1024_12289[] = { + 1283868770400643928u, 6416574995475331444u, 4078260278032692663u, + 2353523259288686585u, 1227179971273316331u, 575931623374121527u, + 242543240509105209u, 91437049221049666u, 30799446349977173u, + 9255276791179340u, 2478152334826140u, 590642893610164u, + 125206034929641u, 23590435911403u, 3948334035941u, + 586753615614u, 77391054539u, 9056793210u, + 940121950u, 86539696u, 7062824u, + 510971u, 32764u, 1862u, + 94u, 4u, 0u +}; + +/* + * Generate a random value with a Gaussian distribution centered on 0. + * The RNG must be ready for extraction (already flipped). + * + * Distribution has standard deviation 1.17*sqrt(q/(2*N)). The + * precomputed table is for N = 1024. Since the sum of two independent + * values of standard deviation sigma has standard deviation + * sigma*sqrt(2), then we can just generate more values and add them + * together for lower dimensions. + */ +static int +mkgauss(RNG_CONTEXT *rng, unsigned logn) { + unsigned u, g; + int val; + + g = 1U << (10 - logn); + val = 0; + for (u = 0; u < g; u ++) { + /* + * Each iteration generates one value with the + * Gaussian distribution for N = 1024. + * + * We use two random 64-bit values. First value + * decides on whether the generated value is 0, and, + * if not, the sign of the value. Second random 64-bit + * word is used to generate the non-zero value. + * + * For constant-time code we have to read the complete + * table. This has negligible cost, compared with the + * remainder of the keygen process (solving the NTRU + * equation). + */ + uint64_t r; + uint32_t f, v, k, neg; + + /* + * First value: + * - flag 'neg' is randomly selected to be 0 or 1. + * - flag 'f' is set to 1 if the generated value is zero, + * or set to 0 otherwise. + */ + r = get_rng_u64(rng); + neg = (uint32_t)(r >> 63); + r &= ~((uint64_t)1 << 63); + f = (uint32_t)((r - gauss_1024_12289[0]) >> 63); + + /* + * We produce a new random 63-bit integer r, and go over + * the array, starting at index 1. We store in v the + * index of the first array element which is not greater + * than r, unless the flag f was already 1. + */ + v = 0; + r = get_rng_u64(rng); + r &= ~((uint64_t)1 << 63); + for (k = 1; k < (uint32_t)((sizeof gauss_1024_12289) + / (sizeof gauss_1024_12289[0])); k ++) { + uint32_t t; + + t = (uint32_t)((r - gauss_1024_12289[k]) >> 63) ^ 1; + v |= k & -(t & (f ^ 1)); + f |= t; + } + + /* + * We apply the sign ('neg' flag). If the value is zero, + * the sign has no effect. + */ + v = (v ^ -neg) + neg; + + /* + * Generated value is added to val. + */ + val += *(int32_t *)&v; + } + return val; +} + +/* + * The MAX_BL_SMALL[] and MAX_BL_LARGE[] contain the lengths, in 31-bit + * words, of intermediate values in the computation: + * + * MAX_BL_SMALL[depth]: length for the input f and g at that depth + * MAX_BL_LARGE[depth]: length for the unreduced F and G at that depth + * + * Rules: + * + * - Within an array, values grow. + * + * - The 'SMALL' array must have an entry for maximum depth, corresponding + * to the size of values used in the binary GCD. There is no such value + * for the 'LARGE' array (the binary GCD yields already reduced + * coefficients). + * + * - MAX_BL_LARGE[depth] >= MAX_BL_SMALL[depth + 1]. + * + * - Values must be large enough to handle the common cases, with some + * margins. + * + * - Values must not be "too large" either because we will convert some + * integers into floating-point values by considering the top 10 words, + * i.e. 310 bits; hence, for values of length more than 10 words, we + * should take care to have the length centered on the expected size. + * + * The following average lengths, in bits, have been measured on thousands + * of random keys (fg = max length of the absolute value of coefficients + * of f and g at that depth; FG = idem for the unreduced F and G; for the + * maximum depth, F and G are the output of binary GCD, multiplied by q; + * for each value, the average and standard deviation are provided). + * + * Binary case: + * depth: 10 fg: 6307.52 (24.48) FG: 6319.66 (24.51) + * depth: 9 fg: 3138.35 (12.25) FG: 9403.29 (27.55) + * depth: 8 fg: 1576.87 ( 7.49) FG: 4703.30 (14.77) + * depth: 7 fg: 794.17 ( 4.98) FG: 2361.84 ( 9.31) + * depth: 6 fg: 400.67 ( 3.10) FG: 1188.68 ( 6.04) + * depth: 5 fg: 202.22 ( 1.87) FG: 599.81 ( 3.87) + * depth: 4 fg: 101.62 ( 1.02) FG: 303.49 ( 2.38) + * depth: 3 fg: 50.37 ( 0.53) FG: 153.65 ( 1.39) + * depth: 2 fg: 24.07 ( 0.25) FG: 78.20 ( 0.73) + * depth: 1 fg: 10.99 ( 0.08) FG: 39.82 ( 0.41) + * depth: 0 fg: 4.00 ( 0.00) FG: 19.61 ( 0.49) + * + * Integers are actually represented either in binary notation over + * 31-bit words (signed, using two's complement), or in RNS, modulo + * many small primes. These small primes are close to, but slightly + * lower than, 2^31. Use of RNS loses less than two bits, even for + * the largest values. + * + * IMPORTANT: if these values are modified, then the temporary buffer + * sizes (FALCON_KEYGEN_TEMP_*, in inner.h) must be recomputed + * accordingly. + */ + +static const size_t MAX_BL_SMALL[] = { + 1, 1, 2, 2, 4, 7, 14, 27, 53, 106, 209 +}; + +static const size_t MAX_BL_LARGE[] = { + 2, 2, 5, 7, 12, 21, 40, 78, 157, 308 +}; + +/* + * Average and standard deviation for the maximum size (in bits) of + * coefficients of (f,g), depending on depth. These values are used + * to compute bounds for Babai's reduction. + */ +static const struct { + int avg; + int std; +} BITLENGTH[] = { + { 4, 0 }, + { 11, 1 }, + { 24, 1 }, + { 50, 1 }, + { 102, 1 }, + { 202, 2 }, + { 401, 4 }, + { 794, 5 }, + { 1577, 8 }, + { 3138, 13 }, + { 6308, 25 } +}; + +/* + * Minimal recursion depth at which we rebuild intermediate values + * when reconstructing f and g. + */ +#define DEPTH_INT_FG 4 + +/* + * Compute squared norm of a short vector. Returned value is saturated to + * 2^32-1 if it is not lower than 2^31. + */ +static uint32_t +poly_small_sqnorm(const int8_t *f, unsigned logn) { + size_t n, u; + uint32_t s, ng; + + n = MKN(logn); + s = 0; + ng = 0; + for (u = 0; u < n; u ++) { + int32_t z; + + z = f[u]; + s += (uint32_t)(z * z); + ng |= s; + } + return s | -(ng >> 31); +} + +/* + * Align (upwards) the provided 'data' pointer with regards to 'base' + * so that the offset is a multiple of the size of 'fpr'. + */ +static fpr * +align_fpr(void *base, void *data) { + uint8_t *cb, *cd; + size_t k, km; + + cb = base; + cd = data; + k = (size_t)(cd - cb); + km = k % sizeof(fpr); + if (km) { + k += (sizeof(fpr)) - km; + } + return (fpr *)(cb + k); +} + +/* + * Align (upwards) the provided 'data' pointer with regards to 'base' + * so that the offset is a multiple of the size of 'uint32_t'. + */ +static uint32_t * +align_u32(void *base, void *data) { + uint8_t *cb, *cd; + size_t k, km; + + cb = base; + cd = data; + k = (size_t)(cd - cb); + km = k % sizeof(uint32_t); + if (km) { + k += (sizeof(uint32_t)) - km; + } + return (uint32_t *)(cb + k); +} + +/* + * Convert a small vector to floating point. + */ +static void +poly_small_to_fp(fpr *x, const int8_t *f, unsigned logn) { + size_t n, u; + + n = MKN(logn); + for (u = 0; u < n; u ++) { + x[u] = fpr_of(f[u]); + } +} + +/* + * Input: f,g of degree N = 2^logn; 'depth' is used only to get their + * individual length. + * + * Output: f',g' of degree N/2, with the length for 'depth+1'. + * + * Values are in RNS; input and/or output may also be in NTT. + */ +static void +make_fg_step(uint32_t *data, unsigned logn, unsigned depth, + int in_ntt, int out_ntt) { + size_t n, hn, u; + size_t slen, tlen; + uint32_t *fd, *gd, *fs, *gs, *gm, *igm, *t1; + const small_prime *primes; + + n = (size_t)1 << logn; + hn = n >> 1; + slen = MAX_BL_SMALL[depth]; + tlen = MAX_BL_SMALL[depth + 1]; + primes = PRIMES; + + /* + * Prepare room for the result. + */ + fd = data; + gd = fd + hn * tlen; + fs = gd + hn * tlen; + gs = fs + n * slen; + gm = gs + n * slen; + igm = gm + n; + t1 = igm + n; + memmove(fs, data, 2 * n * slen * sizeof * data); + + /* + * First slen words: we use the input values directly, and apply + * inverse NTT as we go. + */ + for (u = 0; u < slen; u ++) { + uint32_t p, p0i, R2; + size_t v; + uint32_t *x; + + p = primes[u].p; + p0i = modp_ninv31(p); + R2 = modp_R2(p, p0i); + modp_mkgm2(gm, igm, logn, primes[u].g, p, p0i); + + for (v = 0, x = fs + u; v < n; v ++, x += slen) { + t1[v] = *x; + } + if (!in_ntt) { + modp_NTT2(t1, gm, logn, p, p0i); + } + for (v = 0, x = fd + u; v < hn; v ++, x += tlen) { + uint32_t w0, w1; + + w0 = t1[(v << 1) + 0]; + w1 = t1[(v << 1) + 1]; + *x = modp_montymul( + modp_montymul(w0, w1, p, p0i), R2, p, p0i); + } + if (in_ntt) { + modp_iNTT2_ext(fs + u, slen, igm, logn, p, p0i); + } + + for (v = 0, x = gs + u; v < n; v ++, x += slen) { + t1[v] = *x; + } + if (!in_ntt) { + modp_NTT2(t1, gm, logn, p, p0i); + } + for (v = 0, x = gd + u; v < hn; v ++, x += tlen) { + uint32_t w0, w1; + + w0 = t1[(v << 1) + 0]; + w1 = t1[(v << 1) + 1]; + *x = modp_montymul( + modp_montymul(w0, w1, p, p0i), R2, p, p0i); + } + if (in_ntt) { + modp_iNTT2_ext(gs + u, slen, igm, logn, p, p0i); + } + + if (!out_ntt) { + modp_iNTT2_ext(fd + u, tlen, igm, logn - 1, p, p0i); + modp_iNTT2_ext(gd + u, tlen, igm, logn - 1, p, p0i); + } + } + + /* + * Since the fs and gs words have been de-NTTized, we can use the + * CRT to rebuild the values. + */ + zint_rebuild_CRT(fs, slen, slen, n, primes, 1, gm); + zint_rebuild_CRT(gs, slen, slen, n, primes, 1, gm); + + /* + * Remaining words: use modular reductions to extract the values. + */ + for (u = slen; u < tlen; u ++) { + uint32_t p, p0i, R2, Rx; + size_t v; + uint32_t *x; + + p = primes[u].p; + p0i = modp_ninv31(p); + R2 = modp_R2(p, p0i); + Rx = modp_Rx((unsigned)slen, p, p0i, R2); + modp_mkgm2(gm, igm, logn, primes[u].g, p, p0i); + for (v = 0, x = fs; v < n; v ++, x += slen) { + t1[v] = zint_mod_small_signed(x, slen, p, p0i, R2, Rx); + } + modp_NTT2(t1, gm, logn, p, p0i); + for (v = 0, x = fd + u; v < hn; v ++, x += tlen) { + uint32_t w0, w1; + + w0 = t1[(v << 1) + 0]; + w1 = t1[(v << 1) + 1]; + *x = modp_montymul( + modp_montymul(w0, w1, p, p0i), R2, p, p0i); + } + for (v = 0, x = gs; v < n; v ++, x += slen) { + t1[v] = zint_mod_small_signed(x, slen, p, p0i, R2, Rx); + } + modp_NTT2(t1, gm, logn, p, p0i); + for (v = 0, x = gd + u; v < hn; v ++, x += tlen) { + uint32_t w0, w1; + + w0 = t1[(v << 1) + 0]; + w1 = t1[(v << 1) + 1]; + *x = modp_montymul( + modp_montymul(w0, w1, p, p0i), R2, p, p0i); + } + + if (!out_ntt) { + modp_iNTT2_ext(fd + u, tlen, igm, logn - 1, p, p0i); + modp_iNTT2_ext(gd + u, tlen, igm, logn - 1, p, p0i); + } + } +} + +/* + * Compute f and g at a specific depth, in RNS notation. + * + * Returned values are stored in the data[] array, at slen words per integer. + * + * Conditions: + * 0 <= depth <= logn + * + * Space use in data[]: enough room for any two successive values (f', g', + * f and g). + */ +static void +make_fg(uint32_t *data, const int8_t *f, const int8_t *g, + unsigned logn, unsigned depth, int out_ntt) { + size_t n, u; + uint32_t *ft, *gt, p0; + unsigned d; + const small_prime *primes; + + n = MKN(logn); + ft = data; + gt = ft + n; + primes = PRIMES; + p0 = primes[0].p; + for (u = 0; u < n; u ++) { + ft[u] = modp_set(f[u], p0); + gt[u] = modp_set(g[u], p0); + } + + if (depth == 0 && out_ntt) { + uint32_t *gm, *igm; + uint32_t p, p0i; + + p = primes[0].p; + p0i = modp_ninv31(p); + gm = gt + n; + igm = gm + MKN(logn); + modp_mkgm2(gm, igm, logn, primes[0].g, p, p0i); + modp_NTT2(ft, gm, logn, p, p0i); + modp_NTT2(gt, gm, logn, p, p0i); + return; + } + + if (depth == 0) { + return; + } + if (depth == 1) { + make_fg_step(data, logn, 0, 0, out_ntt); + return; + } + make_fg_step(data, logn, 0, 0, 1); + for (d = 1; d + 1 < depth; d ++) { + make_fg_step(data, logn - d, d, 1, 1); + } + make_fg_step(data, logn - depth + 1, depth - 1, 1, out_ntt); +} + +/* + * Solving the NTRU equation, deepest level: compute the resultants of + * f and g with X^N+1, and use binary GCD. The F and G values are + * returned in tmp[]. + * + * Returned value: 1 on success, 0 on error. + */ +static int +solve_NTRU_deepest(unsigned logn_top, + const int8_t *f, const int8_t *g, uint32_t *tmp) { + size_t len; + uint32_t *Fp, *Gp, *fp, *gp, *t1, q; + const small_prime *primes; + + len = MAX_BL_SMALL[logn_top]; + primes = PRIMES; + + Fp = tmp; + Gp = Fp + len; + fp = Gp + len; + gp = fp + len; + t1 = gp + len; + + make_fg(fp, f, g, logn_top, logn_top, 0); + + /* + * We use the CRT to rebuild the resultants as big integers. + * There are two such big integers. The resultants are always + * nonnegative. + */ + zint_rebuild_CRT(fp, len, len, 2, primes, 0, t1); + + /* + * Apply the binary GCD. The zint_bezout() function works only + * if both inputs are odd. + * + * We can test on the result and return 0 because that would + * imply failure of the NTRU solving equation, and the (f,g) + * values will be abandoned in that case. + */ + if (!zint_bezout(Gp, Fp, fp, gp, len, t1)) { + return 0; + } + + /* + * Multiply the two values by the target value q. Values must + * fit in the destination arrays. + * We can again test on the returned words: a non-zero output + * of zint_mul_small() means that we exceeded our array + * capacity, and that implies failure and rejection of (f,g). + */ + q = 12289; + if (zint_mul_small(Fp, len, q) != 0 + || zint_mul_small(Gp, len, q) != 0) { + return 0; + } + + return 1; +} + +/* + * Solving the NTRU equation, intermediate level. Upon entry, the F and G + * from the previous level should be in the tmp[] array. + * This function MAY be invoked for the top-level (in which case depth = 0). + * + * Returned value: 1 on success, 0 on error. + */ +static int +solve_NTRU_intermediate(unsigned logn_top, + const int8_t *f, const int8_t *g, unsigned depth, uint32_t *tmp) { + /* + * In this function, 'logn' is the log2 of the degree for + * this step. If N = 2^logn, then: + * - the F and G values already in fk->tmp (from the deeper + * levels) have degree N/2; + * - this function should return F and G of degree N. + */ + unsigned logn; + size_t n, hn, slen, dlen, llen, rlen, FGlen, u; + uint32_t *Fd, *Gd, *Ft, *Gt, *ft, *gt, *t1; + fpr *rt1, *rt2, *rt3, *rt4, *rt5; + int scale_fg, minbl_fg, maxbl_fg, maxbl_FG, scale_k; + uint32_t *x, *y; + int32_t *k; + const small_prime *primes; + + logn = logn_top - depth; + n = (size_t)1 << logn; + hn = n >> 1; + + /* + * slen = size for our input f and g; also size of the reduced + * F and G we return (degree N) + * + * dlen = size of the F and G obtained from the deeper level + * (degree N/2 or N/3) + * + * llen = size for intermediary F and G before reduction (degree N) + * + * We build our non-reduced F and G as two independent halves each, + * of degree N/2 (F = F0 + X*F1, G = G0 + X*G1). + */ + slen = MAX_BL_SMALL[depth]; + dlen = MAX_BL_SMALL[depth + 1]; + llen = MAX_BL_LARGE[depth]; + primes = PRIMES; + + /* + * Fd and Gd are the F and G from the deeper level. + */ + Fd = tmp; + Gd = Fd + dlen * hn; + + /* + * Compute the input f and g for this level. Note that we get f + * and g in RNS + NTT representation. + */ + ft = Gd + dlen * hn; + make_fg(ft, f, g, logn_top, depth, 1); + + /* + * Move the newly computed f and g to make room for our candidate + * F and G (unreduced). + */ + Ft = tmp; + Gt = Ft + n * llen; + t1 = Gt + n * llen; + memmove(t1, ft, 2 * n * slen * sizeof * ft); + ft = t1; + gt = ft + slen * n; + t1 = gt + slen * n; + + /* + * Move Fd and Gd _after_ f and g. + */ + memmove(t1, Fd, 2 * hn * dlen * sizeof * Fd); + Fd = t1; + Gd = Fd + hn * dlen; + + /* + * We reduce Fd and Gd modulo all the small primes we will need, + * and store the values in Ft and Gt (only n/2 values in each). + */ + for (u = 0; u < llen; u ++) { + uint32_t p, p0i, R2, Rx; + size_t v; + uint32_t *xs, *ys, *xd, *yd; + + p = primes[u].p; + p0i = modp_ninv31(p); + R2 = modp_R2(p, p0i); + Rx = modp_Rx((unsigned)dlen, p, p0i, R2); + for (v = 0, xs = Fd, ys = Gd, xd = Ft + u, yd = Gt + u; + v < hn; + v ++, xs += dlen, ys += dlen, xd += llen, yd += llen) { + *xd = zint_mod_small_signed(xs, dlen, p, p0i, R2, Rx); + *yd = zint_mod_small_signed(ys, dlen, p, p0i, R2, Rx); + } + } + + /* + * We do not need Fd and Gd after that point. + */ + + /* + * Compute our F and G modulo sufficiently many small primes. + */ + for (u = 0; u < llen; u ++) { + uint32_t p, p0i, R2; + uint32_t *gm, *igm, *fx, *gx, *Fp, *Gp; + size_t v; + + /* + * All computations are done modulo p. + */ + p = primes[u].p; + p0i = modp_ninv31(p); + R2 = modp_R2(p, p0i); + + /* + * If we processed slen words, then f and g have been + * de-NTTized, and are in RNS; we can rebuild them. + */ + if (u == slen) { + zint_rebuild_CRT(ft, slen, slen, n, primes, 1, t1); + zint_rebuild_CRT(gt, slen, slen, n, primes, 1, t1); + } + + gm = t1; + igm = gm + n; + fx = igm + n; + gx = fx + n; + + modp_mkgm2(gm, igm, logn, primes[u].g, p, p0i); + + if (u < slen) { + for (v = 0, x = ft + u, y = gt + u; + v < n; v ++, x += slen, y += slen) { + fx[v] = *x; + gx[v] = *y; + } + modp_iNTT2_ext(ft + u, slen, igm, logn, p, p0i); + modp_iNTT2_ext(gt + u, slen, igm, logn, p, p0i); + } else { + uint32_t Rx; + + Rx = modp_Rx((unsigned)slen, p, p0i, R2); + for (v = 0, x = ft, y = gt; + v < n; v ++, x += slen, y += slen) { + fx[v] = zint_mod_small_signed(x, slen, + p, p0i, R2, Rx); + gx[v] = zint_mod_small_signed(y, slen, + p, p0i, R2, Rx); + } + modp_NTT2(fx, gm, logn, p, p0i); + modp_NTT2(gx, gm, logn, p, p0i); + } + + /* + * Get F' and G' modulo p and in NTT representation + * (they have degree n/2). These values were computed in + * a previous step, and stored in Ft and Gt. + */ + Fp = gx + n; + Gp = Fp + hn; + for (v = 0, x = Ft + u, y = Gt + u; + v < hn; v ++, x += llen, y += llen) { + Fp[v] = *x; + Gp[v] = *y; + } + modp_NTT2(Fp, gm, logn - 1, p, p0i); + modp_NTT2(Gp, gm, logn - 1, p, p0i); + + /* + * Compute our F and G modulo p. + * + * General case: + * + * we divide degree by d = 2 or 3 + * f'(x^d) = N(f)(x^d) = f * adj(f) + * g'(x^d) = N(g)(x^d) = g * adj(g) + * f'*G' - g'*F' = q + * F = F'(x^d) * adj(g) + * G = G'(x^d) * adj(f) + * + * We compute things in the NTT. We group roots of phi + * such that all roots x in a group share the same x^d. + * If the roots in a group are x_1, x_2... x_d, then: + * + * N(f)(x_1^d) = f(x_1)*f(x_2)*...*f(x_d) + * + * Thus, we have: + * + * G(x_1) = f(x_2)*f(x_3)*...*f(x_d)*G'(x_1^d) + * G(x_2) = f(x_1)*f(x_3)*...*f(x_d)*G'(x_1^d) + * ... + * G(x_d) = f(x_1)*f(x_2)*...*f(x_{d-1})*G'(x_1^d) + * + * In all cases, we can thus compute F and G in NTT + * representation by a few simple multiplications. + * Moreover, in our chosen NTT representation, roots + * from the same group are consecutive in RAM. + */ + for (v = 0, x = Ft + u, y = Gt + u; v < hn; + v ++, x += (llen << 1), y += (llen << 1)) { + uint32_t ftA, ftB, gtA, gtB; + uint32_t mFp, mGp; + + ftA = fx[(v << 1) + 0]; + ftB = fx[(v << 1) + 1]; + gtA = gx[(v << 1) + 0]; + gtB = gx[(v << 1) + 1]; + mFp = modp_montymul(Fp[v], R2, p, p0i); + mGp = modp_montymul(Gp[v], R2, p, p0i); + x[0] = modp_montymul(gtB, mFp, p, p0i); + x[llen] = modp_montymul(gtA, mFp, p, p0i); + y[0] = modp_montymul(ftB, mGp, p, p0i); + y[llen] = modp_montymul(ftA, mGp, p, p0i); + } + modp_iNTT2_ext(Ft + u, llen, igm, logn, p, p0i); + modp_iNTT2_ext(Gt + u, llen, igm, logn, p, p0i); + } + + /* + * Rebuild F and G with the CRT. + */ + zint_rebuild_CRT(Ft, llen, llen, n, primes, 1, t1); + zint_rebuild_CRT(Gt, llen, llen, n, primes, 1, t1); + + /* + * At that point, Ft, Gt, ft and gt are consecutive in RAM (in that + * order). + */ + + /* + * Apply Babai reduction to bring back F and G to size slen. + * + * We use the FFT to compute successive approximations of the + * reduction coefficient. We first isolate the top bits of + * the coefficients of f and g, and convert them to floating + * point; with the FFT, we compute adj(f), adj(g), and + * 1/(f*adj(f)+g*adj(g)). + * + * Then, we repeatedly apply the following: + * + * - Get the top bits of the coefficients of F and G into + * floating point, and use the FFT to compute: + * (F*adj(f)+G*adj(g))/(f*adj(f)+g*adj(g)) + * + * - Convert back that value into normal representation, and + * round it to the nearest integers, yielding a polynomial k. + * Proper scaling is applied to f, g, F and G so that the + * coefficients fit on 32 bits (signed). + * + * - Subtract k*f from F and k*g from G. + * + * Under normal conditions, this process reduces the size of F + * and G by some bits at each iteration. For constant-time + * operation, we do not want to measure the actual length of + * F and G; instead, we do the following: + * + * - f and g are converted to floating-point, with some scaling + * if necessary to keep values in the representable range. + * + * - For each iteration, we _assume_ a maximum size for F and G, + * and use the values at that size. If we overreach, then + * we get zeros, which is harmless: the resulting coefficients + * of k will be 0 and the value won't be reduced. + * + * - We conservatively assume that F and G will be reduced by + * at least 25 bits at each iteration. + * + * Even when reaching the bottom of the reduction, reduction + * coefficient will remain low. If it goes out-of-range, then + * something wrong occurred and the whole NTRU solving fails. + */ + + /* + * Memory layout: + * - We need to compute and keep adj(f), adj(g), and + * 1/(f*adj(f)+g*adj(g)) (sizes N, N and N/2 fp numbers, + * respectively). + * - At each iteration we need two extra fp buffer (N fp values), + * and produce a k (N 32-bit words). k will be shared with one + * of the fp buffers. + * - To compute k*f and k*g efficiently (with the NTT), we need + * some extra room; we reuse the space of the temporary buffers. + * + * Arrays of 'fpr' are obtained from the temporary array itself. + * We ensure that the base is at a properly aligned offset (the + * source array tmp[] is supposed to be already aligned). + */ + + rt3 = align_fpr(tmp, t1); + rt4 = rt3 + n; + rt5 = rt4 + n; + rt1 = rt5 + (n >> 1); + k = (int32_t *)align_u32(tmp, rt1); + rt2 = align_fpr(tmp, k + n); + if (rt2 < (rt1 + n)) { + rt2 = rt1 + n; + } + t1 = (uint32_t *)k + n; + + /* + * Get f and g into rt3 and rt4 as floating-point approximations. + * + * We need to "scale down" the floating-point representation of + * coefficients when they are too big. We want to keep the value + * below 2^310 or so. Thus, when values are larger than 10 words, + * we consider only the top 10 words. Array lengths have been + * computed so that average maximum length will fall in the + * middle or the upper half of these top 10 words. + */ + rlen = slen; + if (rlen > 10) { + rlen = 10; + } + poly_big_to_fp(rt3, ft + slen - rlen, rlen, slen, logn); + poly_big_to_fp(rt4, gt + slen - rlen, rlen, slen, logn); + + /* + * Values in rt3 and rt4 are downscaled by 2^(scale_fg). + */ + scale_fg = 31 * (int)(slen - rlen); + + /* + * Estimated boundaries for the maximum size (in bits) of the + * coefficients of (f,g). We use the measured average, and + * allow for a deviation of at most six times the standard + * deviation. + */ + minbl_fg = BITLENGTH[depth].avg - 6 * BITLENGTH[depth].std; + maxbl_fg = BITLENGTH[depth].avg + 6 * BITLENGTH[depth].std; + + /* + * Compute 1/(f*adj(f)+g*adj(g)) in rt5. We also keep adj(f) + * and adj(g) in rt3 and rt4, respectively. + */ + PQCLEAN_FALCON512_CLEAN_FFT(rt3, logn); + PQCLEAN_FALCON512_CLEAN_FFT(rt4, logn); + PQCLEAN_FALCON512_CLEAN_poly_invnorm2_fft(rt5, rt3, rt4, logn); + PQCLEAN_FALCON512_CLEAN_poly_adj_fft(rt3, logn); + PQCLEAN_FALCON512_CLEAN_poly_adj_fft(rt4, logn); + + /* + * Reduce F and G repeatedly. + * + * The expected maximum bit length of coefficients of F and G + * is kept in maxbl_FG, with the corresponding word length in + * FGlen. + */ + FGlen = llen; + maxbl_FG = 31 * (int)llen; + + /* + * Each reduction operation computes the reduction polynomial + * "k". We need that polynomial to have coefficients that fit + * on 32-bit signed integers, with some scaling; thus, we use + * a descending sequence of scaling values, down to zero. + * + * The size of the coefficients of k is (roughly) the difference + * between the size of the coefficients of (F,G) and the size + * of the coefficients of (f,g). Thus, the maximum size of the + * coefficients of k is, at the start, maxbl_FG - minbl_fg; + * this is our starting scale value for k. + * + * We need to estimate the size of (F,G) during the execution of + * the algorithm; we are allowed some overestimation but not too + * much (poly_big_to_fp() uses a 310-bit window). Generally + * speaking, after applying a reduction with k scaled to + * scale_k, the size of (F,G) will be size(f,g) + scale_k + dd, + * where 'dd' is a few bits to account for the fact that the + * reduction is never perfect (intuitively, dd is on the order + * of sqrt(N), so at most 5 bits; we here allow for 10 extra + * bits). + * + * The size of (f,g) is not known exactly, but maxbl_fg is an + * upper bound. + */ + scale_k = maxbl_FG - minbl_fg; + + for (;;) { + int scale_FG, dc, new_maxbl_FG; + uint32_t scl, sch; + fpr pdc, pt; + + /* + * Convert current F and G into floating-point. We apply + * scaling if the current length is more than 10 words. + */ + rlen = FGlen; + if (rlen > 10) { + rlen = 10; + } + scale_FG = 31 * (int)(FGlen - rlen); + poly_big_to_fp(rt1, Ft + FGlen - rlen, rlen, llen, logn); + poly_big_to_fp(rt2, Gt + FGlen - rlen, rlen, llen, logn); + + /* + * Compute (F*adj(f)+G*adj(g))/(f*adj(f)+g*adj(g)) in rt2. + */ + PQCLEAN_FALCON512_CLEAN_FFT(rt1, logn); + PQCLEAN_FALCON512_CLEAN_FFT(rt2, logn); + PQCLEAN_FALCON512_CLEAN_poly_mul_fft(rt1, rt3, logn); + PQCLEAN_FALCON512_CLEAN_poly_mul_fft(rt2, rt4, logn); + PQCLEAN_FALCON512_CLEAN_poly_add(rt2, rt1, logn); + PQCLEAN_FALCON512_CLEAN_poly_mul_autoadj_fft(rt2, rt5, logn); + PQCLEAN_FALCON512_CLEAN_iFFT(rt2, logn); + + /* + * (f,g) are scaled by 'scale_fg', meaning that the + * numbers in rt3/rt4 should be multiplied by 2^(scale_fg) + * to have their true mathematical value. + * + * (F,G) are similarly scaled by 'scale_FG'. Therefore, + * the value we computed in rt2 is scaled by + * 'scale_FG-scale_fg'. + * + * We want that value to be scaled by 'scale_k', hence we + * apply a corrective scaling. After scaling, the values + * should fit in -2^31-1..+2^31-1. + */ + dc = scale_k - scale_FG + scale_fg; + + /* + * We will need to multiply values by 2^(-dc). The value + * 'dc' is not secret, so we can compute 2^(-dc) with a + * non-constant-time process. + * (We could use ldexp(), but we prefer to avoid any + * dependency on libm. When using FP emulation, we could + * use our fpr_ldexp(), which is constant-time.) + */ + if (dc < 0) { + dc = -dc; + pt = fpr_two; + } else { + pt = fpr_onehalf; + } + pdc = fpr_one; + while (dc != 0) { + if ((dc & 1) != 0) { + pdc = fpr_mul(pdc, pt); + } + dc >>= 1; + pt = fpr_sqr(pt); + } + + for (u = 0; u < n; u ++) { + fpr xv; + + xv = fpr_mul(rt2[u], pdc); + + /* + * Sometimes the values can be out-of-bounds if + * the algorithm fails; we must not call + * fpr_rint() (and cast to int32_t) if the value + * is not in-bounds. Note that the test does not + * break constant-time discipline, since any + * failure here implies that we discard the current + * secret key (f,g). + */ + if (!fpr_lt(fpr_mtwo31m1, xv) + || !fpr_lt(xv, fpr_ptwo31m1)) { + return 0; + } + k[u] = (int32_t)fpr_rint(xv); + } + + /* + * Values in k[] are integers. They really are scaled + * down by maxbl_FG - minbl_fg bits. + * + * If we are at low depth, then we use the NTT to + * compute k*f and k*g. + */ + sch = (uint32_t)(scale_k / 31); + scl = (uint32_t)(scale_k % 31); + if (depth <= DEPTH_INT_FG) { + poly_sub_scaled_ntt(Ft, FGlen, llen, ft, slen, slen, + k, sch, scl, logn, t1); + poly_sub_scaled_ntt(Gt, FGlen, llen, gt, slen, slen, + k, sch, scl, logn, t1); + } else { + poly_sub_scaled(Ft, FGlen, llen, ft, slen, slen, + k, sch, scl, logn); + poly_sub_scaled(Gt, FGlen, llen, gt, slen, slen, + k, sch, scl, logn); + } + + /* + * We compute the new maximum size of (F,G), assuming that + * (f,g) has _maximal_ length (i.e. that reduction is + * "late" instead of "early". We also adjust FGlen + * accordingly. + */ + new_maxbl_FG = scale_k + maxbl_fg + 10; + if (new_maxbl_FG < maxbl_FG) { + maxbl_FG = new_maxbl_FG; + if ((int)FGlen * 31 >= maxbl_FG + 31) { + FGlen --; + } + } + + /* + * We suppose that scaling down achieves a reduction by + * at least 25 bits per iteration. We stop when we have + * done the loop with an unscaled k. + */ + if (scale_k <= 0) { + break; + } + scale_k -= 25; + if (scale_k < 0) { + scale_k = 0; + } + } + + /* + * If (F,G) length was lowered below 'slen', then we must take + * care to re-extend the sign. + */ + if (FGlen < slen) { + for (u = 0; u < n; u ++, Ft += llen, Gt += llen) { + size_t v; + uint32_t sw; + + sw = -(Ft[FGlen - 1] >> 30) >> 1; + for (v = FGlen; v < slen; v ++) { + Ft[v] = sw; + } + sw = -(Gt[FGlen - 1] >> 30) >> 1; + for (v = FGlen; v < slen; v ++) { + Gt[v] = sw; + } + } + } + + /* + * Compress encoding of all values to 'slen' words (this is the + * expected output format). + */ + for (u = 0, x = tmp, y = tmp; + u < (n << 1); u ++, x += slen, y += llen) { + memmove(x, y, slen * sizeof * y); + } + return 1; +} + +/* + * Solving the NTRU equation, binary case, depth = 1. Upon entry, the + * F and G from the previous level should be in the tmp[] array. + * + * Returned value: 1 on success, 0 on error. + */ +static int +solve_NTRU_binary_depth1(unsigned logn_top, + const int8_t *f, const int8_t *g, uint32_t *tmp) { + /* + * The first half of this function is a copy of the corresponding + * part in solve_NTRU_intermediate(), for the reconstruction of + * the unreduced F and G. The second half (Babai reduction) is + * done differently, because the unreduced F and G fit in 53 bits + * of precision, allowing a much simpler process with lower RAM + * usage. + */ + unsigned depth, logn; + size_t n_top, n, hn, slen, dlen, llen, u; + uint32_t *Fd, *Gd, *Ft, *Gt, *ft, *gt, *t1; + fpr *rt1, *rt2, *rt3, *rt4, *rt5, *rt6; + uint32_t *x, *y; + + depth = 1; + n_top = (size_t)1 << logn_top; + logn = logn_top - depth; + n = (size_t)1 << logn; + hn = n >> 1; + + /* + * Equations are: + * + * f' = f0^2 - X^2*f1^2 + * g' = g0^2 - X^2*g1^2 + * F' and G' are a solution to f'G' - g'F' = q (from deeper levels) + * F = F'*(g0 - X*g1) + * G = G'*(f0 - X*f1) + * + * f0, f1, g0, g1, f', g', F' and G' are all "compressed" to + * degree N/2 (their odd-indexed coefficients are all zero). + */ + + /* + * slen = size for our input f and g; also size of the reduced + * F and G we return (degree N) + * + * dlen = size of the F and G obtained from the deeper level + * (degree N/2) + * + * llen = size for intermediary F and G before reduction (degree N) + * + * We build our non-reduced F and G as two independent halves each, + * of degree N/2 (F = F0 + X*F1, G = G0 + X*G1). + */ + slen = MAX_BL_SMALL[depth]; + dlen = MAX_BL_SMALL[depth + 1]; + llen = MAX_BL_LARGE[depth]; + + /* + * Fd and Gd are the F and G from the deeper level. Ft and Gt + * are the destination arrays for the unreduced F and G. + */ + Fd = tmp; + Gd = Fd + dlen * hn; + Ft = Gd + dlen * hn; + Gt = Ft + llen * n; + + /* + * We reduce Fd and Gd modulo all the small primes we will need, + * and store the values in Ft and Gt. + */ + for (u = 0; u < llen; u ++) { + uint32_t p, p0i, R2, Rx; + size_t v; + uint32_t *xs, *ys, *xd, *yd; + + p = PRIMES[u].p; + p0i = modp_ninv31(p); + R2 = modp_R2(p, p0i); + Rx = modp_Rx((unsigned)dlen, p, p0i, R2); + for (v = 0, xs = Fd, ys = Gd, xd = Ft + u, yd = Gt + u; + v < hn; + v ++, xs += dlen, ys += dlen, xd += llen, yd += llen) { + *xd = zint_mod_small_signed(xs, dlen, p, p0i, R2, Rx); + *yd = zint_mod_small_signed(ys, dlen, p, p0i, R2, Rx); + } + } + + /* + * Now Fd and Gd are not needed anymore; we can squeeze them out. + */ + memmove(tmp, Ft, llen * n * sizeof(uint32_t)); + Ft = tmp; + memmove(Ft + llen * n, Gt, llen * n * sizeof(uint32_t)); + Gt = Ft + llen * n; + ft = Gt + llen * n; + gt = ft + slen * n; + + t1 = gt + slen * n; + + /* + * Compute our F and G modulo sufficiently many small primes. + */ + for (u = 0; u < llen; u ++) { + uint32_t p, p0i, R2; + uint32_t *gm, *igm, *fx, *gx, *Fp, *Gp; + unsigned e; + size_t v; + + /* + * All computations are done modulo p. + */ + p = PRIMES[u].p; + p0i = modp_ninv31(p); + R2 = modp_R2(p, p0i); + + /* + * We recompute things from the source f and g, of full + * degree. However, we will need only the n first elements + * of the inverse NTT table (igm); the call to modp_mkgm() + * below will fill n_top elements in igm[] (thus overflowing + * into fx[]) but later code will overwrite these extra + * elements. + */ + gm = t1; + igm = gm + n_top; + fx = igm + n; + gx = fx + n_top; + modp_mkgm2(gm, igm, logn_top, PRIMES[u].g, p, p0i); + + /* + * Set ft and gt to f and g modulo p, respectively. + */ + for (v = 0; v < n_top; v ++) { + fx[v] = modp_set(f[v], p); + gx[v] = modp_set(g[v], p); + } + + /* + * Convert to NTT and compute our f and g. + */ + modp_NTT2(fx, gm, logn_top, p, p0i); + modp_NTT2(gx, gm, logn_top, p, p0i); + for (e = logn_top; e > logn; e --) { + modp_poly_rec_res(fx, e, p, p0i, R2); + modp_poly_rec_res(gx, e, p, p0i, R2); + } + + /* + * From that point onward, we only need tables for + * degree n, so we can save some space. + */ + if (depth > 0) { /* always true */ + memmove(gm + n, igm, n * sizeof * igm); + igm = gm + n; + memmove(igm + n, fx, n * sizeof * ft); + fx = igm + n; + memmove(fx + n, gx, n * sizeof * gt); + gx = fx + n; + } + + /* + * Get F' and G' modulo p and in NTT representation + * (they have degree n/2). These values were computed + * in a previous step, and stored in Ft and Gt. + */ + Fp = gx + n; + Gp = Fp + hn; + for (v = 0, x = Ft + u, y = Gt + u; + v < hn; v ++, x += llen, y += llen) { + Fp[v] = *x; + Gp[v] = *y; + } + modp_NTT2(Fp, gm, logn - 1, p, p0i); + modp_NTT2(Gp, gm, logn - 1, p, p0i); + + /* + * Compute our F and G modulo p. + * + * Equations are: + * + * f'(x^2) = N(f)(x^2) = f * adj(f) + * g'(x^2) = N(g)(x^2) = g * adj(g) + * + * f'*G' - g'*F' = q + * + * F = F'(x^2) * adj(g) + * G = G'(x^2) * adj(f) + * + * The NTT representation of f is f(w) for all w which + * are roots of phi. In the binary case, as well as in + * the ternary case for all depth except the deepest, + * these roots can be grouped in pairs (w,-w), and we + * then have: + * + * f(w) = adj(f)(-w) + * f(-w) = adj(f)(w) + * + * and w^2 is then a root for phi at the half-degree. + * + * At the deepest level in the ternary case, this still + * holds, in the following sense: the roots of x^2-x+1 + * are (w,-w^2) (for w^3 = -1, and w != -1), and we + * have: + * + * f(w) = adj(f)(-w^2) + * f(-w^2) = adj(f)(w) + * + * In all case, we can thus compute F and G in NTT + * representation by a few simple multiplications. + * Moreover, the two roots for each pair are consecutive + * in our bit-reversal encoding. + */ + for (v = 0, x = Ft + u, y = Gt + u; + v < hn; v ++, x += (llen << 1), y += (llen << 1)) { + uint32_t ftA, ftB, gtA, gtB; + uint32_t mFp, mGp; + + ftA = fx[(v << 1) + 0]; + ftB = fx[(v << 1) + 1]; + gtA = gx[(v << 1) + 0]; + gtB = gx[(v << 1) + 1]; + mFp = modp_montymul(Fp[v], R2, p, p0i); + mGp = modp_montymul(Gp[v], R2, p, p0i); + x[0] = modp_montymul(gtB, mFp, p, p0i); + x[llen] = modp_montymul(gtA, mFp, p, p0i); + y[0] = modp_montymul(ftB, mGp, p, p0i); + y[llen] = modp_montymul(ftA, mGp, p, p0i); + } + modp_iNTT2_ext(Ft + u, llen, igm, logn, p, p0i); + modp_iNTT2_ext(Gt + u, llen, igm, logn, p, p0i); + + /* + * Also save ft and gt (only up to size slen). + */ + if (u < slen) { + modp_iNTT2(fx, igm, logn, p, p0i); + modp_iNTT2(gx, igm, logn, p, p0i); + for (v = 0, x = ft + u, y = gt + u; + v < n; v ++, x += slen, y += slen) { + *x = fx[v]; + *y = gx[v]; + } + } + } + + /* + * Rebuild f, g, F and G with the CRT. Note that the elements of F + * and G are consecutive, and thus can be rebuilt in a single + * loop; similarly, the elements of f and g are consecutive. + */ + zint_rebuild_CRT(Ft, llen, llen, n << 1, PRIMES, 1, t1); + zint_rebuild_CRT(ft, slen, slen, n << 1, PRIMES, 1, t1); + + /* + * Here starts the Babai reduction, specialized for depth = 1. + * + * Candidates F and G (from Ft and Gt), and base f and g (ft and gt), + * are converted to floating point. There is no scaling, and a + * single pass is sufficient. + */ + + /* + * Convert F and G into floating point (rt1 and rt2). + */ + rt1 = align_fpr(tmp, gt + slen * n); + rt2 = rt1 + n; + poly_big_to_fp(rt1, Ft, llen, llen, logn); + poly_big_to_fp(rt2, Gt, llen, llen, logn); + + /* + * Integer representation of F and G is no longer needed, we + * can remove it. + */ + memmove(tmp, ft, 2 * slen * n * sizeof * ft); + ft = tmp; + gt = ft + slen * n; + rt3 = align_fpr(tmp, gt + slen * n); + memmove(rt3, rt1, 2 * n * sizeof * rt1); + rt1 = rt3; + rt2 = rt1 + n; + rt3 = rt2 + n; + rt4 = rt3 + n; + + /* + * Convert f and g into floating point (rt3 and rt4). + */ + poly_big_to_fp(rt3, ft, slen, slen, logn); + poly_big_to_fp(rt4, gt, slen, slen, logn); + + /* + * Remove unneeded ft and gt. + */ + memmove(tmp, rt1, 4 * n * sizeof * rt1); + rt1 = (fpr *)tmp; + rt2 = rt1 + n; + rt3 = rt2 + n; + rt4 = rt3 + n; + + /* + * We now have: + * rt1 = F + * rt2 = G + * rt3 = f + * rt4 = g + * in that order in RAM. We convert all of them to FFT. + */ + PQCLEAN_FALCON512_CLEAN_FFT(rt1, logn); + PQCLEAN_FALCON512_CLEAN_FFT(rt2, logn); + PQCLEAN_FALCON512_CLEAN_FFT(rt3, logn); + PQCLEAN_FALCON512_CLEAN_FFT(rt4, logn); + + /* + * Compute: + * rt5 = F*adj(f) + G*adj(g) + * rt6 = 1 / (f*adj(f) + g*adj(g)) + * (Note that rt6 is half-length.) + */ + rt5 = rt4 + n; + rt6 = rt5 + n; + PQCLEAN_FALCON512_CLEAN_poly_add_muladj_fft(rt5, rt1, rt2, rt3, rt4, logn); + PQCLEAN_FALCON512_CLEAN_poly_invnorm2_fft(rt6, rt3, rt4, logn); + + /* + * Compute: + * rt5 = (F*adj(f)+G*adj(g)) / (f*adj(f)+g*adj(g)) + */ + PQCLEAN_FALCON512_CLEAN_poly_mul_autoadj_fft(rt5, rt6, logn); + + /* + * Compute k as the rounded version of rt5. Check that none of + * the values is larger than 2^63-1 (in absolute value) + * because that would make the fpr_rint() do something undefined; + * note that any out-of-bounds value here implies a failure and + * (f,g) will be discarded, so we can make a simple test. + */ + PQCLEAN_FALCON512_CLEAN_iFFT(rt5, logn); + for (u = 0; u < n; u ++) { + fpr z; + + z = rt5[u]; + if (!fpr_lt(z, fpr_ptwo63m1) || !fpr_lt(fpr_mtwo63m1, z)) { + return 0; + } + rt5[u] = fpr_of(fpr_rint(z)); + } + PQCLEAN_FALCON512_CLEAN_FFT(rt5, logn); + + /* + * Subtract k*f from F, and k*g from G. + */ + PQCLEAN_FALCON512_CLEAN_poly_mul_fft(rt3, rt5, logn); + PQCLEAN_FALCON512_CLEAN_poly_mul_fft(rt4, rt5, logn); + PQCLEAN_FALCON512_CLEAN_poly_sub(rt1, rt3, logn); + PQCLEAN_FALCON512_CLEAN_poly_sub(rt2, rt4, logn); + PQCLEAN_FALCON512_CLEAN_iFFT(rt1, logn); + PQCLEAN_FALCON512_CLEAN_iFFT(rt2, logn); + + /* + * Convert back F and G to integers, and return. + */ + Ft = tmp; + Gt = Ft + n; + rt3 = align_fpr(tmp, Gt + n); + memmove(rt3, rt1, 2 * n * sizeof * rt1); + rt1 = rt3; + rt2 = rt1 + n; + for (u = 0; u < n; u ++) { + Ft[u] = (uint32_t)fpr_rint(rt1[u]); + Gt[u] = (uint32_t)fpr_rint(rt2[u]); + } + + return 1; +} + +/* + * Solving the NTRU equation, top level. Upon entry, the F and G + * from the previous level should be in the tmp[] array. + * + * Returned value: 1 on success, 0 on error. + */ +static int +solve_NTRU_binary_depth0(unsigned logn, + const int8_t *f, const int8_t *g, uint32_t *tmp) { + size_t n, hn, u; + uint32_t p, p0i, R2; + uint32_t *Fp, *Gp, *t1, *t2, *t3, *t4, *t5; + uint32_t *gm, *igm, *ft, *gt; + fpr *rt2, *rt3; + + n = (size_t)1 << logn; + hn = n >> 1; + + /* + * Equations are: + * + * f' = f0^2 - X^2*f1^2 + * g' = g0^2 - X^2*g1^2 + * F' and G' are a solution to f'G' - g'F' = q (from deeper levels) + * F = F'*(g0 - X*g1) + * G = G'*(f0 - X*f1) + * + * f0, f1, g0, g1, f', g', F' and G' are all "compressed" to + * degree N/2 (their odd-indexed coefficients are all zero). + * + * Everything should fit in 31-bit integers, hence we can just use + * the first small prime p = 2147473409. + */ + p = PRIMES[0].p; + p0i = modp_ninv31(p); + R2 = modp_R2(p, p0i); + + Fp = tmp; + Gp = Fp + hn; + ft = Gp + hn; + gt = ft + n; + gm = gt + n; + igm = gm + n; + + modp_mkgm2(gm, igm, logn, PRIMES[0].g, p, p0i); + + /* + * Convert F' anf G' in NTT representation. + */ + for (u = 0; u < hn; u ++) { + Fp[u] = modp_set(zint_one_to_plain(Fp + u), p); + Gp[u] = modp_set(zint_one_to_plain(Gp + u), p); + } + modp_NTT2(Fp, gm, logn - 1, p, p0i); + modp_NTT2(Gp, gm, logn - 1, p, p0i); + + /* + * Load f and g and convert them to NTT representation. + */ + for (u = 0; u < n; u ++) { + ft[u] = modp_set(f[u], p); + gt[u] = modp_set(g[u], p); + } + modp_NTT2(ft, gm, logn, p, p0i); + modp_NTT2(gt, gm, logn, p, p0i); + + /* + * Build the unreduced F,G in ft and gt. + */ + for (u = 0; u < n; u += 2) { + uint32_t ftA, ftB, gtA, gtB; + uint32_t mFp, mGp; + + ftA = ft[u + 0]; + ftB = ft[u + 1]; + gtA = gt[u + 0]; + gtB = gt[u + 1]; + mFp = modp_montymul(Fp[u >> 1], R2, p, p0i); + mGp = modp_montymul(Gp[u >> 1], R2, p, p0i); + ft[u + 0] = modp_montymul(gtB, mFp, p, p0i); + ft[u + 1] = modp_montymul(gtA, mFp, p, p0i); + gt[u + 0] = modp_montymul(ftB, mGp, p, p0i); + gt[u + 1] = modp_montymul(ftA, mGp, p, p0i); + } + modp_iNTT2(ft, igm, logn, p, p0i); + modp_iNTT2(gt, igm, logn, p, p0i); + + Gp = Fp + n; + t1 = Gp + n; + memmove(Fp, ft, 2 * n * sizeof * ft); + + /* + * We now need to apply the Babai reduction. At that point, + * we have F and G in two n-word arrays. + * + * We can compute F*adj(f)+G*adj(g) and f*adj(f)+g*adj(g) + * modulo p, using the NTT. We still move memory around in + * order to save RAM. + */ + t2 = t1 + n; + t3 = t2 + n; + t4 = t3 + n; + t5 = t4 + n; + + /* + * Compute the NTT tables in t1 and t2. We do not keep t2 + * (we'll recompute it later on). + */ + modp_mkgm2(t1, t2, logn, PRIMES[0].g, p, p0i); + + /* + * Convert F and G to NTT. + */ + modp_NTT2(Fp, t1, logn, p, p0i); + modp_NTT2(Gp, t1, logn, p, p0i); + + /* + * Load f and adj(f) in t4 and t5, and convert them to NTT + * representation. + */ + t4[0] = t5[0] = modp_set(f[0], p); + for (u = 1; u < n; u ++) { + t4[u] = modp_set(f[u], p); + t5[n - u] = modp_set(-f[u], p); + } + modp_NTT2(t4, t1, logn, p, p0i); + modp_NTT2(t5, t1, logn, p, p0i); + + /* + * Compute F*adj(f) in t2, and f*adj(f) in t3. + */ + for (u = 0; u < n; u ++) { + uint32_t w; + + w = modp_montymul(t5[u], R2, p, p0i); + t2[u] = modp_montymul(w, Fp[u], p, p0i); + t3[u] = modp_montymul(w, t4[u], p, p0i); + } + + /* + * Load g and adj(g) in t4 and t5, and convert them to NTT + * representation. + */ + t4[0] = t5[0] = modp_set(g[0], p); + for (u = 1; u < n; u ++) { + t4[u] = modp_set(g[u], p); + t5[n - u] = modp_set(-g[u], p); + } + modp_NTT2(t4, t1, logn, p, p0i); + modp_NTT2(t5, t1, logn, p, p0i); + + /* + * Add G*adj(g) to t2, and g*adj(g) to t3. + */ + for (u = 0; u < n; u ++) { + uint32_t w; + + w = modp_montymul(t5[u], R2, p, p0i); + t2[u] = modp_add(t2[u], + modp_montymul(w, Gp[u], p, p0i), p); + t3[u] = modp_add(t3[u], + modp_montymul(w, t4[u], p, p0i), p); + } + + /* + * Convert back t2 and t3 to normal representation (normalized + * around 0), and then + * move them to t1 and t2. We first need to recompute the + * inverse table for NTT. + */ + modp_mkgm2(t1, t4, logn, PRIMES[0].g, p, p0i); + modp_iNTT2(t2, t4, logn, p, p0i); + modp_iNTT2(t3, t4, logn, p, p0i); + for (u = 0; u < n; u ++) { + t1[u] = (uint32_t)modp_norm(t2[u], p); + t2[u] = (uint32_t)modp_norm(t3[u], p); + } + + /* + * At that point, array contents are: + * + * F (NTT representation) (Fp) + * G (NTT representation) (Gp) + * F*adj(f)+G*adj(g) (t1) + * f*adj(f)+g*adj(g) (t2) + * + * We want to divide t1 by t2. The result is not integral; it + * must be rounded. We thus need to use the FFT. + */ + + /* + * Get f*adj(f)+g*adj(g) in FFT representation. Since this + * polynomial is auto-adjoint, all its coordinates in FFT + * representation are actually real, so we can truncate off + * the imaginary parts. + */ + rt3 = align_fpr(tmp, t3); + for (u = 0; u < n; u ++) { + rt3[u] = fpr_of(((int32_t *)t2)[u]); + } + PQCLEAN_FALCON512_CLEAN_FFT(rt3, logn); + rt2 = align_fpr(tmp, t2); + memmove(rt2, rt3, hn * sizeof * rt3); + + /* + * Convert F*adj(f)+G*adj(g) in FFT representation. + */ + rt3 = rt2 + hn; + for (u = 0; u < n; u ++) { + rt3[u] = fpr_of(((int32_t *)t1)[u]); + } + PQCLEAN_FALCON512_CLEAN_FFT(rt3, logn); + + /* + * Compute (F*adj(f)+G*adj(g))/(f*adj(f)+g*adj(g)) and get + * its rounded normal representation in t1. + */ + PQCLEAN_FALCON512_CLEAN_poly_div_autoadj_fft(rt3, rt2, logn); + PQCLEAN_FALCON512_CLEAN_iFFT(rt3, logn); + for (u = 0; u < n; u ++) { + t1[u] = modp_set((int32_t)fpr_rint(rt3[u]), p); + } + + /* + * RAM contents are now: + * + * F (NTT representation) (Fp) + * G (NTT representation) (Gp) + * k (t1) + * + * We want to compute F-k*f, and G-k*g. + */ + t2 = t1 + n; + t3 = t2 + n; + t4 = t3 + n; + t5 = t4 + n; + modp_mkgm2(t2, t3, logn, PRIMES[0].g, p, p0i); + for (u = 0; u < n; u ++) { + t4[u] = modp_set(f[u], p); + t5[u] = modp_set(g[u], p); + } + modp_NTT2(t1, t2, logn, p, p0i); + modp_NTT2(t4, t2, logn, p, p0i); + modp_NTT2(t5, t2, logn, p, p0i); + for (u = 0; u < n; u ++) { + uint32_t kw; + + kw = modp_montymul(t1[u], R2, p, p0i); + Fp[u] = modp_sub(Fp[u], + modp_montymul(kw, t4[u], p, p0i), p); + Gp[u] = modp_sub(Gp[u], + modp_montymul(kw, t5[u], p, p0i), p); + } + modp_iNTT2(Fp, t3, logn, p, p0i); + modp_iNTT2(Gp, t3, logn, p, p0i); + for (u = 0; u < n; u ++) { + Fp[u] = (uint32_t)modp_norm(Fp[u], p); + Gp[u] = (uint32_t)modp_norm(Gp[u], p); + } + + return 1; +} + +/* + * Solve the NTRU equation. Returned value is 1 on success, 0 on error. + * G can be NULL, in which case that value is computed but not returned. + * If any of the coefficients of F and G exceeds lim (in absolute value), + * then 0 is returned. + */ +static int +solve_NTRU(unsigned logn, int8_t *F, int8_t *G, + const int8_t *f, const int8_t *g, int lim, uint32_t *tmp) { + size_t n, u; + uint32_t *ft, *gt, *Ft, *Gt, *gm; + uint32_t p, p0i, r; + const small_prime *primes; + + n = MKN(logn); + + if (!solve_NTRU_deepest(logn, f, g, tmp)) { + return 0; + } + + /* + * For logn <= 2, we need to use solve_NTRU_intermediate() + * directly, because coefficients are a bit too large and + * do not fit the hypotheses in solve_NTRU_binary_depth0(). + */ + if (logn <= 2) { + unsigned depth; + + depth = logn; + while (depth -- > 0) { + if (!solve_NTRU_intermediate(logn, f, g, depth, tmp)) { + return 0; + } + } + } else { + unsigned depth; + + depth = logn; + while (depth -- > 2) { + if (!solve_NTRU_intermediate(logn, f, g, depth, tmp)) { + return 0; + } + } + if (!solve_NTRU_binary_depth1(logn, f, g, tmp)) { + return 0; + } + if (!solve_NTRU_binary_depth0(logn, f, g, tmp)) { + return 0; + } + } + + /* + * If no buffer has been provided for G, use a temporary one. + */ + if (G == NULL) { + G = (int8_t *)(tmp + 2 * n); + } + + /* + * Final F and G are in fk->tmp, one word per coefficient + * (signed value over 31 bits). + */ + if (!poly_big_to_small(F, tmp, lim, logn) + || !poly_big_to_small(G, tmp + n, lim, logn)) { + return 0; + } + + /* + * Verify that the NTRU equation is fulfilled. Since all elements + * have short lengths, verifying modulo a small prime p works, and + * allows using the NTT. + * + * We put Gt[] first in tmp[], and process it first, so that it does + * not overlap with G[] in case we allocated it ourselves. + */ + Gt = tmp; + ft = Gt + n; + gt = ft + n; + Ft = gt + n; + gm = Ft + n; + + primes = PRIMES; + p = primes[0].p; + p0i = modp_ninv31(p); + modp_mkgm2(gm, tmp, logn, primes[0].g, p, p0i); + for (u = 0; u < n; u ++) { + Gt[u] = modp_set(G[u], p); + } + for (u = 0; u < n; u ++) { + ft[u] = modp_set(f[u], p); + gt[u] = modp_set(g[u], p); + Ft[u] = modp_set(F[u], p); + } + modp_NTT2(ft, gm, logn, p, p0i); + modp_NTT2(gt, gm, logn, p, p0i); + modp_NTT2(Ft, gm, logn, p, p0i); + modp_NTT2(Gt, gm, logn, p, p0i); + r = modp_montymul(12289, 1, p, p0i); + for (u = 0; u < n; u ++) { + uint32_t z; + + z = modp_sub(modp_montymul(ft[u], Gt[u], p, p0i), + modp_montymul(gt[u], Ft[u], p, p0i), p); + if (z != r) { + return 0; + } + } + + return 1; +} + +/* + * Generate a random polynomial with a Gaussian distribution. This function + * also makes sure that the resultant of the polynomial with phi is odd. + */ +static void +poly_small_mkgauss(RNG_CONTEXT *rng, int8_t *f, unsigned logn) { + size_t n, u; + unsigned mod2; + + n = MKN(logn); + mod2 = 0; + for (u = 0; u < n; u ++) { + int s; + +restart: + s = mkgauss(rng, logn); + + /* + * We need the coefficient to fit within -127..+127; + * realistically, this is always the case except for + * the very low degrees (N = 2 or 4), for which there + * is no real security anyway. + */ + if (s < -127 || s > 127) { + goto restart; + } + + /* + * We need the sum of all coefficients to be 1; otherwise, + * the resultant of the polynomial with X^N+1 will be even, + * and the binary GCD will fail. + */ + if (u == n - 1) { + if ((mod2 ^ (unsigned)(s & 1)) == 0) { + goto restart; + } + } else { + mod2 ^= (unsigned)(s & 1); + } + f[u] = (int8_t)s; + } +} + +/* see falcon.h */ +void +PQCLEAN_FALCON512_CLEAN_keygen(inner_shake256_context *rng, + int8_t *f, int8_t *g, int8_t *F, int8_t *G, uint16_t *h, + unsigned logn, uint8_t *tmp) { + /* + * Algorithm is the following: + * + * - Generate f and g with the Gaussian distribution. + * + * - If either Res(f,phi) or Res(g,phi) is even, try again. + * + * - If ||(f,g)|| is too large, try again. + * + * - If ||B~_{f,g}|| is too large, try again. + * + * - If f is not invertible mod phi mod q, try again. + * + * - Compute h = g/f mod phi mod q. + * + * - Solve the NTRU equation fG - gF = q; if the solving fails, + * try again. Usual failure condition is when Res(f,phi) + * and Res(g,phi) are not prime to each other. + */ + size_t n, u; + uint16_t *h2, *tmp2; + RNG_CONTEXT *rc; + + n = MKN(logn); + rc = rng; + + /* + * We need to generate f and g randomly, until we find values + * such that the norm of (g,-f), and of the orthogonalized + * vector, are satisfying. The orthogonalized vector is: + * (q*adj(f)/(f*adj(f)+g*adj(g)), q*adj(g)/(f*adj(f)+g*adj(g))) + * (it is actually the (N+1)-th row of the Gram-Schmidt basis). + * + * In the binary case, coefficients of f and g are generated + * independently of each other, with a discrete Gaussian + * distribution of standard deviation 1.17*sqrt(q/(2*N)). Then, + * the two vectors have expected norm 1.17*sqrt(q), which is + * also our acceptance bound: we require both vectors to be no + * larger than that (this will be satisfied about 1/4th of the + * time, thus we expect sampling new (f,g) about 4 times for that + * step). + * + * We require that Res(f,phi) and Res(g,phi) are both odd (the + * NTRU equation solver requires it). + */ + for (;;) { + fpr *rt1, *rt2, *rt3; + fpr bnorm; + uint32_t normf, normg, norm; + int lim; + + /* + * The poly_small_mkgauss() function makes sure + * that the sum of coefficients is 1 modulo 2 + * (i.e. the resultant of the polynomial with phi + * will be odd). + */ + poly_small_mkgauss(rc, f, logn); + poly_small_mkgauss(rc, g, logn); + + /* + * Verify that all coefficients are within the bounds + * defined in max_fg_bits. This is the case with + * overwhelming probability; this guarantees that the + * key will be encodable with FALCON_COMP_TRIM. + */ + lim = 1 << (PQCLEAN_FALCON512_CLEAN_max_fg_bits[logn] - 1); + for (u = 0; u < n; u ++) { + /* + * We can use non-CT tests since on any failure + * we will discard f and g. + */ + if (f[u] >= lim || f[u] <= -lim + || g[u] >= lim || g[u] <= -lim) { + lim = -1; + break; + } + } + if (lim < 0) { + continue; + } + + /* + * Bound is 1.17*sqrt(q). We compute the squared + * norms. With q = 12289, the squared bound is: + * (1.17^2)* 12289 = 16822.4121 + * Since f and g are integral, the squared norm + * of (g,-f) is an integer. + */ + normf = poly_small_sqnorm(f, logn); + normg = poly_small_sqnorm(g, logn); + norm = (normf + normg) | -((normf | normg) >> 31); + if (norm >= 16823) { + continue; + } + + /* + * We compute the orthogonalized vector norm. + */ + rt1 = (fpr *)tmp; + rt2 = rt1 + n; + rt3 = rt2 + n; + poly_small_to_fp(rt1, f, logn); + poly_small_to_fp(rt2, g, logn); + PQCLEAN_FALCON512_CLEAN_FFT(rt1, logn); + PQCLEAN_FALCON512_CLEAN_FFT(rt2, logn); + PQCLEAN_FALCON512_CLEAN_poly_invnorm2_fft(rt3, rt1, rt2, logn); + PQCLEAN_FALCON512_CLEAN_poly_adj_fft(rt1, logn); + PQCLEAN_FALCON512_CLEAN_poly_adj_fft(rt2, logn); + PQCLEAN_FALCON512_CLEAN_poly_mulconst(rt1, fpr_q, logn); + PQCLEAN_FALCON512_CLEAN_poly_mulconst(rt2, fpr_q, logn); + PQCLEAN_FALCON512_CLEAN_poly_mul_autoadj_fft(rt1, rt3, logn); + PQCLEAN_FALCON512_CLEAN_poly_mul_autoadj_fft(rt2, rt3, logn); + PQCLEAN_FALCON512_CLEAN_iFFT(rt1, logn); + PQCLEAN_FALCON512_CLEAN_iFFT(rt2, logn); + bnorm = fpr_zero; + for (u = 0; u < n; u ++) { + bnorm = fpr_add(bnorm, fpr_sqr(rt1[u])); + bnorm = fpr_add(bnorm, fpr_sqr(rt2[u])); + } + if (!fpr_lt(bnorm, fpr_bnorm_max)) { + continue; + } + + /* + * Compute public key h = g/f mod X^N+1 mod q. If this + * fails, we must restart. + */ + if (h == NULL) { + h2 = (uint16_t *)tmp; + tmp2 = h2 + n; + } else { + h2 = h; + tmp2 = (uint16_t *)tmp; + } + if (!PQCLEAN_FALCON512_CLEAN_compute_public(h2, f, g, logn, (uint8_t *)tmp2)) { + continue; + } + + /* + * Solve the NTRU equation to get F and G. + */ + lim = (1 << (PQCLEAN_FALCON512_CLEAN_max_FG_bits[logn] - 1)) - 1; + if (!solve_NTRU(logn, F, G, f, g, lim, (uint32_t *)tmp)) { + continue; + } + + /* + * Key pair is generated. + */ + break; + } +} diff --git a/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/manifest.mn b/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/manifest.mn new file mode 100644 index 000000000..979f06cc6 --- /dev/null +++ b/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/manifest.mn @@ -0,0 +1,32 @@ +# DO NOT EDIT: generated from manifest.mn.subdirs.template +# +# This Source Code Form is subject to the terms of the Mozilla Public +# License, v. 2.0. If a copy of the MPL was not distributed with this +# file, You can obtain one at http://mozilla.org/MPL/2.0/. +CORE_DEPTH = ../../../../../.. + +MODULE = oqs + +LIBRARY_NAME = oqs_src_sig_falcon_pqclean_falcon-512_clean +SHARED_LIBRARY = $(NULL) + +CSRCS = \ + codec.c \ + common.c \ + fft.c \ + fpr.c \ + inner.c \ + keygen.c \ + pqclean.c \ + rng.c \ + sign.c \ + vrfy.c \ + $(NULL) + +# only add module debugging in opt builds if DEBUG_PKCS11 is set +ifdef DEBUG_PKCS11 + DEFINES += -DDEBUG_MODULE +endif + +# This part of the code, including all sub-dirs, can be optimized for size +export ALLOW_OPT_CODE_SIZE = 1 diff --git a/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/pqclean.c b/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/pqclean.c new file mode 100644 index 000000000..3abf68149 --- /dev/null +++ b/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/pqclean.c @@ -0,0 +1,384 @@ +#include "api.h" +#include "inner.h" +#include "randombytes.h" +#include <stddef.h> +#include <string.h> +/* + * Wrapper for implementing the PQClean API. + */ + + + +#define NONCELEN 40 +#define SEEDLEN 48 + +/* + * Encoding formats (nnnn = log of degree, 9 for Falcon-512, 10 for Falcon-1024) + * + * private key: + * header byte: 0101nnnn + * private f (6 or 5 bits by element, depending on degree) + * private g (6 or 5 bits by element, depending on degree) + * private F (8 bits by element) + * + * public key: + * header byte: 0000nnnn + * public h (14 bits by element) + * + * signature: + * header byte: 0011nnnn + * nonce 40 bytes + * value (12 bits by element) + * + * message + signature: + * signature length (2 bytes, big-endian) + * nonce 40 bytes + * message + * header byte: 0010nnnn + * value (12 bits by element) + * (signature length is 1+len(value), not counting the nonce) + */ + +/* see api.h */ +int +PQCLEAN_FALCON512_CLEAN_crypto_sign_keypair(unsigned char *pk, unsigned char *sk) { + union { + uint8_t b[FALCON_KEYGEN_TEMP_9]; + uint64_t dummy_u64; + fpr dummy_fpr; + } tmp; + int8_t f[512], g[512], F[512]; + uint16_t h[512]; + unsigned char seed[SEEDLEN]; + inner_shake256_context rng; + size_t u, v; + + /* + * Generate key pair. + */ + randombytes(seed, sizeof seed); + inner_shake256_init(&rng); + inner_shake256_inject(&rng, seed, sizeof seed); + inner_shake256_flip(&rng); + PQCLEAN_FALCON512_CLEAN_keygen(&rng, f, g, F, NULL, h, 9, tmp.b); + inner_shake256_ctx_release(&rng); + + /* + * Encode private key. + */ + sk[0] = 0x50 + 9; + u = 1; + v = PQCLEAN_FALCON512_CLEAN_trim_i8_encode( + sk + u, PQCLEAN_FALCON512_CLEAN_CRYPTO_SECRETKEYBYTES - u, + f, 9, PQCLEAN_FALCON512_CLEAN_max_fg_bits[9]); + if (v == 0) { + return -1; + } + u += v; + v = PQCLEAN_FALCON512_CLEAN_trim_i8_encode( + sk + u, PQCLEAN_FALCON512_CLEAN_CRYPTO_SECRETKEYBYTES - u, + g, 9, PQCLEAN_FALCON512_CLEAN_max_fg_bits[9]); + if (v == 0) { + return -1; + } + u += v; + v = PQCLEAN_FALCON512_CLEAN_trim_i8_encode( + sk + u, PQCLEAN_FALCON512_CLEAN_CRYPTO_SECRETKEYBYTES - u, + F, 9, PQCLEAN_FALCON512_CLEAN_max_FG_bits[9]); + if (v == 0) { + return -1; + } + u += v; + if (u != PQCLEAN_FALCON512_CLEAN_CRYPTO_SECRETKEYBYTES) { + return -1; + } + + /* + * Encode public key. + */ + pk[0] = 0x00 + 9; + v = PQCLEAN_FALCON512_CLEAN_modq_encode( + pk + 1, PQCLEAN_FALCON512_CLEAN_CRYPTO_PUBLICKEYBYTES - 1, + h, 9); + if (v != PQCLEAN_FALCON512_CLEAN_CRYPTO_PUBLICKEYBYTES - 1) { + return -1; + } + + return 0; +} + +/* + * Compute the signature. nonce[] receives the nonce and must have length + * NONCELEN bytes. sigbuf[] receives the signature value (without nonce + * or header byte), with *sigbuflen providing the maximum value length and + * receiving the actual value length. + * + * If a signature could be computed but not encoded because it would + * exceed the output buffer size, then a new signature is computed. If + * the provided buffer size is too low, this could loop indefinitely, so + * the caller must provide a size that can accommodate signatures with a + * large enough probability. + * + * Return value: 0 on success, -1 on error. + */ +static int +do_sign(uint8_t *nonce, uint8_t *sigbuf, size_t *sigbuflen, + const uint8_t *m, size_t mlen, const uint8_t *sk) { + union { + uint8_t b[72 * 512]; + uint64_t dummy_u64; + fpr dummy_fpr; + } tmp; + int8_t f[512], g[512], F[512], G[512]; + union { + int16_t sig[512]; + uint16_t hm[512]; + } r; + unsigned char seed[SEEDLEN]; + inner_shake256_context sc; + size_t u, v; + + /* + * Decode the private key. + */ + if (sk[0] != 0x50 + 9) { + return -1; + } + u = 1; + v = PQCLEAN_FALCON512_CLEAN_trim_i8_decode( + f, 9, PQCLEAN_FALCON512_CLEAN_max_fg_bits[9], + sk + u, PQCLEAN_FALCON512_CLEAN_CRYPTO_SECRETKEYBYTES - u); + if (v == 0) { + return -1; + } + u += v; + v = PQCLEAN_FALCON512_CLEAN_trim_i8_decode( + g, 9, PQCLEAN_FALCON512_CLEAN_max_fg_bits[9], + sk + u, PQCLEAN_FALCON512_CLEAN_CRYPTO_SECRETKEYBYTES - u); + if (v == 0) { + return -1; + } + u += v; + v = PQCLEAN_FALCON512_CLEAN_trim_i8_decode( + F, 9, PQCLEAN_FALCON512_CLEAN_max_FG_bits[9], + sk + u, PQCLEAN_FALCON512_CLEAN_CRYPTO_SECRETKEYBYTES - u); + if (v == 0) { + return -1; + } + u += v; + if (u != PQCLEAN_FALCON512_CLEAN_CRYPTO_SECRETKEYBYTES) { + return -1; + } + if (!PQCLEAN_FALCON512_CLEAN_complete_private(G, f, g, F, 9, tmp.b)) { + return -1; + } + + /* + * Create a random nonce (40 bytes). + */ + randombytes(nonce, NONCELEN); + + /* + * Hash message nonce + message into a vector. + */ + inner_shake256_init(&sc); + inner_shake256_inject(&sc, nonce, NONCELEN); + inner_shake256_inject(&sc, m, mlen); + inner_shake256_flip(&sc); + PQCLEAN_FALCON512_CLEAN_hash_to_point_ct(&sc, r.hm, 9, tmp.b); + inner_shake256_ctx_release(&sc); + + /* + * Initialize a RNG. + */ + randombytes(seed, sizeof seed); + inner_shake256_init(&sc); + inner_shake256_inject(&sc, seed, sizeof seed); + inner_shake256_flip(&sc); + + /* + * Compute and return the signature. This loops until a signature + * value is found that fits in the provided buffer. + */ + for (;;) { + PQCLEAN_FALCON512_CLEAN_sign_dyn(r.sig, &sc, f, g, F, G, r.hm, 9, tmp.b); + v = PQCLEAN_FALCON512_CLEAN_comp_encode(sigbuf, *sigbuflen, r.sig, 9); + if (v != 0) { + inner_shake256_ctx_release(&sc); + *sigbuflen = v; + return 0; + } + } +} + +/* + * Verify a sigature. The nonce has size NONCELEN bytes. sigbuf[] + * (of size sigbuflen) contains the signature value, not including the + * header byte or nonce. Return value is 0 on success, -1 on error. + */ +static int +do_verify( + const uint8_t *nonce, const uint8_t *sigbuf, size_t sigbuflen, + const uint8_t *m, size_t mlen, const uint8_t *pk) { + union { + uint8_t b[2 * 512]; + uint64_t dummy_u64; + fpr dummy_fpr; + } tmp; + uint16_t h[512], hm[512]; + int16_t sig[512]; + inner_shake256_context sc; + + /* + * Decode public key. + */ + if (pk[0] != 0x00 + 9) { + return -1; + } + if (PQCLEAN_FALCON512_CLEAN_modq_decode(h, 9, + pk + 1, PQCLEAN_FALCON512_CLEAN_CRYPTO_PUBLICKEYBYTES - 1) + != PQCLEAN_FALCON512_CLEAN_CRYPTO_PUBLICKEYBYTES - 1) { + return -1; + } + PQCLEAN_FALCON512_CLEAN_to_ntt_monty(h, 9); + + /* + * Decode signature. + */ + if (sigbuflen == 0) { + return -1; + } + if (PQCLEAN_FALCON512_CLEAN_comp_decode(sig, 9, sigbuf, sigbuflen) != sigbuflen) { + return -1; + } + + /* + * Hash nonce + message into a vector. + */ + inner_shake256_init(&sc); + inner_shake256_inject(&sc, nonce, NONCELEN); + inner_shake256_inject(&sc, m, mlen); + inner_shake256_flip(&sc); + PQCLEAN_FALCON512_CLEAN_hash_to_point_ct(&sc, hm, 9, tmp.b); + inner_shake256_ctx_release(&sc); + + /* + * Verify signature. + */ + if (!PQCLEAN_FALCON512_CLEAN_verify_raw(hm, sig, h, 9, tmp.b)) { + return -1; + } + return 0; +} + +/* see api.h */ +int +PQCLEAN_FALCON512_CLEAN_crypto_sign_signature( + uint8_t *sig, size_t *siglen, + const uint8_t *m, size_t mlen, const uint8_t *sk) { + /* + * The PQCLEAN_FALCON512_CLEAN_CRYPTO_BYTES constant is used for + * the signed message object (as produced by PQCLEAN_FALCON512_CLEAN_crypto_sign()) + * and includes a two-byte length value, so we take care here + * to only generate signatures that are two bytes shorter than + * the maximum. This is done to ensure that PQCLEAN_FALCON512_CLEAN_crypto_sign() + * and PQCLEAN_FALCON512_CLEAN_crypto_sign_signature() produce the exact same signature + * value, if used on the same message, with the same private key, + * and using the same output from randombytes() (this is for + * reproducibility of tests). + */ + size_t vlen; + + vlen = PQCLEAN_FALCON512_CLEAN_CRYPTO_BYTES - NONCELEN - 3; + if (do_sign(sig + 1, sig + 1 + NONCELEN, &vlen, m, mlen, sk) < 0) { + return -1; + } + sig[0] = 0x30 + 9; + *siglen = 1 + NONCELEN + vlen; + return 0; +} + +/* see api.h */ +int +PQCLEAN_FALCON512_CLEAN_crypto_sign_verify( + const uint8_t *sig, size_t siglen, + const uint8_t *m, size_t mlen, const uint8_t *pk) { + if (siglen < 1 + NONCELEN) { + return -1; + } + if (sig[0] != 0x30 + 9) { + return -1; + } + return do_verify(sig + 1, + sig + 1 + NONCELEN, siglen - 1 - NONCELEN, m, mlen, pk); +} + +/* see api.h */ +int +PQCLEAN_FALCON512_CLEAN_crypto_sign( + uint8_t *sm, size_t *smlen, + const uint8_t *m, size_t mlen, const uint8_t *sk) { + uint8_t *pm, *sigbuf; + size_t sigbuflen; + + /* + * Move the message to its final location; this is a memmove() so + * it handles overlaps properly. + */ + memmove(sm + 2 + NONCELEN, m, mlen); + pm = sm + 2 + NONCELEN; + sigbuf = pm + 1 + mlen; + sigbuflen = PQCLEAN_FALCON512_CLEAN_CRYPTO_BYTES - NONCELEN - 3; + if (do_sign(sm + 2, sigbuf, &sigbuflen, pm, mlen, sk) < 0) { + return -1; + } + pm[mlen] = 0x20 + 9; + sigbuflen ++; + sm[0] = (uint8_t)(sigbuflen >> 8); + sm[1] = (uint8_t)sigbuflen; + *smlen = mlen + 2 + NONCELEN + sigbuflen; + return 0; +} + +/* see api.h */ +int +PQCLEAN_FALCON512_CLEAN_crypto_sign_open( + uint8_t *m, size_t *mlen, + const uint8_t *sm, size_t smlen, const uint8_t *pk) { + const uint8_t *sigbuf; + size_t pmlen, sigbuflen; + + if (smlen < 3 + NONCELEN) { + return -1; + } + sigbuflen = ((size_t)sm[0] << 8) | (size_t)sm[1]; + if (sigbuflen < 2 || sigbuflen > (smlen - NONCELEN - 2)) { + return -1; + } + sigbuflen --; + pmlen = smlen - NONCELEN - 3 - sigbuflen; + if (sm[2 + NONCELEN + pmlen] != 0x20 + 9) { + return -1; + } + sigbuf = sm + 2 + NONCELEN + pmlen + 1; + + /* + * The 2-byte length header and the one-byte signature header + * have been verified. Nonce is at sm+2, followed by the message + * itself. Message length is in pmlen. sigbuf/sigbuflen point to + * the signature value (excluding the header byte). + */ + if (do_verify(sm + 2, sigbuf, sigbuflen, + sm + 2 + NONCELEN, pmlen, pk) < 0) { + return -1; + } + + /* + * Signature is correct, we just have to copy/move the message + * to its final destination. The memmove() properly handles + * overlaps. + */ + memmove(m, sm + 2 + NONCELEN, pmlen); + *mlen = pmlen; + return 0; +} diff --git a/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/pqclean_falcon-512_clean.gyp b/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/pqclean_falcon-512_clean.gyp new file mode 100644 index 000000000..ec88d54ad --- /dev/null +++ b/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/pqclean_falcon-512_clean.gyp @@ -0,0 +1,48 @@ +# DO NOT EDIT: generated from subdir.gyp.template +# This Source Code Form is subject to the terms of the Mozilla Public +# License, v. 2.0. If a copy of the MPL was not distributed with this +# file, You can obtain one at http://mozilla.org/MPL/2.0/. +{ + 'includes': [ + '../../../../../../coreconf/config.gypi' + ], + 'targets': [ + { + 'target_name': 'oqs_src_sig_falcon_pqclean_falcon-512_clean', + 'type': 'static_library', + 'sources': [ + 'codec.c', + 'common.c', + 'fft.c', + 'fpr.c', + 'inner.c', + 'keygen.c', + 'pqclean.c', + 'rng.c', + 'sign.c', + 'vrfy.c', + ], + 'dependencies': [ + '<(DEPTH)/exports.gyp:nss_exports' + ] + } + ], + 'target_defaults': { + 'defines': [ + ], + 'include_dirs': [ + '<(DEPTH)/lib/liboqs/src/common/pqclean_shims', + '<(DEPTH)/lib/liboqs/src/common/sha3/xkcp_low/KeccakP-1600/plain-64bits', + ], + [ 'OS=="mac"', { + 'defines': [ + 'OQS_HAVE_POSIX_MEMALIGN', + 'OQS_HAVE_ALIGNED_ALLOC', + 'OQS_HAVE_MEMALIGN' + ] + }] + }, + 'variables': { + 'module': 'oqs' + } +} diff --git a/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/rng.c b/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/rng.c new file mode 100644 index 000000000..266db7572 --- /dev/null +++ b/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/rng.c @@ -0,0 +1,201 @@ +#include "inner.h" +#include <assert.h> +/* + * PRNG and interface to the system RNG. + * + * ==========================(LICENSE BEGIN)============================ + * + * Copyright (c) 2017-2019 Falcon Project + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the + * "Software"), to deal in the Software without restriction, including + * without limitation the rights to use, copy, modify, merge, publish, + * distribute, sublicense, and/or sell copies of the Software, and to + * permit persons to whom the Software is furnished to do so, subject to + * the following conditions: + * + * The above copyright notice and this permission notice shall be + * included in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, + * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF + * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. + * IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY + * CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, + * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE + * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. + * + * ===========================(LICENSE END)============================= + * + * @author Thomas Pornin <thomas.pornin@nccgroup.com> + */ + + + +/* + * Include relevant system header files. For Win32, this will also need + * linking with advapi32.dll, which we trigger with an appropriate #pragma. + */ + +/* see inner.h */ +int +PQCLEAN_FALCON512_CLEAN_get_seed(void *seed, size_t len) { + (void)seed; + if (len == 0) { + return 1; + } + return 0; +} + +/* see inner.h */ +void +PQCLEAN_FALCON512_CLEAN_prng_init(prng *p, inner_shake256_context *src) { + /* + * To ensure reproducibility for a given seed, we + * must enforce little-endian interpretation of + * the state words. + */ + uint8_t tmp[56]; + uint64_t th, tl; + int i; + + inner_shake256_extract(src, tmp, 56); + for (i = 0; i < 14; i ++) { + uint32_t w; + + w = (uint32_t)tmp[(i << 2) + 0] + | ((uint32_t)tmp[(i << 2) + 1] << 8) + | ((uint32_t)tmp[(i << 2) + 2] << 16) + | ((uint32_t)tmp[(i << 2) + 3] << 24); + *(uint32_t *)(p->state.d + (i << 2)) = w; + } + tl = *(uint32_t *)(p->state.d + 48); + th = *(uint32_t *)(p->state.d + 52); + *(uint64_t *)(p->state.d + 48) = tl + (th << 32); + PQCLEAN_FALCON512_CLEAN_prng_refill(p); +} + +/* + * PRNG based on ChaCha20. + * + * State consists in key (32 bytes) then IV (16 bytes) and block counter + * (8 bytes). Normally, we should not care about local endianness (this + * is for a PRNG), but for the NIST competition we need reproducible KAT + * vectors that work across architectures, so we enforce little-endian + * interpretation where applicable. Moreover, output words are "spread + * out" over the output buffer with the interleaving pattern that is + * naturally obtained from the AVX2 implementation that runs eight + * ChaCha20 instances in parallel. + * + * The block counter is XORed into the first 8 bytes of the IV. + */ +void +PQCLEAN_FALCON512_CLEAN_prng_refill(prng *p) { + + static const uint32_t CW[] = { + 0x61707865, 0x3320646e, 0x79622d32, 0x6b206574 + }; + + uint64_t cc; + size_t u; + + /* + * State uses local endianness. Only the output bytes must be + * converted to little endian (if used on a big-endian machine). + */ + cc = *(uint64_t *)(p->state.d + 48); + for (u = 0; u < 8; u ++) { + uint32_t state[16]; + size_t v; + int i; + + memcpy(&state[0], CW, sizeof CW); + memcpy(&state[4], p->state.d, 48); + state[14] ^= (uint32_t)cc; + state[15] ^= (uint32_t)(cc >> 32); + for (i = 0; i < 10; i ++) { + +#define QROUND(a, b, c, d) do { \ + state[a] += state[b]; \ + state[d] ^= state[a]; \ + state[d] = (state[d] << 16) | (state[d] >> 16); \ + state[c] += state[d]; \ + state[b] ^= state[c]; \ + state[b] = (state[b] << 12) | (state[b] >> 20); \ + state[a] += state[b]; \ + state[d] ^= state[a]; \ + state[d] = (state[d] << 8) | (state[d] >> 24); \ + state[c] += state[d]; \ + state[b] ^= state[c]; \ + state[b] = (state[b] << 7) | (state[b] >> 25); \ + } while (0) + + QROUND( 0, 4, 8, 12); + QROUND( 1, 5, 9, 13); + QROUND( 2, 6, 10, 14); + QROUND( 3, 7, 11, 15); + QROUND( 0, 5, 10, 15); + QROUND( 1, 6, 11, 12); + QROUND( 2, 7, 8, 13); + QROUND( 3, 4, 9, 14); + +#undef QROUND + + } + + for (v = 0; v < 4; v ++) { + state[v] += CW[v]; + } + for (v = 4; v < 14; v ++) { + state[v] += ((uint32_t *)p->state.d)[v - 4]; + } + state[14] += ((uint32_t *)p->state.d)[10] + ^ (uint32_t)cc; + state[15] += ((uint32_t *)p->state.d)[11] + ^ (uint32_t)(cc >> 32); + cc ++; + + /* + * We mimic the interleaving that is used in the AVX2 + * implementation. + */ + for (v = 0; v < 16; v ++) { + p->buf.d[(u << 2) + (v << 5) + 0] = + (uint8_t)state[v]; + p->buf.d[(u << 2) + (v << 5) + 1] = + (uint8_t)(state[v] >> 8); + p->buf.d[(u << 2) + (v << 5) + 2] = + (uint8_t)(state[v] >> 16); + p->buf.d[(u << 2) + (v << 5) + 3] = + (uint8_t)(state[v] >> 24); + } + } + *(uint64_t *)(p->state.d + 48) = cc; + + + p->ptr = 0; +} + +/* see inner.h */ +void +PQCLEAN_FALCON512_CLEAN_prng_get_bytes(prng *p, void *dst, size_t len) { + uint8_t *buf; + + buf = dst; + while (len > 0) { + size_t clen; + + clen = (sizeof p->buf.d) - p->ptr; + if (clen > len) { + clen = len; + } + memcpy(buf, p->buf.d, clen); + buf += clen; + len -= clen; + p->ptr += clen; + if (p->ptr == sizeof p->buf.d) { + PQCLEAN_FALCON512_CLEAN_prng_refill(p); + } + } +} diff --git a/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/sign.c b/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/sign.c new file mode 100644 index 000000000..469ae3b42 --- /dev/null +++ b/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/sign.c @@ -0,0 +1,1254 @@ +#include "inner.h" + +/* + * Falcon signature generation. + * + * ==========================(LICENSE BEGIN)============================ + * + * Copyright (c) 2017-2019 Falcon Project + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the + * "Software"), to deal in the Software without restriction, including + * without limitation the rights to use, copy, modify, merge, publish, + * distribute, sublicense, and/or sell copies of the Software, and to + * permit persons to whom the Software is furnished to do so, subject to + * the following conditions: + * + * The above copyright notice and this permission notice shall be + * included in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, + * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF + * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. + * IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY + * CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, + * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE + * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. + * + * ===========================(LICENSE END)============================= + * + * @author Thomas Pornin <thomas.pornin@nccgroup.com> + */ + + +/* =================================================================== */ + +/* + * Compute degree N from logarithm 'logn'. + */ +#define MKN(logn) ((size_t)1 << (logn)) + +/* =================================================================== */ +/* + * Binary case: + * N = 2^logn + * phi = X^N+1 + */ + +/* + * Get the size of the LDL tree for an input with polynomials of size + * 2^logn. The size is expressed in the number of elements. + */ +static inline unsigned +ffLDL_treesize(unsigned logn) { + /* + * For logn = 0 (polynomials are constant), the "tree" is a + * single element. Otherwise, the tree node has size 2^logn, and + * has two child trees for size logn-1 each. Thus, treesize s() + * must fulfill these two relations: + * + * s(0) = 1 + * s(logn) = (2^logn) + 2*s(logn-1) + */ + return (logn + 1) << logn; +} + +/* + * Inner function for ffLDL_fft(). It expects the matrix to be both + * auto-adjoint and quasicyclic; also, it uses the source operands + * as modifiable temporaries. + * + * tmp[] must have room for at least one polynomial. + */ +static void +ffLDL_fft_inner(fpr *tree, + fpr *g0, fpr *g1, unsigned logn, fpr *tmp) { + size_t n, hn; + + n = MKN(logn); + if (n == 1) { + tree[0] = g0[0]; + return; + } + hn = n >> 1; + + /* + * The LDL decomposition yields L (which is written in the tree) + * and the diagonal of D. Since d00 = g0, we just write d11 + * into tmp. + */ + PQCLEAN_FALCON512_CLEAN_poly_LDLmv_fft(tmp, tree, g0, g1, g0, logn); + + /* + * Split d00 (currently in g0) and d11 (currently in tmp). We + * reuse g0 and g1 as temporary storage spaces: + * d00 splits into g1, g1+hn + * d11 splits into g0, g0+hn + */ + PQCLEAN_FALCON512_CLEAN_poly_split_fft(g1, g1 + hn, g0, logn); + PQCLEAN_FALCON512_CLEAN_poly_split_fft(g0, g0 + hn, tmp, logn); + + /* + * Each split result is the first row of a new auto-adjoint + * quasicyclic matrix for the next recursive step. + */ + ffLDL_fft_inner(tree + n, + g1, g1 + hn, logn - 1, tmp); + ffLDL_fft_inner(tree + n + ffLDL_treesize(logn - 1), + g0, g0 + hn, logn - 1, tmp); +} + +/* + * Compute the ffLDL tree of an auto-adjoint matrix G. The matrix + * is provided as three polynomials (FFT representation). + * + * The "tree" array is filled with the computed tree, of size + * (logn+1)*(2^logn) elements (see ffLDL_treesize()). + * + * Input arrays MUST NOT overlap, except possibly the three unmodified + * arrays g00, g01 and g11. tmp[] should have room for at least three + * polynomials of 2^logn elements each. + */ +static void +ffLDL_fft(fpr *tree, const fpr *g00, + const fpr *g01, const fpr *g11, + unsigned logn, fpr *tmp) { + size_t n, hn; + fpr *d00, *d11; + + n = MKN(logn); + if (n == 1) { + tree[0] = g00[0]; + return; + } + hn = n >> 1; + d00 = tmp; + d11 = tmp + n; + tmp += n << 1; + + memcpy(d00, g00, n * sizeof * g00); + PQCLEAN_FALCON512_CLEAN_poly_LDLmv_fft(d11, tree, g00, g01, g11, logn); + + PQCLEAN_FALCON512_CLEAN_poly_split_fft(tmp, tmp + hn, d00, logn); + PQCLEAN_FALCON512_CLEAN_poly_split_fft(d00, d00 + hn, d11, logn); + memcpy(d11, tmp, n * sizeof * tmp); + ffLDL_fft_inner(tree + n, + d11, d11 + hn, logn - 1, tmp); + ffLDL_fft_inner(tree + n + ffLDL_treesize(logn - 1), + d00, d00 + hn, logn - 1, tmp); +} + +/* + * Normalize an ffLDL tree: each leaf of value x is replaced with + * sigma / sqrt(x). + */ +static void +ffLDL_binary_normalize(fpr *tree, unsigned logn) { + /* + * TODO: make an iterative version. + */ + size_t n; + + n = MKN(logn); + if (n == 1) { + /* + * We actually store in the tree leaf the inverse of + * the value mandated by the specification: this + * saves a division both here and in the sampler. + */ + tree[0] = fpr_mul(fpr_sqrt(tree[0]), fpr_inv_sigma); + } else { + ffLDL_binary_normalize(tree + n, logn - 1); + ffLDL_binary_normalize(tree + n + ffLDL_treesize(logn - 1), + logn - 1); + } +} + +/* =================================================================== */ + +/* + * Convert an integer polynomial (with small values) into the + * representation with complex numbers. + */ +static void +smallints_to_fpr(fpr *r, const int8_t *t, unsigned logn) { + size_t n, u; + + n = MKN(logn); + for (u = 0; u < n; u ++) { + r[u] = fpr_of(t[u]); + } +} + +/* + * The expanded private key contains: + * - The B0 matrix (four elements) + * - The ffLDL tree + */ + +static inline size_t +skoff_b00(unsigned logn) { + (void)logn; + return 0; +} + +static inline size_t +skoff_b01(unsigned logn) { + return MKN(logn); +} + +static inline size_t +skoff_b10(unsigned logn) { + return 2 * MKN(logn); +} + +static inline size_t +skoff_b11(unsigned logn) { + return 3 * MKN(logn); +} + +static inline size_t +skoff_tree(unsigned logn) { + return 4 * MKN(logn); +} + +/* see inner.h */ +void +PQCLEAN_FALCON512_CLEAN_expand_privkey(fpr *expanded_key, + const int8_t *f, const int8_t *g, + const int8_t *F, const int8_t *G, + unsigned logn, uint8_t *tmp) { + size_t n; + fpr *rf, *rg, *rF, *rG; + fpr *b00, *b01, *b10, *b11; + fpr *g00, *g01, *g11, *gxx; + fpr *tree; + + n = MKN(logn); + b00 = expanded_key + skoff_b00(logn); + b01 = expanded_key + skoff_b01(logn); + b10 = expanded_key + skoff_b10(logn); + b11 = expanded_key + skoff_b11(logn); + tree = expanded_key + skoff_tree(logn); + + /* + * We load the private key elements directly into the B0 matrix, + * since B0 = [[g, -f], [G, -F]]. + */ + rf = b01; + rg = b00; + rF = b11; + rG = b10; + + smallints_to_fpr(rf, f, logn); + smallints_to_fpr(rg, g, logn); + smallints_to_fpr(rF, F, logn); + smallints_to_fpr(rG, G, logn); + + /* + * Compute the FFT for the key elements, and negate f and F. + */ + PQCLEAN_FALCON512_CLEAN_FFT(rf, logn); + PQCLEAN_FALCON512_CLEAN_FFT(rg, logn); + PQCLEAN_FALCON512_CLEAN_FFT(rF, logn); + PQCLEAN_FALCON512_CLEAN_FFT(rG, logn); + PQCLEAN_FALCON512_CLEAN_poly_neg(rf, logn); + PQCLEAN_FALCON512_CLEAN_poly_neg(rF, logn); + + /* + * The Gram matrix is G = B x B*. Formulas are: + * g00 = b00*adj(b00) + b01*adj(b01) + * g01 = b00*adj(b10) + b01*adj(b11) + * g10 = b10*adj(b00) + b11*adj(b01) + * g11 = b10*adj(b10) + b11*adj(b11) + * + * For historical reasons, this implementation uses + * g00, g01 and g11 (upper triangle). + */ + g00 = (fpr *)tmp; + g01 = g00 + n; + g11 = g01 + n; + gxx = g11 + n; + + memcpy(g00, b00, n * sizeof * b00); + PQCLEAN_FALCON512_CLEAN_poly_mulselfadj_fft(g00, logn); + memcpy(gxx, b01, n * sizeof * b01); + PQCLEAN_FALCON512_CLEAN_poly_mulselfadj_fft(gxx, logn); + PQCLEAN_FALCON512_CLEAN_poly_add(g00, gxx, logn); + + memcpy(g01, b00, n * sizeof * b00); + PQCLEAN_FALCON512_CLEAN_poly_muladj_fft(g01, b10, logn); + memcpy(gxx, b01, n * sizeof * b01); + PQCLEAN_FALCON512_CLEAN_poly_muladj_fft(gxx, b11, logn); + PQCLEAN_FALCON512_CLEAN_poly_add(g01, gxx, logn); + + memcpy(g11, b10, n * sizeof * b10); + PQCLEAN_FALCON512_CLEAN_poly_mulselfadj_fft(g11, logn); + memcpy(gxx, b11, n * sizeof * b11); + PQCLEAN_FALCON512_CLEAN_poly_mulselfadj_fft(gxx, logn); + PQCLEAN_FALCON512_CLEAN_poly_add(g11, gxx, logn); + + /* + * Compute the Falcon tree. + */ + ffLDL_fft(tree, g00, g01, g11, logn, gxx); + + /* + * Normalize tree. + */ + ffLDL_binary_normalize(tree, logn); +} + +typedef int (*samplerZ)(void *ctx, fpr mu, fpr sigma); + +/* + * Perform Fast Fourier Sampling for target vector t. The Gram matrix + * is provided (G = [[g00, g01], [adj(g01), g11]]). The sampled vector + * is written over (t0,t1). The Gram matrix is modified as well. The + * tmp[] buffer must have room for four polynomials. + */ +static void +ffSampling_fft_dyntree(samplerZ samp, void *samp_ctx, + fpr *t0, fpr *t1, + fpr *g00, fpr *g01, fpr *g11, + unsigned logn, fpr *tmp) { + size_t n, hn; + fpr *z0, *z1; + + /* + * Deepest level: the LDL tree leaf value is just g00 (the + * array has length only 1 at this point); we normalize it + * with regards to sigma, then use it for sampling. + */ + if (logn == 0) { + fpr leaf; + + leaf = g00[0]; + leaf = fpr_mul(fpr_sqrt(leaf), fpr_inv_sigma); + t0[0] = fpr_of(samp(samp_ctx, t0[0], leaf)); + t1[0] = fpr_of(samp(samp_ctx, t1[0], leaf)); + return; + } + + n = (size_t)1 << logn; + hn = n >> 1; + + /* + * Decompose G into LDL. We only need d00 (identical to g00), + * d11, and l10; we do that in place. + */ + PQCLEAN_FALCON512_CLEAN_poly_LDL_fft(g00, g01, g11, logn); + + /* + * Split d00 and d11 and expand them into half-size quasi-cyclic + * Gram matrices. We also save l10 in tmp[]. + */ + PQCLEAN_FALCON512_CLEAN_poly_split_fft(tmp, tmp + hn, g00, logn); + memcpy(g00, tmp, n * sizeof * tmp); + PQCLEAN_FALCON512_CLEAN_poly_split_fft(tmp, tmp + hn, g11, logn); + memcpy(g11, tmp, n * sizeof * tmp); + memcpy(tmp, g01, n * sizeof * g01); + memcpy(g01, g00, hn * sizeof * g00); + memcpy(g01 + hn, g11, hn * sizeof * g00); + + /* + * The half-size Gram matrices for the recursive LDL tree + * building are now: + * - left sub-tree: g00, g00+hn, g01 + * - right sub-tree: g11, g11+hn, g01+hn + * l10 is in tmp[]. + */ + + /* + * We split t1 and use the first recursive call on the two + * halves, using the right sub-tree. The result is merged + * back into tmp + 2*n. + */ + z1 = tmp + n; + PQCLEAN_FALCON512_CLEAN_poly_split_fft(z1, z1 + hn, t1, logn); + ffSampling_fft_dyntree(samp, samp_ctx, z1, z1 + hn, + g11, g11 + hn, g01 + hn, logn - 1, z1 + n); + PQCLEAN_FALCON512_CLEAN_poly_merge_fft(tmp + (n << 1), z1, z1 + hn, logn); + + /* + * Compute tb0 = t0 + (t1 - z1) * l10. + * At that point, l10 is in tmp, t1 is unmodified, and z1 is + * in tmp + (n << 1). The buffer in z1 is free. + * + * In the end, z1 is written over t1, and tb0 is in t0. + */ + memcpy(z1, t1, n * sizeof * t1); + PQCLEAN_FALCON512_CLEAN_poly_sub(z1, tmp + (n << 1), logn); + memcpy(t1, tmp + (n << 1), n * sizeof * tmp); + PQCLEAN_FALCON512_CLEAN_poly_mul_fft(tmp, z1, logn); + PQCLEAN_FALCON512_CLEAN_poly_add(t0, tmp, logn); + + /* + * Second recursive invocation, on the split tb0 (currently in t0) + * and the left sub-tree. + */ + z0 = tmp; + PQCLEAN_FALCON512_CLEAN_poly_split_fft(z0, z0 + hn, t0, logn); + ffSampling_fft_dyntree(samp, samp_ctx, z0, z0 + hn, + g00, g00 + hn, g01, logn - 1, z0 + n); + PQCLEAN_FALCON512_CLEAN_poly_merge_fft(t0, z0, z0 + hn, logn); +} + +/* + * Perform Fast Fourier Sampling for target vector t and LDL tree T. + * tmp[] must have size for at least two polynomials of size 2^logn. + */ +static void +ffSampling_fft(samplerZ samp, void *samp_ctx, + fpr *z0, fpr *z1, + const fpr *tree, + const fpr *t0, const fpr *t1, unsigned logn, + fpr *tmp) { + size_t n, hn; + const fpr *tree0, *tree1; + + /* + * When logn == 2, we inline the last two recursion levels. + */ + if (logn == 2) { + fpr x0, x1, y0, y1, w0, w1, w2, w3, sigma; + fpr a_re, a_im, b_re, b_im, c_re, c_im; + + tree0 = tree + 4; + tree1 = tree + 8; + + /* + * We split t1 into w*, then do the recursive invocation, + * with output in w*. We finally merge back into z1. + */ + a_re = t1[0]; + a_im = t1[2]; + b_re = t1[1]; + b_im = t1[3]; + c_re = fpr_add(a_re, b_re); + c_im = fpr_add(a_im, b_im); + w0 = fpr_half(c_re); + w1 = fpr_half(c_im); + c_re = fpr_sub(a_re, b_re); + c_im = fpr_sub(a_im, b_im); + w2 = fpr_mul(fpr_add(c_re, c_im), fpr_invsqrt8); + w3 = fpr_mul(fpr_sub(c_im, c_re), fpr_invsqrt8); + + x0 = w2; + x1 = w3; + sigma = tree1[3]; + w2 = fpr_of(samp(samp_ctx, x0, sigma)); + w3 = fpr_of(samp(samp_ctx, x1, sigma)); + a_re = fpr_sub(x0, w2); + a_im = fpr_sub(x1, w3); + b_re = tree1[0]; + b_im = tree1[1]; + c_re = fpr_sub(fpr_mul(a_re, b_re), fpr_mul(a_im, b_im)); + c_im = fpr_add(fpr_mul(a_re, b_im), fpr_mul(a_im, b_re)); + x0 = fpr_add(c_re, w0); + x1 = fpr_add(c_im, w1); + sigma = tree1[2]; + w0 = fpr_of(samp(samp_ctx, x0, sigma)); + w1 = fpr_of(samp(samp_ctx, x1, sigma)); + + a_re = w0; + a_im = w1; + b_re = w2; + b_im = w3; + c_re = fpr_mul(fpr_sub(b_re, b_im), fpr_invsqrt2); + c_im = fpr_mul(fpr_add(b_re, b_im), fpr_invsqrt2); + z1[0] = w0 = fpr_add(a_re, c_re); + z1[2] = w2 = fpr_add(a_im, c_im); + z1[1] = w1 = fpr_sub(a_re, c_re); + z1[3] = w3 = fpr_sub(a_im, c_im); + + /* + * Compute tb0 = t0 + (t1 - z1) * L. Value tb0 ends up in w*. + */ + w0 = fpr_sub(t1[0], w0); + w1 = fpr_sub(t1[1], w1); + w2 = fpr_sub(t1[2], w2); + w3 = fpr_sub(t1[3], w3); + + a_re = w0; + a_im = w2; + b_re = tree[0]; + b_im = tree[2]; + w0 = fpr_sub(fpr_mul(a_re, b_re), fpr_mul(a_im, b_im)); + w2 = fpr_add(fpr_mul(a_re, b_im), fpr_mul(a_im, b_re)); + a_re = w1; + a_im = w3; + b_re = tree[1]; + b_im = tree[3]; + w1 = fpr_sub(fpr_mul(a_re, b_re), fpr_mul(a_im, b_im)); + w3 = fpr_add(fpr_mul(a_re, b_im), fpr_mul(a_im, b_re)); + + w0 = fpr_add(w0, t0[0]); + w1 = fpr_add(w1, t0[1]); + w2 = fpr_add(w2, t0[2]); + w3 = fpr_add(w3, t0[3]); + + /* + * Second recursive invocation. + */ + a_re = w0; + a_im = w2; + b_re = w1; + b_im = w3; + c_re = fpr_add(a_re, b_re); + c_im = fpr_add(a_im, b_im); + w0 = fpr_half(c_re); + w1 = fpr_half(c_im); + c_re = fpr_sub(a_re, b_re); + c_im = fpr_sub(a_im, b_im); + w2 = fpr_mul(fpr_add(c_re, c_im), fpr_invsqrt8); + w3 = fpr_mul(fpr_sub(c_im, c_re), fpr_invsqrt8); + + x0 = w2; + x1 = w3; + sigma = tree0[3]; + w2 = y0 = fpr_of(samp(samp_ctx, x0, sigma)); + w3 = y1 = fpr_of(samp(samp_ctx, x1, sigma)); + a_re = fpr_sub(x0, y0); + a_im = fpr_sub(x1, y1); + b_re = tree0[0]; + b_im = tree0[1]; + c_re = fpr_sub(fpr_mul(a_re, b_re), fpr_mul(a_im, b_im)); + c_im = fpr_add(fpr_mul(a_re, b_im), fpr_mul(a_im, b_re)); + x0 = fpr_add(c_re, w0); + x1 = fpr_add(c_im, w1); + sigma = tree0[2]; + w0 = fpr_of(samp(samp_ctx, x0, sigma)); + w1 = fpr_of(samp(samp_ctx, x1, sigma)); + + a_re = w0; + a_im = w1; + b_re = w2; + b_im = w3; + c_re = fpr_mul(fpr_sub(b_re, b_im), fpr_invsqrt2); + c_im = fpr_mul(fpr_add(b_re, b_im), fpr_invsqrt2); + z0[0] = fpr_add(a_re, c_re); + z0[2] = fpr_add(a_im, c_im); + z0[1] = fpr_sub(a_re, c_re); + z0[3] = fpr_sub(a_im, c_im); + + return; + } + + /* + * Case logn == 1 is reachable only when using Falcon-2 (the + * smallest size for which Falcon is mathematically defined, but + * of course way too insecure to be of any use). + */ + if (logn == 1) { + fpr x0, x1, y0, y1, sigma; + fpr a_re, a_im, b_re, b_im, c_re, c_im; + + x0 = t1[0]; + x1 = t1[1]; + sigma = tree[3]; + z1[0] = y0 = fpr_of(samp(samp_ctx, x0, sigma)); + z1[1] = y1 = fpr_of(samp(samp_ctx, x1, sigma)); + a_re = fpr_sub(x0, y0); + a_im = fpr_sub(x1, y1); + b_re = tree[0]; + b_im = tree[1]; + c_re = fpr_sub(fpr_mul(a_re, b_re), fpr_mul(a_im, b_im)); + c_im = fpr_add(fpr_mul(a_re, b_im), fpr_mul(a_im, b_re)); + x0 = fpr_add(c_re, t0[0]); + x1 = fpr_add(c_im, t0[1]); + sigma = tree[2]; + z0[0] = fpr_of(samp(samp_ctx, x0, sigma)); + z0[1] = fpr_of(samp(samp_ctx, x1, sigma)); + + return; + } + + /* + * Normal end of recursion is for logn == 0. Since the last + * steps of the recursions were inlined in the blocks above + * (when logn == 1 or 2), this case is not reachable, and is + * retained here only for documentation purposes. + + if (logn == 0) { + fpr x0, x1, sigma; + + x0 = t0[0]; + x1 = t1[0]; + sigma = tree[0]; + z0[0] = fpr_of(samp(samp_ctx, x0, sigma)); + z1[0] = fpr_of(samp(samp_ctx, x1, sigma)); + return; + } + + */ + + /* + * General recursive case (logn >= 3). + */ + + n = (size_t)1 << logn; + hn = n >> 1; + tree0 = tree + n; + tree1 = tree + n + ffLDL_treesize(logn - 1); + + /* + * We split t1 into z1 (reused as temporary storage), then do + * the recursive invocation, with output in tmp. We finally + * merge back into z1. + */ + PQCLEAN_FALCON512_CLEAN_poly_split_fft(z1, z1 + hn, t1, logn); + ffSampling_fft(samp, samp_ctx, tmp, tmp + hn, + tree1, z1, z1 + hn, logn - 1, tmp + n); + PQCLEAN_FALCON512_CLEAN_poly_merge_fft(z1, tmp, tmp + hn, logn); + + /* + * Compute tb0 = t0 + (t1 - z1) * L. Value tb0 ends up in tmp[]. + */ + memcpy(tmp, t1, n * sizeof * t1); + PQCLEAN_FALCON512_CLEAN_poly_sub(tmp, z1, logn); + PQCLEAN_FALCON512_CLEAN_poly_mul_fft(tmp, tree, logn); + PQCLEAN_FALCON512_CLEAN_poly_add(tmp, t0, logn); + + /* + * Second recursive invocation. + */ + PQCLEAN_FALCON512_CLEAN_poly_split_fft(z0, z0 + hn, tmp, logn); + ffSampling_fft(samp, samp_ctx, tmp, tmp + hn, + tree0, z0, z0 + hn, logn - 1, tmp + n); + PQCLEAN_FALCON512_CLEAN_poly_merge_fft(z0, tmp, tmp + hn, logn); +} + +/* + * Compute a signature: the signature contains two vectors, s1 and s2. + * The s1 vector is not returned. The squared norm of (s1,s2) is + * computed, and if it is short enough, then s2 is returned into the + * s2[] buffer, and 1 is returned; otherwise, s2[] is untouched and 0 is + * returned; the caller should then try again. This function uses an + * expanded key. + * + * tmp[] must have room for at least six polynomials. + */ +static int +do_sign_tree(samplerZ samp, void *samp_ctx, int16_t *s2, + const fpr *expanded_key, + const uint16_t *hm, + unsigned logn, fpr *tmp) { + size_t n, u; + fpr *t0, *t1, *tx, *ty; + const fpr *b00, *b01, *b10, *b11, *tree; + fpr ni; + uint32_t sqn, ng; + int16_t *s1tmp, *s2tmp; + + n = MKN(logn); + t0 = tmp; + t1 = t0 + n; + b00 = expanded_key + skoff_b00(logn); + b01 = expanded_key + skoff_b01(logn); + b10 = expanded_key + skoff_b10(logn); + b11 = expanded_key + skoff_b11(logn); + tree = expanded_key + skoff_tree(logn); + + /* + * Set the target vector to [hm, 0] (hm is the hashed message). + */ + for (u = 0; u < n; u ++) { + t0[u] = fpr_of(hm[u]); + /* This is implicit. + t1[u] = fpr_zero; + */ + } + + /* + * Apply the lattice basis to obtain the real target + * vector (after normalization with regards to modulus). + */ + PQCLEAN_FALCON512_CLEAN_FFT(t0, logn); + ni = fpr_inverse_of_q; + memcpy(t1, t0, n * sizeof * t0); + PQCLEAN_FALCON512_CLEAN_poly_mul_fft(t1, b01, logn); + PQCLEAN_FALCON512_CLEAN_poly_mulconst(t1, fpr_neg(ni), logn); + PQCLEAN_FALCON512_CLEAN_poly_mul_fft(t0, b11, logn); + PQCLEAN_FALCON512_CLEAN_poly_mulconst(t0, ni, logn); + + tx = t1 + n; + ty = tx + n; + + /* + * Apply sampling. Output is written back in [tx, ty]. + */ + ffSampling_fft(samp, samp_ctx, tx, ty, tree, t0, t1, logn, ty + n); + + /* + * Get the lattice point corresponding to that tiny vector. + */ + memcpy(t0, tx, n * sizeof * tx); + memcpy(t1, ty, n * sizeof * ty); + PQCLEAN_FALCON512_CLEAN_poly_mul_fft(tx, b00, logn); + PQCLEAN_FALCON512_CLEAN_poly_mul_fft(ty, b10, logn); + PQCLEAN_FALCON512_CLEAN_poly_add(tx, ty, logn); + memcpy(ty, t0, n * sizeof * t0); + PQCLEAN_FALCON512_CLEAN_poly_mul_fft(ty, b01, logn); + + memcpy(t0, tx, n * sizeof * tx); + PQCLEAN_FALCON512_CLEAN_poly_mul_fft(t1, b11, logn); + PQCLEAN_FALCON512_CLEAN_poly_add(t1, ty, logn); + + PQCLEAN_FALCON512_CLEAN_iFFT(t0, logn); + PQCLEAN_FALCON512_CLEAN_iFFT(t1, logn); + + /* + * Compute the signature. + */ + s1tmp = (int16_t *)tx; + sqn = 0; + ng = 0; + for (u = 0; u < n; u ++) { + int32_t z; + + z = (int32_t)hm[u] - (int32_t)fpr_rint(t0[u]); + sqn += (uint32_t)(z * z); + ng |= sqn; + s1tmp[u] = (int16_t)z; + } + sqn |= -(ng >> 31); + + /* + * With "normal" degrees (e.g. 512 or 1024), it is very + * improbable that the computed vector is not short enough; + * however, it may happen in practice for the very reduced + * versions (e.g. degree 16 or below). In that case, the caller + * will loop, and we must not write anything into s2[] because + * s2[] may overlap with the hashed message hm[] and we need + * hm[] for the next iteration. + */ + s2tmp = (int16_t *)tmp; + for (u = 0; u < n; u ++) { + s2tmp[u] = (int16_t) - fpr_rint(t1[u]); + } + if (PQCLEAN_FALCON512_CLEAN_is_short_half(sqn, s2tmp, logn)) { + memcpy(s2, s2tmp, n * sizeof * s2); + memcpy(tmp, s1tmp, n * sizeof * s1tmp); + return 1; + } + return 0; +} + +/* + * Compute a signature: the signature contains two vectors, s1 and s2. + * The s1 vector is not returned. The squared norm of (s1,s2) is + * computed, and if it is short enough, then s2 is returned into the + * s2[] buffer, and 1 is returned; otherwise, s2[] is untouched and 0 is + * returned; the caller should then try again. + * + * tmp[] must have room for at least nine polynomials. + */ +static int +do_sign_dyn(samplerZ samp, void *samp_ctx, int16_t *s2, + const int8_t *f, const int8_t *g, + const int8_t *F, const int8_t *G, + const uint16_t *hm, unsigned logn, fpr *tmp) { + size_t n, u; + fpr *t0, *t1, *tx, *ty; + fpr *b00, *b01, *b10, *b11, *g00, *g01, *g11; + fpr ni; + uint32_t sqn, ng; + int16_t *s1tmp, *s2tmp; + + n = MKN(logn); + + /* + * Lattice basis is B = [[g, -f], [G, -F]]. We convert it to FFT. + */ + b00 = tmp; + b01 = b00 + n; + b10 = b01 + n; + b11 = b10 + n; + smallints_to_fpr(b01, f, logn); + smallints_to_fpr(b00, g, logn); + smallints_to_fpr(b11, F, logn); + smallints_to_fpr(b10, G, logn); + PQCLEAN_FALCON512_CLEAN_FFT(b01, logn); + PQCLEAN_FALCON512_CLEAN_FFT(b00, logn); + PQCLEAN_FALCON512_CLEAN_FFT(b11, logn); + PQCLEAN_FALCON512_CLEAN_FFT(b10, logn); + PQCLEAN_FALCON512_CLEAN_poly_neg(b01, logn); + PQCLEAN_FALCON512_CLEAN_poly_neg(b11, logn); + + /* + * Compute the Gram matrix G = B x B*. Formulas are: + * g00 = b00*adj(b00) + b01*adj(b01) + * g01 = b00*adj(b10) + b01*adj(b11) + * g10 = b10*adj(b00) + b11*adj(b01) + * g11 = b10*adj(b10) + b11*adj(b11) + * + * For historical reasons, this implementation uses + * g00, g01 and g11 (upper triangle). g10 is not kept + * since it is equal to adj(g01). + * + * We _replace_ the matrix B with the Gram matrix, but we + * must keep b01 and b11 for computing the target vector. + */ + t0 = b11 + n; + t1 = t0 + n; + + memcpy(t0, b01, n * sizeof * b01); + PQCLEAN_FALCON512_CLEAN_poly_mulselfadj_fft(t0, logn); // t0 <- b01*adj(b01) + + memcpy(t1, b00, n * sizeof * b00); + PQCLEAN_FALCON512_CLEAN_poly_muladj_fft(t1, b10, logn); // t1 <- b00*adj(b10) + PQCLEAN_FALCON512_CLEAN_poly_mulselfadj_fft(b00, logn); // b00 <- b00*adj(b00) + PQCLEAN_FALCON512_CLEAN_poly_add(b00, t0, logn); // b00 <- g00 + memcpy(t0, b01, n * sizeof * b01); + PQCLEAN_FALCON512_CLEAN_poly_muladj_fft(b01, b11, logn); // b01 <- b01*adj(b11) + PQCLEAN_FALCON512_CLEAN_poly_add(b01, t1, logn); // b01 <- g01 + + PQCLEAN_FALCON512_CLEAN_poly_mulselfadj_fft(b10, logn); // b10 <- b10*adj(b10) + memcpy(t1, b11, n * sizeof * b11); + PQCLEAN_FALCON512_CLEAN_poly_mulselfadj_fft(t1, logn); // t1 <- b11*adj(b11) + PQCLEAN_FALCON512_CLEAN_poly_add(b10, t1, logn); // b10 <- g11 + + /* + * We rename variables to make things clearer. The three elements + * of the Gram matrix uses the first 3*n slots of tmp[], followed + * by b11 and b01 (in that order). + */ + g00 = b00; + g01 = b01; + g11 = b10; + b01 = t0; + t0 = b01 + n; + t1 = t0 + n; + + /* + * Memory layout at that point: + * g00 g01 g11 b11 b01 t0 t1 + */ + + /* + * Set the target vector to [hm, 0] (hm is the hashed message). + */ + for (u = 0; u < n; u ++) { + t0[u] = fpr_of(hm[u]); + /* This is implicit. + t1[u] = fpr_zero; + */ + } + + /* + * Apply the lattice basis to obtain the real target + * vector (after normalization with regards to modulus). + */ + PQCLEAN_FALCON512_CLEAN_FFT(t0, logn); + ni = fpr_inverse_of_q; + memcpy(t1, t0, n * sizeof * t0); + PQCLEAN_FALCON512_CLEAN_poly_mul_fft(t1, b01, logn); + PQCLEAN_FALCON512_CLEAN_poly_mulconst(t1, fpr_neg(ni), logn); + PQCLEAN_FALCON512_CLEAN_poly_mul_fft(t0, b11, logn); + PQCLEAN_FALCON512_CLEAN_poly_mulconst(t0, ni, logn); + + /* + * b01 and b11 can be discarded, so we move back (t0,t1). + * Memory layout is now: + * g00 g01 g11 t0 t1 + */ + memcpy(b11, t0, n * 2 * sizeof * t0); + t0 = g11 + n; + t1 = t0 + n; + + /* + * Apply sampling; result is written over (t0,t1). + */ + ffSampling_fft_dyntree(samp, samp_ctx, + t0, t1, g00, g01, g11, logn, t1 + n); + + /* + * We arrange the layout back to: + * b00 b01 b10 b11 t0 t1 + * + * We did not conserve the matrix basis, so we must recompute + * it now. + */ + b00 = tmp; + b01 = b00 + n; + b10 = b01 + n; + b11 = b10 + n; + memmove(b11 + n, t0, n * 2 * sizeof * t0); + t0 = b11 + n; + t1 = t0 + n; + smallints_to_fpr(b01, f, logn); + smallints_to_fpr(b00, g, logn); + smallints_to_fpr(b11, F, logn); + smallints_to_fpr(b10, G, logn); + PQCLEAN_FALCON512_CLEAN_FFT(b01, logn); + PQCLEAN_FALCON512_CLEAN_FFT(b00, logn); + PQCLEAN_FALCON512_CLEAN_FFT(b11, logn); + PQCLEAN_FALCON512_CLEAN_FFT(b10, logn); + PQCLEAN_FALCON512_CLEAN_poly_neg(b01, logn); + PQCLEAN_FALCON512_CLEAN_poly_neg(b11, logn); + tx = t1 + n; + ty = tx + n; + + /* + * Get the lattice point corresponding to that tiny vector. + */ + memcpy(tx, t0, n * sizeof * t0); + memcpy(ty, t1, n * sizeof * t1); + PQCLEAN_FALCON512_CLEAN_poly_mul_fft(tx, b00, logn); + PQCLEAN_FALCON512_CLEAN_poly_mul_fft(ty, b10, logn); + PQCLEAN_FALCON512_CLEAN_poly_add(tx, ty, logn); + memcpy(ty, t0, n * sizeof * t0); + PQCLEAN_FALCON512_CLEAN_poly_mul_fft(ty, b01, logn); + + memcpy(t0, tx, n * sizeof * tx); + PQCLEAN_FALCON512_CLEAN_poly_mul_fft(t1, b11, logn); + PQCLEAN_FALCON512_CLEAN_poly_add(t1, ty, logn); + PQCLEAN_FALCON512_CLEAN_iFFT(t0, logn); + PQCLEAN_FALCON512_CLEAN_iFFT(t1, logn); + + s1tmp = (int16_t *)tx; + sqn = 0; + ng = 0; + for (u = 0; u < n; u ++) { + int32_t z; + + z = (int32_t)hm[u] - (int32_t)fpr_rint(t0[u]); + sqn += (uint32_t)(z * z); + ng |= sqn; + s1tmp[u] = (int16_t)z; + } + sqn |= -(ng >> 31); + + /* + * With "normal" degrees (e.g. 512 or 1024), it is very + * improbable that the computed vector is not short enough; + * however, it may happen in practice for the very reduced + * versions (e.g. degree 16 or below). In that case, the caller + * will loop, and we must not write anything into s2[] because + * s2[] may overlap with the hashed message hm[] and we need + * hm[] for the next iteration. + */ + s2tmp = (int16_t *)tmp; + for (u = 0; u < n; u ++) { + s2tmp[u] = (int16_t) - fpr_rint(t1[u]); + } + if (PQCLEAN_FALCON512_CLEAN_is_short_half(sqn, s2tmp, logn)) { + memcpy(s2, s2tmp, n * sizeof * s2); + memcpy(tmp, s1tmp, n * sizeof * s1tmp); + return 1; + } + return 0; +} + +/* + * Sample an integer value along a half-gaussian distribution centered + * on zero and standard deviation 1.8205, with a precision of 72 bits. + */ +int +PQCLEAN_FALCON512_CLEAN_gaussian0_sampler(prng *p) { + + static const uint32_t dist[] = { + 10745844u, 3068844u, 3741698u, + 5559083u, 1580863u, 8248194u, + 2260429u, 13669192u, 2736639u, + 708981u, 4421575u, 10046180u, + 169348u, 7122675u, 4136815u, + 30538u, 13063405u, 7650655u, + 4132u, 14505003u, 7826148u, + 417u, 16768101u, 11363290u, + 31u, 8444042u, 8086568u, + 1u, 12844466u, 265321u, + 0u, 1232676u, 13644283u, + 0u, 38047u, 9111839u, + 0u, 870u, 6138264u, + 0u, 14u, 12545723u, + 0u, 0u, 3104126u, + 0u, 0u, 28824u, + 0u, 0u, 198u, + 0u, 0u, 1u + }; + + uint32_t v0, v1, v2, hi; + uint64_t lo; + size_t u; + int z; + + /* + * Get a random 72-bit value, into three 24-bit limbs v0..v2. + */ + lo = prng_get_u64(p); + hi = prng_get_u8(p); + v0 = (uint32_t)lo & 0xFFFFFF; + v1 = (uint32_t)(lo >> 24) & 0xFFFFFF; + v2 = (uint32_t)(lo >> 48) | (hi << 16); + + /* + * Sampled value is z, such that v0..v2 is lower than the first + * z elements of the table. + */ + z = 0; + for (u = 0; u < (sizeof dist) / sizeof(dist[0]); u += 3) { + uint32_t w0, w1, w2, cc; + + w0 = dist[u + 2]; + w1 = dist[u + 1]; + w2 = dist[u + 0]; + cc = (v0 - w0) >> 31; + cc = (v1 - w1 - cc) >> 31; + cc = (v2 - w2 - cc) >> 31; + z += (int)cc; + } + return z; + +} + +/* + * Sample a bit with probability exp(-x) for some x >= 0. + */ +static int +BerExp(prng *p, fpr x, fpr ccs) { + int s, i; + fpr r; + uint32_t sw, w; + uint64_t z; + + /* + * Reduce x modulo log(2): x = s*log(2) + r, with s an integer, + * and 0 <= r < log(2). Since x >= 0, we can use fpr_trunc(). + */ + s = (int)fpr_trunc(fpr_mul(x, fpr_inv_log2)); + r = fpr_sub(x, fpr_mul(fpr_of(s), fpr_log2)); + + /* + * It may happen (quite rarely) that s >= 64; if sigma = 1.2 + * (the minimum value for sigma), r = 0 and b = 1, then we get + * s >= 64 if the half-Gaussian produced a z >= 13, which happens + * with probability about 0.000000000230383991, which is + * approximatively equal to 2^(-32). In any case, if s >= 64, + * then BerExp will be non-zero with probability less than + * 2^(-64), so we can simply saturate s at 63. + */ + sw = (uint32_t)s; + sw ^= (sw ^ 63) & -((63 - sw) >> 31); + s = (int)sw; + + /* + * Compute exp(-r); we know that 0 <= r < log(2) at this point, so + * we can use fpr_expm_p63(), which yields a result scaled to 2^63. + * We scale it up to 2^64, then right-shift it by s bits because + * we really want exp(-x) = 2^(-s)*exp(-r). + * + * The "-1" operation makes sure that the value fits on 64 bits + * (i.e. if r = 0, we may get 2^64, and we prefer 2^64-1 in that + * case). The bias is negligible since fpr_expm_p63() only computes + * with 51 bits of precision or so. + */ + z = ((fpr_expm_p63(r, ccs) << 1) - 1) >> s; + + /* + * Sample a bit with probability exp(-x). Since x = s*log(2) + r, + * exp(-x) = 2^-s * exp(-r), we compare lazily exp(-x) with the + * PRNG output to limit its consumption, the sign of the difference + * yields the expected result. + */ + i = 64; + do { + i -= 8; + w = prng_get_u8(p) - ((uint32_t)(z >> i) & 0xFF); + } while (!w && i > 0); + return (int)(w >> 31); +} + +/* + * The sampler produces a random integer that follows a discrete Gaussian + * distribution, centered on mu, and with standard deviation sigma. The + * provided parameter isigma is equal to 1/sigma. + * + * The value of sigma MUST lie between 1 and 2 (i.e. isigma lies between + * 0.5 and 1); in Falcon, sigma should always be between 1.2 and 1.9. + */ +int +PQCLEAN_FALCON512_CLEAN_sampler(void *ctx, fpr mu, fpr isigma) { + sampler_context *spc; + int s, z0, z, b; + fpr r, dss, ccs, x; + + spc = ctx; + + /* + * Center is mu. We compute mu = s + r where s is an integer + * and 0 <= r < 1. + */ + s = (int)fpr_floor(mu); + r = fpr_sub(mu, fpr_of(s)); + + /* + * dss = 1/(2*sigma^2) = 0.5*(isigma^2). + */ + dss = fpr_half(fpr_sqr(isigma)); + + /* + * ccs = sigma_min / sigma = sigma_min * isigma. + */ + ccs = fpr_mul(isigma, spc->sigma_min); + + /* + * We now need to sample on center r. + */ + for (;;) { + /* + * Sample z for a Gaussian distribution. Then get a + * random bit b to turn the sampling into a bimodal + * distribution: if b = 1, we use z+1, otherwise we + * use -z. We thus have two situations: + * + * - b = 1: z >= 1 and sampled against a Gaussian + * centered on 1. + * - b = 0: z <= 0 and sampled against a Gaussian + * centered on 0. + */ + z0 = PQCLEAN_FALCON512_CLEAN_gaussian0_sampler(&spc->p); + b = (int)prng_get_u8(&spc->p) & 1; + z = b + ((b << 1) - 1) * z0; + + /* + * Rejection sampling. We want a Gaussian centered on r; + * but we sampled against a Gaussian centered on b (0 or + * 1). But we know that z is always in the range where + * our sampling distribution is greater than the Gaussian + * distribution, so rejection works. + * + * We got z with distribution: + * G(z) = exp(-((z-b)^2)/(2*sigma0^2)) + * We target distribution: + * S(z) = exp(-((z-r)^2)/(2*sigma^2)) + * Rejection sampling works by keeping the value z with + * probability S(z)/G(z), and starting again otherwise. + * This requires S(z) <= G(z), which is the case here. + * Thus, we simply need to keep our z with probability: + * P = exp(-x) + * where: + * x = ((z-r)^2)/(2*sigma^2) - ((z-b)^2)/(2*sigma0^2) + * + * Here, we scale up the Bernouilli distribution, which + * makes rejection more probable, but makes rejection + * rate sufficiently decorrelated from the Gaussian + * center and standard deviation that the whole sampler + * can be said to be constant-time. + */ + x = fpr_mul(fpr_sqr(fpr_sub(fpr_of(z), r)), dss); + x = fpr_sub(x, fpr_mul(fpr_of(z0 * z0), fpr_inv_2sqrsigma0)); + if (BerExp(&spc->p, x, ccs)) { + /* + * Rejection sampling was centered on r, but the + * actual center is mu = s + r. + */ + return s + z; + } + } +} + +/* see inner.h */ +void +PQCLEAN_FALCON512_CLEAN_sign_tree(int16_t *sig, inner_shake256_context *rng, + const fpr *expanded_key, + const uint16_t *hm, unsigned logn, uint8_t *tmp) { + fpr *ftmp; + + ftmp = (fpr *)tmp; + for (;;) { + /* + * Signature produces short vectors s1 and s2. The + * signature is acceptable only if the aggregate vector + * s1,s2 is short; we must use the same bound as the + * verifier. + * + * If the signature is acceptable, then we return only s2 + * (the verifier recomputes s1 from s2, the hashed message, + * and the public key). + */ + sampler_context spc; + samplerZ samp; + void *samp_ctx; + + /* + * Normal sampling. We use a fast PRNG seeded from our + * SHAKE context ('rng'). + */ + if (logn == 10) { + spc.sigma_min = fpr_sigma_min_10; + } else { + spc.sigma_min = fpr_sigma_min_9; + } + PQCLEAN_FALCON512_CLEAN_prng_init(&spc.p, rng); + samp = PQCLEAN_FALCON512_CLEAN_sampler; + samp_ctx = &spc; + + /* + * Do the actual signature. + */ + if (do_sign_tree(samp, samp_ctx, sig, + expanded_key, hm, logn, ftmp)) { + break; + } + } +} + +/* see inner.h */ +void +PQCLEAN_FALCON512_CLEAN_sign_dyn(int16_t *sig, inner_shake256_context *rng, + const int8_t *f, const int8_t *g, + const int8_t *F, const int8_t *G, + const uint16_t *hm, unsigned logn, uint8_t *tmp) { + fpr *ftmp; + + ftmp = (fpr *)tmp; + for (;;) { + /* + * Signature produces short vectors s1 and s2. The + * signature is acceptable only if the aggregate vector + * s1,s2 is short; we must use the same bound as the + * verifier. + * + * If the signature is acceptable, then we return only s2 + * (the verifier recomputes s1 from s2, the hashed message, + * and the public key). + */ + sampler_context spc; + samplerZ samp; + void *samp_ctx; + + /* + * Normal sampling. We use a fast PRNG seeded from our + * SHAKE context ('rng'). + */ + if (logn == 10) { + spc.sigma_min = fpr_sigma_min_10; + } else { + spc.sigma_min = fpr_sigma_min_9; + } + PQCLEAN_FALCON512_CLEAN_prng_init(&spc.p, rng); + samp = PQCLEAN_FALCON512_CLEAN_sampler; + samp_ctx = &spc; + + /* + * Do the actual signature. + */ + if (do_sign_dyn(samp, samp_ctx, sig, + f, g, F, G, hm, logn, ftmp)) { + break; + } + } +} diff --git a/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/vrfy.c b/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/vrfy.c new file mode 100644 index 000000000..cf89f69f6 --- /dev/null +++ b/lib/liboqs/src/sig/falcon/pqclean_falcon-512_clean/vrfy.c @@ -0,0 +1,853 @@ +#include "inner.h" + +/* + * Falcon signature verification. + * + * ==========================(LICENSE BEGIN)============================ + * + * Copyright (c) 2017-2019 Falcon Project + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the + * "Software"), to deal in the Software without restriction, including + * without limitation the rights to use, copy, modify, merge, publish, + * distribute, sublicense, and/or sell copies of the Software, and to + * permit persons to whom the Software is furnished to do so, subject to + * the following conditions: + * + * The above copyright notice and this permission notice shall be + * included in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, + * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF + * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. + * IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY + * CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, + * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE + * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. + * + * ===========================(LICENSE END)============================= + * + * @author Thomas Pornin <thomas.pornin@nccgroup.com> + */ + + +/* ===================================================================== */ +/* + * Constants for NTT. + * + * n = 2^logn (2 <= n <= 1024) + * phi = X^n + 1 + * q = 12289 + * q0i = -1/q mod 2^16 + * R = 2^16 mod q + * R2 = 2^32 mod q + */ + +#define Q 12289 +#define Q0I 12287 +#define R 4091 +#define R2 10952 + +/* + * Table for NTT, binary case: + * GMb[x] = R*(g^rev(x)) mod q + * where g = 7 (it is a 2048-th primitive root of 1 modulo q) + * and rev() is the bit-reversal function over 10 bits. + */ +static const uint16_t GMb[] = { + 4091, 7888, 11060, 11208, 6960, 4342, 6275, 9759, + 1591, 6399, 9477, 5266, 586, 5825, 7538, 9710, + 1134, 6407, 1711, 965, 7099, 7674, 3743, 6442, + 10414, 8100, 1885, 1688, 1364, 10329, 10164, 9180, + 12210, 6240, 997, 117, 4783, 4407, 1549, 7072, + 2829, 6458, 4431, 8877, 7144, 2564, 5664, 4042, + 12189, 432, 10751, 1237, 7610, 1534, 3983, 7863, + 2181, 6308, 8720, 6570, 4843, 1690, 14, 3872, + 5569, 9368, 12163, 2019, 7543, 2315, 4673, 7340, + 1553, 1156, 8401, 11389, 1020, 2967, 10772, 7045, + 3316, 11236, 5285, 11578, 10637, 10086, 9493, 6180, + 9277, 6130, 3323, 883, 10469, 489, 1502, 2851, + 11061, 9729, 2742, 12241, 4970, 10481, 10078, 1195, + 730, 1762, 3854, 2030, 5892, 10922, 9020, 5274, + 9179, 3604, 3782, 10206, 3180, 3467, 4668, 2446, + 7613, 9386, 834, 7703, 6836, 3403, 5351, 12276, + 3580, 1739, 10820, 9787, 10209, 4070, 12250, 8525, + 10401, 2749, 7338, 10574, 6040, 943, 9330, 1477, + 6865, 9668, 3585, 6633, 12145, 4063, 3684, 7680, + 8188, 6902, 3533, 9807, 6090, 727, 10099, 7003, + 6945, 1949, 9731, 10559, 6057, 378, 7871, 8763, + 8901, 9229, 8846, 4551, 9589, 11664, 7630, 8821, + 5680, 4956, 6251, 8388, 10156, 8723, 2341, 3159, + 1467, 5460, 8553, 7783, 2649, 2320, 9036, 6188, + 737, 3698, 4699, 5753, 9046, 3687, 16, 914, + 5186, 10531, 4552, 1964, 3509, 8436, 7516, 5381, + 10733, 3281, 7037, 1060, 2895, 7156, 8887, 5357, + 6409, 8197, 2962, 6375, 5064, 6634, 5625, 278, + 932, 10229, 8927, 7642, 351, 9298, 237, 5858, + 7692, 3146, 12126, 7586, 2053, 11285, 3802, 5204, + 4602, 1748, 11300, 340, 3711, 4614, 300, 10993, + 5070, 10049, 11616, 12247, 7421, 10707, 5746, 5654, + 3835, 5553, 1224, 8476, 9237, 3845, 250, 11209, + 4225, 6326, 9680, 12254, 4136, 2778, 692, 8808, + 6410, 6718, 10105, 10418, 3759, 7356, 11361, 8433, + 6437, 3652, 6342, 8978, 5391, 2272, 6476, 7416, + 8418, 10824, 11986, 5733, 876, 7030, 2167, 2436, + 3442, 9217, 8206, 4858, 5964, 2746, 7178, 1434, + 7389, 8879, 10661, 11457, 4220, 1432, 10832, 4328, + 8557, 1867, 9454, 2416, 3816, 9076, 686, 5393, + 2523, 4339, 6115, 619, 937, 2834, 7775, 3279, + 2363, 7488, 6112, 5056, 824, 10204, 11690, 1113, + 2727, 9848, 896, 2028, 5075, 2654, 10464, 7884, + 12169, 5434, 3070, 6400, 9132, 11672, 12153, 4520, + 1273, 9739, 11468, 9937, 10039, 9720, 2262, 9399, + 11192, 315, 4511, 1158, 6061, 6751, 11865, 357, + 7367, 4550, 983, 8534, 8352, 10126, 7530, 9253, + 4367, 5221, 3999, 8777, 3161, 6990, 4130, 11652, + 3374, 11477, 1753, 292, 8681, 2806, 10378, 12188, + 5800, 11811, 3181, 1988, 1024, 9340, 2477, 10928, + 4582, 6750, 3619, 5503, 5233, 2463, 8470, 7650, + 7964, 6395, 1071, 1272, 3474, 11045, 3291, 11344, + 8502, 9478, 9837, 1253, 1857, 6233, 4720, 11561, + 6034, 9817, 3339, 1797, 2879, 6242, 5200, 2114, + 7962, 9353, 11363, 5475, 6084, 9601, 4108, 7323, + 10438, 9471, 1271, 408, 6911, 3079, 360, 8276, + 11535, 9156, 9049, 11539, 850, 8617, 784, 7919, + 8334, 12170, 1846, 10213, 12184, 7827, 11903, 5600, + 9779, 1012, 721, 2784, 6676, 6552, 5348, 4424, + 6816, 8405, 9959, 5150, 2356, 5552, 5267, 1333, + 8801, 9661, 7308, 5788, 4910, 909, 11613, 4395, + 8238, 6686, 4302, 3044, 2285, 12249, 1963, 9216, + 4296, 11918, 695, 4371, 9793, 4884, 2411, 10230, + 2650, 841, 3890, 10231, 7248, 8505, 11196, 6688, + 4059, 6060, 3686, 4722, 11853, 5816, 7058, 6868, + 11137, 7926, 4894, 12284, 4102, 3908, 3610, 6525, + 7938, 7982, 11977, 6755, 537, 4562, 1623, 8227, + 11453, 7544, 906, 11816, 9548, 10858, 9703, 2815, + 11736, 6813, 6979, 819, 8903, 6271, 10843, 348, + 7514, 8339, 6439, 694, 852, 5659, 2781, 3716, + 11589, 3024, 1523, 8659, 4114, 10738, 3303, 5885, + 2978, 7289, 11884, 9123, 9323, 11830, 98, 2526, + 2116, 4131, 11407, 1844, 3645, 3916, 8133, 2224, + 10871, 8092, 9651, 5989, 7140, 8480, 1670, 159, + 10923, 4918, 128, 7312, 725, 9157, 5006, 6393, + 3494, 6043, 10972, 6181, 11838, 3423, 10514, 7668, + 3693, 6658, 6905, 11953, 10212, 11922, 9101, 8365, + 5110, 45, 2400, 1921, 4377, 2720, 1695, 51, + 2808, 650, 1896, 9997, 9971, 11980, 8098, 4833, + 4135, 4257, 5838, 4765, 10985, 11532, 590, 12198, + 482, 12173, 2006, 7064, 10018, 3912, 12016, 10519, + 11362, 6954, 2210, 284, 5413, 6601, 3865, 10339, + 11188, 6231, 517, 9564, 11281, 3863, 1210, 4604, + 8160, 11447, 153, 7204, 5763, 5089, 9248, 12154, + 11748, 1354, 6672, 179, 5532, 2646, 5941, 12185, + 862, 3158, 477, 7279, 5678, 7914, 4254, 302, + 2893, 10114, 6890, 9560, 9647, 11905, 4098, 9824, + 10269, 1353, 10715, 5325, 6254, 3951, 1807, 6449, + 5159, 1308, 8315, 3404, 1877, 1231, 112, 6398, + 11724, 12272, 7286, 1459, 12274, 9896, 3456, 800, + 1397, 10678, 103, 7420, 7976, 936, 764, 632, + 7996, 8223, 8445, 7758, 10870, 9571, 2508, 1946, + 6524, 10158, 1044, 4338, 2457, 3641, 1659, 4139, + 4688, 9733, 11148, 3946, 2082, 5261, 2036, 11850, + 7636, 12236, 5366, 2380, 1399, 7720, 2100, 3217, + 10912, 8898, 7578, 11995, 2791, 1215, 3355, 2711, + 2267, 2004, 8568, 10176, 3214, 2337, 1750, 4729, + 4997, 7415, 6315, 12044, 4374, 7157, 4844, 211, + 8003, 10159, 9290, 11481, 1735, 2336, 5793, 9875, + 8192, 986, 7527, 1401, 870, 3615, 8465, 2756, + 9770, 2034, 10168, 3264, 6132, 54, 2880, 4763, + 11805, 3074, 8286, 9428, 4881, 6933, 1090, 10038, + 2567, 708, 893, 6465, 4962, 10024, 2090, 5718, + 10743, 780, 4733, 4623, 2134, 2087, 4802, 884, + 5372, 5795, 5938, 4333, 6559, 7549, 5269, 10664, + 4252, 3260, 5917, 10814, 5768, 9983, 8096, 7791, + 6800, 7491, 6272, 1907, 10947, 6289, 11803, 6032, + 11449, 1171, 9201, 7933, 2479, 7970, 11337, 7062, + 8911, 6728, 6542, 8114, 8828, 6595, 3545, 4348, + 4610, 2205, 6999, 8106, 5560, 10390, 9321, 2499, + 2413, 7272, 6881, 10582, 9308, 9437, 3554, 3326, + 5991, 11969, 3415, 12283, 9838, 12063, 4332, 7830, + 11329, 6605, 12271, 2044, 11611, 7353, 11201, 11582, + 3733, 8943, 9978, 1627, 7168, 3935, 5050, 2762, + 7496, 10383, 755, 1654, 12053, 4952, 10134, 4394, + 6592, 7898, 7497, 8904, 12029, 3581, 10748, 5674, + 10358, 4901, 7414, 8771, 710, 6764, 8462, 7193, + 5371, 7274, 11084, 290, 7864, 6827, 11822, 2509, + 6578, 4026, 5807, 1458, 5721, 5762, 4178, 2105, + 11621, 4852, 8897, 2856, 11510, 9264, 2520, 8776, + 7011, 2647, 1898, 7039, 5950, 11163, 5488, 6277, + 9182, 11456, 633, 10046, 11554, 5633, 9587, 2333, + 7008, 7084, 5047, 7199, 9865, 8997, 569, 6390, + 10845, 9679, 8268, 11472, 4203, 1997, 2, 9331, + 162, 6182, 2000, 3649, 9792, 6363, 7557, 6187, + 8510, 9935, 5536, 9019, 3706, 12009, 1452, 3067, + 5494, 9692, 4865, 6019, 7106, 9610, 4588, 10165, + 6261, 5887, 2652, 10172, 1580, 10379, 4638, 9949 +}; + +/* + * Table for inverse NTT, binary case: + * iGMb[x] = R*((1/g)^rev(x)) mod q + * Since g = 7, 1/g = 8778 mod 12289. + */ +static const uint16_t iGMb[] = { + 4091, 4401, 1081, 1229, 2530, 6014, 7947, 5329, + 2579, 4751, 6464, 11703, 7023, 2812, 5890, 10698, + 3109, 2125, 1960, 10925, 10601, 10404, 4189, 1875, + 5847, 8546, 4615, 5190, 11324, 10578, 5882, 11155, + 8417, 12275, 10599, 7446, 5719, 3569, 5981, 10108, + 4426, 8306, 10755, 4679, 11052, 1538, 11857, 100, + 8247, 6625, 9725, 5145, 3412, 7858, 5831, 9460, + 5217, 10740, 7882, 7506, 12172, 11292, 6049, 79, + 13, 6938, 8886, 5453, 4586, 11455, 2903, 4676, + 9843, 7621, 8822, 9109, 2083, 8507, 8685, 3110, + 7015, 3269, 1367, 6397, 10259, 8435, 10527, 11559, + 11094, 2211, 1808, 7319, 48, 9547, 2560, 1228, + 9438, 10787, 11800, 1820, 11406, 8966, 6159, 3012, + 6109, 2796, 2203, 1652, 711, 7004, 1053, 8973, + 5244, 1517, 9322, 11269, 900, 3888, 11133, 10736, + 4949, 7616, 9974, 4746, 10270, 126, 2921, 6720, + 6635, 6543, 1582, 4868, 42, 673, 2240, 7219, + 1296, 11989, 7675, 8578, 11949, 989, 10541, 7687, + 7085, 8487, 1004, 10236, 4703, 163, 9143, 4597, + 6431, 12052, 2991, 11938, 4647, 3362, 2060, 11357, + 12011, 6664, 5655, 7225, 5914, 9327, 4092, 5880, + 6932, 3402, 5133, 9394, 11229, 5252, 9008, 1556, + 6908, 4773, 3853, 8780, 10325, 7737, 1758, 7103, + 11375, 12273, 8602, 3243, 6536, 7590, 8591, 11552, + 6101, 3253, 9969, 9640, 4506, 3736, 6829, 10822, + 9130, 9948, 3566, 2133, 3901, 6038, 7333, 6609, + 3468, 4659, 625, 2700, 7738, 3443, 3060, 3388, + 3526, 4418, 11911, 6232, 1730, 2558, 10340, 5344, + 5286, 2190, 11562, 6199, 2482, 8756, 5387, 4101, + 4609, 8605, 8226, 144, 5656, 8704, 2621, 5424, + 10812, 2959, 11346, 6249, 1715, 4951, 9540, 1888, + 3764, 39, 8219, 2080, 2502, 1469, 10550, 8709, + 5601, 1093, 3784, 5041, 2058, 8399, 11448, 9639, + 2059, 9878, 7405, 2496, 7918, 11594, 371, 7993, + 3073, 10326, 40, 10004, 9245, 7987, 5603, 4051, + 7894, 676, 11380, 7379, 6501, 4981, 2628, 3488, + 10956, 7022, 6737, 9933, 7139, 2330, 3884, 5473, + 7865, 6941, 5737, 5613, 9505, 11568, 11277, 2510, + 6689, 386, 4462, 105, 2076, 10443, 119, 3955, + 4370, 11505, 3672, 11439, 750, 3240, 3133, 754, + 4013, 11929, 9210, 5378, 11881, 11018, 2818, 1851, + 4966, 8181, 2688, 6205, 6814, 926, 2936, 4327, + 10175, 7089, 6047, 9410, 10492, 8950, 2472, 6255, + 728, 7569, 6056, 10432, 11036, 2452, 2811, 3787, + 945, 8998, 1244, 8815, 11017, 11218, 5894, 4325, + 4639, 3819, 9826, 7056, 6786, 8670, 5539, 7707, + 1361, 9812, 2949, 11265, 10301, 9108, 478, 6489, + 101, 1911, 9483, 3608, 11997, 10536, 812, 8915, + 637, 8159, 5299, 9128, 3512, 8290, 7068, 7922, + 3036, 4759, 2163, 3937, 3755, 11306, 7739, 4922, + 11932, 424, 5538, 6228, 11131, 7778, 11974, 1097, + 2890, 10027, 2569, 2250, 2352, 821, 2550, 11016, + 7769, 136, 617, 3157, 5889, 9219, 6855, 120, + 4405, 1825, 9635, 7214, 10261, 11393, 2441, 9562, + 11176, 599, 2085, 11465, 7233, 6177, 4801, 9926, + 9010, 4514, 9455, 11352, 11670, 6174, 7950, 9766, + 6896, 11603, 3213, 8473, 9873, 2835, 10422, 3732, + 7961, 1457, 10857, 8069, 832, 1628, 3410, 4900, + 10855, 5111, 9543, 6325, 7431, 4083, 3072, 8847, + 9853, 10122, 5259, 11413, 6556, 303, 1465, 3871, + 4873, 5813, 10017, 6898, 3311, 5947, 8637, 5852, + 3856, 928, 4933, 8530, 1871, 2184, 5571, 5879, + 3481, 11597, 9511, 8153, 35, 2609, 5963, 8064, + 1080, 12039, 8444, 3052, 3813, 11065, 6736, 8454, + 2340, 7651, 1910, 10709, 2117, 9637, 6402, 6028, + 2124, 7701, 2679, 5183, 6270, 7424, 2597, 6795, + 9222, 10837, 280, 8583, 3270, 6753, 2354, 3779, + 6102, 4732, 5926, 2497, 8640, 10289, 6107, 12127, + 2958, 12287, 10292, 8086, 817, 4021, 2610, 1444, + 5899, 11720, 3292, 2424, 5090, 7242, 5205, 5281, + 9956, 2702, 6656, 735, 2243, 11656, 833, 3107, + 6012, 6801, 1126, 6339, 5250, 10391, 9642, 5278, + 3513, 9769, 3025, 779, 9433, 3392, 7437, 668, + 10184, 8111, 6527, 6568, 10831, 6482, 8263, 5711, + 9780, 467, 5462, 4425, 11999, 1205, 5015, 6918, + 5096, 3827, 5525, 11579, 3518, 4875, 7388, 1931, + 6615, 1541, 8708, 260, 3385, 4792, 4391, 5697, + 7895, 2155, 7337, 236, 10635, 11534, 1906, 4793, + 9527, 7239, 8354, 5121, 10662, 2311, 3346, 8556, + 707, 1088, 4936, 678, 10245, 18, 5684, 960, + 4459, 7957, 226, 2451, 6, 8874, 320, 6298, + 8963, 8735, 2852, 2981, 1707, 5408, 5017, 9876, + 9790, 2968, 1899, 6729, 4183, 5290, 10084, 7679, + 7941, 8744, 5694, 3461, 4175, 5747, 5561, 3378, + 5227, 952, 4319, 9810, 4356, 3088, 11118, 840, + 6257, 486, 6000, 1342, 10382, 6017, 4798, 5489, + 4498, 4193, 2306, 6521, 1475, 6372, 9029, 8037, + 1625, 7020, 4740, 5730, 7956, 6351, 6494, 6917, + 11405, 7487, 10202, 10155, 7666, 7556, 11509, 1546, + 6571, 10199, 2265, 7327, 5824, 11396, 11581, 9722, + 2251, 11199, 5356, 7408, 2861, 4003, 9215, 484, + 7526, 9409, 12235, 6157, 9025, 2121, 10255, 2519, + 9533, 3824, 8674, 11419, 10888, 4762, 11303, 4097, + 2414, 6496, 9953, 10554, 808, 2999, 2130, 4286, + 12078, 7445, 5132, 7915, 245, 5974, 4874, 7292, + 7560, 10539, 9952, 9075, 2113, 3721, 10285, 10022, + 9578, 8934, 11074, 9498, 294, 4711, 3391, 1377, + 9072, 10189, 4569, 10890, 9909, 6923, 53, 4653, + 439, 10253, 7028, 10207, 8343, 1141, 2556, 7601, + 8150, 10630, 8648, 9832, 7951, 11245, 2131, 5765, + 10343, 9781, 2718, 1419, 4531, 3844, 4066, 4293, + 11657, 11525, 11353, 4313, 4869, 12186, 1611, 10892, + 11489, 8833, 2393, 15, 10830, 5003, 17, 565, + 5891, 12177, 11058, 10412, 8885, 3974, 10981, 7130, + 5840, 10482, 8338, 6035, 6964, 1574, 10936, 2020, + 2465, 8191, 384, 2642, 2729, 5399, 2175, 9396, + 11987, 8035, 4375, 6611, 5010, 11812, 9131, 11427, + 104, 6348, 9643, 6757, 12110, 5617, 10935, 541, + 135, 3041, 7200, 6526, 5085, 12136, 842, 4129, + 7685, 11079, 8426, 1008, 2725, 11772, 6058, 1101, + 1950, 8424, 5688, 6876, 12005, 10079, 5335, 927, + 1770, 273, 8377, 2271, 5225, 10283, 116, 11807, + 91, 11699, 757, 1304, 7524, 6451, 8032, 8154, + 7456, 4191, 309, 2318, 2292, 10393, 11639, 9481, + 12238, 10594, 9569, 7912, 10368, 9889, 12244, 7179, + 3924, 3188, 367, 2077, 336, 5384, 5631, 8596, + 4621, 1775, 8866, 451, 6108, 1317, 6246, 8795, + 5896, 7283, 3132, 11564, 4977, 12161, 7371, 1366, + 12130, 10619, 3809, 5149, 6300, 2638, 4197, 1418, + 10065, 4156, 8373, 8644, 10445, 882, 8158, 10173, + 9763, 12191, 459, 2966, 3166, 405, 5000, 9311, + 6404, 8986, 1551, 8175, 3630, 10766, 9265, 700, + 8573, 9508, 6630, 11437, 11595, 5850, 3950, 4775, + 11941, 1446, 6018, 3386, 11470, 5310, 5476, 553, + 9474, 2586, 1431, 2741, 473, 11383, 4745, 836, + 4062, 10666, 7727, 11752, 5534, 312, 4307, 4351, + 5764, 8679, 8381, 8187, 5, 7395, 4363, 1152, + 5421, 5231, 6473, 436, 7567, 8603, 6229, 8230 +}; + +/* + * Reduce a small signed integer modulo q. The source integer MUST + * be between -q/2 and +q/2. + */ +static inline uint32_t +mq_conv_small(int x) { + /* + * If x < 0, the cast to uint32_t will set the high bit to 1. + */ + uint32_t y; + + y = (uint32_t)x; + y += Q & -(y >> 31); + return y; +} + +/* + * Addition modulo q. Operands must be in the 0..q-1 range. + */ +static inline uint32_t +mq_add(uint32_t x, uint32_t y) { + /* + * We compute x + y - q. If the result is negative, then the + * high bit will be set, and 'd >> 31' will be equal to 1; + * thus '-(d >> 31)' will be an all-one pattern. Otherwise, + * it will be an all-zero pattern. In other words, this + * implements a conditional addition of q. + */ + uint32_t d; + + d = x + y - Q; + d += Q & -(d >> 31); + return d; +} + +/* + * Subtraction modulo q. Operands must be in the 0..q-1 range. + */ +static inline uint32_t +mq_sub(uint32_t x, uint32_t y) { + /* + * As in mq_add(), we use a conditional addition to ensure the + * result is in the 0..q-1 range. + */ + uint32_t d; + + d = x - y; + d += Q & -(d >> 31); + return d; +} + +/* + * Division by 2 modulo q. Operand must be in the 0..q-1 range. + */ +static inline uint32_t +mq_rshift1(uint32_t x) { + x += Q & -(x & 1); + return (x >> 1); +} + +/* + * Montgomery multiplication modulo q. If we set R = 2^16 mod q, then + * this function computes: x * y / R mod q + * Operands must be in the 0..q-1 range. + */ +static inline uint32_t +mq_montymul(uint32_t x, uint32_t y) { + uint32_t z, w; + + /* + * We compute x*y + k*q with a value of k chosen so that the 16 + * low bits of the result are 0. We can then shift the value. + * After the shift, result may still be larger than q, but it + * will be lower than 2*q, so a conditional subtraction works. + */ + + z = x * y; + w = ((z * Q0I) & 0xFFFF) * Q; + + /* + * When adding z and w, the result will have its low 16 bits + * equal to 0. Since x, y and z are lower than q, the sum will + * be no more than (2^15 - 1) * q + (q - 1)^2, which will + * fit on 29 bits. + */ + z = (z + w) >> 16; + + /* + * After the shift, analysis shows that the value will be less + * than 2q. We do a subtraction then conditional subtraction to + * ensure the result is in the expected range. + */ + z -= Q; + z += Q & -(z >> 31); + return z; +} + +/* + * Montgomery squaring (computes (x^2)/R). + */ +static inline uint32_t +mq_montysqr(uint32_t x) { + return mq_montymul(x, x); +} + +/* + * Divide x by y modulo q = 12289. + */ +static inline uint32_t +mq_div_12289(uint32_t x, uint32_t y) { + /* + * We invert y by computing y^(q-2) mod q. + * + * We use the following addition chain for exponent e = 12287: + * + * e0 = 1 + * e1 = 2 * e0 = 2 + * e2 = e1 + e0 = 3 + * e3 = e2 + e1 = 5 + * e4 = 2 * e3 = 10 + * e5 = 2 * e4 = 20 + * e6 = 2 * e5 = 40 + * e7 = 2 * e6 = 80 + * e8 = 2 * e7 = 160 + * e9 = e8 + e2 = 163 + * e10 = e9 + e8 = 323 + * e11 = 2 * e10 = 646 + * e12 = 2 * e11 = 1292 + * e13 = e12 + e9 = 1455 + * e14 = 2 * e13 = 2910 + * e15 = 2 * e14 = 5820 + * e16 = e15 + e10 = 6143 + * e17 = 2 * e16 = 12286 + * e18 = e17 + e0 = 12287 + * + * Additions on exponents are converted to Montgomery + * multiplications. We define all intermediate results as so + * many local variables, and let the C compiler work out which + * must be kept around. + */ + uint32_t y0, y1, y2, y3, y4, y5, y6, y7, y8, y9; + uint32_t y10, y11, y12, y13, y14, y15, y16, y17, y18; + + y0 = mq_montymul(y, R2); + y1 = mq_montysqr(y0); + y2 = mq_montymul(y1, y0); + y3 = mq_montymul(y2, y1); + y4 = mq_montysqr(y3); + y5 = mq_montysqr(y4); + y6 = mq_montysqr(y5); + y7 = mq_montysqr(y6); + y8 = mq_montysqr(y7); + y9 = mq_montymul(y8, y2); + y10 = mq_montymul(y9, y8); + y11 = mq_montysqr(y10); + y12 = mq_montysqr(y11); + y13 = mq_montymul(y12, y9); + y14 = mq_montysqr(y13); + y15 = mq_montysqr(y14); + y16 = mq_montymul(y15, y10); + y17 = mq_montysqr(y16); + y18 = mq_montymul(y17, y0); + + /* + * Final multiplication with x, which is not in Montgomery + * representation, computes the correct division result. + */ + return mq_montymul(y18, x); +} + +/* + * Compute NTT on a ring element. + */ +static void +mq_NTT(uint16_t *a, unsigned logn) { + size_t n, t, m; + + n = (size_t)1 << logn; + t = n; + for (m = 1; m < n; m <<= 1) { + size_t ht, i, j1; + + ht = t >> 1; + for (i = 0, j1 = 0; i < m; i ++, j1 += t) { + size_t j, j2; + uint32_t s; + + s = GMb[m + i]; + j2 = j1 + ht; + for (j = j1; j < j2; j ++) { + uint32_t u, v; + + u = a[j]; + v = mq_montymul(a[j + ht], s); + a[j] = (uint16_t)mq_add(u, v); + a[j + ht] = (uint16_t)mq_sub(u, v); + } + } + t = ht; + } +} + +/* + * Compute the inverse NTT on a ring element, binary case. + */ +static void +mq_iNTT(uint16_t *a, unsigned logn) { + size_t n, t, m; + uint32_t ni; + + n = (size_t)1 << logn; + t = 1; + m = n; + while (m > 1) { + size_t hm, dt, i, j1; + + hm = m >> 1; + dt = t << 1; + for (i = 0, j1 = 0; i < hm; i ++, j1 += dt) { + size_t j, j2; + uint32_t s; + + j2 = j1 + t; + s = iGMb[hm + i]; + for (j = j1; j < j2; j ++) { + uint32_t u, v, w; + + u = a[j]; + v = a[j + t]; + a[j] = (uint16_t)mq_add(u, v); + w = mq_sub(u, v); + a[j + t] = (uint16_t) + mq_montymul(w, s); + } + } + t = dt; + m = hm; + } + + /* + * To complete the inverse NTT, we must now divide all values by + * n (the vector size). We thus need the inverse of n, i.e. we + * need to divide 1 by 2 logn times. But we also want it in + * Montgomery representation, i.e. we also want to multiply it + * by R = 2^16. In the common case, this should be a simple right + * shift. The loop below is generic and works also in corner cases; + * its computation time is negligible. + */ + ni = R; + for (m = n; m > 1; m >>= 1) { + ni = mq_rshift1(ni); + } + for (m = 0; m < n; m ++) { + a[m] = (uint16_t)mq_montymul(a[m], ni); + } +} + +/* + * Convert a polynomial (mod q) to Montgomery representation. + */ +static void +mq_poly_tomonty(uint16_t *f, unsigned logn) { + size_t u, n; + + n = (size_t)1 << logn; + for (u = 0; u < n; u ++) { + f[u] = (uint16_t)mq_montymul(f[u], R2); + } +} + +/* + * Multiply two polynomials together (NTT representation, and using + * a Montgomery multiplication). Result f*g is written over f. + */ +static void +mq_poly_montymul_ntt(uint16_t *f, const uint16_t *g, unsigned logn) { + size_t u, n; + + n = (size_t)1 << logn; + for (u = 0; u < n; u ++) { + f[u] = (uint16_t)mq_montymul(f[u], g[u]); + } +} + +/* + * Subtract polynomial g from polynomial f. + */ +static void +mq_poly_sub(uint16_t *f, const uint16_t *g, unsigned logn) { + size_t u, n; + + n = (size_t)1 << logn; + for (u = 0; u < n; u ++) { + f[u] = (uint16_t)mq_sub(f[u], g[u]); + } +} + +/* ===================================================================== */ + +/* see inner.h */ +void +PQCLEAN_FALCON512_CLEAN_to_ntt_monty(uint16_t *h, unsigned logn) { + mq_NTT(h, logn); + mq_poly_tomonty(h, logn); +} + +/* see inner.h */ +int +PQCLEAN_FALCON512_CLEAN_verify_raw(const uint16_t *c0, const int16_t *s2, + const uint16_t *h, unsigned logn, uint8_t *tmp) { + size_t u, n; + uint16_t *tt; + + n = (size_t)1 << logn; + tt = (uint16_t *)tmp; + + /* + * Reduce s2 elements modulo q ([0..q-1] range). + */ + for (u = 0; u < n; u ++) { + uint32_t w; + + w = (uint32_t)s2[u]; + w += Q & -(w >> 31); + tt[u] = (uint16_t)w; + } + + /* + * Compute -s1 = s2*h - c0 mod phi mod q (in tt[]). + */ + mq_NTT(tt, logn); + mq_poly_montymul_ntt(tt, h, logn); + mq_iNTT(tt, logn); + mq_poly_sub(tt, c0, logn); + + /* + * Normalize -s1 elements into the [-q/2..q/2] range. + */ + for (u = 0; u < n; u ++) { + int32_t w; + + w = (int32_t)tt[u]; + w -= (int32_t)(Q & -(((Q >> 1) - (uint32_t)w) >> 31)); + ((int16_t *)tt)[u] = (int16_t)w; + } + + /* + * Signature is valid if and only if the aggregate (-s1,s2) vector + * is short enough. + */ + return PQCLEAN_FALCON512_CLEAN_is_short((int16_t *)tt, s2, logn); +} + +/* see inner.h */ +int +PQCLEAN_FALCON512_CLEAN_compute_public(uint16_t *h, + const int8_t *f, const int8_t *g, unsigned logn, uint8_t *tmp) { + size_t u, n; + uint16_t *tt; + + n = (size_t)1 << logn; + tt = (uint16_t *)tmp; + for (u = 0; u < n; u ++) { + tt[u] = (uint16_t)mq_conv_small(f[u]); + h[u] = (uint16_t)mq_conv_small(g[u]); + } + mq_NTT(h, logn); + mq_NTT(tt, logn); + for (u = 0; u < n; u ++) { + if (tt[u] == 0) { + return 0; + } + h[u] = (uint16_t)mq_div_12289(h[u], tt[u]); + } + mq_iNTT(h, logn); + return 1; +} + +/* see inner.h */ +int +PQCLEAN_FALCON512_CLEAN_complete_private(int8_t *G, + const int8_t *f, const int8_t *g, const int8_t *F, + unsigned logn, uint8_t *tmp) { + size_t u, n; + uint16_t *t1, *t2; + + n = (size_t)1 << logn; + t1 = (uint16_t *)tmp; + t2 = t1 + n; + for (u = 0; u < n; u ++) { + t1[u] = (uint16_t)mq_conv_small(g[u]); + t2[u] = (uint16_t)mq_conv_small(F[u]); + } + mq_NTT(t1, logn); + mq_NTT(t2, logn); + mq_poly_tomonty(t1, logn); + mq_poly_montymul_ntt(t1, t2, logn); + for (u = 0; u < n; u ++) { + t2[u] = (uint16_t)mq_conv_small(f[u]); + } + mq_NTT(t2, logn); + for (u = 0; u < n; u ++) { + if (t2[u] == 0) { + return 0; + } + t1[u] = (uint16_t)mq_div_12289(t1[u], t2[u]); + } + mq_iNTT(t1, logn); + for (u = 0; u < n; u ++) { + uint32_t w; + int32_t gi; + + w = t1[u]; + w -= (Q & ~ -((w - (Q >> 1)) >> 31)); + gi = *(int32_t *)&w; + if (gi < -127 || gi > +127) { + return 0; + } + G[u] = (int8_t)gi; + } + return 1; +} + +/* see inner.h */ +int +PQCLEAN_FALCON512_CLEAN_is_invertible( + const int16_t *s2, unsigned logn, uint8_t *tmp) { + size_t u, n; + uint16_t *tt; + uint32_t r; + + n = (size_t)1 << logn; + tt = (uint16_t *)tmp; + for (u = 0; u < n; u ++) { + uint32_t w; + + w = (uint32_t)s2[u]; + w += Q & -(w >> 31); + tt[u] = (uint16_t)w; + } + mq_NTT(tt, logn); + r = 0; + for (u = 0; u < n; u ++) { + r |= (uint32_t)(tt[u] - 1); + } + return (int)(1u - (r >> 31)); +} + +/* see inner.h */ +int +PQCLEAN_FALCON512_CLEAN_verify_recover(uint16_t *h, + const uint16_t *c0, const int16_t *s1, const int16_t *s2, + unsigned logn, uint8_t *tmp) { + size_t u, n; + uint16_t *tt; + uint32_t r; + + n = (size_t)1 << logn; + + /* + * Reduce elements of s1 and s2 modulo q; then write s2 into tt[] + * and c0 - s1 into h[]. + */ + tt = (uint16_t *)tmp; + for (u = 0; u < n; u ++) { + uint32_t w; + + w = (uint32_t)s2[u]; + w += Q & -(w >> 31); + tt[u] = (uint16_t)w; + + w = (uint32_t)s1[u]; + w += Q & -(w >> 31); + w = mq_sub(c0[u], w); + h[u] = (uint16_t)w; + } + + /* + * Compute h = (c0 - s1) / s2. If one of the coefficients of s2 + * is zero (in NTT representation) then the operation fails. We + * keep that information into a flag so that we do not deviate + * from strict constant-time processing; if all coefficients of + * s2 are non-zero, then the high bit of r will be zero. + */ + mq_NTT(tt, logn); + mq_NTT(h, logn); + r = 0; + for (u = 0; u < n; u ++) { + r |= (uint32_t)(tt[u] - 1); + h[u] = (uint16_t)mq_div_12289(h[u], tt[u]); + } + mq_iNTT(h, logn); + + /* + * Signature is acceptable if and only if it is short enough, + * and s2 was invertible mod phi mod q. The caller must still + * check that the rebuilt public key matches the expected + * value (e.g. through a hash). + */ + r = ~r & (uint32_t) - PQCLEAN_FALCON512_CLEAN_is_short(s1, s2, logn); + return (int)(r >> 31); +} + +/* see inner.h */ +int +PQCLEAN_FALCON512_CLEAN_count_nttzero(const int16_t *sig, unsigned logn, uint8_t *tmp) { + uint16_t *s2; + size_t u, n; + uint32_t r; + + n = (size_t)1 << logn; + s2 = (uint16_t *)tmp; + for (u = 0; u < n; u ++) { + uint32_t w; + + w = (uint32_t)sig[u]; + w += Q & -(w >> 31); + s2[u] = (uint16_t)w; + } + mq_NTT(s2, logn); + r = 0; + for (u = 0; u < n; u ++) { + uint32_t w; + + w = (uint32_t)s2[u] - 1u; + r += (w >> 31); + } + return (int)r; +} diff --git a/lib/liboqs/src/sig/falcon/sig_falcon.h b/lib/liboqs/src/sig/falcon/sig_falcon.h new file mode 100644 index 000000000..2cd661617 --- /dev/null +++ b/lib/liboqs/src/sig/falcon/sig_falcon.h @@ -0,0 +1,30 @@ +// SPDX-License-Identifier: MIT + +#ifndef OQS_SIG_FALCON_H +#define OQS_SIG_FALCON_H + +#include <oqs/oqs.h> + +#ifdef OQS_ENABLE_SIG_falcon_512 +#define OQS_SIG_falcon_512_length_public_key 897 +#define OQS_SIG_falcon_512_length_secret_key 1281 +#define OQS_SIG_falcon_512_length_signature 690 + +OQS_SIG *OQS_SIG_falcon_512_new(void); +OQS_API OQS_STATUS OQS_SIG_falcon_512_keypair(uint8_t *public_key, uint8_t *secret_key); +OQS_API OQS_STATUS OQS_SIG_falcon_512_sign(uint8_t *signature, size_t *signature_len, const uint8_t *message, size_t message_len, const uint8_t *secret_key); +OQS_API OQS_STATUS OQS_SIG_falcon_512_verify(const uint8_t *message, size_t message_len, const uint8_t *signature, size_t signature_len, const uint8_t *public_key); +#endif + +#ifdef OQS_ENABLE_SIG_falcon_1024 +#define OQS_SIG_falcon_1024_length_public_key 1793 +#define OQS_SIG_falcon_1024_length_secret_key 2305 +#define OQS_SIG_falcon_1024_length_signature 1330 + +OQS_SIG *OQS_SIG_falcon_1024_new(void); +OQS_API OQS_STATUS OQS_SIG_falcon_1024_keypair(uint8_t *public_key, uint8_t *secret_key); +OQS_API OQS_STATUS OQS_SIG_falcon_1024_sign(uint8_t *signature, size_t *signature_len, const uint8_t *message, size_t message_len, const uint8_t *secret_key); +OQS_API OQS_STATUS OQS_SIG_falcon_1024_verify(const uint8_t *message, size_t message_len, const uint8_t *signature, size_t signature_len, const uint8_t *public_key); +#endif + +#endif diff --git a/lib/liboqs/src/sig/falcon/sig_falcon_1024.c b/lib/liboqs/src/sig/falcon/sig_falcon_1024.c new file mode 100644 index 000000000..cdb3cd0d7 --- /dev/null +++ b/lib/liboqs/src/sig/falcon/sig_falcon_1024.c @@ -0,0 +1,90 @@ +// SPDX-License-Identifier: MIT + +#include <stdlib.h> + +#include <oqs/sig_falcon.h> + +#if defined(OQS_ENABLE_SIG_falcon_1024) + +OQS_SIG *OQS_SIG_falcon_1024_new(void) { + + OQS_SIG *sig = malloc(sizeof(OQS_SIG)); + if (sig == NULL) { + return NULL; + } + sig->method_name = OQS_SIG_alg_falcon_1024; + sig->alg_version = "supercop-20201018 via https://github.com/jschanck/package-pqclean/tree/cea1fa5a/falcon"; + + sig->claimed_nist_level = 5; + sig->euf_cma = true; + + sig->length_public_key = OQS_SIG_falcon_1024_length_public_key; + sig->length_secret_key = OQS_SIG_falcon_1024_length_secret_key; + sig->length_signature = OQS_SIG_falcon_1024_length_signature; + + sig->keypair = OQS_SIG_falcon_1024_keypair; + sig->sign = OQS_SIG_falcon_1024_sign; + sig->verify = OQS_SIG_falcon_1024_verify; + + return sig; +} + +extern int PQCLEAN_FALCON1024_CLEAN_crypto_sign_keypair(uint8_t *pk, uint8_t *sk); +extern int PQCLEAN_FALCON1024_CLEAN_crypto_sign_signature(uint8_t *sig, size_t *siglen, const uint8_t *m, size_t mlen, const uint8_t *sk); +extern int PQCLEAN_FALCON1024_CLEAN_crypto_sign_verify(const uint8_t *sig, size_t siglen, const uint8_t *m, size_t mlen, const uint8_t *pk); + +#if defined(OQS_ENABLE_SIG_falcon_1024_avx2) +extern int PQCLEAN_FALCON1024_AVX2_crypto_sign_keypair(uint8_t *pk, uint8_t *sk); +extern int PQCLEAN_FALCON1024_AVX2_crypto_sign_signature(uint8_t *sig, size_t *siglen, const uint8_t *m, size_t mlen, const uint8_t *sk); +extern int PQCLEAN_FALCON1024_AVX2_crypto_sign_verify(const uint8_t *sig, size_t siglen, const uint8_t *m, size_t mlen, const uint8_t *pk); +#endif + +OQS_API OQS_STATUS OQS_SIG_falcon_1024_keypair(uint8_t *public_key, uint8_t *secret_key) { +#if defined(OQS_ENABLE_SIG_falcon_1024_avx2) +#if defined(OQS_DIST_BUILD) + if (OQS_CPU_has_extension(OQS_CPU_EXT_AVX2)) { +#endif /* OQS_DIST_BUILD */ + return (OQS_STATUS) PQCLEAN_FALCON1024_AVX2_crypto_sign_keypair(public_key, secret_key); +#if defined(OQS_DIST_BUILD) + } else { + return (OQS_STATUS) PQCLEAN_FALCON1024_CLEAN_crypto_sign_keypair(public_key, secret_key); + } +#endif /* OQS_DIST_BUILD */ +#else + return (OQS_STATUS) PQCLEAN_FALCON1024_CLEAN_crypto_sign_keypair(public_key, secret_key); +#endif +} + +OQS_API OQS_STATUS OQS_SIG_falcon_1024_sign(uint8_t *signature, size_t *signature_len, const uint8_t *message, size_t message_len, const uint8_t *secret_key) { +#if defined(OQS_ENABLE_SIG_falcon_1024_avx2) +#if defined(OQS_DIST_BUILD) + if (OQS_CPU_has_extension(OQS_CPU_EXT_AVX2)) { +#endif /* OQS_DIST_BUILD */ + return (OQS_STATUS) PQCLEAN_FALCON1024_AVX2_crypto_sign_signature(signature, signature_len, message, message_len, secret_key); +#if defined(OQS_DIST_BUILD) + } else { + return (OQS_STATUS) PQCLEAN_FALCON1024_CLEAN_crypto_sign_signature(signature, signature_len, message, message_len, secret_key); + } +#endif /* OQS_DIST_BUILD */ +#else + return (OQS_STATUS) PQCLEAN_FALCON1024_CLEAN_crypto_sign_signature(signature, signature_len, message, message_len, secret_key); +#endif +} + +OQS_API OQS_STATUS OQS_SIG_falcon_1024_verify(const uint8_t *message, size_t message_len, const uint8_t *signature, size_t signature_len, const uint8_t *public_key) { +#if defined(OQS_ENABLE_SIG_falcon_1024_avx2) +#if defined(OQS_DIST_BUILD) + if (OQS_CPU_has_extension(OQS_CPU_EXT_AVX2)) { +#endif /* OQS_DIST_BUILD */ + return (OQS_STATUS) PQCLEAN_FALCON1024_AVX2_crypto_sign_verify(signature, signature_len, message, message_len, public_key); +#if defined(OQS_DIST_BUILD) + } else { + return (OQS_STATUS) PQCLEAN_FALCON1024_CLEAN_crypto_sign_verify(signature, signature_len, message, message_len, public_key); + } +#endif /* OQS_DIST_BUILD */ +#else + return (OQS_STATUS) PQCLEAN_FALCON1024_CLEAN_crypto_sign_verify(signature, signature_len, message, message_len, public_key); +#endif +} + +#endif diff --git a/lib/liboqs/src/sig/falcon/sig_falcon_512.c b/lib/liboqs/src/sig/falcon/sig_falcon_512.c new file mode 100644 index 000000000..1b09cff54 --- /dev/null +++ b/lib/liboqs/src/sig/falcon/sig_falcon_512.c @@ -0,0 +1,90 @@ +// SPDX-License-Identifier: MIT + +#include <stdlib.h> + +#include <oqs/sig_falcon.h> + +#if defined(OQS_ENABLE_SIG_falcon_512) + +OQS_SIG *OQS_SIG_falcon_512_new(void) { + + OQS_SIG *sig = malloc(sizeof(OQS_SIG)); + if (sig == NULL) { + return NULL; + } + sig->method_name = OQS_SIG_alg_falcon_512; + sig->alg_version = "supercop-20201018 via https://github.com/jschanck/package-pqclean/tree/cea1fa5a/falcon"; + + sig->claimed_nist_level = 1; + sig->euf_cma = true; + + sig->length_public_key = OQS_SIG_falcon_512_length_public_key; + sig->length_secret_key = OQS_SIG_falcon_512_length_secret_key; + sig->length_signature = OQS_SIG_falcon_512_length_signature; + + sig->keypair = OQS_SIG_falcon_512_keypair; + sig->sign = OQS_SIG_falcon_512_sign; + sig->verify = OQS_SIG_falcon_512_verify; + + return sig; +} + +extern int PQCLEAN_FALCON512_CLEAN_crypto_sign_keypair(uint8_t *pk, uint8_t *sk); +extern int PQCLEAN_FALCON512_CLEAN_crypto_sign_signature(uint8_t *sig, size_t *siglen, const uint8_t *m, size_t mlen, const uint8_t *sk); +extern int PQCLEAN_FALCON512_CLEAN_crypto_sign_verify(const uint8_t *sig, size_t siglen, const uint8_t *m, size_t mlen, const uint8_t *pk); + +#if defined(OQS_ENABLE_SIG_falcon_512_avx2) +extern int PQCLEAN_FALCON512_AVX2_crypto_sign_keypair(uint8_t *pk, uint8_t *sk); +extern int PQCLEAN_FALCON512_AVX2_crypto_sign_signature(uint8_t *sig, size_t *siglen, const uint8_t *m, size_t mlen, const uint8_t *sk); +extern int PQCLEAN_FALCON512_AVX2_crypto_sign_verify(const uint8_t *sig, size_t siglen, const uint8_t *m, size_t mlen, const uint8_t *pk); +#endif + +OQS_API OQS_STATUS OQS_SIG_falcon_512_keypair(uint8_t *public_key, uint8_t *secret_key) { +#if defined(OQS_ENABLE_SIG_falcon_512_avx2) +#if defined(OQS_DIST_BUILD) + if (OQS_CPU_has_extension(OQS_CPU_EXT_AVX2)) { +#endif /* OQS_DIST_BUILD */ + return (OQS_STATUS) PQCLEAN_FALCON512_AVX2_crypto_sign_keypair(public_key, secret_key); +#if defined(OQS_DIST_BUILD) + } else { + return (OQS_STATUS) PQCLEAN_FALCON512_CLEAN_crypto_sign_keypair(public_key, secret_key); + } +#endif /* OQS_DIST_BUILD */ +#else + return (OQS_STATUS) PQCLEAN_FALCON512_CLEAN_crypto_sign_keypair(public_key, secret_key); +#endif +} + +OQS_API OQS_STATUS OQS_SIG_falcon_512_sign(uint8_t *signature, size_t *signature_len, const uint8_t *message, size_t message_len, const uint8_t *secret_key) { +#if defined(OQS_ENABLE_SIG_falcon_512_avx2) +#if defined(OQS_DIST_BUILD) + if (OQS_CPU_has_extension(OQS_CPU_EXT_AVX2)) { +#endif /* OQS_DIST_BUILD */ + return (OQS_STATUS) PQCLEAN_FALCON512_AVX2_crypto_sign_signature(signature, signature_len, message, message_len, secret_key); +#if defined(OQS_DIST_BUILD) + } else { + return (OQS_STATUS) PQCLEAN_FALCON512_CLEAN_crypto_sign_signature(signature, signature_len, message, message_len, secret_key); + } +#endif /* OQS_DIST_BUILD */ +#else + return (OQS_STATUS) PQCLEAN_FALCON512_CLEAN_crypto_sign_signature(signature, signature_len, message, message_len, secret_key); +#endif +} + +OQS_API OQS_STATUS OQS_SIG_falcon_512_verify(const uint8_t *message, size_t message_len, const uint8_t *signature, size_t signature_len, const uint8_t *public_key) { +#if defined(OQS_ENABLE_SIG_falcon_512_avx2) +#if defined(OQS_DIST_BUILD) + if (OQS_CPU_has_extension(OQS_CPU_EXT_AVX2)) { +#endif /* OQS_DIST_BUILD */ + return (OQS_STATUS) PQCLEAN_FALCON512_AVX2_crypto_sign_verify(signature, signature_len, message, message_len, public_key); +#if defined(OQS_DIST_BUILD) + } else { + return (OQS_STATUS) PQCLEAN_FALCON512_CLEAN_crypto_sign_verify(signature, signature_len, message, message_len, public_key); + } +#endif /* OQS_DIST_BUILD */ +#else + return (OQS_STATUS) PQCLEAN_FALCON512_CLEAN_crypto_sign_verify(signature, signature_len, message, message_len, public_key); +#endif +} + +#endif |