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authorVincent Palatin <vpalatin@chromium.org>2017-02-16 14:15:30 +0100
committerchrome-bot <chrome-bot@chromium.org>2017-02-23 16:02:03 -0800
commit0d858f1544cfd50f4a63f348d722bb16d638c0b1 (patch)
treec4fe70955629048828b9fdb4369a667d4f26c515
parentbff020fc6b25fe5dc0245c811d9f53b7c518aa08 (diff)
downloadchrome-ec-0d858f1544cfd50f4a63f348d722bb16d638c0b1.tar.gz
curve25519: strip-down, build and test
Keep only the most compact version of the curve25519 code and remove the remaining unused code for easier compilation. Do the minimal changes to make it compile in the EC code base, there should be no real functional changes. Re-use the wording from BoringSSL include/openssl/curve25519.h for the header. Signed-off-by: Vincent Palatin <vpalatin@chromium.org> BRANCH=none BUG=chrome-os-partner:62991 TEST=run x25519 on host (ie 'make run-x25519') and the STM32L4 target: make BOARD=eve_fp PROJECT=x25519 TEST_BUILD=y ./util/flash_ec --board=eve_fp --image=build/eve_fp/x25519.bin execute 'runtest' in the console. Change-Id: I13dbe453eff39b461effb1b3ffa549afc1749fef Reviewed-on: https://chromium-review.googlesource.com/444187 Commit-Ready: Vincent Palatin <vpalatin@chromium.org> Tested-by: Vincent Palatin <vpalatin@chromium.org> Reviewed-by: Adam Langley <agl@chromium.org> Reviewed-by: Randall Spangler <rspangler@chromium.org>
Diffstat
-rw-r--r--builtin/stdint.h7
-rw-r--r--common/build.mk1
-rw-r--r--common/curve25519.c4105
-rw-r--r--include/config.h4
-rw-r--r--include/curve25519.h62
-rw-r--r--test/build.mk2
-rw-r--r--test/test_config.h4
-rw-r--r--test/x25519.c243
-rw-r--r--test/x25519.tasklist17
9 files changed, 257 insertions, 4188 deletions
diff --git a/builtin/stdint.h b/builtin/stdint.h
index b82268b409..fe4a92e2ea 100644
--- a/builtin/stdint.h
+++ b/builtin/stdint.h
@@ -44,4 +44,11 @@ typedef uint8_t uint_least8_t;
#define INT32_MAX (2147483647U)
#endif
+#ifndef UINT64_C
+#define UINT64_C(c) c ## ULL
+#endif
+#ifndef INT64_C
+#define INT64_C(c) c ## LL
+#endif
+
#endif /* __CROS_EC_STDINT_H__ */
diff --git a/common/build.mk b/common/build.mk
index a34ef11d3b..c3a9023fcb 100644
--- a/common/build.mk
+++ b/common/build.mk
@@ -43,6 +43,7 @@ common-$(CONFIG_COMMON_PANIC_OUTPUT)+=panic_output.o
common-$(CONFIG_COMMON_RUNTIME)+=hooks.o main.o system.o
common-$(CONFIG_COMMON_TIMER)+=timer.o
common-$(CONFIG_CRC8)+= crc8.o
+common-$(CONFIG_CURVE25519)+=curve25519.o
common-$(CONFIG_DEVICE_STATE)+=device_state.o
common-$(CONFIG_DPTF)+=dptf.o
common-$(CONFIG_EXTENSION_COMMAND)+=extension.o
diff --git a/common/curve25519.c b/common/curve25519.c
index d660b6c616..5faa53dc11 100644
--- a/common/curve25519.c
+++ b/common/curve25519.c
@@ -19,17 +19,19 @@
*
* The field functions are shared by Ed25519 and X25519 where possible. */
-#include <openssl/curve25519.h>
+#include "curve25519.h"
+#include "trng.h"
+#include "util.h"
+#define CRYPTO_memcmp safe_memcmp
-#include <string.h>
-
-#include <openssl/cpu.h>
-#include <openssl/mem.h>
-#include <openssl/rand.h>
-#include <openssl/sha.h>
-
-#include "internal.h"
+/*
+ * fe means field element. Here the field is \Z/(2^255-19). An element t,
+ * entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77
+ * t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on
+ * context.
+ */
+typedef int32_t fe[10];
static const int64_t kBottom25Bits = INT64_C(0x1ffffff);
static const int64_t kBottom26Bits = INT64_C(0x3ffffff);
@@ -690,4038 +692,13 @@ static void fe_invert(fe out, const fe z) {
fe_mul(out, t1, t0);
}
-/* h = -f
- *
- * Preconditions:
- * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
- *
- * Postconditions:
- * |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. */
-static void fe_neg(fe h, const fe f) {
- unsigned i;
- for (i = 0; i < 10; i++) {
- h[i] = -f[i];
- }
-}
-
-/* Replace (f,g) with (g,g) if b == 1;
- * replace (f,g) with (f,g) if b == 0.
- *
- * Preconditions: b in {0,1}. */
-static void fe_cmov(fe f, const fe g, unsigned b) {
- b = 0-b;
- unsigned i;
- for (i = 0; i < 10; i++) {
- int32_t x = f[i] ^ g[i];
- x &= b;
- f[i] ^= x;
- }
-}
-
-/* return 0 if f == 0
- * return 1 if f != 0
- *
- * Preconditions:
- * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */
-static int fe_isnonzero(const fe f) {
- uint8_t s[32];
- fe_tobytes(s, f);
-
- static const uint8_t zero[32] = {0};
- return CRYPTO_memcmp(s, zero, sizeof(zero)) != 0;
-}
-
-/* return 1 if f is in {1,3,5,...,q-2}
- * return 0 if f is in {0,2,4,...,q-1}
- *
- * Preconditions:
- * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */
-static int fe_isnegative(const fe f) {
- uint8_t s[32];
- fe_tobytes(s, f);
- return s[0] & 1;
-}
-
-/* h = 2 * f * f
- * Can overlap h with f.
- *
- * Preconditions:
- * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
- *
- * Postconditions:
- * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
- *
- * See fe_mul.c for discussion of implementation strategy. */
-static void fe_sq2(fe h, const fe f) {
- int32_t f0 = f[0];
- int32_t f1 = f[1];
- int32_t f2 = f[2];
- int32_t f3 = f[3];
- int32_t f4 = f[4];
- int32_t f5 = f[5];
- int32_t f6 = f[6];
- int32_t f7 = f[7];
- int32_t f8 = f[8];
- int32_t f9 = f[9];
- int32_t f0_2 = 2 * f0;
- int32_t f1_2 = 2 * f1;
- int32_t f2_2 = 2 * f2;
- int32_t f3_2 = 2 * f3;
- int32_t f4_2 = 2 * f4;
- int32_t f5_2 = 2 * f5;
- int32_t f6_2 = 2 * f6;
- int32_t f7_2 = 2 * f7;
- int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
- int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
- int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
- int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
- int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
- int64_t f0f0 = f0 * (int64_t) f0;
- int64_t f0f1_2 = f0_2 * (int64_t) f1;
- int64_t f0f2_2 = f0_2 * (int64_t) f2;
- int64_t f0f3_2 = f0_2 * (int64_t) f3;
- int64_t f0f4_2 = f0_2 * (int64_t) f4;
- int64_t f0f5_2 = f0_2 * (int64_t) f5;
- int64_t f0f6_2 = f0_2 * (int64_t) f6;
- int64_t f0f7_2 = f0_2 * (int64_t) f7;
- int64_t f0f8_2 = f0_2 * (int64_t) f8;
- int64_t f0f9_2 = f0_2 * (int64_t) f9;
- int64_t f1f1_2 = f1_2 * (int64_t) f1;
- int64_t f1f2_2 = f1_2 * (int64_t) f2;
- int64_t f1f3_4 = f1_2 * (int64_t) f3_2;
- int64_t f1f4_2 = f1_2 * (int64_t) f4;
- int64_t f1f5_4 = f1_2 * (int64_t) f5_2;
- int64_t f1f6_2 = f1_2 * (int64_t) f6;
- int64_t f1f7_4 = f1_2 * (int64_t) f7_2;
- int64_t f1f8_2 = f1_2 * (int64_t) f8;
- int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
- int64_t f2f2 = f2 * (int64_t) f2;
- int64_t f2f3_2 = f2_2 * (int64_t) f3;
- int64_t f2f4_2 = f2_2 * (int64_t) f4;
- int64_t f2f5_2 = f2_2 * (int64_t) f5;
- int64_t f2f6_2 = f2_2 * (int64_t) f6;
- int64_t f2f7_2 = f2_2 * (int64_t) f7;
- int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
- int64_t f2f9_38 = f2 * (int64_t) f9_38;
- int64_t f3f3_2 = f3_2 * (int64_t) f3;
- int64_t f3f4_2 = f3_2 * (int64_t) f4;
- int64_t f3f5_4 = f3_2 * (int64_t) f5_2;
- int64_t f3f6_2 = f3_2 * (int64_t) f6;
- int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
- int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
- int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
- int64_t f4f4 = f4 * (int64_t) f4;
- int64_t f4f5_2 = f4_2 * (int64_t) f5;
- int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
- int64_t f4f7_38 = f4 * (int64_t) f7_38;
- int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
- int64_t f4f9_38 = f4 * (int64_t) f9_38;
- int64_t f5f5_38 = f5 * (int64_t) f5_38;
- int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
- int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
- int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
- int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
- int64_t f6f6_19 = f6 * (int64_t) f6_19;
- int64_t f6f7_38 = f6 * (int64_t) f7_38;
- int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
- int64_t f6f9_38 = f6 * (int64_t) f9_38;
- int64_t f7f7_38 = f7 * (int64_t) f7_38;
- int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
- int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
- int64_t f8f8_19 = f8 * (int64_t) f8_19;
- int64_t f8f9_38 = f8 * (int64_t) f9_38;
- int64_t f9f9_38 = f9 * (int64_t) f9_38;
- int64_t h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
- int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
- int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
- int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
- int64_t h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38;
- int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
- int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
- int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
- int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38;
- int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
- int64_t carry0;
- int64_t carry1;
- int64_t carry2;
- int64_t carry3;
- int64_t carry4;
- int64_t carry5;
- int64_t carry6;
- int64_t carry7;
- int64_t carry8;
- int64_t carry9;
-
- h0 += h0;
- h1 += h1;
- h2 += h2;
- h3 += h3;
- h4 += h4;
- h5 += h5;
- h6 += h6;
- h7 += h7;
- h8 += h8;
- h9 += h9;
-
- carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
- carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
-
- carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
- carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
-
- carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
- carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
-
- carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
- carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
-
- carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
- carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
-
- carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
-
- carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
-
- h[0] = h0;
- h[1] = h1;
- h[2] = h2;
- h[3] = h3;
- h[4] = h4;
- h[5] = h5;
- h[6] = h6;
- h[7] = h7;
- h[8] = h8;
- h[9] = h9;
-}
-
-static void fe_pow22523(fe out, const fe z) {
- fe t0;
- fe t1;
- fe t2;
- int i;
-
- fe_sq(t0, z);
- fe_sq(t1, t0);
- for (i = 1; i < 2; ++i) {
- fe_sq(t1, t1);
- }
- fe_mul(t1, z, t1);
- fe_mul(t0, t0, t1);
- fe_sq(t0, t0);
- fe_mul(t0, t1, t0);
- fe_sq(t1, t0);
- for (i = 1; i < 5; ++i) {
- fe_sq(t1, t1);
- }
- fe_mul(t0, t1, t0);
- fe_sq(t1, t0);
- for (i = 1; i < 10; ++i) {
- fe_sq(t1, t1);
- }
- fe_mul(t1, t1, t0);
- fe_sq(t2, t1);
- for (i = 1; i < 20; ++i) {
- fe_sq(t2, t2);
- }
- fe_mul(t1, t2, t1);
- fe_sq(t1, t1);
- for (i = 1; i < 10; ++i) {
- fe_sq(t1, t1);
- }
- fe_mul(t0, t1, t0);
- fe_sq(t1, t0);
- for (i = 1; i < 50; ++i) {
- fe_sq(t1, t1);
- }
- fe_mul(t1, t1, t0);
- fe_sq(t2, t1);
- for (i = 1; i < 100; ++i) {
- fe_sq(t2, t2);
- }
- fe_mul(t1, t2, t1);
- fe_sq(t1, t1);
- for (i = 1; i < 50; ++i) {
- fe_sq(t1, t1);
- }
- fe_mul(t0, t1, t0);
- fe_sq(t0, t0);
- for (i = 1; i < 2; ++i) {
- fe_sq(t0, t0);
- }
- fe_mul(out, t0, z);
-}
-
-void x25519_ge_tobytes(uint8_t *s, const ge_p2 *h) {
- fe recip;
- fe x;
- fe y;
-
- fe_invert(recip, h->Z);
- fe_mul(x, h->X, recip);
- fe_mul(y, h->Y, recip);
- fe_tobytes(s, y);
- s[31] ^= fe_isnegative(x) << 7;
-}
-
-static void ge_p3_tobytes(uint8_t *s, const ge_p3 *h) {
- fe recip;
- fe x;
- fe y;
-
- fe_invert(recip, h->Z);
- fe_mul(x, h->X, recip);
- fe_mul(y, h->Y, recip);
- fe_tobytes(s, y);
- s[31] ^= fe_isnegative(x) << 7;
-}
-
-static const fe d = {-10913610, 13857413, -15372611, 6949391, 114729,
- -8787816, -6275908, -3247719, -18696448, -12055116};
-
-static const fe sqrtm1 = {-32595792, -7943725, 9377950, 3500415, 12389472,
- -272473, -25146209, -2005654, 326686, 11406482};
-
-int x25519_ge_frombytes_vartime(ge_p3 *h, const uint8_t *s) {
- fe u;
- fe v;
- fe v3;
- fe vxx;
- fe check;
-
- fe_frombytes(h->Y, s);
- fe_1(h->Z);
- fe_sq(u, h->Y);
- fe_mul(v, u, d);
- fe_sub(u, u, h->Z); /* u = y^2-1 */
- fe_add(v, v, h->Z); /* v = dy^2+1 */
-
- fe_sq(v3, v);
- fe_mul(v3, v3, v); /* v3 = v^3 */
- fe_sq(h->X, v3);
- fe_mul(h->X, h->X, v);
- fe_mul(h->X, h->X, u); /* x = uv^7 */
-
- fe_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */
- fe_mul(h->X, h->X, v3);
- fe_mul(h->X, h->X, u); /* x = uv^3(uv^7)^((q-5)/8) */
-
- fe_sq(vxx, h->X);
- fe_mul(vxx, vxx, v);
- fe_sub(check, vxx, u); /* vx^2-u */
- if (fe_isnonzero(check)) {
- fe_add(check, vxx, u); /* vx^2+u */
- if (fe_isnonzero(check)) {
- return -1;
- }
- fe_mul(h->X, h->X, sqrtm1);
- }
-
- if (fe_isnegative(h->X) != (s[31] >> 7)) {
- fe_neg(h->X, h->X);
- }
-
- fe_mul(h->T, h->X, h->Y);
- return 0;
-}
-
-static void ge_p2_0(ge_p2 *h) {
- fe_0(h->X);
- fe_1(h->Y);
- fe_1(h->Z);
-}
-
-static void ge_p3_0(ge_p3 *h) {
- fe_0(h->X);
- fe_1(h->Y);
- fe_1(h->Z);
- fe_0(h->T);
-}
-
-static void ge_cached_0(ge_cached *h) {
- fe_1(h->YplusX);
- fe_1(h->YminusX);
- fe_1(h->Z);
- fe_0(h->T2d);
-}
-
-static void ge_precomp_0(ge_precomp *h) {
- fe_1(h->yplusx);
- fe_1(h->yminusx);
- fe_0(h->xy2d);
-}
-
-/* r = p */
-static void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p) {
- fe_copy(r->X, p->X);
- fe_copy(r->Y, p->Y);
- fe_copy(r->Z, p->Z);
-}
-
-static const fe d2 = {-21827239, -5839606, -30745221, 13898782, 229458,
- 15978800, -12551817, -6495438, 29715968, 9444199};
-
-/* r = p */
-void x25519_ge_p3_to_cached(ge_cached *r, const ge_p3 *p) {
- fe_add(r->YplusX, p->Y, p->X);
- fe_sub(r->YminusX, p->Y, p->X);
- fe_copy(r->Z, p->Z);
- fe_mul(r->T2d, p->T, d2);
-}
-
-/* r = p */
-void x25519_ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p) {
- fe_mul(r->X, p->X, p->T);
- fe_mul(r->Y, p->Y, p->Z);
- fe_mul(r->Z, p->Z, p->T);
-}
-
-/* r = p */
-void x25519_ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p) {
- fe_mul(r->X, p->X, p->T);
- fe_mul(r->Y, p->Y, p->Z);
- fe_mul(r->Z, p->Z, p->T);
- fe_mul(r->T, p->X, p->Y);
-}
-
-/* r = p */
-static void ge_p1p1_to_cached(ge_cached *r, const ge_p1p1 *p) {
- ge_p3 t;
- x25519_ge_p1p1_to_p3(&t, p);
- x25519_ge_p3_to_cached(r, &t);
-}
-
-/* r = 2 * p */
-static void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p) {
- fe t0;
-
- fe_sq(r->X, p->X);
- fe_sq(r->Z, p->Y);
- fe_sq2(r->T, p->Z);
- fe_add(r->Y, p->X, p->Y);
- fe_sq(t0, r->Y);
- fe_add(r->Y, r->Z, r->X);
- fe_sub(r->Z, r->Z, r->X);
- fe_sub(r->X, t0, r->Y);
- fe_sub(r->T, r->T, r->Z);
-}
-
-/* r = 2 * p */
-static void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p) {
- ge_p2 q;
- ge_p3_to_p2(&q, p);
- ge_p2_dbl(r, &q);
-}
-
-/* r = p + q */
-static void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) {
- fe t0;
-
- fe_add(r->X, p->Y, p->X);
- fe_sub(r->Y, p->Y, p->X);
- fe_mul(r->Z, r->X, q->yplusx);
- fe_mul(r->Y, r->Y, q->yminusx);
- fe_mul(r->T, q->xy2d, p->T);
- fe_add(t0, p->Z, p->Z);
- fe_sub(r->X, r->Z, r->Y);
- fe_add(r->Y, r->Z, r->Y);
- fe_add(r->Z, t0, r->T);
- fe_sub(r->T, t0, r->T);
-}
-
-/* r = p - q */
-static void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) {
- fe t0;
-
- fe_add(r->X, p->Y, p->X);
- fe_sub(r->Y, p->Y, p->X);
- fe_mul(r->Z, r->X, q->yminusx);
- fe_mul(r->Y, r->Y, q->yplusx);
- fe_mul(r->T, q->xy2d, p->T);
- fe_add(t0, p->Z, p->Z);
- fe_sub(r->X, r->Z, r->Y);
- fe_add(r->Y, r->Z, r->Y);
- fe_sub(r->Z, t0, r->T);
- fe_add(r->T, t0, r->T);
-}
-
-/* r = p + q */
-void x25519_ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) {
- fe t0;
-
- fe_add(r->X, p->Y, p->X);
- fe_sub(r->Y, p->Y, p->X);
- fe_mul(r->Z, r->X, q->YplusX);
- fe_mul(r->Y, r->Y, q->YminusX);
- fe_mul(r->T, q->T2d, p->T);
- fe_mul(r->X, p->Z, q->Z);
- fe_add(t0, r->X, r->X);
- fe_sub(r->X, r->Z, r->Y);
- fe_add(r->Y, r->Z, r->Y);
- fe_add(r->Z, t0, r->T);
- fe_sub(r->T, t0, r->T);
-}
-
-/* r = p - q */
-void x25519_ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) {
- fe t0;
-
- fe_add(r->X, p->Y, p->X);
- fe_sub(r->Y, p->Y, p->X);
- fe_mul(r->Z, r->X, q->YminusX);
- fe_mul(r->Y, r->Y, q->YplusX);
- fe_mul(r->T, q->T2d, p->T);
- fe_mul(r->X, p->Z, q->Z);
- fe_add(t0, r->X, r->X);
- fe_sub(r->X, r->Z, r->Y);
- fe_add(r->Y, r->Z, r->Y);
- fe_sub(r->Z, t0, r->T);
- fe_add(r->T, t0, r->T);
-}
-
-static uint8_t equal(signed char b, signed char c) {
- uint8_t ub = b;
- uint8_t uc = c;
- uint8_t x = ub ^ uc; /* 0: yes; 1..255: no */
- uint32_t y = x; /* 0: yes; 1..255: no */
- y -= 1; /* 4294967295: yes; 0..254: no */
- y >>= 31; /* 1: yes; 0: no */
- return y;
-}
-
-static void cmov(ge_precomp *t, const ge_precomp *u, uint8_t b) {
- fe_cmov(t->yplusx, u->yplusx, b);
- fe_cmov(t->yminusx, u->yminusx, b);
- fe_cmov(t->xy2d, u->xy2d, b);
-}
-
-void x25519_ge_scalarmult_small_precomp(
- ge_p3 *h, const uint8_t a[32], const uint8_t precomp_table[15 * 2 * 32]) {
- /* precomp_table is first expanded into matching |ge_precomp|
- * elements. */
- ge_precomp multiples[15];
-
- unsigned i;
- for (i = 0; i < 15; i++) {
- const uint8_t *bytes = &precomp_table[i*(2 * 32)];
- fe x, y;
- fe_frombytes(x, bytes);
- fe_frombytes(y, bytes + 32);
-
- ge_precomp *out = &multiples[i];
- fe_add(out->yplusx, y, x);
- fe_sub(out->yminusx, y, x);
- fe_mul(out->xy2d, x, y);
- fe_mul(out->xy2d, out->xy2d, d2);
- }
-
- /* See the comment above |k25519SmallPrecomp| about the structure of the
- * precomputed elements. This loop does 64 additions and 64 doublings to
- * calculate the result. */
- ge_p3_0(h);
-
- for (i = 63; i < 64; i--) {
- unsigned j;
- signed char index = 0;
-
- for (j = 0; j < 4; j++) {
- const uint8_t bit = 1 & (a[(8 * j) + (i / 8)] >> (i & 7));
- index |= (bit << j);
- }
-
- ge_precomp e;
- ge_precomp_0(&e);
-
- for (j = 1; j < 16; j++) {
- cmov(&e, &multiples[j-1], equal(index, j));
- }
-
- ge_cached cached;
- ge_p1p1 r;
- x25519_ge_p3_to_cached(&cached, h);
- x25519_ge_add(&r, h, &cached);
- x25519_ge_p1p1_to_p3(h, &r);
-
- ge_madd(&r, h, &e);
- x25519_ge_p1p1_to_p3(h, &r);
- }
-}
-
-#if defined(OPENSSL_SMALL)
-
-/* This block of code replaces the standard base-point table with a much smaller
- * one. The standard table is 30,720 bytes while this one is just 960.
- *
- * This table contains 15 pairs of group elements, (x, y), where each field
- * element is serialised with |fe_tobytes|. If |i| is the index of the group
- * element then consider i+1 as a four-bit number: (i₀, i₁, i₂, i₃) (where i₀
- * is the most significant bit). The value of the group element is then:
- * (i₀×2^192 + i₁×2^128 + i₂×2^64 + i₃)G, where G is the generator. */
-static const uint8_t k25519SmallPrecomp[15 * 2 * 32] = {
- 0x1a, 0xd5, 0x25, 0x8f, 0x60, 0x2d, 0x56, 0xc9, 0xb2, 0xa7, 0x25, 0x95,
- 0x60, 0xc7, 0x2c, 0x69, 0x5c, 0xdc, 0xd6, 0xfd, 0x31, 0xe2, 0xa4, 0xc0,
- 0xfe, 0x53, 0x6e, 0xcd, 0xd3, 0x36, 0x69, 0x21, 0x58, 0x66, 0x66, 0x66,
- 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
- 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
- 0x66, 0x66, 0x66, 0x66, 0x02, 0xa2, 0xed, 0xf4, 0x8f, 0x6b, 0x0b, 0x3e,
- 0xeb, 0x35, 0x1a, 0xd5, 0x7e, 0xdb, 0x78, 0x00, 0x96, 0x8a, 0xa0, 0xb4,
- 0xcf, 0x60, 0x4b, 0xd4, 0xd5, 0xf9, 0x2d, 0xbf, 0x88, 0xbd, 0x22, 0x62,
- 0x13, 0x53, 0xe4, 0x82, 0x57, 0xfa, 0x1e, 0x8f, 0x06, 0x2b, 0x90, 0xba,
- 0x08, 0xb6, 0x10, 0x54, 0x4f, 0x7c, 0x1b, 0x26, 0xed, 0xda, 0x6b, 0xdd,
- 0x25, 0xd0, 0x4e, 0xea, 0x42, 0xbb, 0x25, 0x03, 0xa2, 0xfb, 0xcc, 0x61,
- 0x67, 0x06, 0x70, 0x1a, 0xc4, 0x78, 0x3a, 0xff, 0x32, 0x62, 0xdd, 0x2c,
- 0xab, 0x50, 0x19, 0x3b, 0xf2, 0x9b, 0x7d, 0xb8, 0xfd, 0x4f, 0x29, 0x9c,
- 0xa7, 0x91, 0xba, 0x0e, 0x46, 0x5e, 0x51, 0xfe, 0x1d, 0xbf, 0xe5, 0xe5,
- 0x9b, 0x95, 0x0d, 0x67, 0xf8, 0xd1, 0xb5, 0x5a, 0xa1, 0x93, 0x2c, 0xc3,
- 0xde, 0x0e, 0x97, 0x85, 0x2d, 0x7f, 0xea, 0xab, 0x3e, 0x47, 0x30, 0x18,
- 0x24, 0xe8, 0xb7, 0x60, 0xae, 0x47, 0x80, 0xfc, 0xe5, 0x23, 0xe7, 0xc2,
- 0xc9, 0x85, 0xe6, 0x98, 0xa0, 0x29, 0x4e, 0xe1, 0x84, 0x39, 0x2d, 0x95,
- 0x2c, 0xf3, 0x45, 0x3c, 0xff, 0xaf, 0x27, 0x4c, 0x6b, 0xa6, 0xf5, 0x4b,
- 0x11, 0xbd, 0xba, 0x5b, 0x9e, 0xc4, 0xa4, 0x51, 0x1e, 0xbe, 0xd0, 0x90,
- 0x3a, 0x9c, 0xc2, 0x26, 0xb6, 0x1e, 0xf1, 0x95, 0x7d, 0xc8, 0x6d, 0x52,
- 0xe6, 0x99, 0x2c, 0x5f, 0x9a, 0x96, 0x0c, 0x68, 0x29, 0xfd, 0xe2, 0xfb,
- 0xe6, 0xbc, 0xec, 0x31, 0x08, 0xec, 0xe6, 0xb0, 0x53, 0x60, 0xc3, 0x8c,
- 0xbe, 0xc1, 0xb3, 0x8a, 0x8f, 0xe4, 0x88, 0x2b, 0x55, 0xe5, 0x64, 0x6e,
- 0x9b, 0xd0, 0xaf, 0x7b, 0x64, 0x2a, 0x35, 0x25, 0x10, 0x52, 0xc5, 0x9e,
- 0x58, 0x11, 0x39, 0x36, 0x45, 0x51, 0xb8, 0x39, 0x93, 0xfc, 0x9d, 0x6a,
- 0xbe, 0x58, 0xcb, 0xa4, 0x0f, 0x51, 0x3c, 0x38, 0x05, 0xca, 0xab, 0x43,
- 0x63, 0x0e, 0xf3, 0x8b, 0x41, 0xa6, 0xf8, 0x9b, 0x53, 0x70, 0x80, 0x53,
- 0x86, 0x5e, 0x8f, 0xe3, 0xc3, 0x0d, 0x18, 0xc8, 0x4b, 0x34, 0x1f, 0xd8,
- 0x1d, 0xbc, 0xf2, 0x6d, 0x34, 0x3a, 0xbe, 0xdf, 0xd9, 0xf6, 0xf3, 0x89,
- 0xa1, 0xe1, 0x94, 0x9f, 0x5d, 0x4c, 0x5d, 0xe9, 0xa1, 0x49, 0x92, 0xef,
- 0x0e, 0x53, 0x81, 0x89, 0x58, 0x87, 0xa6, 0x37, 0xf1, 0xdd, 0x62, 0x60,
- 0x63, 0x5a, 0x9d, 0x1b, 0x8c, 0xc6, 0x7d, 0x52, 0xea, 0x70, 0x09, 0x6a,
- 0xe1, 0x32, 0xf3, 0x73, 0x21, 0x1f, 0x07, 0x7b, 0x7c, 0x9b, 0x49, 0xd8,
- 0xc0, 0xf3, 0x25, 0x72, 0x6f, 0x9d, 0xed, 0x31, 0x67, 0x36, 0x36, 0x54,
- 0x40, 0x92, 0x71, 0xe6, 0x11, 0x28, 0x11, 0xad, 0x93, 0x32, 0x85, 0x7b,
- 0x3e, 0xb7, 0x3b, 0x49, 0x13, 0x1c, 0x07, 0xb0, 0x2e, 0x93, 0xaa, 0xfd,
- 0xfd, 0x28, 0x47, 0x3d, 0x8d, 0xd2, 0xda, 0xc7, 0x44, 0xd6, 0x7a, 0xdb,
- 0x26, 0x7d, 0x1d, 0xb8, 0xe1, 0xde, 0x9d, 0x7a, 0x7d, 0x17, 0x7e, 0x1c,
- 0x37, 0x04, 0x8d, 0x2d, 0x7c, 0x5e, 0x18, 0x38, 0x1e, 0xaf, 0xc7, 0x1b,
- 0x33, 0x48, 0x31, 0x00, 0x59, 0xf6, 0xf2, 0xca, 0x0f, 0x27, 0x1b, 0x63,
- 0x12, 0x7e, 0x02, 0x1d, 0x49, 0xc0, 0x5d, 0x79, 0x87, 0xef, 0x5e, 0x7a,
- 0x2f, 0x1f, 0x66, 0x55, 0xd8, 0x09, 0xd9, 0x61, 0x38, 0x68, 0xb0, 0x07,
- 0xa3, 0xfc, 0xcc, 0x85, 0x10, 0x7f, 0x4c, 0x65, 0x65, 0xb3, 0xfa, 0xfa,
- 0xa5, 0x53, 0x6f, 0xdb, 0x74, 0x4c, 0x56, 0x46, 0x03, 0xe2, 0xd5, 0x7a,
- 0x29, 0x1c, 0xc6, 0x02, 0xbc, 0x59, 0xf2, 0x04, 0x75, 0x63, 0xc0, 0x84,
- 0x2f, 0x60, 0x1c, 0x67, 0x76, 0xfd, 0x63, 0x86, 0xf3, 0xfa, 0xbf, 0xdc,
- 0xd2, 0x2d, 0x90, 0x91, 0xbd, 0x33, 0xa9, 0xe5, 0x66, 0x0c, 0xda, 0x42,
- 0x27, 0xca, 0xf4, 0x66, 0xc2, 0xec, 0x92, 0x14, 0x57, 0x06, 0x63, 0xd0,
- 0x4d, 0x15, 0x06, 0xeb, 0x69, 0x58, 0x4f, 0x77, 0xc5, 0x8b, 0xc7, 0xf0,
- 0x8e, 0xed, 0x64, 0xa0, 0xb3, 0x3c, 0x66, 0x71, 0xc6, 0x2d, 0xda, 0x0a,
- 0x0d, 0xfe, 0x70, 0x27, 0x64, 0xf8, 0x27, 0xfa, 0xf6, 0x5f, 0x30, 0xa5,
- 0x0d, 0x6c, 0xda, 0xf2, 0x62, 0x5e, 0x78, 0x47, 0xd3, 0x66, 0x00, 0x1c,
- 0xfd, 0x56, 0x1f, 0x5d, 0x3f, 0x6f, 0xf4, 0x4c, 0xd8, 0xfd, 0x0e, 0x27,
- 0xc9, 0x5c, 0x2b, 0xbc, 0xc0, 0xa4, 0xe7, 0x23, 0x29, 0x02, 0x9f, 0x31,
- 0xd6, 0xe9, 0xd7, 0x96, 0xf4, 0xe0, 0x5e, 0x0b, 0x0e, 0x13, 0xee, 0x3c,
- 0x09, 0xed, 0xf2, 0x3d, 0x76, 0x91, 0xc3, 0xa4, 0x97, 0xae, 0xd4, 0x87,
- 0xd0, 0x5d, 0xf6, 0x18, 0x47, 0x1f, 0x1d, 0x67, 0xf2, 0xcf, 0x63, 0xa0,
- 0x91, 0x27, 0xf8, 0x93, 0x45, 0x75, 0x23, 0x3f, 0xd1, 0xf1, 0xad, 0x23,
- 0xdd, 0x64, 0x93, 0x96, 0x41, 0x70, 0x7f, 0xf7, 0xf5, 0xa9, 0x89, 0xa2,
- 0x34, 0xb0, 0x8d, 0x1b, 0xae, 0x19, 0x15, 0x49, 0x58, 0x23, 0x6d, 0x87,
- 0x15, 0x4f, 0x81, 0x76, 0xfb, 0x23, 0xb5, 0xea, 0xcf, 0xac, 0x54, 0x8d,
- 0x4e, 0x42, 0x2f, 0xeb, 0x0f, 0x63, 0xdb, 0x68, 0x37, 0xa8, 0xcf, 0x8b,
- 0xab, 0xf5, 0xa4, 0x6e, 0x96, 0x2a, 0xb2, 0xd6, 0xbe, 0x9e, 0xbd, 0x0d,
- 0xb4, 0x42, 0xa9, 0xcf, 0x01, 0x83, 0x8a, 0x17, 0x47, 0x76, 0xc4, 0xc6,
- 0x83, 0x04, 0x95, 0x0b, 0xfc, 0x11, 0xc9, 0x62, 0xb8, 0x0c, 0x76, 0x84,
- 0xd9, 0xb9, 0x37, 0xfa, 0xfc, 0x7c, 0xc2, 0x6d, 0x58, 0x3e, 0xb3, 0x04,
- 0xbb, 0x8c, 0x8f, 0x48, 0xbc, 0x91, 0x27, 0xcc, 0xf9, 0xb7, 0x22, 0x19,
- 0x83, 0x2e, 0x09, 0xb5, 0x72, 0xd9, 0x54, 0x1c, 0x4d, 0xa1, 0xea, 0x0b,
- 0xf1, 0xc6, 0x08, 0x72, 0x46, 0x87, 0x7a, 0x6e, 0x80, 0x56, 0x0a, 0x8a,
- 0xc0, 0xdd, 0x11, 0x6b, 0xd6, 0xdd, 0x47, 0xdf, 0x10, 0xd9, 0xd8, 0xea,
- 0x7c, 0xb0, 0x8f, 0x03, 0x00, 0x2e, 0xc1, 0x8f, 0x44, 0xa8, 0xd3, 0x30,
- 0x06, 0x89, 0xa2, 0xf9, 0x34, 0xad, 0xdc, 0x03, 0x85, 0xed, 0x51, 0xa7,
- 0x82, 0x9c, 0xe7, 0x5d, 0x52, 0x93, 0x0c, 0x32, 0x9a, 0x5b, 0xe1, 0xaa,
- 0xca, 0xb8, 0x02, 0x6d, 0x3a, 0xd4, 0xb1, 0x3a, 0xf0, 0x5f, 0xbe, 0xb5,
- 0x0d, 0x10, 0x6b, 0x38, 0x32, 0xac, 0x76, 0x80, 0xbd, 0xca, 0x94, 0x71,
- 0x7a, 0xf2, 0xc9, 0x35, 0x2a, 0xde, 0x9f, 0x42, 0x49, 0x18, 0x01, 0xab,
- 0xbc, 0xef, 0x7c, 0x64, 0x3f, 0x58, 0x3d, 0x92, 0x59, 0xdb, 0x13, 0xdb,
- 0x58, 0x6e, 0x0a, 0xe0, 0xb7, 0x91, 0x4a, 0x08, 0x20, 0xd6, 0x2e, 0x3c,
- 0x45, 0xc9, 0x8b, 0x17, 0x79, 0xe7, 0xc7, 0x90, 0x99, 0x3a, 0x18, 0x25,
-};
-
-void x25519_ge_scalarmult_base(ge_p3 *h, const uint8_t a[32]) {
- x25519_ge_scalarmult_small_precomp(h, a, k25519SmallPrecomp);
-}
-
-#else
-
-/* k25519Precomp[i][j] = (j+1)*256^i*B */
-static const ge_precomp k25519Precomp[32][8] = {
- {
- {
- {25967493, -14356035, 29566456, 3660896, -12694345, 4014787,
- 27544626, -11754271, -6079156, 2047605},
- {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692,
- 5043384, 19500929, -15469378},
- {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380,
- 29287919, 11864899, -24514362, -4438546},
- },
- {
- {-12815894, -12976347, -21581243, 11784320, -25355658, -2750717,
- -11717903, -3814571, -358445, -10211303},
- {-21703237, 6903825, 27185491, 6451973, -29577724, -9554005,
- -15616551, 11189268, -26829678, -5319081},
- {26966642, 11152617, 32442495, 15396054, 14353839, -12752335,
- -3128826, -9541118, -15472047, -4166697},
- },
- {
- {15636291, -9688557, 24204773, -7912398, 616977, -16685262,
- 27787600, -14772189, 28944400, -1550024},
- {16568933, 4717097, -11556148, -1102322, 15682896, -11807043,
- 16354577, -11775962, 7689662, 11199574},
- {30464156, -5976125, -11779434, -15670865, 23220365, 15915852,
- 7512774, 10017326, -17749093, -9920357},
- },
- {
- {-17036878, 13921892, 10945806, -6033431, 27105052, -16084379,
- -28926210, 15006023, 3284568, -6276540},
- {23599295, -8306047, -11193664, -7687416, 13236774, 10506355,
- 7464579, 9656445, 13059162, 10374397},
- {7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664,
- -3839045, -641708, -101325},
- },
- {
- {10861363, 11473154, 27284546, 1981175, -30064349, 12577861,
- 32867885, 14515107, -15438304, 10819380},
- {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668,
- 12483688, -12668491, 5581306},
- {19563160, 16186464, -29386857, 4097519, 10237984, -4348115,
- 28542350, 13850243, -23678021, -15815942},
- },
- {
- {-15371964, -12862754, 32573250, 4720197, -26436522, 5875511,
- -19188627, -15224819, -9818940, -12085777},
- {-8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240,
- -15689887, 1762328, 14866737},
- {-18199695, -15951423, -10473290, 1707278, -17185920, 3916101,
- -28236412, 3959421, 27914454, 4383652},
- },
- {
- {5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852,
- 5230134, -23952439, -15175766},
- {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722,
- 20654025, 16520125, 30598449, 7715701},
- {28881845, 14381568, 9657904, 3680757, -20181635, 7843316,
- -31400660, 1370708, 29794553, -1409300},
- },
- {
- {14499471, -2729599, -33191113, -4254652, 28494862, 14271267,
- 30290735, 10876454, -33154098, 2381726},
- {-7195431, -2655363, -14730155, 462251, -27724326, 3941372,
- -6236617, 3696005, -32300832, 15351955},
- {27431194, 8222322, 16448760, -3907995, -18707002, 11938355,
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- },
- {
- {-5037580, -13028295, -2970559, -3061767, 15640974, -6701666,
- -26739026, 926050, -1684339, -13333647},
- {13908495, -3549272, 30919928, -6273825, -21521863, 7989039,
- 9021034, 9078865, 3353509, 4033511},
- {-29663431, -15113610, 32259991, -344482, 24295849, -12912123,
- 23161163, 8839127, 27485041, 7356032},
- },
- },
- {
- {
- {9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142,
- 2625015, 28431036, -16771834},
- {-23839233, -8311415, -25945511, 7480958, -17681669, -8354183,
- -22545972, 14150565, 15970762, 4099461},
- {29262576, 16756590, 26350592, -8793563, 8529671, -11208050,
- 13617293, -9937143, 11465739, 8317062},
- },
- {
- {-25493081, -6962928, 32500200, -9419051, -23038724, -2302222,
- 14898637, 3848455, 20969334, -5157516},
- {-20384450, -14347713, -18336405, 13884722, -33039454, 2842114,
- -21610826, -3649888, 11177095, 14989547},
- {-24496721, -11716016, 16959896, 2278463, 12066309, 10137771,
- 13515641, 2581286, -28487508, 9930240},
- },
- {
- {-17751622, -2097826, 16544300, -13009300, -15914807, -14949081,
- 18345767, -13403753, 16291481, -5314038},
- {-33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774,
- 6957617, 4368891, 9788741},
- {16660756, 7281060, -10830758, 12911820, 20108584, -8101676,
- -21722536, -8613148, 16250552, -11111103},
- },
- {
- {-19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584,
- 10604807, -30190403, 4782747},
- {-1354539, 14736941, -7367442, -13292886, 7710542, -14155590,
- -9981571, 4383045, 22546403, 437323},
- {31665577, -12180464, -16186830, 1491339, -18368625, 3294682,
- 27343084, 2786261, -30633590, -14097016},
- },
- {
- {-14467279, -683715, -33374107, 7448552, 19294360, 14334329,
- -19690631, 2355319, -19284671, -6114373},
- {15121312, -15796162, 6377020, -6031361, -10798111, -12957845,
- 18952177, 15496498, -29380133, 11754228},
- {-2637277, -13483075, 8488727, -14303896, 12728761, -1622493,
- 7141596, 11724556, 22761615, -10134141},
- },
- {
- {16918416, 11729663, -18083579, 3022987, -31015732, -13339659,
- -28741185, -12227393, 32851222, 11717399},
- {11166634, 7338049, -6722523, 4531520, -29468672, -7302055,
- 31474879, 3483633, -1193175, -4030831},
- {-185635, 9921305, 31456609, -13536438, -12013818, 13348923,
- 33142652, 6546660, -19985279, -3948376},
- },
- {
- {-32460596, 11266712, -11197107, -7899103, 31703694, 3855903,
- -8537131, -12833048, -30772034, -15486313},
- {-18006477, 12709068, 3991746, -6479188, -21491523, -10550425,
- -31135347, -16049879, 10928917, 3011958},
- {-6957757, -15594337, 31696059, 334240, 29576716, 14796075,
- -30831056, -12805180, 18008031, 10258577},
- },
- {
- {-22448644, 15655569, 7018479, -4410003, -30314266, -1201591,
- -1853465, 1367120, 25127874, 6671743},
- {29701166, -14373934, -10878120, 9279288, -17568, 13127210,
- 21382910, 11042292, 25838796, 4642684},
- {-20430234, 14955537, -24126347, 8124619, -5369288, -5990470,
- 30468147, -13900640, 18423289, 4177476},
- },
- },
-};
-
-static uint8_t negative(signed char b) {
- uint32_t x = b;
- x >>= 31; /* 1: yes; 0: no */
- return x;
-}
-
-static void table_select(ge_precomp *t, int pos, signed char b) {
- ge_precomp minust;
- uint8_t bnegative = negative(b);
- uint8_t babs = b - ((uint8_t)((-bnegative) & b) << 1);
-
- ge_precomp_0(t);
- cmov(t, &k25519Precomp[pos][0], equal(babs, 1));
- cmov(t, &k25519Precomp[pos][1], equal(babs, 2));
- cmov(t, &k25519Precomp[pos][2], equal(babs, 3));
- cmov(t, &k25519Precomp[pos][3], equal(babs, 4));
- cmov(t, &k25519Precomp[pos][4], equal(babs, 5));
- cmov(t, &k25519Precomp[pos][5], equal(babs, 6));
- cmov(t, &k25519Precomp[pos][6], equal(babs, 7));
- cmov(t, &k25519Precomp[pos][7], equal(babs, 8));
- fe_copy(minust.yplusx, t->yminusx);
- fe_copy(minust.yminusx, t->yplusx);
- fe_neg(minust.xy2d, t->xy2d);
- cmov(t, &minust, bnegative);
-}
-
-/* h = a * B
- * where a = a[0]+256*a[1]+...+256^31 a[31]
- * B is the Ed25519 base point (x,4/5) with x positive.
- *
- * Preconditions:
- * a[31] <= 127 */
-void x25519_ge_scalarmult_base(ge_p3 *h, const uint8_t *a) {
- signed char e[64];
- signed char carry;
- ge_p1p1 r;
- ge_p2 s;
- ge_precomp t;
- int i;
-
- for (i = 0; i < 32; ++i) {
- e[2 * i + 0] = (a[i] >> 0) & 15;
- e[2 * i + 1] = (a[i] >> 4) & 15;
- }
- /* each e[i] is between 0 and 15 */
- /* e[63] is between 0 and 7 */
-
- carry = 0;
- for (i = 0; i < 63; ++i) {
- e[i] += carry;
- carry = e[i] + 8;
- carry >>= 4;
- e[i] -= carry << 4;
- }
- e[63] += carry;
- /* each e[i] is between -8 and 8 */
-
- ge_p3_0(h);
- for (i = 1; i < 64; i += 2) {
- table_select(&t, i / 2, e[i]);
- ge_madd(&r, h, &t);
- x25519_ge_p1p1_to_p3(h, &r);
- }
-
- ge_p3_dbl(&r, h);
- x25519_ge_p1p1_to_p2(&s, &r);
- ge_p2_dbl(&r, &s);
- x25519_ge_p1p1_to_p2(&s, &r);
- ge_p2_dbl(&r, &s);
- x25519_ge_p1p1_to_p2(&s, &r);
- ge_p2_dbl(&r, &s);
- x25519_ge_p1p1_to_p3(h, &r);
-
- for (i = 0; i < 64; i += 2) {
- table_select(&t, i / 2, e[i]);
- ge_madd(&r, h, &t);
- x25519_ge_p1p1_to_p3(h, &r);
- }
-}
-
-#endif
-
-static void cmov_cached(ge_cached *t, ge_cached *u, uint8_t b) {
- fe_cmov(t->YplusX, u->YplusX, b);
- fe_cmov(t->YminusX, u->YminusX, b);
- fe_cmov(t->Z, u->Z, b);
- fe_cmov(t->T2d, u->T2d, b);
-}
-
-/* r = scalar * A.
- * where a = a[0]+256*a[1]+...+256^31 a[31]. */
-void x25519_ge_scalarmult(ge_p2 *r, const uint8_t *scalar, const ge_p3 *A) {
- ge_p2 Ai_p2[8];
- ge_cached Ai[16];
- ge_p1p1 t;
-
- ge_cached_0(&Ai[0]);
- x25519_ge_p3_to_cached(&Ai[1], A);
- ge_p3_to_p2(&Ai_p2[1], A);
-
- unsigned i;
- for (i = 2; i < 16; i += 2) {
- ge_p2_dbl(&t, &Ai_p2[i / 2]);
- ge_p1p1_to_cached(&Ai[i], &t);
- if (i < 8) {
- x25519_ge_p1p1_to_p2(&Ai_p2[i], &t);
- }
- x25519_ge_add(&t, A, &Ai[i]);
- ge_p1p1_to_cached(&Ai[i + 1], &t);
- if (i < 7) {
- x25519_ge_p1p1_to_p2(&Ai_p2[i + 1], &t);
- }
- }
-
- ge_p2_0(r);
- ge_p3 u;
-
- for (i = 0; i < 256; i += 4) {
- ge_p2_dbl(&t, r);
- x25519_ge_p1p1_to_p2(r, &t);
- ge_p2_dbl(&t, r);
- x25519_ge_p1p1_to_p2(r, &t);
- ge_p2_dbl(&t, r);
- x25519_ge_p1p1_to_p2(r, &t);
- ge_p2_dbl(&t, r);
- x25519_ge_p1p1_to_p3(&u, &t);
-
- uint8_t index = scalar[31 - i/8];
- index >>= 4 - (i & 4);
- index &= 0xf;
-
- unsigned j;
- ge_cached selected;
- ge_cached_0(&selected);
- for (j = 0; j < 16; j++) {
- cmov_cached(&selected, &Ai[j], equal(j, index));
- }
-
- x25519_ge_add(&t, &u, &selected);
- x25519_ge_p1p1_to_p2(r, &t);
- }
-}
-
-static void slide(signed char *r, const uint8_t *a) {
- int i;
- int b;
- int k;
-
- for (i = 0; i < 256; ++i) {
- r[i] = 1 & (a[i >> 3] >> (i & 7));
- }
-
- for (i = 0; i < 256; ++i) {
- if (r[i]) {
- for (b = 1; b <= 6 && i + b < 256; ++b) {
- if (r[i + b]) {
- if (r[i] + (r[i + b] << b) <= 15) {
- r[i] += r[i + b] << b;
- r[i + b] = 0;
- } else if (r[i] - (r[i + b] << b) >= -15) {
- r[i] -= r[i + b] << b;
- for (k = i + b; k < 256; ++k) {
- if (!r[k]) {
- r[k] = 1;
- break;
- }
- r[k] = 0;
- }
- } else {
- break;
- }
- }
- }
- }
- }
-}
-
-static const ge_precomp Bi[8] = {
- {
- {25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626,
- -11754271, -6079156, 2047605},
- {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692,
- 5043384, 19500929, -15469378},
- {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919,
- 11864899, -24514362, -4438546},
- },
- {
- {15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600,
- -14772189, 28944400, -1550024},
- {16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577,
- -11775962, 7689662, 11199574},
- {30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774,
- 10017326, -17749093, -9920357},
- },
- {
- {10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885,
- 14515107, -15438304, 10819380},
- {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668,
- 12483688, -12668491, 5581306},
- {19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350,
- 13850243, -23678021, -15815942},
- },
- {
- {5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852,
- 5230134, -23952439, -15175766},
- {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025,
- 16520125, 30598449, 7715701},
- {28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660,
- 1370708, 29794553, -1409300},
- },
- {
- {-22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211,
- -1361450, -13062696, 13821877},
- {-6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028,
- -7212327, 18853322, -14220951},
- {4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358,
- -10431137, 2207753, -3209784},
- },
- {
- {-25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364,
- -663000, -31111463, -16132436},
- {25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789,
- 15725684, 171356, 6466918},
- {23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339,
- -14088058, -30714912, 16193877},
- },
- {
- {-33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398,
- 4729455, -18074513, 9256800},
- {-25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405,
- 9761698, -19827198, 630305},
- {-13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551,
- -15960994, -2449256, -14291300},
- },
- {
- {-3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575,
- 15033784, 25105118, -7894876},
- {-24326370, 15950226, -31801215, -14592823, -11662737, -5090925,
- 1573892, -2625887, 2198790, -15804619},
- {-3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022,
- -16236442, -32461234, -12290683},
- },
-};
-
-/* r = a * A + b * B
- * where a = a[0]+256*a[1]+...+256^31 a[31].
- * and b = b[0]+256*b[1]+...+256^31 b[31].
- * B is the Ed25519 base point (x,4/5) with x positive. */
-static void ge_double_scalarmult_vartime(ge_p2 *r, const uint8_t *a,
- const ge_p3 *A, const uint8_t *b) {
- signed char aslide[256];
- signed char bslide[256];
- ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */
- ge_p1p1 t;
- ge_p3 u;
- ge_p3 A2;
- int i;
-
- slide(aslide, a);
- slide(bslide, b);
-
- x25519_ge_p3_to_cached(&Ai[0], A);
- ge_p3_dbl(&t, A);
- x25519_ge_p1p1_to_p3(&A2, &t);
- x25519_ge_add(&t, &A2, &Ai[0]);
- x25519_ge_p1p1_to_p3(&u, &t);
- x25519_ge_p3_to_cached(&Ai[1], &u);
- x25519_ge_add(&t, &A2, &Ai[1]);
- x25519_ge_p1p1_to_p3(&u, &t);
- x25519_ge_p3_to_cached(&Ai[2], &u);
- x25519_ge_add(&t, &A2, &Ai[2]);
- x25519_ge_p1p1_to_p3(&u, &t);
- x25519_ge_p3_to_cached(&Ai[3], &u);
- x25519_ge_add(&t, &A2, &Ai[3]);
- x25519_ge_p1p1_to_p3(&u, &t);
- x25519_ge_p3_to_cached(&Ai[4], &u);
- x25519_ge_add(&t, &A2, &Ai[4]);
- x25519_ge_p1p1_to_p3(&u, &t);
- x25519_ge_p3_to_cached(&Ai[5], &u);
- x25519_ge_add(&t, &A2, &Ai[5]);
- x25519_ge_p1p1_to_p3(&u, &t);
- x25519_ge_p3_to_cached(&Ai[6], &u);
- x25519_ge_add(&t, &A2, &Ai[6]);
- x25519_ge_p1p1_to_p3(&u, &t);
- x25519_ge_p3_to_cached(&Ai[7], &u);
-
- ge_p2_0(r);
-
- for (i = 255; i >= 0; --i) {
- if (aslide[i] || bslide[i]) {
- break;
- }
- }
-
- for (; i >= 0; --i) {
- ge_p2_dbl(&t, r);
-
- if (aslide[i] > 0) {
- x25519_ge_p1p1_to_p3(&u, &t);
- x25519_ge_add(&t, &u, &Ai[aslide[i] / 2]);
- } else if (aslide[i] < 0) {
- x25519_ge_p1p1_to_p3(&u, &t);
- x25519_ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]);
- }
-
- if (bslide[i] > 0) {
- x25519_ge_p1p1_to_p3(&u, &t);
- ge_madd(&t, &u, &Bi[bslide[i] / 2]);
- } else if (bslide[i] < 0) {
- x25519_ge_p1p1_to_p3(&u, &t);
- ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]);
- }
-
- x25519_ge_p1p1_to_p2(r, &t);
- }
-}
-
-/* The set of scalars is \Z/l
- * where l = 2^252 + 27742317777372353535851937790883648493. */
-
-/* Input:
- * s[0]+256*s[1]+...+256^63*s[63] = s
- *
- * Output:
- * s[0]+256*s[1]+...+256^31*s[31] = s mod l
- * where l = 2^252 + 27742317777372353535851937790883648493.
- * Overwrites s in place. */
-void x25519_sc_reduce(uint8_t *s) {
- int64_t s0 = 2097151 & load_3(s);
- int64_t s1 = 2097151 & (load_4(s + 2) >> 5);
- int64_t s2 = 2097151 & (load_3(s + 5) >> 2);
- int64_t s3 = 2097151 & (load_4(s + 7) >> 7);
- int64_t s4 = 2097151 & (load_4(s + 10) >> 4);
- int64_t s5 = 2097151 & (load_3(s + 13) >> 1);
- int64_t s6 = 2097151 & (load_4(s + 15) >> 6);
- int64_t s7 = 2097151 & (load_3(s + 18) >> 3);
- int64_t s8 = 2097151 & load_3(s + 21);
- int64_t s9 = 2097151 & (load_4(s + 23) >> 5);
- int64_t s10 = 2097151 & (load_3(s + 26) >> 2);
- int64_t s11 = 2097151 & (load_4(s + 28) >> 7);
- int64_t s12 = 2097151 & (load_4(s + 31) >> 4);
- int64_t s13 = 2097151 & (load_3(s + 34) >> 1);
- int64_t s14 = 2097151 & (load_4(s + 36) >> 6);
- int64_t s15 = 2097151 & (load_3(s + 39) >> 3);
- int64_t s16 = 2097151 & load_3(s + 42);
- int64_t s17 = 2097151 & (load_4(s + 44) >> 5);
- int64_t s18 = 2097151 & (load_3(s + 47) >> 2);
- int64_t s19 = 2097151 & (load_4(s + 49) >> 7);
- int64_t s20 = 2097151 & (load_4(s + 52) >> 4);
- int64_t s21 = 2097151 & (load_3(s + 55) >> 1);
- int64_t s22 = 2097151 & (load_4(s + 57) >> 6);
- int64_t s23 = (load_4(s + 60) >> 3);
- int64_t carry0;
- int64_t carry1;
- int64_t carry2;
- int64_t carry3;
- int64_t carry4;
- int64_t carry5;
- int64_t carry6;
- int64_t carry7;
- int64_t carry8;
- int64_t carry9;
- int64_t carry10;
- int64_t carry11;
- int64_t carry12;
- int64_t carry13;
- int64_t carry14;
- int64_t carry15;
- int64_t carry16;
-
- s11 += s23 * 666643;
- s12 += s23 * 470296;
- s13 += s23 * 654183;
- s14 -= s23 * 997805;
- s15 += s23 * 136657;
- s16 -= s23 * 683901;
- s23 = 0;
-
- s10 += s22 * 666643;
- s11 += s22 * 470296;
- s12 += s22 * 654183;
- s13 -= s22 * 997805;
- s14 += s22 * 136657;
- s15 -= s22 * 683901;
- s22 = 0;
-
- s9 += s21 * 666643;
- s10 += s21 * 470296;
- s11 += s21 * 654183;
- s12 -= s21 * 997805;
- s13 += s21 * 136657;
- s14 -= s21 * 683901;
- s21 = 0;
-
- s8 += s20 * 666643;
- s9 += s20 * 470296;
- s10 += s20 * 654183;
- s11 -= s20 * 997805;
- s12 += s20 * 136657;
- s13 -= s20 * 683901;
- s20 = 0;
-
- s7 += s19 * 666643;
- s8 += s19 * 470296;
- s9 += s19 * 654183;
- s10 -= s19 * 997805;
- s11 += s19 * 136657;
- s12 -= s19 * 683901;
- s19 = 0;
-
- s6 += s18 * 666643;
- s7 += s18 * 470296;
- s8 += s18 * 654183;
- s9 -= s18 * 997805;
- s10 += s18 * 136657;
- s11 -= s18 * 683901;
- s18 = 0;
-
- carry6 = (s6 + (1 << 20)) >> 21;
- s7 += carry6;
- s6 -= carry6 << 21;
- carry8 = (s8 + (1 << 20)) >> 21;
- s9 += carry8;
- s8 -= carry8 << 21;
- carry10 = (s10 + (1 << 20)) >> 21;
- s11 += carry10;
- s10 -= carry10 << 21;
- carry12 = (s12 + (1 << 20)) >> 21;
- s13 += carry12;
- s12 -= carry12 << 21;
- carry14 = (s14 + (1 << 20)) >> 21;
- s15 += carry14;
- s14 -= carry14 << 21;
- carry16 = (s16 + (1 << 20)) >> 21;
- s17 += carry16;
- s16 -= carry16 << 21;
-
- carry7 = (s7 + (1 << 20)) >> 21;
- s8 += carry7;
- s7 -= carry7 << 21;
- carry9 = (s9 + (1 << 20)) >> 21;
- s10 += carry9;
- s9 -= carry9 << 21;
- carry11 = (s11 + (1 << 20)) >> 21;
- s12 += carry11;
- s11 -= carry11 << 21;
- carry13 = (s13 + (1 << 20)) >> 21;
- s14 += carry13;
- s13 -= carry13 << 21;
- carry15 = (s15 + (1 << 20)) >> 21;
- s16 += carry15;
- s15 -= carry15 << 21;
-
- s5 += s17 * 666643;
- s6 += s17 * 470296;
- s7 += s17 * 654183;
- s8 -= s17 * 997805;
- s9 += s17 * 136657;
- s10 -= s17 * 683901;
- s17 = 0;
-
- s4 += s16 * 666643;
- s5 += s16 * 470296;
- s6 += s16 * 654183;
- s7 -= s16 * 997805;
- s8 += s16 * 136657;
- s9 -= s16 * 683901;
- s16 = 0;
-
- s3 += s15 * 666643;
- s4 += s15 * 470296;
- s5 += s15 * 654183;
- s6 -= s15 * 997805;
- s7 += s15 * 136657;
- s8 -= s15 * 683901;
- s15 = 0;
-
- s2 += s14 * 666643;
- s3 += s14 * 470296;
- s4 += s14 * 654183;
- s5 -= s14 * 997805;
- s6 += s14 * 136657;
- s7 -= s14 * 683901;
- s14 = 0;
-
- s1 += s13 * 666643;
- s2 += s13 * 470296;
- s3 += s13 * 654183;
- s4 -= s13 * 997805;
- s5 += s13 * 136657;
- s6 -= s13 * 683901;
- s13 = 0;
-
- s0 += s12 * 666643;
- s1 += s12 * 470296;
- s2 += s12 * 654183;
- s3 -= s12 * 997805;
- s4 += s12 * 136657;
- s5 -= s12 * 683901;
- s12 = 0;
-
- carry0 = (s0 + (1 << 20)) >> 21;
- s1 += carry0;
- s0 -= carry0 << 21;
- carry2 = (s2 + (1 << 20)) >> 21;
- s3 += carry2;
- s2 -= carry2 << 21;
- carry4 = (s4 + (1 << 20)) >> 21;
- s5 += carry4;
- s4 -= carry4 << 21;
- carry6 = (s6 + (1 << 20)) >> 21;
- s7 += carry6;
- s6 -= carry6 << 21;
- carry8 = (s8 + (1 << 20)) >> 21;
- s9 += carry8;
- s8 -= carry8 << 21;
- carry10 = (s10 + (1 << 20)) >> 21;
- s11 += carry10;
- s10 -= carry10 << 21;
-
- carry1 = (s1 + (1 << 20)) >> 21;
- s2 += carry1;
- s1 -= carry1 << 21;
- carry3 = (s3 + (1 << 20)) >> 21;
- s4 += carry3;
- s3 -= carry3 << 21;
- carry5 = (s5 + (1 << 20)) >> 21;
- s6 += carry5;
- s5 -= carry5 << 21;
- carry7 = (s7 + (1 << 20)) >> 21;
- s8 += carry7;
- s7 -= carry7 << 21;
- carry9 = (s9 + (1 << 20)) >> 21;
- s10 += carry9;
- s9 -= carry9 << 21;
- carry11 = (s11 + (1 << 20)) >> 21;
- s12 += carry11;
- s11 -= carry11 << 21;
-
- s0 += s12 * 666643;
- s1 += s12 * 470296;
- s2 += s12 * 654183;
- s3 -= s12 * 997805;
- s4 += s12 * 136657;
- s5 -= s12 * 683901;
- s12 = 0;
-
- carry0 = s0 >> 21;
- s1 += carry0;
- s0 -= carry0 << 21;
- carry1 = s1 >> 21;
- s2 += carry1;
- s1 -= carry1 << 21;
- carry2 = s2 >> 21;
- s3 += carry2;
- s2 -= carry2 << 21;
- carry3 = s3 >> 21;
- s4 += carry3;
- s3 -= carry3 << 21;
- carry4 = s4 >> 21;
- s5 += carry4;
- s4 -= carry4 << 21;
- carry5 = s5 >> 21;
- s6 += carry5;
- s5 -= carry5 << 21;
- carry6 = s6 >> 21;
- s7 += carry6;
- s6 -= carry6 << 21;
- carry7 = s7 >> 21;
- s8 += carry7;
- s7 -= carry7 << 21;
- carry8 = s8 >> 21;
- s9 += carry8;
- s8 -= carry8 << 21;
- carry9 = s9 >> 21;
- s10 += carry9;
- s9 -= carry9 << 21;
- carry10 = s10 >> 21;
- s11 += carry10;
- s10 -= carry10 << 21;
- carry11 = s11 >> 21;
- s12 += carry11;
- s11 -= carry11 << 21;
-
- s0 += s12 * 666643;
- s1 += s12 * 470296;
- s2 += s12 * 654183;
- s3 -= s12 * 997805;
- s4 += s12 * 136657;
- s5 -= s12 * 683901;
- s12 = 0;
-
- carry0 = s0 >> 21;
- s1 += carry0;
- s0 -= carry0 << 21;
- carry1 = s1 >> 21;
- s2 += carry1;
- s1 -= carry1 << 21;
- carry2 = s2 >> 21;
- s3 += carry2;
- s2 -= carry2 << 21;
- carry3 = s3 >> 21;
- s4 += carry3;
- s3 -= carry3 << 21;
- carry4 = s4 >> 21;
- s5 += carry4;
- s4 -= carry4 << 21;
- carry5 = s5 >> 21;
- s6 += carry5;
- s5 -= carry5 << 21;
- carry6 = s6 >> 21;
- s7 += carry6;
- s6 -= carry6 << 21;
- carry7 = s7 >> 21;
- s8 += carry7;
- s7 -= carry7 << 21;
- carry8 = s8 >> 21;
- s9 += carry8;
- s8 -= carry8 << 21;
- carry9 = s9 >> 21;
- s10 += carry9;
- s9 -= carry9 << 21;
- carry10 = s10 >> 21;
- s11 += carry10;
- s10 -= carry10 << 21;
-
- s[0] = s0 >> 0;
- s[1] = s0 >> 8;
- s[2] = (s0 >> 16) | (s1 << 5);
- s[3] = s1 >> 3;
- s[4] = s1 >> 11;
- s[5] = (s1 >> 19) | (s2 << 2);
- s[6] = s2 >> 6;
- s[7] = (s2 >> 14) | (s3 << 7);
- s[8] = s3 >> 1;
- s[9] = s3 >> 9;
- s[10] = (s3 >> 17) | (s4 << 4);
- s[11] = s4 >> 4;
- s[12] = s4 >> 12;
- s[13] = (s4 >> 20) | (s5 << 1);
- s[14] = s5 >> 7;
- s[15] = (s5 >> 15) | (s6 << 6);
- s[16] = s6 >> 2;
- s[17] = s6 >> 10;
- s[18] = (s6 >> 18) | (s7 << 3);
- s[19] = s7 >> 5;
- s[20] = s7 >> 13;
- s[21] = s8 >> 0;
- s[22] = s8 >> 8;
- s[23] = (s8 >> 16) | (s9 << 5);
- s[24] = s9 >> 3;
- s[25] = s9 >> 11;
- s[26] = (s9 >> 19) | (s10 << 2);
- s[27] = s10 >> 6;
- s[28] = (s10 >> 14) | (s11 << 7);
- s[29] = s11 >> 1;
- s[30] = s11 >> 9;
- s[31] = s11 >> 17;
-}
-
-/* Input:
- * a[0]+256*a[1]+...+256^31*a[31] = a
- * b[0]+256*b[1]+...+256^31*b[31] = b
- * c[0]+256*c[1]+...+256^31*c[31] = c
- *
- * Output:
- * s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l
- * where l = 2^252 + 27742317777372353535851937790883648493. */
-static void sc_muladd(uint8_t *s, const uint8_t *a, const uint8_t *b,
- const uint8_t *c) {
- int64_t a0 = 2097151 & load_3(a);
- int64_t a1 = 2097151 & (load_4(a + 2) >> 5);
- int64_t a2 = 2097151 & (load_3(a + 5) >> 2);
- int64_t a3 = 2097151 & (load_4(a + 7) >> 7);
- int64_t a4 = 2097151 & (load_4(a + 10) >> 4);
- int64_t a5 = 2097151 & (load_3(a + 13) >> 1);
- int64_t a6 = 2097151 & (load_4(a + 15) >> 6);
- int64_t a7 = 2097151 & (load_3(a + 18) >> 3);
- int64_t a8 = 2097151 & load_3(a + 21);
- int64_t a9 = 2097151 & (load_4(a + 23) >> 5);
- int64_t a10 = 2097151 & (load_3(a + 26) >> 2);
- int64_t a11 = (load_4(a + 28) >> 7);
- int64_t b0 = 2097151 & load_3(b);
- int64_t b1 = 2097151 & (load_4(b + 2) >> 5);
- int64_t b2 = 2097151 & (load_3(b + 5) >> 2);
- int64_t b3 = 2097151 & (load_4(b + 7) >> 7);
- int64_t b4 = 2097151 & (load_4(b + 10) >> 4);
- int64_t b5 = 2097151 & (load_3(b + 13) >> 1);
- int64_t b6 = 2097151 & (load_4(b + 15) >> 6);
- int64_t b7 = 2097151 & (load_3(b + 18) >> 3);
- int64_t b8 = 2097151 & load_3(b + 21);
- int64_t b9 = 2097151 & (load_4(b + 23) >> 5);
- int64_t b10 = 2097151 & (load_3(b + 26) >> 2);
- int64_t b11 = (load_4(b + 28) >> 7);
- int64_t c0 = 2097151 & load_3(c);
- int64_t c1 = 2097151 & (load_4(c + 2) >> 5);
- int64_t c2 = 2097151 & (load_3(c + 5) >> 2);
- int64_t c3 = 2097151 & (load_4(c + 7) >> 7);
- int64_t c4 = 2097151 & (load_4(c + 10) >> 4);
- int64_t c5 = 2097151 & (load_3(c + 13) >> 1);
- int64_t c6 = 2097151 & (load_4(c + 15) >> 6);
- int64_t c7 = 2097151 & (load_3(c + 18) >> 3);
- int64_t c8 = 2097151 & load_3(c + 21);
- int64_t c9 = 2097151 & (load_4(c + 23) >> 5);
- int64_t c10 = 2097151 & (load_3(c + 26) >> 2);
- int64_t c11 = (load_4(c + 28) >> 7);
- int64_t s0;
- int64_t s1;
- int64_t s2;
- int64_t s3;
- int64_t s4;
- int64_t s5;
- int64_t s6;
- int64_t s7;
- int64_t s8;
- int64_t s9;
- int64_t s10;
- int64_t s11;
- int64_t s12;
- int64_t s13;
- int64_t s14;
- int64_t s15;
- int64_t s16;
- int64_t s17;
- int64_t s18;
- int64_t s19;
- int64_t s20;
- int64_t s21;
- int64_t s22;
- int64_t s23;
- int64_t carry0;
- int64_t carry1;
- int64_t carry2;
- int64_t carry3;
- int64_t carry4;
- int64_t carry5;
- int64_t carry6;
- int64_t carry7;
- int64_t carry8;
- int64_t carry9;
- int64_t carry10;
- int64_t carry11;
- int64_t carry12;
- int64_t carry13;
- int64_t carry14;
- int64_t carry15;
- int64_t carry16;
- int64_t carry17;
- int64_t carry18;
- int64_t carry19;
- int64_t carry20;
- int64_t carry21;
- int64_t carry22;
-
- s0 = c0 + a0 * b0;
- s1 = c1 + a0 * b1 + a1 * b0;
- s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0;
- s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0;
- s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0;
- s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0;
- s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0;
- s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 +
- a6 * b1 + a7 * b0;
- s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 +
- a6 * b2 + a7 * b1 + a8 * b0;
- s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 +
- a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0;
- s10 = c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 +
- a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0;
- s11 = c11 + a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 +
- a6 * b5 + a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0;
- s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 +
- a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1;
- s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 +
- a9 * b4 + a10 * b3 + a11 * b2;
- s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 +
- a10 * b4 + a11 * b3;
- s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 +
- a11 * b4;
- s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5;
- s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6;
- s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7;
- s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8;
- s20 = a9 * b11 + a10 * b10 + a11 * b9;
- s21 = a10 * b11 + a11 * b10;
- s22 = a11 * b11;
- s23 = 0;
-
- carry0 = (s0 + (1 << 20)) >> 21;
- s1 += carry0;
- s0 -= carry0 << 21;
- carry2 = (s2 + (1 << 20)) >> 21;
- s3 += carry2;
- s2 -= carry2 << 21;
- carry4 = (s4 + (1 << 20)) >> 21;
- s5 += carry4;
- s4 -= carry4 << 21;
- carry6 = (s6 + (1 << 20)) >> 21;
- s7 += carry6;
- s6 -= carry6 << 21;
- carry8 = (s8 + (1 << 20)) >> 21;
- s9 += carry8;
- s8 -= carry8 << 21;
- carry10 = (s10 + (1 << 20)) >> 21;
- s11 += carry10;
- s10 -= carry10 << 21;
- carry12 = (s12 + (1 << 20)) >> 21;
- s13 += carry12;
- s12 -= carry12 << 21;
- carry14 = (s14 + (1 << 20)) >> 21;
- s15 += carry14;
- s14 -= carry14 << 21;
- carry16 = (s16 + (1 << 20)) >> 21;
- s17 += carry16;
- s16 -= carry16 << 21;
- carry18 = (s18 + (1 << 20)) >> 21;
- s19 += carry18;
- s18 -= carry18 << 21;
- carry20 = (s20 + (1 << 20)) >> 21;
- s21 += carry20;
- s20 -= carry20 << 21;
- carry22 = (s22 + (1 << 20)) >> 21;
- s23 += carry22;
- s22 -= carry22 << 21;
-
- carry1 = (s1 + (1 << 20)) >> 21;
- s2 += carry1;
- s1 -= carry1 << 21;
- carry3 = (s3 + (1 << 20)) >> 21;
- s4 += carry3;
- s3 -= carry3 << 21;
- carry5 = (s5 + (1 << 20)) >> 21;
- s6 += carry5;
- s5 -= carry5 << 21;
- carry7 = (s7 + (1 << 20)) >> 21;
- s8 += carry7;
- s7 -= carry7 << 21;
- carry9 = (s9 + (1 << 20)) >> 21;
- s10 += carry9;
- s9 -= carry9 << 21;
- carry11 = (s11 + (1 << 20)) >> 21;
- s12 += carry11;
- s11 -= carry11 << 21;
- carry13 = (s13 + (1 << 20)) >> 21;
- s14 += carry13;
- s13 -= carry13 << 21;
- carry15 = (s15 + (1 << 20)) >> 21;
- s16 += carry15;
- s15 -= carry15 << 21;
- carry17 = (s17 + (1 << 20)) >> 21;
- s18 += carry17;
- s17 -= carry17 << 21;
- carry19 = (s19 + (1 << 20)) >> 21;
- s20 += carry19;
- s19 -= carry19 << 21;
- carry21 = (s21 + (1 << 20)) >> 21;
- s22 += carry21;
- s21 -= carry21 << 21;
-
- s11 += s23 * 666643;
- s12 += s23 * 470296;
- s13 += s23 * 654183;
- s14 -= s23 * 997805;
- s15 += s23 * 136657;
- s16 -= s23 * 683901;
- s23 = 0;
-
- s10 += s22 * 666643;
- s11 += s22 * 470296;
- s12 += s22 * 654183;
- s13 -= s22 * 997805;
- s14 += s22 * 136657;
- s15 -= s22 * 683901;
- s22 = 0;
-
- s9 += s21 * 666643;
- s10 += s21 * 470296;
- s11 += s21 * 654183;
- s12 -= s21 * 997805;
- s13 += s21 * 136657;
- s14 -= s21 * 683901;
- s21 = 0;
-
- s8 += s20 * 666643;
- s9 += s20 * 470296;
- s10 += s20 * 654183;
- s11 -= s20 * 997805;
- s12 += s20 * 136657;
- s13 -= s20 * 683901;
- s20 = 0;
-
- s7 += s19 * 666643;
- s8 += s19 * 470296;
- s9 += s19 * 654183;
- s10 -= s19 * 997805;
- s11 += s19 * 136657;
- s12 -= s19 * 683901;
- s19 = 0;
-
- s6 += s18 * 666643;
- s7 += s18 * 470296;
- s8 += s18 * 654183;
- s9 -= s18 * 997805;
- s10 += s18 * 136657;
- s11 -= s18 * 683901;
- s18 = 0;
-
- carry6 = (s6 + (1 << 20)) >> 21;
- s7 += carry6;
- s6 -= carry6 << 21;
- carry8 = (s8 + (1 << 20)) >> 21;
- s9 += carry8;
- s8 -= carry8 << 21;
- carry10 = (s10 + (1 << 20)) >> 21;
- s11 += carry10;
- s10 -= carry10 << 21;
- carry12 = (s12 + (1 << 20)) >> 21;
- s13 += carry12;
- s12 -= carry12 << 21;
- carry14 = (s14 + (1 << 20)) >> 21;
- s15 += carry14;
- s14 -= carry14 << 21;
- carry16 = (s16 + (1 << 20)) >> 21;
- s17 += carry16;
- s16 -= carry16 << 21;
-
- carry7 = (s7 + (1 << 20)) >> 21;
- s8 += carry7;
- s7 -= carry7 << 21;
- carry9 = (s9 + (1 << 20)) >> 21;
- s10 += carry9;
- s9 -= carry9 << 21;
- carry11 = (s11 + (1 << 20)) >> 21;
- s12 += carry11;
- s11 -= carry11 << 21;
- carry13 = (s13 + (1 << 20)) >> 21;
- s14 += carry13;
- s13 -= carry13 << 21;
- carry15 = (s15 + (1 << 20)) >> 21;
- s16 += carry15;
- s15 -= carry15 << 21;
-
- s5 += s17 * 666643;
- s6 += s17 * 470296;
- s7 += s17 * 654183;
- s8 -= s17 * 997805;
- s9 += s17 * 136657;
- s10 -= s17 * 683901;
- s17 = 0;
-
- s4 += s16 * 666643;
- s5 += s16 * 470296;
- s6 += s16 * 654183;
- s7 -= s16 * 997805;
- s8 += s16 * 136657;
- s9 -= s16 * 683901;
- s16 = 0;
-
- s3 += s15 * 666643;
- s4 += s15 * 470296;
- s5 += s15 * 654183;
- s6 -= s15 * 997805;
- s7 += s15 * 136657;
- s8 -= s15 * 683901;
- s15 = 0;
-
- s2 += s14 * 666643;
- s3 += s14 * 470296;
- s4 += s14 * 654183;
- s5 -= s14 * 997805;
- s6 += s14 * 136657;
- s7 -= s14 * 683901;
- s14 = 0;
-
- s1 += s13 * 666643;
- s2 += s13 * 470296;
- s3 += s13 * 654183;
- s4 -= s13 * 997805;
- s5 += s13 * 136657;
- s6 -= s13 * 683901;
- s13 = 0;
-
- s0 += s12 * 666643;
- s1 += s12 * 470296;
- s2 += s12 * 654183;
- s3 -= s12 * 997805;
- s4 += s12 * 136657;
- s5 -= s12 * 683901;
- s12 = 0;
-
- carry0 = (s0 + (1 << 20)) >> 21;
- s1 += carry0;
- s0 -= carry0 << 21;
- carry2 = (s2 + (1 << 20)) >> 21;
- s3 += carry2;
- s2 -= carry2 << 21;
- carry4 = (s4 + (1 << 20)) >> 21;
- s5 += carry4;
- s4 -= carry4 << 21;
- carry6 = (s6 + (1 << 20)) >> 21;
- s7 += carry6;
- s6 -= carry6 << 21;
- carry8 = (s8 + (1 << 20)) >> 21;
- s9 += carry8;
- s8 -= carry8 << 21;
- carry10 = (s10 + (1 << 20)) >> 21;
- s11 += carry10;
- s10 -= carry10 << 21;
-
- carry1 = (s1 + (1 << 20)) >> 21;
- s2 += carry1;
- s1 -= carry1 << 21;
- carry3 = (s3 + (1 << 20)) >> 21;
- s4 += carry3;
- s3 -= carry3 << 21;
- carry5 = (s5 + (1 << 20)) >> 21;
- s6 += carry5;
- s5 -= carry5 << 21;
- carry7 = (s7 + (1 << 20)) >> 21;
- s8 += carry7;
- s7 -= carry7 << 21;
- carry9 = (s9 + (1 << 20)) >> 21;
- s10 += carry9;
- s9 -= carry9 << 21;
- carry11 = (s11 + (1 << 20)) >> 21;
- s12 += carry11;
- s11 -= carry11 << 21;
-
- s0 += s12 * 666643;
- s1 += s12 * 470296;
- s2 += s12 * 654183;
- s3 -= s12 * 997805;
- s4 += s12 * 136657;
- s5 -= s12 * 683901;
- s12 = 0;
-
- carry0 = s0 >> 21;
- s1 += carry0;
- s0 -= carry0 << 21;
- carry1 = s1 >> 21;
- s2 += carry1;
- s1 -= carry1 << 21;
- carry2 = s2 >> 21;
- s3 += carry2;
- s2 -= carry2 << 21;
- carry3 = s3 >> 21;
- s4 += carry3;
- s3 -= carry3 << 21;
- carry4 = s4 >> 21;
- s5 += carry4;
- s4 -= carry4 << 21;
- carry5 = s5 >> 21;
- s6 += carry5;
- s5 -= carry5 << 21;
- carry6 = s6 >> 21;
- s7 += carry6;
- s6 -= carry6 << 21;
- carry7 = s7 >> 21;
- s8 += carry7;
- s7 -= carry7 << 21;
- carry8 = s8 >> 21;
- s9 += carry8;
- s8 -= carry8 << 21;
- carry9 = s9 >> 21;
- s10 += carry9;
- s9 -= carry9 << 21;
- carry10 = s10 >> 21;
- s11 += carry10;
- s10 -= carry10 << 21;
- carry11 = s11 >> 21;
- s12 += carry11;
- s11 -= carry11 << 21;
-
- s0 += s12 * 666643;
- s1 += s12 * 470296;
- s2 += s12 * 654183;
- s3 -= s12 * 997805;
- s4 += s12 * 136657;
- s5 -= s12 * 683901;
- s12 = 0;
-
- carry0 = s0 >> 21;
- s1 += carry0;
- s0 -= carry0 << 21;
- carry1 = s1 >> 21;
- s2 += carry1;
- s1 -= carry1 << 21;
- carry2 = s2 >> 21;
- s3 += carry2;
- s2 -= carry2 << 21;
- carry3 = s3 >> 21;
- s4 += carry3;
- s3 -= carry3 << 21;
- carry4 = s4 >> 21;
- s5 += carry4;
- s4 -= carry4 << 21;
- carry5 = s5 >> 21;
- s6 += carry5;
- s5 -= carry5 << 21;
- carry6 = s6 >> 21;
- s7 += carry6;
- s6 -= carry6 << 21;
- carry7 = s7 >> 21;
- s8 += carry7;
- s7 -= carry7 << 21;
- carry8 = s8 >> 21;
- s9 += carry8;
- s8 -= carry8 << 21;
- carry9 = s9 >> 21;
- s10 += carry9;
- s9 -= carry9 << 21;
- carry10 = s10 >> 21;
- s11 += carry10;
- s10 -= carry10 << 21;
-
- s[0] = s0 >> 0;
- s[1] = s0 >> 8;
- s[2] = (s0 >> 16) | (s1 << 5);
- s[3] = s1 >> 3;
- s[4] = s1 >> 11;
- s[5] = (s1 >> 19) | (s2 << 2);
- s[6] = s2 >> 6;
- s[7] = (s2 >> 14) | (s3 << 7);
- s[8] = s3 >> 1;
- s[9] = s3 >> 9;
- s[10] = (s3 >> 17) | (s4 << 4);
- s[11] = s4 >> 4;
- s[12] = s4 >> 12;
- s[13] = (s4 >> 20) | (s5 << 1);
- s[14] = s5 >> 7;
- s[15] = (s5 >> 15) | (s6 << 6);
- s[16] = s6 >> 2;
- s[17] = s6 >> 10;
- s[18] = (s6 >> 18) | (s7 << 3);
- s[19] = s7 >> 5;
- s[20] = s7 >> 13;
- s[21] = s8 >> 0;
- s[22] = s8 >> 8;
- s[23] = (s8 >> 16) | (s9 << 5);
- s[24] = s9 >> 3;
- s[25] = s9 >> 11;
- s[26] = (s9 >> 19) | (s10 << 2);
- s[27] = s10 >> 6;
- s[28] = (s10 >> 14) | (s11 << 7);
- s[29] = s11 >> 1;
- s[30] = s11 >> 9;
- s[31] = s11 >> 17;
-}
-
-void ED25519_keypair(uint8_t out_public_key[32], uint8_t out_private_key[64]) {
- uint8_t seed[32];
- RAND_bytes(seed, 32);
- ED25519_keypair_from_seed(out_public_key, out_private_key, seed);
-}
-
-int ED25519_sign(uint8_t *out_sig, const uint8_t *message, size_t message_len,
- const uint8_t private_key[64]) {
- uint8_t az[SHA512_DIGEST_LENGTH];
- SHA512(private_key, 32, az);
-
- az[0] &= 248;
- az[31] &= 63;
- az[31] |= 64;
-
- SHA512_CTX hash_ctx;
- SHA512_Init(&hash_ctx);
- SHA512_Update(&hash_ctx, az + 32, 32);
- SHA512_Update(&hash_ctx, message, message_len);
- uint8_t nonce[SHA512_DIGEST_LENGTH];
- SHA512_Final(nonce, &hash_ctx);
-
- x25519_sc_reduce(nonce);
- ge_p3 R;
- x25519_ge_scalarmult_base(&R, nonce);
- ge_p3_tobytes(out_sig, &R);
-
- SHA512_Init(&hash_ctx);
- SHA512_Update(&hash_ctx, out_sig, 32);
- SHA512_Update(&hash_ctx, private_key + 32, 32);
- SHA512_Update(&hash_ctx, message, message_len);
- uint8_t hram[SHA512_DIGEST_LENGTH];
- SHA512_Final(hram, &hash_ctx);
-
- x25519_sc_reduce(hram);
- sc_muladd(out_sig + 32, hram, az, nonce);
-
- return 1;
-}
-
-int ED25519_verify(const uint8_t *message, size_t message_len,
- const uint8_t signature[64], const uint8_t public_key[32]) {
- ge_p3 A;
- if ((signature[63] & 224) != 0 ||
- x25519_ge_frombytes_vartime(&A, public_key) != 0) {
- return 0;
- }
-
- fe_neg(A.X, A.X);
- fe_neg(A.T, A.T);
-
- uint8_t pkcopy[32];
- memcpy(pkcopy, public_key, 32);
- uint8_t rcopy[32];
- memcpy(rcopy, signature, 32);
- uint8_t scopy[32];
- memcpy(scopy, signature + 32, 32);
-
- SHA512_CTX hash_ctx;
- SHA512_Init(&hash_ctx);
- SHA512_Update(&hash_ctx, signature, 32);
- SHA512_Update(&hash_ctx, public_key, 32);
- SHA512_Update(&hash_ctx, message, message_len);
- uint8_t h[SHA512_DIGEST_LENGTH];
- SHA512_Final(h, &hash_ctx);
-
- x25519_sc_reduce(h);
-
- ge_p2 R;
- ge_double_scalarmult_vartime(&R, h, &A, scopy);
-
- uint8_t rcheck[32];
- x25519_ge_tobytes(rcheck, &R);
-
- return CRYPTO_memcmp(rcheck, rcopy, sizeof(rcheck)) == 0;
-}
-
-void ED25519_keypair_from_seed(uint8_t out_public_key[32],
- uint8_t out_private_key[64],
- const uint8_t seed[32]) {
- uint8_t az[SHA512_DIGEST_LENGTH];
- SHA512(seed, 32, az);
-
- az[0] &= 248;
- az[31] &= 63;
- az[31] |= 64;
-
- ge_p3 A;
- x25519_ge_scalarmult_base(&A, az);
- ge_p3_tobytes(out_public_key, &A);
-
- memcpy(out_private_key, seed, 32);
- memcpy(out_private_key + 32, out_public_key, 32);
-}
-
-
-#if defined(BORINGSSL_X25519_X86_64)
-
-static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
- const uint8_t point[32]) {
- x25519_x86_64(out, scalar, point);
-}
-
-#else
-
/* Replace (f,g) with (g,f) if b == 1;
* replace (f,g) with (f,g) if b == 0.
*
* Preconditions: b in {0,1}. */
static void fe_cswap(fe f, fe g, unsigned int b) {
- b = 0-b;
unsigned i;
+ b = 0-b;
for (i = 0; i < 10; i++) {
int32_t x = f[i] ^ g[i];
x &= b;
@@ -4798,6 +775,8 @@ static void x25519_scalar_mult_generic(uint8_t out[32],
const uint8_t scalar[32],
const uint8_t point[32]) {
fe x1, x2, z2, x3, z3, tmp0, tmp1;
+ unsigned swap;
+ int pos;
uint8_t e[32];
memcpy(e, scalar, 32);
@@ -4810,8 +789,7 @@ static void x25519_scalar_mult_generic(uint8_t out[32],
fe_copy(x3, x1);
fe_1(z3);
- unsigned swap = 0;
- int pos;
+ swap = 0;
for (pos = 254; pos >= 0; --pos) {
unsigned b = 1 & (e[pos / 8] >> (pos & 7));
swap ^= b;
@@ -4847,21 +825,12 @@ static void x25519_scalar_mult_generic(uint8_t out[32],
static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
const uint8_t point[32]) {
-#if defined(BORINGSSL_X25519_NEON)
- if (CRYPTO_is_NEON_capable()) {
- x25519_NEON(out, scalar, point);
- return;
- }
-#endif
-
x25519_scalar_mult_generic(out, scalar, point);
}
-#endif /* BORINGSSL_X25519_X86_64 */
-
-
+#ifdef CONFIG_RNG
void X25519_keypair(uint8_t out_public_value[32], uint8_t out_private_key[32]) {
- RAND_bytes(out_private_key, 32);
+ rand_bytes(out_private_key, 32);
/* All X25519 implementations should decode scalars correctly (see
* https://tools.ietf.org/html/rfc7748#section-5). However, if an
@@ -4882,6 +851,7 @@ void X25519_keypair(uint8_t out_public_value[32], uint8_t out_private_key[32]) {
X25519_public_from_private(out_public_value, out_private_key);
}
+#endif
int X25519(uint8_t out_shared_key[32], const uint8_t private_key[32],
const uint8_t peer_public_value[32]) {
@@ -4891,47 +861,8 @@ int X25519(uint8_t out_shared_key[32], const uint8_t private_key[32],
return CRYPTO_memcmp(kZeros, out_shared_key, 32) != 0;
}
-#if defined(BORINGSSL_X25519_X86_64)
-
-/* When |BORINGSSL_X25519_X86_64| is set, base point multiplication is done with
- * the Montgomery ladder because it's faster. Otherwise it's done using the
- * Ed25519 tables. */
-
void X25519_public_from_private(uint8_t out_public_value[32],
const uint8_t private_key[32]) {
static const uint8_t kMongomeryBasePoint[32] = {9};
x25519_scalar_mult(out_public_value, private_key, kMongomeryBasePoint);
}
-
-#else
-
-void X25519_public_from_private(uint8_t out_public_value[32],
- const uint8_t private_key[32]) {
-#if defined(BORINGSSL_X25519_NEON)
- if (CRYPTO_is_NEON_capable()) {
- static const uint8_t kMongomeryBasePoint[32] = {9};
- x25519_NEON(out_public_value, private_key, kMongomeryBasePoint);
- return;
- }
-#endif
-
- uint8_t e[32];
- memcpy(e, private_key, 32);
- e[0] &= 248;
- e[31] &= 127;
- e[31] |= 64;
-
- ge_p3 A;
- x25519_ge_scalarmult_base(&A, e);
-
- /* We only need the u-coordinate of the curve25519 point. The map is
- * u=(y+1)/(1-y). Since y=Y/Z, this gives u=(Z+Y)/(Z-Y). */
- fe zplusy, zminusy, zminusy_inv;
- fe_add(zplusy, A.Z, A.Y);
- fe_sub(zminusy, A.Z, A.Y);
- fe_invert(zminusy_inv, zminusy);
- fe_mul(zplusy, zplusy, zminusy_inv);
- fe_tobytes(out_public_value, zplusy);
-}
-
-#endif /* BORINGSSL_X25519_X86_64 */
diff --git a/include/config.h b/include/config.h
index f6b8c2a443..cf3e6e19dd 100644
--- a/include/config.h
+++ b/include/config.h
@@ -613,6 +613,10 @@
#undef CONFIG_STM32_CLOCK_HSE_HZ
/*****************************************************************************/
+/* Support curve25519 public key cryptography */
+#undef CONFIG_CURVE25519
+
+/*****************************************************************************/
/* PMIC config */
/* Support firmware long press power-off timer */
diff --git a/include/curve25519.h b/include/curve25519.h
new file mode 100644
index 0000000000..4b75373da1
--- /dev/null
+++ b/include/curve25519.h
@@ -0,0 +1,62 @@
+/* Copyright 2017 The Chromium OS Authors. All rights reserved.
+ * Use of this source code is governed by a BSD-style license that can be
+ * found in the LICENSE file.
+ */
+
+#ifndef __CROS_EC_CURVE25519_H
+#define __CROS_EC_CURVE25519_H
+
+#include <stdint.h>
+
+/* Curve25519.
+ *
+ * Curve25519 is an elliptic curve. See https://tools.ietf.org/html/rfc7748.
+ */
+
+
+/* X25519.
+ *
+ * X25519 is the Diffie-Hellman primitive built from curve25519. It is
+ * sometimes referred to as “curve25519”, but “X25519” is a more precise
+ * name.
+ * See http://cr.yp.to/ecdh.html and https://tools.ietf.org/html/rfc7748.
+ */
+
+#define X25519_PRIVATE_KEY_LEN 32
+#define X25519_PUBLIC_VALUE_LEN 32
+
+/**
+ * Generate a public/private key pair.
+ * @param out_public_value generated public key.
+ * @param out_private_value generated private key.
+ */
+void X25519_keypair(uint8_t out_public_value[32], uint8_t out_private_key[32]);
+
+/**
+ * Diffie-Hellman function.
+ * @param out_shared_key
+ * @param private_key
+ * @param out_public_value
+ * @return one on success and zero on error.
+ *
+ * X25519() writes a shared key to @out_shared_key that is calculated from the
+ * given private key and the peer's public value.
+ *
+ * Don't use the shared key directly, rather use a KDF and also include the two
+ * public values as inputs.
+ */
+int X25519(uint8_t out_shared_key[32], const uint8_t private_key[32],
+ const uint8_t peers_public_value[32]);
+
+/**
+ * Compute the matching public key.
+ * @param out_public_value computed public key.
+ * @param private_key private key to use.
+ *
+ * X25519_public_from_private() calculates a Diffie-Hellman public value from
+ * the given private key and writes it to @out_public_value.
+ */
+void X25519_public_from_private(uint8_t out_public_value[32],
+ const uint8_t private_key[32]);
+
+#endif /* __CROS_EC_CURVE25519_H */
diff --git a/test/build.mk b/test/build.mk
index c5aa29638f..0079c21f48 100644
--- a/test/build.mk
+++ b/test/build.mk
@@ -73,6 +73,7 @@ test-list-host += timer_dos
test-list-host += usb_pd
test-list-host += usb_pd_giveback
test-list-host += utils
+test-list-host += x25519
endif
battery_get_params_smart-y=battery_get_params_smart.o
@@ -118,3 +119,4 @@ timer_dos-y=timer_dos.o
usb_pd-y=usb_pd.o
usb_pd_giveback-y=usb_pd.o
utils-y=utils.o
+x25519-y=x25519.o
diff --git a/test/test_config.h b/test/test_config.h
index 36bebe8a01..029ce9bd70 100644
--- a/test/test_config.h
+++ b/test/test_config.h
@@ -203,6 +203,10 @@ enum nvmem_users {
#define CONFIG_FLASH_NVMEM_VARS_USER_SIZE 600
#endif /* TEST_NVMEM_VARS */
+#ifdef TEST_X25519
+#define CONFIG_CURVE25519
+#endif /* TEST_X25519 */
+
#ifndef __ASSEMBLER__
/* Callback function from charge_manager to send host event */
static inline void pd_send_host_event(int mask) { }
diff --git a/test/x25519.c b/test/x25519.c
index 24dfa650c9..7f6f70f16c 100644
--- a/test/x25519.c
+++ b/test/x25519.c
@@ -12,115 +12,156 @@
* OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
* CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */
-#include <stdint.h>
-#include <stdio.h>
-#include <string.h>
-
-#include <openssl/curve25519.h>
-
-
-static bool TestX25519() {
- /* Taken from https://tools.ietf.org/html/rfc7748#section-5.2 */
- static const uint8_t kScalar1[32] = {
- 0xa5, 0x46, 0xe3, 0x6b, 0xf0, 0x52, 0x7c, 0x9d, 0x3b, 0x16, 0x15,
- 0x4b, 0x82, 0x46, 0x5e, 0xdd, 0x62, 0x14, 0x4c, 0x0a, 0xc1, 0xfc,
- 0x5a, 0x18, 0x50, 0x6a, 0x22, 0x44, 0xba, 0x44, 0x9a, 0xc4,
- };
- static const uint8_t kPoint1[32] = {
- 0xe6, 0xdb, 0x68, 0x67, 0x58, 0x30, 0x30, 0xdb, 0x35, 0x94, 0xc1,
- 0xa4, 0x24, 0xb1, 0x5f, 0x7c, 0x72, 0x66, 0x24, 0xec, 0x26, 0xb3,
- 0x35, 0x3b, 0x10, 0xa9, 0x03, 0xa6, 0xd0, 0xab, 0x1c, 0x4c,
- };
-
- uint8_t out[32];
- X25519(out, kScalar1, kPoint1);
-
- static const uint8_t kExpected1[32] = {
- 0xc3, 0xda, 0x55, 0x37, 0x9d, 0xe9, 0xc6, 0x90, 0x8e, 0x94, 0xea,
- 0x4d, 0xf2, 0x8d, 0x08, 0x4f, 0x32, 0xec, 0xcf, 0x03, 0x49, 0x1c,
- 0x71, 0xf7, 0x54, 0xb4, 0x07, 0x55, 0x77, 0xa2, 0x85, 0x52,
- };
- if (memcmp(kExpected1, out, sizeof(out)) != 0) {
- fprintf(stderr, "X25519 test one failed.\n");
- return false;
- }
-
- static const uint8_t kScalar2[32] = {
- 0x4b, 0x66, 0xe9, 0xd4, 0xd1, 0xb4, 0x67, 0x3c, 0x5a, 0xd2, 0x26,
- 0x91, 0x95, 0x7d, 0x6a, 0xf5, 0xc1, 0x1b, 0x64, 0x21, 0xe0, 0xea,
- 0x01, 0xd4, 0x2c, 0xa4, 0x16, 0x9e, 0x79, 0x18, 0xba, 0x0d,
- };
- static const uint8_t kPoint2[32] = {
- 0xe5, 0x21, 0x0f, 0x12, 0x78, 0x68, 0x11, 0xd3, 0xf4, 0xb7, 0x95,
- 0x9d, 0x05, 0x38, 0xae, 0x2c, 0x31, 0xdb, 0xe7, 0x10, 0x6f, 0xc0,
- 0x3c, 0x3e, 0xfc, 0x4c, 0xd5, 0x49, 0xc7, 0x15, 0xa4, 0x93,
- };
-
- X25519(out, kScalar2, kPoint2);
-
- static const uint8_t kExpected2[32] = {
- 0x95, 0xcb, 0xde, 0x94, 0x76, 0xe8, 0x90, 0x7d, 0x7a, 0xad, 0xe4,
- 0x5c, 0xb4, 0xb8, 0x73, 0xf8, 0x8b, 0x59, 0x5a, 0x68, 0x79, 0x9f,
- 0xa1, 0x52, 0xe6, 0xf8, 0xf7, 0x64, 0x7a, 0xac, 0x79, 0x57,
- };
- if (memcmp(kExpected2, out, sizeof(out)) != 0) {
- fprintf(stderr, "X25519 test two failed.\n");
- return false;
- }
-
- return true;
+#include "console.h"
+#include "common.h"
+#include "curve25519.h"
+#include "test_util.h"
+#include "timer.h"
+#include "util.h"
+#include "watchdog.h"
+
+
+static int test_x25519(void)
+{
+ /* Taken from https://tools.ietf.org/html/rfc7748#section-5.2 */
+ static const uint8_t scalar1[32] = {
+ 0xa5, 0x46, 0xe3, 0x6b, 0xf0, 0x52, 0x7c, 0x9d,
+ 0x3b, 0x16, 0x15, 0x4b, 0x82, 0x46, 0x5e, 0xdd,
+ 0x62, 0x14, 0x4c, 0x0a, 0xc1, 0xfc, 0x5a, 0x18,
+ 0x50, 0x6a, 0x22, 0x44, 0xba, 0x44, 0x9a, 0xc4,
+ };
+ static const uint8_t point1[32] = {
+ 0xe6, 0xdb, 0x68, 0x67, 0x58, 0x30, 0x30, 0xdb,
+ 0x35, 0x94, 0xc1, 0xa4, 0x24, 0xb1, 0x5f, 0x7c,
+ 0x72, 0x66, 0x24, 0xec, 0x26, 0xb3, 0x35, 0x3b,
+ 0x10, 0xa9, 0x03, 0xa6, 0xd0, 0xab, 0x1c, 0x4c,
+ };
+ static const uint8_t expected1[32] = {
+ 0xc3, 0xda, 0x55, 0x37, 0x9d, 0xe9, 0xc6, 0x90,
+ 0x8e, 0x94, 0xea, 0x4d, 0xf2, 0x8d, 0x08, 0x4f,
+ 0x32, 0xec, 0xcf, 0x03, 0x49, 0x1c, 0x71, 0xf7,
+ 0x54, 0xb4, 0x07, 0x55, 0x77, 0xa2, 0x85, 0x52,
+ };
+ static const uint8_t scalar2[32] = {
+ 0x4b, 0x66, 0xe9, 0xd4, 0xd1, 0xb4, 0x67, 0x3c,
+ 0x5a, 0xd2, 0x26, 0x91, 0x95, 0x7d, 0x6a, 0xf5,
+ 0xc1, 0x1b, 0x64, 0x21, 0xe0, 0xea, 0x01, 0xd4,
+ 0x2c, 0xa4, 0x16, 0x9e, 0x79, 0x18, 0xba, 0x0d,
+ };
+ static const uint8_t point2[32] = {
+ 0xe5, 0x21, 0x0f, 0x12, 0x78, 0x68, 0x11, 0xd3,
+ 0xf4, 0xb7, 0x95, 0x9d, 0x05, 0x38, 0xae, 0x2c,
+ 0x31, 0xdb, 0xe7, 0x10, 0x6f, 0xc0, 0x3c, 0x3e,
+ 0xfc, 0x4c, 0xd5, 0x49, 0xc7, 0x15, 0xa4, 0x93,
+ };
+ static const uint8_t expected2[32] = {
+ 0x95, 0xcb, 0xde, 0x94, 0x76, 0xe8, 0x90, 0x7d,
+ 0x7a, 0xad, 0xe4, 0x5c, 0xb4, 0xb8, 0x73, 0xf8,
+ 0x8b, 0x59, 0x5a, 0x68, 0x79, 0x9f, 0xa1, 0x52,
+ 0xe6, 0xf8, 0xf7, 0x64, 0x7a, 0xac, 0x79, 0x57,
+ };
+ uint8_t out[32];
+
+ X25519(out, scalar1, point1);
+
+ if (memcmp(expected1, out, sizeof(out)) != 0) {
+ ccprintf("X25519 test one failed.\n");
+ return 0;
+ }
+
+
+ X25519(out, scalar2, point2);
+
+ if (memcmp(expected2, out, sizeof(out)) != 0) {
+ ccprintf("X25519 test two failed.\n");
+ return 0;
+ }
+
+ return 1;
}
-static bool TestX25519SmallOrder() {
- static const uint8_t kSmallOrderPoint[32] = {
- 0xe0, 0xeb, 0x7a, 0x7c, 0x3b, 0x41, 0xb8, 0xae, 0x16, 0x56, 0xe3,
- 0xfa, 0xf1, 0x9f, 0xc4, 0x6a, 0xda, 0x09, 0x8d, 0xeb, 0x9c, 0x32,
- 0xb1, 0xfd, 0x86, 0x62, 0x05, 0x16, 0x5f, 0x49, 0xb8,
- };
+static int test_x25519_small_order(void)
+{
+ static const uint8_t kSmallOrderPoint[32] = {
+ 0xe0, 0xeb, 0x7a, 0x7c, 0x3b, 0x41, 0xb8, 0xae,
+ 0x16, 0x56, 0xe3, 0xfa, 0xf1, 0x9f, 0xc4, 0x6a,
+ 0xda, 0x09, 0x8d, 0xeb, 0x9c, 0x32, 0xb1, 0xfd,
+ 0x86, 0x62, 0x05, 0x16, 0x5f, 0x49, 0xb8,
+ };
+ uint8_t out[32], private_key[32];
- uint8_t out[32], private_key[32];
- memset(private_key, 0x11, sizeof(private_key));
+ memset(private_key, 0x11, sizeof(private_key));
- if (X25519(out, private_key, kSmallOrderPoint)) {
- fprintf(stderr, "X25519 returned success with a small-order input.\n");
- return false;
- }
+ if (X25519(out, private_key, kSmallOrderPoint)) {
+ ccprintf("X25519 returned success with a small-order input.\n");
+ return 0;
+ }
- return true;
+ return 1;
}
-static bool TestX25519Iterated() {
- /* Taken from https://tools.ietf.org/html/rfc7748#section-5.2 */
- uint8_t scalar[32] = {9}, point[32] = {9}, out[32];
-
- unsigned i;
- for (i = 0; i < 1000; i++) {
- X25519(out, scalar, point);
- memcpy(point, scalar, sizeof(point));
- memcpy(scalar, out, sizeof(scalar));
- }
-
- static const uint8_t kExpected[32] = {
- 0x68, 0x4c, 0xf5, 0x9b, 0xa8, 0x33, 0x09, 0x55, 0x28, 0x00, 0xef,
- 0x56, 0x6f, 0x2f, 0x4d, 0x3c, 0x1c, 0x38, 0x87, 0xc4, 0x93, 0x60,
- 0xe3, 0x87, 0x5f, 0x2e, 0xb9, 0x4d, 0x99, 0x53, 0x2c, 0x51,
- };
-
- if (memcmp(kExpected, scalar, sizeof(kExpected)) != 0) {
- fprintf(stderr, "Iterated X25519 test failed\n");
- return false;
- }
-
- return true;
+static int test_x25519_iterated(void)
+{
+ /* Taken from https://tools.ietf.org/html/rfc7748#section-5.2 */
+ static const uint8_t expected[32] = {
+ 0x68, 0x4c, 0xf5, 0x9b, 0xa8, 0x33, 0x09, 0x55,
+ 0x28, 0x00, 0xef, 0x56, 0x6f, 0x2f, 0x4d, 0x3c,
+ 0x1c, 0x38, 0x87, 0xc4, 0x93, 0x60, 0xe3, 0x87,
+ 0x5f, 0x2e, 0xb9, 0x4d, 0x99, 0x53, 0x2c, 0x51,
+ };
+ uint8_t scalar[32] = {9}, point[32] = {9}, out[32];
+ unsigned i;
+
+ for (i = 0; i < 1000; i++) {
+ watchdog_reload();
+ X25519(out, scalar, point);
+ memcpy(point, scalar, sizeof(point));
+ memcpy(scalar, out, sizeof(scalar));
+ }
+
+ if (memcmp(expected, scalar, sizeof(expected)) != 0) {
+ ccprintf("Iterated X25519 test failed\n");
+ return 0;
+ }
+
+ return 1;
}
-int main(int argc, char **argv) {
- if (!TestX25519() ||
- !TestX25519Iterated() ||
- !TestX25519SmallOrder()) {
- return 1;
- }
+static void test_x25519_speed(void)
+{
+ static const uint8_t scalar1[32] = {
+ 0xa5, 0x46, 0xe3, 0x6b, 0xf0, 0x52, 0x7c, 0x9d,
+ 0x3b, 0x16, 0x15, 0x4b, 0x82, 0x46, 0x5e, 0xdd,
+ 0x62, 0x14, 0x4c, 0x0a, 0xc1, 0xfc, 0x5a, 0x18,
+ 0x50, 0x6a, 0x22, 0x44, 0xba, 0x44, 0x9a, 0xc4,
+ };
+ static const uint8_t point1[32] = {
+ 0xe6, 0xdb, 0x68, 0x67, 0x58, 0x30, 0x30, 0xdb,
+ 0x35, 0x94, 0xc1, 0xa4, 0x24, 0xb1, 0x5f, 0x7c,
+ 0x72, 0x66, 0x24, 0xec, 0x26, 0xb3, 0x35, 0x3b,
+ 0x10, 0xa9, 0x03, 0xa6, 0xd0, 0xab, 0x1c, 0x4c,
+ };
+ uint8_t out[32];
+ timestamp_t t0, t1;
+
+ X25519(out, scalar1, point1);
+ t0 = get_time();
+ X25519(out, scalar1, point1);
+ t1 = get_time();
+ ccprintf("X25519 duration %ld us\n", t1.val - t0.val);
+}
- printf("PASS\n");
- return 0;
+void run_test(void)
+{
+ watchdog_reload();
+ if (!test_x25519() || !test_x25519_iterated() ||
+ !test_x25519_small_order()) {
+ test_fail();
+ return;
+ }
+ watchdog_reload();
+ /* do not check speed, just as a benchmark */
+ test_x25519_speed();
+
+ test_pass();
}
diff --git a/test/x25519.tasklist b/test/x25519.tasklist
new file mode 100644
index 0000000000..e76178ba0a
--- /dev/null
+++ b/test/x25519.tasklist
@@ -0,0 +1,17 @@
+/* Copyright 2017 The Chromium OS Authors. All rights reserved.
+ * Use of this source code is governed by a BSD-style license that can be
+ * found in the LICENSE file.
+ */
+
+/**
+ * List of enabled tasks in the priority order
+ *
+ * The first one has the lowest priority.
+ *
+ * For each task, use the macro TASK_TEST(n, r, d, s) where :
+ * 'n' in the name of the task
+ * 'r' in the main routine of the task
+ * 'd' in an opaque parameter passed to the routine at startup
+ * 's' is the stack size in bytes; must be a multiple of 8
+ */
+#define CONFIG_TEST_TASK_LIST
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