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authornagendra modadugu <ngm@google.com>2016-03-25 14:35:38 -0700
committerchrome-bot <chrome-bot@chromium.org>2016-04-20 03:14:30 -0700
commit045a593203db69ad576113dab97f0ad5cd26d4a4 (patch)
tree5da452d6e8f981c6983a3c928b431771094b3221
parentf00d4621a480f12293214f14716ac33a90281ce7 (diff)
downloadchrome-ec-045a593203db69ad576113dab97f0ad5cd26d4a4.tar.gz
CR50: add support for RSA key generation
Prime generation uses a sieve to amortize division with small primes. Otherwise this a standard Miller-Rabin implementation. BRANCH=none BUG=chrome-os-partner:43025,chrome-os-partner:47524 TEST=tests under test/tpm2 pass Change-Id: I9f84d1f9c911f6146e4bd80296f75157a191552d Signed-off-by: nagendra modadugu <ngm@google.com> Reviewed-on: https://chromium-review.googlesource.com/335222 Commit-Ready: Nagendra Modadugu <ngm@google.com> Tested-by: Nagendra Modadugu <ngm@google.com> Reviewed-by: Nagendra Modadugu <ngm@google.com>
Diffstat
-rw-r--r--board/cr50/tpm2/rsa.c150
-rw-r--r--board/cr50/tpm2/stubs.c17
-rw-r--r--chip/g/dcrypto/bn.c480
-rw-r--r--chip/g/dcrypto/dcrypto.h8
-rw-r--r--chip/g/dcrypto/internal.h1
-rw-r--r--chip/g/dcrypto/rsa.c2
-rw-r--r--test/tpm_test/ftdi_spi_tpm.c4
-rw-r--r--test/tpm_test/rsa_test.py513
8 files changed, 1150 insertions, 25 deletions
diff --git a/board/cr50/tpm2/rsa.c b/board/cr50/tpm2/rsa.c
index e48e4fb352..43e7d4e23d 100644
--- a/board/cr50/tpm2/rsa.c
+++ b/board/cr50/tpm2/rsa.c
@@ -6,6 +6,7 @@
#include "CryptoEngine.h"
#include "dcrypto.h"
+#include "trng.h"
#include <assert.h>
@@ -13,6 +14,9 @@ static void reverse_tpm2b(TPM2B *b)
{
reverse(b->buffer, b->size);
}
+TPM2B_BYTE_VALUE(4);
+
+#define RSA_F4 65537
static int check_key(const RSA_KEY *key)
{
@@ -251,6 +255,109 @@ CRYPT_RESULT _cpri__TestKeyRSA(TPM2B *d_buf, uint32_t e,
}
}
+/* Each 1024-bit prime generation attempt fails with probability
+ * ~0.5%. Setting an upper limit on the attempts allows for an
+ * application to display a message and then reattempt.
+ * TODO(ngm): tweak this value along with performance improvements. */
+#define MAX_GENERATE_ATTEMPTS 3
+
+static int generate_prime(struct BIGNUM *b, TPM_ALG_ID hashing, TPM2B *seed,
+ const char *label, TPM2B *extra, uint32_t *counter)
+{
+ TPM2B_4_BYTE_VALUE marshaled_counter = { .t = {4} };
+ uint32_t initial_counter;
+
+ initial_counter = *counter;
+ for (; *counter - initial_counter < MAX_GENERATE_ATTEMPTS;
+ *counter += 1) {
+ UINT32_TO_BYTE_ARRAY(*counter, marshaled_counter.t.buffer);
+ _cpri__KDFa(hashing, seed, label, extra, &marshaled_counter.b,
+ bn_bits(b), (uint8_t *) b->d, NULL, FALSE);
+
+ if (DCRYPTO_bn_generate_prime(b))
+ return 1;
+ }
+
+ return 0;
+}
+
+CRYPT_RESULT _cpri__GenerateKeyRSA(
+ TPM2B *N_buf, TPM2B *p_buf, uint16_t num_bits,
+ uint32_t e_buf, TPM_ALG_ID hashing, TPM2B *seed,
+ const char *label, TPM2B *extra, uint32_t *counter_in)
+{
+ const char *label_p = "RSA p!";
+ const char *label_q = "RSA q!";
+ /* Numbers from NIST SP800-57.
+ * Fallback conservatively for keys larger than 2048 bits. */
+ const uint32_t security_strength =
+ num_bits <= 1024 ? 80 :
+ num_bits <= 2048 ? 112 :
+ 256;
+
+ const uint16_t num_bytes = num_bits / 8;
+ uint8_t q_buf[RSA_MAX_BYTES / 2];
+
+ struct BIGNUM e;
+ struct BIGNUM p;
+ struct BIGNUM q;
+ struct BIGNUM N;
+
+ uint32_t counter;
+
+ if (num_bits & 0xF)
+ return CRYPT_FAIL;
+ if (num_bytes / 2 > p_buf->size)
+ return CRYPT_FAIL;
+ if (N_buf->size > 0 && num_bytes > N_buf->size)
+ return CRYPT_FAIL;
+ if (num_bytes > RSA_MAX_BYTES)
+ return CRYPT_FAIL;
+ /* Seed size must be at least 2*security_strength per TPM 2.0 spec. */
+ if (seed == NULL || seed->size * 8 < 2 * security_strength)
+ return CRYPT_FAIL;
+
+ if (e_buf == 0)
+ e_buf = RSA_F4;
+
+ N_buf->size = num_bytes;
+ DCRYPTO_bn_wrap(&e, &e_buf, sizeof(e_buf));
+ DCRYPTO_bn_wrap(&p, p_buf->buffer, num_bytes / 2);
+ DCRYPTO_bn_wrap(&q, q_buf, num_bytes / 2);
+
+ if (label == NULL)
+ label = label_p;
+ if (counter_in != NULL)
+ counter = *counter_in;
+ else
+ counter = 1;
+ if (!generate_prime(&p, hashing, seed, label, extra, &counter)) {
+ if (counter_in != NULL)
+ *counter_in = counter;
+ return CRYPT_FAIL;
+ }
+
+ if (label == label_p)
+ label = label_q;
+ if (!generate_prime(&q, hashing, seed, label, extra, &counter)) {
+ if (counter_in != NULL)
+ *counter_in = counter;
+ return CRYPT_FAIL;
+ }
+
+ if (counter_in != NULL)
+ *counter_in = counter;
+ N_buf->size = num_bytes;
+ p_buf->size = num_bytes / 2;
+ DCRYPTO_bn_wrap(&N, N_buf->buffer, num_bytes);
+ DCRYPTO_bn_mul(&N, &p, &q);
+ reverse_tpm2b(N_buf);
+ reverse_tpm2b(p_buf);
+ /* TODO(ngm): replace with secure memset. */
+ memset(q_buf, 0, sizeof(q_buf));
+ return CRYPT_SUCCESS;
+}
+
#ifdef CRYPTO_TEST_SETUP
#include "extension.h"
@@ -261,7 +368,8 @@ enum {
TEST_RSA_SIGN = 2,
TEST_RSA_VERIFY = 3,
TEST_RSA_KEYGEN = 4,
- TEST_RSA_KEYTEST = 5
+ TEST_RSA_KEYTEST = 5,
+ TEST_BN_PRIMEGEN = 6,
};
static const TPM2B_PUBLIC_KEY_RSA RSA_768_N = {
@@ -454,6 +562,11 @@ static const RSA_KEY RSA_2048 = {
#define MAX_MSG_BYTES RSA_MAX_BYTES
+/* 128-byte buffer to hold entropy for generating a
+ * 2048-bit RSA key (assuming ~112 bits of security strength,
+ * the TPM spec requires a seed of minimum size 28-bytes). */
+TPM2B_BYTE_VALUE(128);
+
static void rsa_command_handler(void *cmd_body,
size_t cmd_size,
size_t *response_size_out)
@@ -477,6 +590,10 @@ static void rsa_command_handler(void *cmd_body,
TPM2B_PUBLIC_KEY_RSA rsa_d;
TPM2B_PUBLIC_KEY_RSA rsa_n;
+ TPM2B_128_BYTE_VALUE seed;
+ uint8_t bn_buf[RSA_MAX_BYTES];
+ struct BIGNUM bn;
+
assert(sizeof(size_t) == sizeof(uint32_t));
/* Command format.
@@ -577,9 +694,6 @@ static void rsa_command_handler(void *cmd_body,
*response_size = 1;
}
return;
- case TEST_RSA_KEYGEN:
- *response_size = 0;
- break;
case TEST_RSA_KEYTEST:
if (_cpri__TestKeyRSA(&rsa_d.b, 65537, &rsa_n.b, &p.b, &q.b)
!= CRYPT_SUCCESS) {
@@ -607,6 +721,34 @@ static void rsa_command_handler(void *cmd_body,
*out = 1;
*response_size = 1;
return;
+ case TEST_RSA_KEYGEN:
+ N.b.size = sizeof(N.t.buffer);
+ p.b.size = sizeof(p.t.buffer);
+ seed.b.size = sizeof(seed.t.buffer);
+ rand_bytes(seed.b.buffer, seed.b.size);
+ if (_cpri__GenerateKeyRSA(
+ &N.b, &p.b, key_len, RSA_F4, TPM_ALG_SHA256,
+ &seed.b, NULL, NULL, NULL) != CRYPT_SUCCESS) {
+ *response_size = 0;
+ } else {
+ memcpy(out, N.b.buffer, N.b.size);
+ memcpy(out + N.b.size, p.b.buffer, p.b.size);
+ *response_size = N.b.size + p.b.size;
+ }
+ return;
+ case TEST_BN_PRIMEGEN:
+ if (in_len > sizeof(bn_buf)) {
+ *response_size = 0;
+ return;
+ }
+ DCRYPTO_bn_wrap(&bn, bn_buf, in_len);
+ memcpy(bn_buf, in, in_len);
+ if (DCRYPTO_bn_generate_prime(&bn)) {
+ memcpy(out, bn.d, bn_size(&bn));
+ *response_size = bn_size(&bn);
+ } else {
+ *response_size = 0;
+ }
}
}
diff --git a/board/cr50/tpm2/stubs.c b/board/cr50/tpm2/stubs.c
index 257889a652..d3e8710604 100644
--- a/board/cr50/tpm2/stubs.c
+++ b/board/cr50/tpm2/stubs.c
@@ -46,23 +46,6 @@ CRYPT_RESULT _cpri__EccCommitCompute(
return CRYPT_FAIL;
}
-CRYPT_RESULT _cpri__GenerateKeyRSA(
- TPM2B * n, // OUT: The public modulu
- TPM2B * p, // OUT: One of the prime factors of n
- UINT16 keySizeInBits, // IN: Size of the public modulus in bit
- UINT32 e, // IN: The public exponent
- TPM_ALG_ID hashAlg, // IN: hash algorithm to use in the key generation proce
- TPM2B * seed, // IN: the seed to use
- const char *label, // IN: A label for the generation process.
- TPM2B * extra, // IN: Party 1 data for the KDF
- UINT32 * counter // IN/OUT: Counter value to allow KFD iteration to be
- // propagated across multiple routine
- )
-{
- ecprintf("%s called\n", __func__);
- return CRYPT_FAIL;
-}
-
BOOL _cpri__Startup(
void)
{
diff --git a/chip/g/dcrypto/bn.c b/chip/g/dcrypto/bn.c
index 52a1abfc1a..bd2cf6bedd 100644
--- a/chip/g/dcrypto/bn.c
+++ b/chip/g/dcrypto/bn.c
@@ -6,6 +6,8 @@
#include "dcrypto.h"
#include "internal.h"
+#include "trng.h"
+
#include <assert.h>
#ifdef CONFIG_WATCHDOG
@@ -28,6 +30,34 @@ void DCRYPTO_bn_wrap(struct BIGNUM *b, void *buf, size_t len)
b->d = (struct access_helper *) buf;
}
+static int bn_eq(const struct BIGNUM *a, const struct BIGNUM *b)
+{
+ int i;
+ uint32_t top = 0;
+
+ for (i = a->dmax - 1; i > b->dmax - 1; --i)
+ top |= BN_DIGIT(a, i);
+ if (top)
+ return 0;
+
+ for (i = b->dmax - 1; i > a->dmax - 1; --i)
+ top |= BN_DIGIT(b, i);
+ if (top)
+ return 0;
+
+ for (i = MIN(a->dmax, b->dmax) - 1; i >= 0; --i)
+ if (BN_DIGIT(a, i) != BN_DIGIT(b, i))
+ return 0;
+
+ return 1;
+}
+
+static void bn_copy(struct BIGNUM *dst, const struct BIGNUM *src)
+{
+ dst->dmax = src->dmax;
+ memcpy(dst->d, src->d, bn_size(dst));
+}
+
int bn_check_topbit(const struct BIGNUM *N)
{
return BN_DIGIT(N, N->dmax - 1) >> 31;
@@ -49,6 +79,22 @@ static int bn_is_bit_set(const struct BIGNUM *a, int n)
return (BN_DIGIT(a, i) >> j) & 1;
}
+static int bn_set_bit(const struct BIGNUM *a, int n)
+{
+ int i, j;
+
+ if (n < 0)
+ return 0;
+
+ i = n / BN_BITS2;
+ j = n % BN_BITS2;
+ if (a->dmax <= i)
+ return 0;
+
+ BN_DIGIT(a, i) |= 1 << j;
+ return 1;
+}
+
/* a[] >= b[]. */
/* TODO(ngm): constant time. */
static int bn_gte(const struct BIGNUM *a, const struct BIGNUM *b)
@@ -356,7 +402,8 @@ static uint32_t bn_mul_add(struct BIGNUM *c, uint32_t a,
}
/* c[] = a[] * b[] */
-void bn_mul(struct BIGNUM *c, const struct BIGNUM *a, const struct BIGNUM *b)
+void DCRYPTO_bn_mul(struct BIGNUM *c, const struct BIGNUM *a,
+ const struct BIGNUM *b)
{
int i;
uint32_t carry = 0;
@@ -485,3 +532,434 @@ int bn_modinv_vartime(struct BIGNUM *d, const struct BIGNUM *e,
return 0; /* Inverse not found. */
}
}
+
+#define NUM_PRIMES 4095
+#define PRIME1 3
+
+/* First NUM_PRIMES worth of primes starting with PRIME1. The entries
+ * are a delta / 2 encoding, i.e.:
+ * prime(x) = prime(x - 1) + (PRIME_DELTAS[x] * 2)
+ *
+ * Using 4096 of the first primes results in a 5-10% improvement in
+ * running time over using the first 2048. */
+const uint8_t PRIME_DELTAS[NUM_PRIMES] = {
+ 0, 1, 1, 2, 1, 2, 1, 2, 3, 1, 3, 2, 1, 2, 3,
+ 3, 1, 3, 2, 1, 3, 2, 3, 4, 2, 1, 2, 1, 2, 7, 2,
+ 3, 1, 5, 1, 3, 3, 2, 3, 3, 1, 5, 1, 2, 1, 6, 6,
+ 2, 1, 2, 3, 1, 5, 3, 3, 3, 1, 3, 2, 1, 5, 7, 2,
+ 1, 2, 7, 3, 5, 1, 2, 3, 4, 3, 3, 2, 3, 4, 2, 4,
+ 5, 1, 5, 1, 3, 2, 3, 4, 2, 1, 2, 6, 4, 2, 4, 2,
+ 3, 6, 1, 9, 3, 5, 3, 3, 1, 3, 5, 3, 3, 1, 3, 3,
+ 2, 1, 6, 5, 1, 2, 3, 3, 1, 6, 2, 3, 4, 5, 4, 5,
+ 4, 3, 3, 2, 4, 3, 2, 4, 2, 7, 5, 6, 1, 5, 1, 2,
+ 1, 5, 7, 2, 1, 2, 7, 2, 1, 2, 10, 2, 4, 5, 4, 2,
+ 3, 3, 7, 2, 3, 3, 4, 3, 6, 2, 3, 1, 5, 1, 3, 5,
+ 1, 5, 1, 3, 9, 2, 1, 2, 3, 3, 4, 3, 3, 11, 1, 5,
+ 4, 5, 3, 3, 4, 6, 2, 3, 3, 1, 3, 6, 5, 9, 1, 2,
+ 3, 1, 3, 2, 1, 2, 6, 1, 3, 17, 3, 3, 4, 9, 5, 7,
+ 2, 1, 2, 3, 4, 2, 1, 3, 6, 5, 1, 2, 1, 2, 3, 6,
+ 6, 4, 6, 3, 2, 3, 4, 2, 4, 2, 7, 2, 3, 1, 2, 3,
+ 1, 3, 5, 10, 3, 2, 1, 12, 2, 1, 5, 6, 1, 5, 4, 3,
+ 3, 3, 9, 3, 2, 1, 6, 5, 6, 4, 8, 7, 3, 2, 1, 2,
+ 1, 5, 6, 3, 3, 9, 1, 8, 1, 11, 3, 4, 3, 2, 1, 2,
+ 4, 3, 5, 1, 5, 7, 5, 3, 6, 1, 2, 1, 5, 6, 1, 8,
+ 1, 3, 2, 1, 5, 4, 9, 12, 2, 3, 4, 8, 1, 2, 4, 8,
+ 1, 2, 4, 3, 3, 2, 6, 1, 11, 3, 1, 3, 2, 3, 7, 3,
+ 2, 1, 3, 2, 3, 6, 3, 3, 7, 2, 3, 6, 4, 3, 2, 13,
+ 9, 5, 4, 2, 3, 1, 3, 11, 6, 1, 8, 4, 2, 6, 7, 5,
+ 1, 2, 4, 3, 3, 2, 1, 2, 3, 4, 2, 1, 3, 5, 1, 5,
+ 4, 2, 7, 5, 6, 1, 3, 2, 1, 8, 7, 2, 3, 4, 3, 2,
+ 9, 4, 5, 3, 3, 4, 5, 6, 7, 2, 3, 3, 1, 14, 1, 5,
+ 4, 2, 7, 2, 4, 6, 3, 6, 2, 3, 10, 5, 1, 8, 13, 2,
+ 1, 6, 3, 2, 6, 3, 4, 2, 4, 11, 1, 2, 1, 6, 14, 1,
+ 3, 3, 3, 2, 3, 1, 6, 2, 6, 1, 5, 1, 8, 1, 8, 3,
+ 10, 8, 4, 2, 1, 2, 1, 11, 4, 6, 3, 5, 1, 2, 3, 1,
+ 3, 5, 1, 6, 5, 1, 5, 7, 3, 2, 3, 4, 3, 3, 8, 6,
+ 1, 2, 7, 3, 2, 4, 5, 4, 3, 3, 11, 3, 1, 5, 7, 2,
+ 3, 9, 1, 5, 7, 2, 1, 5, 7, 2, 4, 9, 2, 3, 1, 2,
+ 3, 1, 6, 2, 10, 11, 6, 1, 2, 3, 3, 1, 3, 11, 1, 3,
+ 8, 3, 6, 1, 3, 6, 8, 1, 2, 3, 7, 2, 1, 9, 12, 5,
+ 3, 1, 5, 1, 5, 1, 5, 3, 1, 5, 1, 5, 3, 4, 15, 5,
+ 1, 5, 4, 3, 5, 9, 3, 6, 6, 1, 9, 3, 2, 3, 3, 9,
+ 1, 5, 7, 3, 2, 1, 2, 12, 1, 6, 3, 8, 4, 3, 3, 9,
+ 8, 1, 2, 3, 1, 3, 3, 5, 3, 6, 6, 9, 1, 3, 2, 9,
+ 4, 12, 2, 1, 2, 3, 1, 6, 2, 7, 15, 5, 3, 6, 7, 3,
+ 5, 6, 1, 2, 3, 4, 3, 5, 1, 2, 7, 3, 3, 2, 3, 1,
+ 5, 1, 8, 6, 4, 9, 2, 3, 6, 1, 3, 3, 3, 14, 3, 7,
+ 2, 4, 5, 4, 6, 9, 2, 1, 2, 12, 6, 3, 1, 8, 3, 3,
+ 7, 5, 7, 2, 15, 3, 3, 3, 4, 3, 2, 1, 6, 3, 2, 1,
+ 3, 11, 3, 1, 2, 9, 1, 2, 6, 1, 3, 2, 13, 3, 3, 2,
+ 4, 5, 16, 8, 1, 3, 2, 1, 2, 1, 5, 7, 3, 2, 4, 5,
+ 3, 10, 2, 1, 3, 15, 2, 4, 5, 3, 3, 4, 3, 6, 2, 3,
+ 1, 3, 2, 3, 1, 5, 1, 8, 3, 10, 2, 6, 7, 14, 3, 10,
+ 2, 9, 4, 3, 2, 3, 7, 3, 3, 5, 1, 5, 6, 4, 5, 1,
+ 5, 4, 6, 5, 12, 1, 2, 4, 3, 2, 4, 9, 5, 3, 3, 1,
+ 3, 5, 6, 1, 5, 3, 3, 3, 4, 3, 5, 3, 1, 3, 3, 3,
+ 5, 4, 12, 3, 11, 1, 9, 2, 4, 5, 15, 4, 9, 2, 1, 5,
+ 3, 1, 3, 2, 9, 4, 6, 9, 8, 3, 1, 6, 3, 5, 1, 5,
+ 1, 3, 5, 7, 2, 12, 1, 8, 1, 5, 1, 5, 10, 2, 1, 2,
+ 4, 8, 3, 3, 1, 6, 8, 4, 2, 3, 15, 1, 5, 1, 3, 2,
+ 3, 3, 4, 3, 2, 6, 3, 4, 6, 2, 7, 6, 5, 12, 3, 6,
+ 3, 1, 11, 4, 9, 5, 3, 7, 2, 1, 3, 5, 4, 3, 2, 3,
+ 15, 7, 5, 1, 6, 5, 1, 8, 1, 9, 12, 9, 3, 8, 9, 3,
+ 1, 9, 2, 3, 1, 5, 4, 5, 3, 3, 4, 2, 3, 1, 5, 1,
+ 6, 2, 3, 3, 1, 6, 2, 7, 9, 2, 3, 10, 2, 4, 3, 2,
+ 4, 2, 7, 3, 2, 7, 6, 2, 1, 15, 2, 12, 3, 3, 6, 6,
+ 7, 3, 2, 1, 2, 9, 3, 6, 4, 3, 2, 6, 1, 6, 15, 8,
+ 1, 3, 11, 7, 3, 5, 6, 3, 1, 2, 4, 5, 3, 3, 12, 7,
+ 3, 2, 4, 6, 9, 5, 1, 5, 1, 2, 3, 10, 3, 2, 7, 2,
+ 1, 2, 7, 3, 6, 12, 5, 3, 4, 5, 1, 15, 2, 3, 1, 6,
+ 2, 7, 3, 17, 6, 4, 3, 5, 1, 2, 10, 5, 4, 8, 1, 5,
+ 7, 2, 1, 6, 3, 8, 3, 4, 2, 4, 2, 3, 4, 3, 3, 6,
+ 3, 2, 3, 3, 4, 9, 2, 10, 2, 6, 1, 5, 3, 1, 5, 6,
+ 1, 2, 10, 3, 15, 3, 2, 4, 5, 6, 3, 1, 14, 1, 3, 2,
+ 1, 8, 6, 1, 3, 5, 4, 12, 6, 3, 9, 3, 2, 7, 3, 2,
+ 6, 4, 3, 6, 2, 3, 6, 3, 6, 1, 8, 10, 2, 1, 5, 9,
+ 4, 2, 7, 2, 1, 3, 11, 3, 7, 3, 3, 5, 3, 1, 5, 1,
+ 2, 1, 11, 1, 2, 3, 3, 6, 3, 7, 5, 6, 3, 4, 2, 18,
+ 7, 6, 3, 2, 3, 1, 6, 3, 6, 8, 1, 5, 4, 11, 1, 6,
+ 3, 2, 3, 9, 1, 6, 3, 2, 6, 4, 3, 6, 2, 3, 6, 3,
+ 1, 6, 6, 2, 7, 3, 8, 3, 1, 5, 4, 9, 3, 17, 1, 14,
+ 1, 11, 3, 1, 5, 6, 1, 3, 2, 4, 11, 3, 1, 5, 4, 2,
+ 3, 4, 2, 6, 9, 6, 10, 2, 3, 3, 4, 2, 1, 8, 6, 1,
+ 5, 4, 5, 1, 2, 3, 7, 6, 11, 4, 14, 1, 2, 10, 2, 1,
+ 2, 7, 5, 6, 1, 6, 8, 1, 14, 4, 11, 4, 2, 3, 3, 7,
+ 2, 4, 6, 3, 3, 2, 10, 2, 9, 1, 6, 3, 2, 3, 7, 9,
+ 5, 4, 5, 16, 3, 5, 3, 3, 1, 3, 8, 3, 1, 6, 3, 14,
+ 1, 5, 4, 8, 3, 4, 3, 5, 12, 10, 5, 1, 5, 1, 6, 2,
+ 3, 10, 2, 1, 6, 9, 5, 1, 5, 1, 2, 10, 8, 13, 2, 4,
+ 3, 2, 6, 3, 4, 6, 6, 3, 2, 4, 11, 1, 8, 7, 5, 3,
+ 6, 6, 7, 3, 2, 10, 2, 6, 3, 1, 3, 3, 8, 4, 11, 1,
+ 14, 4, 3, 2, 10, 2, 6, 12, 10, 2, 4, 5, 1, 8, 1, 6,
+ 6, 17, 1, 2, 3, 6, 3, 3, 4, 3, 2, 1, 3, 12, 2, 10,
+ 5, 3, 3, 7, 2, 3, 3, 1, 6, 3, 5, 1, 5, 3, 10, 2,
+ 13, 2, 1, 3, 11, 1, 12, 2, 3, 1, 2, 3, 12, 3, 4, 2,
+ 1, 17, 3, 4, 8, 6, 1, 5, 1, 5, 3, 4, 2, 4, 6, 11,
+ 3, 7, 2, 13, 2, 1, 6, 5, 4, 2, 4, 6, 2, 7, 3, 8,
+ 3, 4, 2, 3, 3, 4, 3, 5, 6, 1, 3, 3, 8, 4, 3, 3,
+ 6, 5, 1, 3, 9, 2, 3, 3, 3, 6, 9, 4, 3, 5, 4, 9,
+ 2, 7, 3, 9, 5, 4, 5, 6, 1, 3, 6, 6, 18, 2, 3, 4,
+ 2, 3, 1, 2, 9, 6, 3, 4, 3, 3, 2, 9, 1, 2, 1, 12,
+ 2, 3, 3, 7, 15, 3, 2, 3, 6, 3, 10, 2, 4, 2, 4, 3,
+ 3, 2, 15, 1, 5, 6, 4, 5, 4, 12, 3, 6, 2, 7, 2, 3,
+ 1, 14, 7, 8, 1, 6, 3, 2, 10, 5, 3, 3, 3, 4, 5, 6,
+ 7, 5, 7, 8, 7, 5, 7, 3, 8, 3, 4, 3, 8, 10, 5, 1,
+ 3, 2, 1, 2, 6, 1, 5, 1, 3, 11, 3, 1, 2, 9, 4, 5,
+ 4, 11, 1, 5, 9, 7, 2, 1, 2, 9, 1, 2, 3, 4, 5, 1,
+ 15, 2, 15, 1, 5, 1, 9, 2, 9, 3, 7, 5, 1, 2, 10, 18,
+ 3, 2, 3, 7, 2, 10, 5, 7, 11, 3, 1, 15, 6, 5, 9, 1,
+ 2, 7, 3, 11, 9, 1, 6, 3, 2, 4, 2, 4, 3, 5, 1, 6,
+ 9, 5, 7, 8, 7, 2, 3, 3, 1, 3, 2, 1, 14, 1, 14, 3,
+ 1, 2, 3, 7, 2, 6, 7, 8, 7, 2, 3, 4, 3, 2, 3, 3,
+ 3, 4, 2, 4, 2, 7, 8, 4, 3, 2, 6, 4, 8, 1, 5, 4,
+ 2, 3, 13, 3, 5, 4, 2, 3, 6, 7, 15, 2, 7, 11, 4, 6,
+ 2, 3, 4, 5, 3, 7, 5, 3, 1, 5, 6, 6, 7, 3, 3, 9,
+ 5, 3, 4, 9, 2, 3, 1, 3, 5, 1, 5, 4, 3, 3, 5, 1,
+ 9, 5, 1, 6, 2, 3, 4, 5, 6, 7, 6, 2, 4, 5, 3, 3,
+ 10, 2, 7, 8, 7, 5, 4, 5, 6, 1, 9, 3, 6, 5, 6, 1,
+ 2, 1, 6, 3, 2, 4, 2, 22, 2, 1, 2, 1, 5, 6, 3, 3,
+ 7, 2, 3, 3, 3, 4, 3, 18, 9, 2, 3, 1, 6, 3, 3, 3,
+ 2, 7, 11, 6, 1, 9, 5, 3, 13, 12, 2, 1, 2, 1, 2, 7,
+ 2, 3, 3, 4, 8, 6, 1, 21, 2, 1, 2, 12, 3, 3, 1, 9,
+ 2, 7, 3, 14, 9, 7, 3, 5, 6, 1, 3, 6, 15, 3, 2, 3,
+ 3, 7, 2, 1, 12, 2, 3, 3, 13, 5, 9, 3, 4, 3, 3, 15,
+ 2, 6, 6, 1, 8, 1, 3, 2, 6, 9, 1, 3, 2, 13, 6, 3,
+ 6, 2, 12, 12, 6, 3, 1, 6, 14, 4, 2, 3, 6, 1, 9, 3,
+ 2, 3, 3, 10, 8, 1, 3, 3, 9, 5, 3, 1, 2, 4, 3, 3,
+ 12, 8, 3, 4, 5, 3, 7, 11, 4, 8, 3, 1, 6, 2, 1, 11,
+ 4, 9, 17, 1, 3, 9, 2, 3, 3, 4, 5, 4, 9, 3, 2, 1,
+ 2, 4, 8, 1, 6, 6, 3, 9, 2, 3, 3, 3, 1, 3, 6, 5,
+ 10, 6, 9, 2, 3, 1, 8, 1, 5, 7, 2, 15, 1, 5, 6, 1,
+ 12, 3, 8, 4, 5, 1, 6, 11, 3, 1, 8, 10, 5, 1, 6, 6,
+ 9, 5, 6, 3, 1, 5, 1, 3, 5, 9, 1, 6, 3, 2, 3, 1,
+ 12, 14, 1, 2, 1, 5, 1, 8, 6, 4, 11, 1, 3, 2, 1, 5,
+ 3, 10, 6, 5, 4, 6, 3, 3, 3, 2, 9, 1, 2, 6, 9, 1,
+ 6, 3, 2, 1, 8, 6, 6, 7, 2, 4, 9, 2, 6, 7, 3, 3,
+ 2, 4, 3, 2, 10, 6, 5, 7, 2, 1, 8, 1, 6, 15, 2, 3,
+ 12, 10, 12, 5, 4, 6, 5, 6, 3, 6, 6, 3, 4, 8, 7, 3,
+ 2, 3, 18, 10, 5, 15, 6, 1, 2, 1, 14, 6, 7, 3, 11, 4,
+ 2, 9, 3, 7, 9, 2, 3, 1, 3, 17, 9, 1, 8, 3, 9, 1,
+ 12, 2, 1, 3, 6, 3, 6, 5, 4, 3, 8, 6, 4, 5, 7, 20,
+ 3, 1, 3, 2, 6, 7, 2, 1, 2, 1, 2, 4, 3, 5, 3, 3,
+ 1, 3, 3, 3, 6, 3, 12, 5, 1, 5, 3, 6, 3, 3, 7, 3,
+ 3, 26, 10, 3, 5, 1, 5, 4, 5, 6, 6, 1, 3, 2, 7, 8,
+ 4, 6, 3, 11, 1, 5, 4, 3, 11, 1, 11, 3, 4, 5, 6, 6,
+ 1, 5, 3, 6, 1, 2, 7, 5, 1, 3, 9, 2, 6, 4, 9, 6,
+ 3, 3, 2, 3, 3, 7, 2, 1, 6, 6, 2, 3, 9, 9, 6, 1,
+ 8, 6, 4, 9, 5, 13, 2, 3, 4, 3, 3, 2, 1, 5, 10, 2,
+ 3, 4, 2, 10, 5, 1, 17, 1, 2, 12, 1, 6, 6, 5, 3, 1,
+ 6, 15, 3, 6, 8, 6, 1, 11, 9, 6, 7, 5, 1, 6, 6, 2,
+ 1, 2, 3, 6, 1, 8, 9, 1, 20, 4, 8, 3, 4, 5, 1, 2,
+ 9, 4, 5, 4, 6, 2, 9, 1, 9, 5, 1, 2, 1, 2, 4, 14,
+ 1, 3, 11, 6, 3, 7, 9, 2, 3, 4, 3, 3, 5, 4, 2, 1,
+ 9, 5, 3, 10, 11, 4, 3, 15, 2, 1, 2, 9, 3, 15, 1, 2,
+ 4, 3, 2, 3, 6, 7, 17, 7, 3, 2, 1, 3, 2, 7, 2, 1,
+ 3, 14, 1, 2, 3, 4, 5, 1, 5, 1, 5, 1, 2, 15, 1, 6,
+ 6, 5, 9, 6, 7, 5, 1, 6, 3, 5, 3, 7, 6, 2, 7, 2,
+ 9, 1, 5, 4, 2, 4, 5, 6, 9, 9, 4, 3, 9, 8, 7, 3,
+ 3, 5, 7, 2, 3, 1, 6, 6, 2, 3, 3, 6, 1, 8, 1, 6,
+ 3, 2, 7, 3, 2, 1, 6, 9, 2, 18, 9, 6, 6, 1, 2, 1,
+ 2, 4, 6, 2, 18, 3, 9, 1, 6, 5, 3, 6, 12, 4, 3, 3,
+ 8, 6, 1, 9, 5, 10, 5, 1, 3, 9, 2, 1, 20, 3, 1, 8,
+ 1, 2, 4, 9, 5, 6, 3, 1, 5, 4, 2, 3, 6, 1, 5, 9,
+ 4, 3, 2, 10, 2, 3, 18, 3, 1, 5, 3, 12, 3, 7, 8, 3,
+ 9, 1, 5, 10, 5, 4, 3, 2, 3, 1, 5, 1, 6, 2, 1, 2,
+ 4, 5, 3, 6, 9, 7, 6, 8, 4, 3, 8, 4, 2, 1, 3, 9,
+ 12, 9, 5, 6, 1, 2, 7, 5, 3, 3, 3, 9, 6, 1, 14, 9,
+ 7, 8, 6, 7, 12, 6, 11, 3, 1, 5, 4, 2, 1, 2, 7, 6,
+ 3, 2, 3, 7, 2, 1, 2, 15, 3, 1, 3, 5, 1, 15, 11, 1,
+ 2, 3, 4, 3, 3, 8, 6, 6, 3, 4, 2, 1, 12, 6, 2, 3,
+ 4, 3, 3, 5, 1, 3, 6, 14, 7, 3, 2, 6, 4, 3, 6, 2,
+ 3, 7, 3, 6, 5, 3, 3, 4, 3, 3, 2, 1, 2, 4, 6, 2,
+ 7, 9, 5, 1, 8, 3, 10, 3, 5, 4, 2, 15, 18, 6, 4, 11,
+ 6, 1, 3, 6, 8, 3, 3, 1, 9, 2, 13, 2, 4, 9, 5, 4,
+ 5, 3, 7, 2, 10, 11, 9, 6, 4, 14, 6, 3, 3, 4, 3, 6,
+ 12, 8, 7, 2, 7, 6, 3, 5, 6, 10, 3, 2, 4, 9, 6, 9,
+ 5, 1, 2, 10, 5, 7, 2, 3, 1, 5, 12, 9, 1, 2, 10, 8,
+ 7, 5, 7, 3, 2, 3, 10, 3, 5, 3, 1, 6, 3, 15, 5, 4,
+ 3, 2, 3, 4, 20, 1, 2, 1, 6, 9, 2, 3, 4, 5, 3, 9,
+ 9, 1, 6, 8, 4, 3, 2, 3, 3, 1, 26, 7, 2, 10, 8, 1,
+ 2, 3, 6, 1, 3, 6, 6, 3, 2, 7, 5, 3, 3, 7, 5, 7,
+ 8, 4, 3, 6, 2, 4, 11, 3, 1, 9, 11, 3, 1, 9, 3, 8,
+ 7, 5, 3, 6, 1, 3, 2, 4, 9, 6, 8, 1, 2, 7, 2, 4,
+ 6, 6, 15, 8, 4, 2, 1, 3, 11, 6, 4, 5, 3, 3, 3, 7,
+ 3, 9, 5, 6, 1, 5, 1, 2, 13, 2, 6, 4, 2, 9, 4, 5,
+ 7, 8, 3, 3, 4, 5, 3, 4, 3, 6, 5, 10, 5, 4, 2, 6,
+ 13, 9, 2, 6, 9, 3, 15, 3, 4, 3, 11, 6, 1, 2, 3, 3,
+ 1, 5, 1, 2, 3, 3, 1, 3, 11, 9, 3, 9, 6, 4, 6, 3,
+ 5, 6, 1, 8, 1, 5, 1, 5, 9, 3, 10, 2, 1, 3, 11, 3,
+ 3, 9, 3, 7, 6, 8, 1, 3, 3, 2, 7, 6, 2, 1, 9, 8,
+ 18, 6, 3, 7, 14, 1, 6, 3, 6, 3, 2, 1, 8, 15, 4, 12,
+ 3, 15, 5, 1, 9, 2, 3, 6, 4, 11, 1, 3, 11, 9, 1, 5,
+ 1, 5, 15, 1, 14, 3, 7, 8, 3, 10, 8, 1, 3, 2, 16, 2,
+ 1, 2, 3, 1, 6, 2, 3, 3, 6, 1, 3, 2, 3, 4, 3, 2,
+ 10, 2, 16, 5, 4, 8, 1, 11, 1, 2, 3, 4, 3, 8, 7, 2,
+ 9, 4, 2, 10, 3, 6, 6, 3, 5, 1, 5, 1, 6, 14, 6, 9,
+ 1, 9, 5, 4, 5, 24, 1, 2, 3, 4, 5, 1, 5, 15, 1, 18,
+ 3, 5, 3, 1, 9, 2, 3, 4, 8, 7, 8, 3, 7, 2, 10, 2,
+ 3, 1, 5, 6, 1, 3, 6, 3, 3, 2, 6, 1, 3, 2, 6, 3,
+ 4, 2, 1, 3, 9, 5, 3, 4, 6, 3, 11, 1, 3, 6, 9, 2,
+ 7, 3, 2, 10, 3, 8, 4, 2, 4, 11, 4, 6, 3, 3, 8, 6,
+ 9, 15, 4, 2, 1, 2, 3, 13, 2, 7, 12, 11, 3, 1, 3, 5,
+ 3, 7, 3, 3, 6, 5, 3, 1, 6, 5, 6, 4, 9, 9, 5, 3,
+ 4, 8, 3, 3, 4, 8, 10, 2, 1, 5, 1, 5, 6, 3, 4, 3,
+ 5, 10, 5, 9, 13, 2, 3, 15, 1, 2, 4, 3, 6, 6, 9, 2,
+ 4, 11, 3, 1, 6, 17, 3, 9, 6, 3, 1, 14, 7, 8, 7, 2,
+ 7, 6, 2, 3, 3, 1, 18, 2, 3, 10, 6, 12, 3, 11, 1, 8,
+ 9, 6, 6, 9, 1, 3, 3, 3, 2, 3, 7, 2, 1, 11, 4, 6,
+ 3, 5, 3, 4, 6, 9, 6, 3, 5, 1, 11, 7, 3, 3, 2, 9,
+ 3, 10, 11, 1, 6, 12, 2, 9, 9, 1, 11, 1, 2, 6, 4, 6,
+ 5, 7, 2, 1, 9, 8, 19, 3, 3, 3, 6, 5, 3, 6, 4, 3,
+ 2, 3, 7, 15, 3, 5, 4, 11, 3, 4, 6, 5, 1, 5, 1, 3,
+ 5, 1, 5, 6, 9, 10, 3, 2, 4, 11, 3, 3, 15, 3, 7, 3,
+ 6, 6, 3, 5, 1, 5, 15, 1, 8, 4, 2, 1, 3, 9, 2, 1,
+ 3, 2, 13, 2, 4, 3, 5, 1, 2, 3, 4, 2, 3, 15, 6, 1,
+ 3, 3, 2, 10, 11, 4, 2, 1, 2, 36, 4, 2, 4, 11, 1, 2,
+ 7, 5, 1, 2, 10, 3, 5, 9, 3, 10, 8, 3, 4, 3, 2, 10,
+ 6, 11, 1, 2, 1, 6, 5, 9, 1, 11, 3, 9, 15, 1, 5, 7,
+ 5, 4, 8, 25, 3, 5, 4, 5, 6, 3, 9, 1, 11, 3, 1, 2,
+ 3, 4, 3, 3, 5, 9, 1, 11, 1, 8, 7, 5, 3, 1, 6, 5,
+ 10, 2, 7, 3, 2, 18, 1, 2, 3, 6, 1, 2, 7, 6, 3, 2,
+ 3, 1, 3, 2, 10, 5, 1, 5, 3, 6, 1, 12, 6, 6, 3, 3,
+ 2, 12, 1, 2, 12, 1, 3, 2, 3, 4, 8, 3, 1, 5, 6, 7,
+ 3, 17, 3, 7, 3, 2, 1, 15, 11, 4, 2, 3, 4, 2, 1, 14,
+ 1, 3, 2, 13, 9, 11, 1, 3, 8, 3, 1, 8, 6, 1, 6, 2,
+ 3, 3, 7, 5, 3, 4, 6, 2, 9, 1, 5, 4, 8, 3, 3, 15,
+ 1, 5, 9, 1, 5, 4, 2, 4, 6, 12, 20, 1, 6, 5, 3, 6,
+ 1, 6, 2, 1, 2, 3, 9, 7, 6, 3, 2, 7, 15, 2, 4, 5,
+ 4, 3, 5, 9, 4, 2, 7, 8, 3, 4, 2, 3, 1, 5, 1, 6,
+ 2, 1, 2, 3, 4, 2, 3, 16, 12, 5, 4, 9, 5, 1, 3, 5,
+ 1, 2, 9, 3, 6, 1, 8, 1, 11, 3, 3, 4, 9, 2, 9, 6,
+ 4, 3, 2, 10, 3, 15, 11, 6, 1, 3, 9, 2, 31, 2, 1, 6,
+ 3, 5, 1, 6, 6, 14, 1, 2, 7, 11, 3, 1, 3, 3, 5, 7,
+ 2, 1, 5, 3, 4, 5, 7, 5, 3, 1, 6, 11, 9, 4, 5, 9,
+ 6, 1, 6, 2, 6, 1, 5, 1, 3, 9, 3, 3, 17, 3, 1, 6,
+ 2, 3, 9, 9, 1, 8, 3, 3, 4, 3, 5, 9, 4, 5, 4, 5,
+ 1, 2, 9, 13, 6, 11, 1, 2, 1, 11, 3, 3, 7, 8, 3, 10,
+ 5, 6, 1, 9, 21, 2, 12, 1, 3, 5, 6, 1, 3, 5, 4, 2,
+ 3, 6, 6, 4, 2, 3, 6, 15, 10, 3, 12, 3, 5, 6, 1, 5,
+ 10, 3, 3, 2, 6, 7, 5, 9, 6, 4, 3, 6, 2, 7, 5, 1,
+ 6, 15, 8, 1, 6, 3, 2, 1, 2, 3, 13, 2, 9, 1, 2, 3,
+ 7, 27, 3, 26, 1, 8, 3, 3, 6, 13, 2, 1, 3, 11, 3, 1,
+ 6, 6, 3, 5, 9, 1, 6, 6, 5, 9, 6, 3, 4, 3, 5, 3,
+ 4, 2, 1, 2, 10, 12, 3, 3, 5, 7, 5, 1, 11, 3, 7, 5,
+ 13, 2, 9, 4, 6, 6, 5, 6, 3, 4, 8, 3, 4, 3, 3, 11,
+ 1, 5, 10, 5, 3, 22, 9, 3, 5, 1, 2, 3, 7, 2, 13, 2,
+ 1, 6, 5, 4, 2, 4, 6, 2, 6, 4, 11, 4, 3, 5, 9, 3,
+ 3, 4, 3, 6, 2, 4, 9, 5, 6, 3, 6, 1, 3, 2, 1, 8,
+ 6, 6, 7, 5, 7, 3, 5, 6, 1, 6, 3, 2, 3, 1, 6, 2,
+ 13, 3, 9, 3, 5, 3, 1, 9, 5, 4, 2, 13, 5, 10, 3, 8,
+ 10, 6, 5, 4, 5, 1, 8, 3, 10, 5, 10, 2, 15, 1, 2, 4,
+ 8, 1, 9, 2, 1, 3, 5, 9, 6, 7, 9, 3, 8, 10, 3, 2,
+ 4, 3, 2, 3, 6, 4, 5, 1, 6, 3, 2, 1, 3, 5, 1, 8,
+ 6, 7, 5, 3, 4, 3, 14, 1, 3, 9, 15, 17, 1, 8, 6, 1,
+ 9, 8, 3, 4, 5, 4, 5, 4, 5, 22, 3, 3, 2, 10, 2, 1,
+ 2, 7, 14, 4, 3, 8, 7, 15, 3, 15, 2, 7, 5, 3, 3, 4,
+ 2, 9, 6, 3, 1, 11, 6, 4, 3, 6, 2, 7, 2, 3, 1, 2,
+ 9, 10, 3, 8, 19, 8, 1, 2, 3, 1, 20, 21, 7, 2, 3, 1,
+ 12, 5, 3, 1, 9, 5, 6, 1, 8, 1, 3, 8, 3, 4, 2, 1,
+ 5, 3, 4, 5, 1, 9, 8, 4, 6, 9, 6, 3, 6, 5, 3, 3
+};
+
+static uint32_t bn_mod_word16(const struct BIGNUM *p, uint16_t word)
+{
+ int i;
+ uint32_t rem = 0;
+
+ for (i = p->dmax - 1; i >= 0; i--) {
+ rem = ((rem << 16) |
+ ((BN_DIGIT(p, i) >> 16) & 0xFFFFUL)) % word;
+ rem = ((rem << 16) | (BN_DIGIT(p, i) & 0xFFFFUL)) % word;
+ }
+
+ return rem;
+}
+
+#define bn_is_even(b) !bn_is_bit_set((b), 0)
+/* From HAC Fact 4.48 (ii), the following number of
+ * rounds suffice for ~2^145 confidence. Each additional
+ * round provides about another k/100 bits of confidence. */
+#define ROUNDS_1024 7
+#define ROUNDS_512 15
+#define ROUNDS_384 22
+
+/* Miller-Rabin from HAC, algorithm 4.24. */
+static int bn_probable_prime(const struct BIGNUM *p)
+{
+ int j;
+ int s = 0;
+
+ uint32_t ONE_buf = 1;
+ uint32_t TWO_buf = 2;
+ uint8_t r_buf[RSA_MAX_BYTES / 2];
+ uint8_t A_buf[RSA_MAX_BYTES / 2];
+ uint8_t y_buf[RSA_MAX_BYTES / 2];
+
+ struct BIGNUM ONE;
+ struct BIGNUM TWO;
+ struct BIGNUM r;
+ struct BIGNUM A;
+ struct BIGNUM y;
+
+ const int rounds = bn_bits(p) >= 1024 ? ROUNDS_1024 :
+ bn_bits(p) >= 512 ? ROUNDS_512 :
+ ROUNDS_384;
+
+ /* Failsafe: update rounds table above to support smaller primes. */
+ if (bn_bits(p) < 384)
+ return 0;
+
+ if (bn_size(p) > sizeof(r_buf))
+ return 0;
+
+ DCRYPTO_bn_wrap(&ONE, &ONE_buf, sizeof(ONE_buf));
+ DCRYPTO_bn_wrap(&r, r_buf, bn_size(p));
+ bn_copy(&r, p);
+
+ /* r * (2 ^ s) = p - 1 */
+ bn_sub(&r, &ONE);
+ while (bn_is_even(&r)) {
+ bn_rshift(&r, 0, 0);
+ s++;
+ }
+
+ DCRYPTO_bn_wrap(&A, A_buf, bn_size(p));
+ DCRYPTO_bn_wrap(&y, y_buf, bn_size(p));
+ DCRYPTO_bn_wrap(&TWO, &TWO_buf, sizeof(TWO_buf));
+ for (j = 0; j < rounds; j++) {
+ int i;
+
+ /* pick random A, such that A < p */
+ rand_bytes(A_buf, bn_size(&A));
+ for (i = A.dmax - 1; i >= 0; i--) {
+ while (BN_DIGIT(&A, i) > BN_DIGIT(p, i))
+ BN_DIGIT(&A, i) = rand();
+ if (BN_DIGIT(&A, i) < BN_DIGIT(p, i))
+ break;
+ }
+
+ /* y = a ^ r mod p */
+ bn_mont_modexp(&y, &A, &r, p);
+ if (bn_eq(&y, &ONE))
+ continue;
+ bn_add(&y, &ONE);
+ if (bn_eq(&y, p))
+ continue;
+ bn_sub(&y, &ONE);
+
+ /* y = y ^ 2 mod p */
+ for (i = 0; i < s - 1; i++) {
+ bn_copy(&A, &y);
+ bn_mont_modexp(&y, &A, &TWO, p);
+
+ if (bn_eq(&y, &ONE))
+ return 0;
+
+ bn_add(&y, &ONE);
+ if (bn_eq(&y, p)) {
+ bn_sub(&y, &ONE);
+ break;
+ }
+ bn_sub(&y, &ONE);
+ }
+ bn_add(&y, &ONE);
+ if (!bn_eq(&y, p))
+ return 0;
+ }
+
+ return 1;
+}
+
+int DCRYPTO_bn_generate_prime(struct BIGNUM *p)
+{
+ int i;
+ int j;
+ /* Using a sieve size of 2048-bits results in a failure rate
+ * of ~0.5% @ 1024-bit candidates. The failure rate rises to ~6%
+ * if the sieve size is halved. */
+ uint8_t composites_buf[256];
+ struct BIGNUM composites;
+ uint16_t prime = PRIME1;
+
+ /* Set top two bits, as well as LSB. */
+ bn_set_bit(p, 0);
+ bn_set_bit(p, bn_bits(p) - 1);
+ bn_set_bit(p, bn_bits(p) - 2);
+
+ /* Save on trial division by marking known composites. */
+ bn_init(&composites, composites_buf, sizeof(composites_buf));
+ for (i = 0; i < sizeof(PRIME_DELTAS) / sizeof(PRIME_DELTAS[0]); i++) {
+ uint16_t rem;
+
+ prime += (PRIME_DELTAS[i] << 1);
+ rem = bn_mod_word16(p, prime);
+ /* Skip marking odd offsets (i.e. even candidates). */
+ for (j = (rem == 0) ? 0 : prime - rem;
+ j < bn_bits(&composites) << 1;
+ j += prime) {
+ if ((j & 1) == 0)
+ bn_set_bit(&composites, j >> 1);
+ }
+ }
+
+ /* composites now marked, apply Miller-Rabin to prime candidates. */
+ j = 0;
+ for (i = 0; i < bn_bits(&composites); i++) {
+ uint32_t diff_buf;
+ struct BIGNUM diff;
+
+ if (bn_is_bit_set(&composites, i))
+ continue;
+
+ /* Recover increment from the composites sieve. */
+ diff_buf = (i << 1) - j;
+ j = (i << 1);
+ DCRYPTO_bn_wrap(&diff, &diff_buf, sizeof(diff_buf));
+ bn_add(p, &diff);
+ if (bn_probable_prime(p))
+ return 1;
+ }
+
+ memset(composites_buf, 0, sizeof(composites_buf));
+ return 0;
+}
diff --git a/chip/g/dcrypto/dcrypto.h b/chip/g/dcrypto/dcrypto.h
index 251eb03685..de30eecaf0 100644
--- a/chip/g/dcrypto/dcrypto.h
+++ b/chip/g/dcrypto/dcrypto.h
@@ -176,4 +176,12 @@ int DCRYPTO_hkdf(uint8_t *OKM, size_t OKM_len,
const uint8_t *IKM, size_t IKM_len,
const uint8_t *info, size_t info_len);
+/*
+ * BN.
+ */
+int DCRYPTO_bn_generate_prime(struct BIGNUM *p);
+void DCRYPTO_bn_wrap(struct BIGNUM *b, void *buf, size_t len);
+void DCRYPTO_bn_mul(struct BIGNUM *c, const struct BIGNUM *a,
+ const struct BIGNUM *b);
+
#endif /* ! __EC_CHIP_G_DCRYPTO_DCRYPTO_H */
diff --git a/chip/g/dcrypto/internal.h b/chip/g/dcrypto/internal.h
index 06288918d4..09a1e09031 100644
--- a/chip/g/dcrypto/internal.h
+++ b/chip/g/dcrypto/internal.h
@@ -112,6 +112,7 @@ struct BIGNUM {
void bn_init(struct BIGNUM *bn, void *buf, size_t len);
#define bn_size(b) ((b)->dmax * BN_BYTES)
+#define bn_bits(b) ((b)->dmax * BN_BITS2)
int bn_check_topbit(const struct BIGNUM *N);
void bn_mont_modexp(struct BIGNUM *output, const struct BIGNUM *input,
const struct BIGNUM *exp, const struct BIGNUM *N);
diff --git a/chip/g/dcrypto/rsa.c b/chip/g/dcrypto/rsa.c
index 7742cea18e..5df3821413 100644
--- a/chip/g/dcrypto/rsa.c
+++ b/chip/g/dcrypto/rsa.c
@@ -650,7 +650,7 @@ int DCRYPTO_rsa_key_compute(struct BIGNUM *N, struct BIGNUM *d,
q = &q_local;
bn_add(&phi, &ONE);
} else {
- bn_mul(N, p, q);
+ DCRYPTO_bn_mul(N, p, q);
memcpy(phi_buf, N->d, bn_size(N));
}
diff --git a/test/tpm_test/ftdi_spi_tpm.c b/test/tpm_test/ftdi_spi_tpm.c
index 752e80bed4..2b9f30992a 100644
--- a/test/tpm_test/ftdi_spi_tpm.c
+++ b/test/tpm_test/ftdi_spi_tpm.c
@@ -272,8 +272,8 @@ int FtdiSpiInit(uint32_t freq, int enable_debug)
return true;
}
-/* This is in seconds. */
-#define MAX_STATUS_TIMEOUT 120
+/* This is in seconds (prime generation may take several minutes). */
+#define MAX_STATUS_TIMEOUT 900
static int WaitForStatus(uint32_t statusMask, uint32_t statusExpected)
{
uint32_t status;
diff --git a/test/tpm_test/rsa_test.py b/test/tpm_test/rsa_test.py
index 14982d5380..6ee474c579 100644
--- a/test/tpm_test/rsa_test.py
+++ b/test/tpm_test/rsa_test.py
@@ -5,7 +5,9 @@
"""Module for testing rsa functions using extended commands."""
+import binascii
import hashlib
+import rsa
import struct
import subcmd
@@ -19,11 +21,13 @@ _RSA_OPCODES = {
'VERIFY': 0x03,
'KEYGEN': 0x04,
'KEYTEST': 0x05,
+ 'PRIMEGEN': 0x06
}
# TPM2 ALG codes.
_RSA_PADDING = {
+ 'NONE': 0x00,
'PKCS1-SSA': 0x14,
'PKCS1-ES': 0x15,
'PKCS1-PSS': 0x16,
@@ -103,6 +107,7 @@ def _verify_cmd(padding, hashing, key_len, sig, msg):
ml=struct.pack('>H', sig_len), msg=sig,
dl=struct.pack('>H', digest_len), dig=digest)
+
def _keytest_cmd(key_len):
op = _RSA_OPCODES['KEYTEST']
return _RSA_CMD_FORMAT.format(o=op, p=0, h=_HASH['NONE'],
@@ -111,6 +116,447 @@ def _keytest_cmd(key_len):
dl='', dig='')
+def _keygen_cmd(key_len, e):
+ op = _RSA_OPCODES['KEYGEN']
+ padding = _RSA_PADDING['NONE']
+ hashing = _HASH['NONE']
+ return _RSA_CMD_FORMAT.format(o=op, p=padding, h=hashing,
+ kl=struct.pack('>H', key_len),
+ ml=struct.pack('>H', 0), msg='',
+ dl=struct.pack('>H', 0), dig='')
+
+
+def _primegen_cmd(seed):
+ op = _RSA_OPCODES['PRIMEGEN']
+ padding = _RSA_PADDING['NONE']
+ hashing = _HASH['NONE']
+ return _RSA_CMD_FORMAT.format(o=op, p=padding, h=hashing,
+ kl=struct.pack('>H', len(seed) * 8 * 2),
+ ml=struct.pack('>H', len(seed)), msg=seed,
+ dl=struct.pack('>H', 0), dig='')
+
+_PRIMES = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53,
+ 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131,
+ 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199,
+ 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281,
+ 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373,
+ 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457,
+ 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557,
+ 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641,
+ 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733,
+ 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827,
+ 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929,
+ 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019,
+ 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091,
+ 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171,
+ 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249,
+ 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319,
+ 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429,
+ 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489,
+ 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571,
+ 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637,
+ 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733,
+ 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823,
+ 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907,
+ 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999,
+ 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083,
+ 2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153,
+ 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267,
+ 2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341,
+ 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411,
+ 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521,
+ 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617,
+ 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689,
+ 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753,
+ 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843,
+ 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939,
+ 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023, 3037,
+ 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137,
+ 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229,
+ 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323,
+ 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407,
+ 3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511,
+ 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581,
+ 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671,
+ 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733, 3739, 3761,
+ 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851,
+ 3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 3929,
+ 3931, 3943, 3947, 3967, 3989, 4001, 4003, 4007, 4013, 4019, 4021,
+ 4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127,
+ 4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219,
+ 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289,
+ 4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409,
+ 4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507,
+ 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597,
+ 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679,
+ 4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759, 4783, 4787, 4789,
+ 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903,
+ 4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973,
+ 4987, 4993, 4999, 5003, 5009, 5011, 5021, 5023, 5039, 5051, 5059,
+ 5077, 5081, 5087, 5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167,
+ 5171, 5179, 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273,
+ 5279, 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387,
+ 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, 5449,
+ 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531,
+ 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639, 5641, 5647, 5651,
+ 5653, 5657, 5659, 5669, 5683, 5689, 5693, 5701, 5711, 5717, 5737,
+ 5741, 5743, 5749, 5779, 5783, 5791, 5801, 5807, 5813, 5821, 5827,
+ 5839, 5843, 5849, 5851, 5857, 5861, 5867, 5869, 5879, 5881, 5897,
+ 5903, 5923, 5927, 5939, 5953, 5981, 5987, 6007, 6011, 6029, 6037,
+ 6043, 6047, 6053, 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121,
+ 6131, 6133, 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217,
+ 6221, 6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301,
+ 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373,
+ 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, 6481, 6491,
+ 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, 6577, 6581, 6599,
+ 6607, 6619, 6637, 6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701,
+ 6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779, 6781, 6791, 6793,
+ 6803, 6823, 6827, 6829, 6833, 6841, 6857, 6863, 6869, 6871, 6883,
+ 6899, 6907, 6911, 6917, 6947, 6949, 6959, 6961, 6967, 6971, 6977,
+ 6983, 6991, 6997, 7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069,
+ 7079, 7103, 7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193,
+ 7207, 7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297,
+ 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411, 7417,
+ 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, 7507, 7517,
+ 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, 7573, 7577, 7583,
+ 7589, 7591, 7603, 7607, 7621, 7639, 7643, 7649, 7669, 7673, 7681,
+ 7687, 7691, 7699, 7703, 7717, 7723, 7727, 7741, 7753, 7757, 7759,
+ 7789, 7793, 7817, 7823, 7829, 7841, 7853, 7867, 7873, 7877, 7879,
+ 7883, 7901, 7907, 7919, 7927, 7933, 7937, 7949, 7951, 7963, 7993,
+ 8009, 8011, 8017, 8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093,
+ 8101, 8111, 8117, 8123, 8147, 8161, 8167, 8171, 8179, 8191, 8209,
+ 8219, 8221, 8231, 8233, 8237, 8243, 8263, 8269, 8273, 8287, 8291,
+ 8293, 8297, 8311, 8317, 8329, 8353, 8363, 8369, 8377, 8387, 8389,
+ 8419, 8423, 8429, 8431, 8443, 8447, 8461, 8467, 8501, 8513, 8521,
+ 8527, 8537, 8539, 8543, 8563, 8573, 8581, 8597, 8599, 8609, 8623,
+ 8627, 8629, 8641, 8647, 8663, 8669, 8677, 8681, 8689, 8693, 8699,
+ 8707, 8713, 8719, 8731, 8737, 8741, 8747, 8753, 8761, 8779, 8783,
+ 8803, 8807, 8819, 8821, 8831, 8837, 8839, 8849, 8861, 8863, 8867,
+ 8887, 8893, 8923, 8929, 8933, 8941, 8951, 8963, 8969, 8971, 8999,
+ 9001, 9007, 9011, 9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091,
+ 9103, 9109, 9127, 9133, 9137, 9151, 9157, 9161, 9173, 9181, 9187,
+ 9199, 9203, 9209, 9221, 9227, 9239, 9241, 9257, 9277, 9281, 9283,
+ 9293, 9311, 9319, 9323, 9337, 9341, 9343, 9349, 9371, 9377, 9391,
+ 9397, 9403, 9413, 9419, 9421, 9431, 9433, 9437, 9439, 9461, 9463,
+ 9467, 9473, 9479, 9491, 9497, 9511, 9521, 9533, 9539, 9547, 9551,
+ 9587, 9601, 9613, 9619, 9623, 9629, 9631, 9643, 9649, 9661, 9677,
+ 9679, 9689, 9697, 9719, 9721, 9733, 9739, 9743, 9749, 9767, 9769,
+ 9781, 9787, 9791, 9803, 9811, 9817, 9829, 9833, 9839, 9851, 9857,
+ 9859, 9871, 9883, 9887, 9901, 9907, 9923, 9929, 9931, 9941, 9949,
+ 9967, 9973, 10007, 10009, 10037, 10039, 10061, 10067, 10069, 10079,
+ 10091, 10093, 10099, 10103, 10111, 10133, 10139, 10141, 10151, 10159,
+ 10163, 10169, 10177, 10181, 10193, 10211, 10223, 10243, 10247, 10253,
+ 10259, 10267, 10271, 10273, 10289, 10301, 10303, 10313, 10321, 10331,
+ 10333, 10337, 10343, 10357, 10369, 10391, 10399, 10427, 10429, 10433,
+ 10453, 10457, 10459, 10463, 10477, 10487, 10499, 10501, 10513, 10529,
+ 10531, 10559, 10567, 10589, 10597, 10601, 10607, 10613, 10627, 10631,
+ 10639, 10651, 10657, 10663, 10667, 10687, 10691, 10709, 10711, 10723,
+ 10729, 10733, 10739, 10753, 10771, 10781, 10789, 10799, 10831, 10837,
+ 10847, 10853, 10859, 10861, 10867, 10883, 10889, 10891, 10903, 10909,
+ 10937, 10939, 10949, 10957, 10973, 10979, 10987, 10993, 11003, 11027,
+ 11047, 11057, 11059, 11069, 11071, 11083, 11087, 11093, 11113, 11117,
+ 11119, 11131, 11149, 11159, 11161, 11171, 11173, 11177, 11197, 11213,
+ 11239, 11243, 11251, 11257, 11261, 11273, 11279, 11287, 11299, 11311,
+ 11317, 11321, 11329, 11351, 11353, 11369, 11383, 11393, 11399, 11411,
+ 11423, 11437, 11443, 11447, 11467, 11471, 11483, 11489, 11491, 11497,
+ 11503, 11519, 11527, 11549, 11551, 11579, 11587, 11593, 11597, 11617,
+ 11621, 11633, 11657, 11677, 11681, 11689, 11699, 11701, 11717, 11719,
+ 11731, 11743, 11777, 11779, 11783, 11789, 11801, 11807, 11813, 11821,
+ 11827, 11831, 11833, 11839, 11863, 11867, 11887, 11897, 11903, 11909,
+ 11923, 11927, 11933, 11939, 11941, 11953, 11959, 11969, 11971, 11981,
+ 11987, 12007, 12011, 12037, 12041, 12043, 12049, 12071, 12073, 12097,
+ 12101, 12107, 12109, 12113, 12119, 12143, 12149, 12157, 12161, 12163,
+ 12197, 12203, 12211, 12227, 12239, 12241, 12251, 12253, 12263, 12269,
+ 12277, 12281, 12289, 12301, 12323, 12329, 12343, 12347, 12373, 12377,
+ 12379, 12391, 12401, 12409, 12413, 12421, 12433, 12437, 12451, 12457,
+ 12473, 12479, 12487, 12491, 12497, 12503, 12511, 12517, 12527, 12539,
+ 12541, 12547, 12553, 12569, 12577, 12583, 12589, 12601, 12611, 12613,
+ 12619, 12637, 12641, 12647, 12653, 12659, 12671, 12689, 12697, 12703,
+ 12713, 12721, 12739, 12743, 12757, 12763, 12781, 12791, 12799, 12809,
+ 12821, 12823, 12829, 12841, 12853, 12889, 12893, 12899, 12907, 12911,
+ 12917, 12919, 12923, 12941, 12953, 12959, 12967, 12973, 12979, 12983,
+ 13001, 13003, 13007, 13009, 13033, 13037, 13043, 13049, 13063, 13093,
+ 13099, 13103, 13109, 13121, 13127, 13147, 13151, 13159, 13163, 13171,
+ 13177, 13183, 13187, 13217, 13219, 13229, 13241, 13249, 13259, 13267,
+ 13291, 13297, 13309, 13313, 13327, 13331, 13337, 13339, 13367, 13381,
+ 13397, 13399, 13411, 13417, 13421, 13441, 13451, 13457, 13463, 13469,
+ 13477, 13487, 13499, 13513, 13523, 13537, 13553, 13567, 13577, 13591,
+ 13597, 13613, 13619, 13627, 13633, 13649, 13669, 13679, 13681, 13687,
+ 13691, 13693, 13697, 13709, 13711, 13721, 13723, 13729, 13751, 13757,
+ 13759, 13763, 13781, 13789, 13799, 13807, 13829, 13831, 13841, 13859,
+ 13873, 13877, 13879, 13883, 13901, 13903, 13907, 13913, 13921, 13931,
+ 13933, 13963, 13967, 13997, 13999, 14009, 14011, 14029, 14033, 14051,
+ 14057, 14071, 14081, 14083, 14087, 14107, 14143, 14149, 14153, 14159,
+ 14173, 14177, 14197, 14207, 14221, 14243, 14249, 14251, 14281, 14293,
+ 14303, 14321, 14323, 14327, 14341, 14347, 14369, 14387, 14389, 14401,
+ 14407, 14411, 14419, 14423, 14431, 14437, 14447, 14449, 14461, 14479,
+ 14489, 14503, 14519, 14533, 14537, 14543, 14549, 14551, 14557, 14561,
+ 14563, 14591, 14593, 14621, 14627, 14629, 14633, 14639, 14653, 14657,
+ 14669, 14683, 14699, 14713, 14717, 14723, 14731, 14737, 14741, 14747,
+ 14753, 14759, 14767, 14771, 14779, 14783, 14797, 14813, 14821, 14827,
+ 14831, 14843, 14851, 14867, 14869, 14879, 14887, 14891, 14897, 14923,
+ 14929, 14939, 14947, 14951, 14957, 14969, 14983, 15013, 15017, 15031,
+ 15053, 15061, 15073, 15077, 15083, 15091, 15101, 15107, 15121, 15131,
+ 15137, 15139, 15149, 15161, 15173, 15187, 15193, 15199, 15217, 15227,
+ 15233, 15241, 15259, 15263, 15269, 15271, 15277, 15287, 15289, 15299,
+ 15307, 15313, 15319, 15329, 15331, 15349, 15359, 15361, 15373, 15377,
+ 15383, 15391, 15401, 15413, 15427, 15439, 15443, 15451, 15461, 15467,
+ 15473, 15493, 15497, 15511, 15527, 15541, 15551, 15559, 15569, 15581,
+ 15583, 15601, 15607, 15619, 15629, 15641, 15643, 15647, 15649, 15661,
+ 15667, 15671, 15679, 15683, 15727, 15731, 15733, 15737, 15739, 15749,
+ 15761, 15767, 15773, 15787, 15791, 15797, 15803, 15809, 15817, 15823,
+ 15859, 15877, 15881, 15887, 15889, 15901, 15907, 15913, 15919, 15923,
+ 15937, 15959, 15971, 15973, 15991, 16001, 16007, 16033, 16057, 16061,
+ 16063, 16067, 16069, 16073, 16087, 16091, 16097, 16103, 16111, 16127,
+ 16139, 16141, 16183, 16187, 16189, 16193, 16217, 16223, 16229, 16231,
+ 16249, 16253, 16267, 16273, 16301, 16319, 16333, 16339, 16349, 16361,
+ 16363, 16369, 16381, 16411, 16417, 16421, 16427, 16433, 16447, 16451,
+ 16453, 16477, 16481, 16487, 16493, 16519, 16529, 16547, 16553, 16561,
+ 16567, 16573, 16603, 16607, 16619, 16631, 16633, 16649, 16651, 16657,
+ 16661, 16673, 16691, 16693, 16699, 16703, 16729, 16741, 16747, 16759,
+ 16763, 16787, 16811, 16823, 16829, 16831, 16843, 16871, 16879, 16883,
+ 16889, 16901, 16903, 16921, 16927, 16931, 16937, 16943, 16963, 16979,
+ 16981, 16987, 16993, 17011, 17021, 17027, 17029, 17033, 17041, 17047,
+ 17053, 17077, 17093, 17099, 17107, 17117, 17123, 17137, 17159, 17167,
+ 17183, 17189, 17191, 17203, 17207, 17209, 17231, 17239, 17257, 17291,
+ 17293, 17299, 17317, 17321, 17327, 17333, 17341, 17351, 17359, 17377,
+ 17383, 17387, 17389, 17393, 17401, 17417, 17419, 17431, 17443, 17449,
+ 17467, 17471, 17477, 17483, 17489, 17491, 17497, 17509, 17519, 17539,
+ 17551, 17569, 17573, 17579, 17581, 17597, 17599, 17609, 17623, 17627,
+ 17657, 17659, 17669, 17681, 17683, 17707, 17713, 17729, 17737, 17747,
+ 17749, 17761, 17783, 17789, 17791, 17807, 17827, 17837, 17839, 17851,
+ 17863, 17881, 17891, 17903, 17909, 17911, 17921, 17923, 17929, 17939,
+ 17957, 17959, 17971, 17977, 17981, 17987, 17989, 18013, 18041, 18043,
+ 18047, 18049, 18059, 18061, 18077, 18089, 18097, 18119, 18121, 18127,
+ 18131, 18133, 18143, 18149, 18169, 18181, 18191, 18199, 18211, 18217,
+ 18223, 18229, 18233, 18251, 18253, 18257, 18269, 18287, 18289, 18301,
+ 18307, 18311, 18313, 18329, 18341, 18353, 18367, 18371, 18379, 18397,
+ 18401, 18413, 18427, 18433, 18439, 18443, 18451, 18457, 18461, 18481,
+ 18493, 18503, 18517, 18521, 18523, 18539, 18541, 18553, 18583, 18587,
+ 18593, 18617, 18637, 18661, 18671, 18679, 18691, 18701, 18713, 18719,
+ 18731, 18743, 18749, 18757, 18773, 18787, 18793, 18797, 18803, 18839,
+ 18859, 18869, 18899, 18911, 18913, 18917, 18919, 18947, 18959, 18973,
+ 18979, 19001, 19009, 19013, 19031, 19037, 19051, 19069, 19073, 19079,
+ 19081, 19087, 19121, 19139, 19141, 19157, 19163, 19181, 19183, 19207,
+ 19211, 19213, 19219, 19231, 19237, 19249, 19259, 19267, 19273, 19289,
+ 19301, 19309, 19319, 19333, 19373, 19379, 19381, 19387, 19391, 19403,
+ 19417, 19421, 19423, 19427, 19429, 19433, 19441, 19447, 19457, 19463,
+ 19469, 19471, 19477, 19483, 19489, 19501, 19507, 19531, 19541, 19543,
+ 19553, 19559, 19571, 19577, 19583, 19597, 19603, 19609, 19661, 19681,
+ 19687, 19697, 19699, 19709, 19717, 19727, 19739, 19751, 19753, 19759,
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+ 19867, 19889, 19891, 19913, 19919, 19927, 19937, 19949, 19961, 19963,
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+ 20347, 20353, 20357, 20359, 20369, 20389, 20393, 20399, 20407, 20411,
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+ 37799, 37811, 37813, 37831, 37847, 37853, 37861, 37871, 37879, 37889,
+ 37897, 37907, 37951, 37957, 37963, 37967, 37987, 37991, 37993, 37997,
+ 38011, 38039, 38047, 38053, 38069, 38083, 38113, 38119, 38149, 38153,
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+ 38261, 38273, 38281, 38287, 38299, 38303, 38317, 38321, 38327, 38329,
+ 38333, 38351, 38371, 38377, 38393, 38431, 38447, 38449, 38453, 38459,
+ 38461, 38501, 38543, 38557, 38561, 38567, 38569, 38593, 38603, 38609,
+ 38611, 38629, 38639, 38651, 38653, 38669, 38671, 38677, 38693, 38699,
+ 38707, 38711, 38713, 38723, 38729, 38737, 38747, 38749, 38767, 38783,
+ 38791, 38803, 38821, 38833, 38839, 38851, 38861, 38867, 38873]
+
+
+def _prime_from_seed(seed):
+ ROUNDS = 7
+
+ def _window(s, primes):
+ w = [0] * 4096
+ for i in primes:
+ rem = s % i
+ if rem != 0:
+ rem = i - rem
+ for j in range(rem, len(w), i):
+ w[j] = 1
+ return w
+
+ # Set LSB, and top two bits.
+ candidate = chr(ord(seed[0]) | 192) + seed[1:-1] + chr(ord(seed[-1]) | 1)
+ candidate = int(binascii.b2a_hex(candidate), 16)
+ assert len(bin(candidate)[2:]) == len(seed) * 8
+ w = _window(candidate, _PRIMES[:4096])
+ for i, bit in enumerate(w):
+ if not bit:
+ if rsa.prime.randomized_primality_testing(candidate + i, ROUNDS):
+ return candidate + i
+ return None
+
+
#
# TEST VECTORS.
#
@@ -135,6 +581,19 @@ _KEYTEST_INPUTS = (
(2048,),
)
+_KEYGEN_INPUTS = (
+ (768, 65537),
+)
+
+
+_PRIMEGEN_INPUTS = (
+ 768,
+ 768,
+ 768,
+ 768,
+ 768
+)
+
def _encrypt_tests(tpm):
msg = 'Hello CR50!'
@@ -198,7 +657,61 @@ def _keytest_tests(tpm):
print('%sSUCCESS: %s' % (utils.cursor_back(), test_name))
+def _keygen_tests(tpm):
+ for data in _KEYGEN_INPUTS:
+ key_len, e = data
+ test_name = 'RSA-KEYGEN:%d:%d' % data
+ cmd = _keygen_cmd(key_len, e)
+
+ wrapped_response = tpm.command(tpm.wrap_ext_command(subcmd.RSA, cmd))
+ result = tpm.unwrap_ext_response(subcmd.RSA, wrapped_response)
+ result_len = len(result)
+ if result_len != int(key_len / 8 * 1.5):
+ raise subcmd.TpmTestError('%s error:%s' % (
+ test_name, utils.hex_dump(result)))
+
+ N = int(binascii.b2a_hex(result[0:result_len * 2 / 3]), 16)
+ p = int(binascii.b2a_hex(result[result_len * 2 / 3:]), 16)
+ q = N / p
+ if not rsa.prime.is_prime(p):
+ raise subcmd.TpmTestError('%s error:%s' % (
+ test_name, utils.hex_dump(result)))
+ if not rsa.prime.is_prime(q):
+ raise subcmd.TpmTestError('%s error:%s' % (
+ test_name, utils.hex_dump(result)))
+ print('%sSUCCESS: %s' % (utils.cursor_back(), test_name))
+
+
+def _primegen_tests(tpm):
+ for data in _PRIMEGEN_INPUTS:
+ key_len = data
+ test_name = 'RSA-PRIMEGEN:%d' % data
+ seed = rsa.randnum.read_random_bits(key_len / 2)
+ assert len(seed) == key_len / 16
+ # dcrypto interface is little-endian.
+ cmd = _primegen_cmd(seed[::-1])
+
+ wrapped_response = tpm.command(tpm.wrap_ext_command(subcmd.RSA, cmd))
+ result = tpm.unwrap_ext_response(subcmd.RSA, wrapped_response)
+ result_len = len(result)
+ if result_len != key_len / 16:
+ raise subcmd.TpmTestError('%s error:%s' % (
+ test_name, utils.hex_dump(result)))
+
+ p = int(binascii.b2a_hex(result[::-1]), 16)
+ if not rsa.prime.is_prime(p):
+ raise subcmd.TpmTestError('%s error:%s' % (
+ test_name, utils.hex_dump(result)))
+ calculated = _prime_from_seed(seed)
+ if p != calculated:
+ raise subcmd.TpmTestError('%s error:%s' % (
+ test_name, utils.hex_dump(result)))
+ print('%sSUCCESS: %s' % (utils.cursor_back(), test_name))
+
+
def rsa_test(tpm):
_encrypt_tests(tpm)
_sign_tests(tpm)
_keytest_tests(tpm)
+ _keygen_tests(tpm)
+ _primegen_tests(tpm)
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