nuts_mpi_t nuts_mpi_new_random(const unsigned int nbits) {
gcry_check();
gcry_mpi_t mpi = gcry_mpi_new(nbits);
gcry_mpi_randomize(mpi, nbits, GCRY_STRONG_RANDOM);
gcry_mpi_set_bit(mpi, nbits - 1);
gcry_mpi_set_bit(mpi, 0);
return nuts_mpi_alloc(mpi);
}
/* This is to check a bug reported by bpgcrypt at itaparica.org on
2006-07-31 against libgcrypt 1.2.2. */
static void
one_bit_only (int highbit)
{
gcry_mpi_t a;
char *result;
int i;
wherestr = "one_bit_only";
show ("checking that set_%sbit does only set one bit\n", highbit?"high":"");
a = gcry_mpi_new (0);
gcry_mpi_randomize (a, 70, GCRY_WEAK_RANDOM);
gcry_mpi_set_ui (a, 0);
if (highbit)
gcry_mpi_set_highbit (a, 42);
else
gcry_mpi_set_bit (a, 42);
if (!gcry_mpi_test_bit (a, 42))
fail ("failed to set a bit\n");
gcry_mpi_clear_bit (a, 42);
if (gcry_mpi_test_bit (a, 42))
fail ("failed to clear a bit\n");
result = mpi2bitstr (a, 70);
assert (strlen (result) == 70);
for (i=0; result[i]; i++)
if ( result[i] != '0' )
break;
if (result[i])
fail ("spurious bits detected\n");
xfree (result);
gcry_mpi_release (a);
}
static void
gen_prime (gcry_mpi_t * ptest, unsigned int nbits, struct GNUNET_HashCode * hc)
{
/* Note: 2 is not included because it can be tested more easily by
* looking at bit 0. The last entry in this list is marked by a zero */
static const uint16_t small_prime_numbers[] = {
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,
0
};
#define DIM(v) (sizeof(v)/sizeof((v)[0]))
static int no_of_small_prime_numbers = DIM (small_prime_numbers) - 1;
gcry_mpi_t prime, pminus1, val_2, val_3, result;
unsigned int i;
unsigned int step;
unsigned int mods[no_of_small_prime_numbers];
gcry_mpi_t tmp;
gcry_mpi_t sp;
GNUNET_assert (nbits >= 16);
/* Make nbits fit into mpz_t implementation. */
val_2 = gcry_mpi_set_ui (NULL, 2);
val_3 = gcry_mpi_set_ui (NULL, 3);
prime = gcry_mpi_snew (0);
result = gcry_mpi_new (0);
pminus1 = gcry_mpi_new (0);
*ptest = gcry_mpi_new (0);
tmp = gcry_mpi_new (0);
sp = gcry_mpi_new (0);
while (1)
{
/* generate a random number */
mpz_randomize (prime, nbits, hc);
/* Set high order bit to 1, set low order bit to 1. If we are
* generating a secret prime we are most probably doing that
* for RSA, to make sure that the modulus does have the
* requested key size we set the 2 high order bits. */
gcry_mpi_set_bit (prime, nbits - 1);
gcry_mpi_set_bit (prime, nbits - 2);
gcry_mpi_set_bit (prime, 0);
/* Calculate all remainders. */
for (i = 0; i < no_of_small_prime_numbers; i++)
{
size_t written;
gcry_mpi_set_ui (sp, small_prime_numbers[i]);
gcry_mpi_div (NULL, tmp, prime, sp, -1);
mods[i] = 0;
written = sizeof (unsigned int);
GNUNET_assert (0 ==
gcry_mpi_print (GCRYMPI_FMT_USG,
(unsigned char *) &mods[i], written,
&written, tmp));
adjust ((unsigned char *) &mods[i], written, sizeof (unsigned int));
mods[i] = ntohl (mods[i]);
}
/* Now try some primes starting with prime. */
for (step = 0; step < 20000; step += 2)
{
/* Check against all the small primes we have in mods. */
for (i = 0; i < no_of_small_prime_numbers; i++)
{
uint16_t x = small_prime_numbers[i];
while (mods[i] + step >= x)
mods[i] -= x;
if (!(mods[i] + step))
break;
}
if (i < no_of_small_prime_numbers)
continue; /* Found a multiple of an already known prime. */
gcry_mpi_add_ui (*ptest, prime, step);
if (!gcry_mpi_test_bit (*ptest, nbits - 2))
break;
/* Do a fast Fermat test now. */
gcry_mpi_sub_ui (pminus1, *ptest, 1);
gcry_mpi_powm (result, val_2, pminus1, *ptest);
if ((!gcry_mpi_cmp_ui (result, 1)) && (is_prime (*ptest, 5, hc)))
{
/* Got it. */
gcry_mpi_release (sp);
gcry_mpi_release (tmp);
gcry_mpi_release (val_2);
gcry_mpi_release (val_3);
gcry_mpi_release (result);
gcry_mpi_release (pminus1);
gcry_mpi_release (prime);
return;
}
}
}
}
/*
* Test iterative X25519 computation through lower layer MPI routines.
*
* Input: K (as hex string), ITER, R (as hex string)
*
* where R is expected result of iterating X25519 by ITER times.
*
*/
static void
test_it (int testno, const char *k_str, int iter, const char *result_str)
{
gcry_ctx_t ctx;
gpg_error_t err;
void *buffer = NULL;
size_t buflen;
gcry_mpi_t mpi_k = NULL;
gcry_mpi_t mpi_x = NULL;
gcry_mpi_point_t P = NULL;
gcry_mpi_point_t Q;
int i;
gcry_mpi_t mpi_kk = NULL;
if (verbose > 1)
info ("Running test %d: iteration=%d\n", testno, iter);
gcry_mpi_ec_new (&ctx, NULL, "Curve25519");
Q = gcry_mpi_point_new (0);
if (!(buffer = hex2buffer (k_str, &buflen)) || buflen != 32)
{
fail ("error scanning MPI for test %d, %s: %s",
testno, "k", "invalid hex string");
goto leave;
}
reverse_buffer (buffer, buflen);
if ((err = gcry_mpi_scan (&mpi_x, GCRYMPI_FMT_USG, buffer, buflen, NULL)))
{
fail ("error scanning MPI for test %d, %s: %s",
testno, "x", gpg_strerror (err));
goto leave;
}
xfree (buffer);
buffer = NULL;
P = gcry_mpi_point_set (NULL, mpi_x, NULL, GCRYMPI_CONST_ONE);
mpi_k = gcry_mpi_copy (mpi_x);
if (debug)
print_mpi ("k", mpi_k);
for (i = 0; i < iter; i++)
{
/*
* Another variant of decodeScalar25519 thing.
*/
mpi_kk = gcry_mpi_set (mpi_kk, mpi_k);
gcry_mpi_set_bit (mpi_kk, 254);
gcry_mpi_clear_bit (mpi_kk, 255);
gcry_mpi_clear_bit (mpi_kk, 0);
gcry_mpi_clear_bit (mpi_kk, 1);
gcry_mpi_clear_bit (mpi_kk, 2);
gcry_mpi_ec_mul (Q, mpi_kk, P, ctx);
P = gcry_mpi_point_set (P, mpi_k, NULL, GCRYMPI_CONST_ONE);
gcry_mpi_ec_get_affine (mpi_k, NULL, Q, ctx);
if (debug)
print_mpi ("k", mpi_k);
}
{
unsigned char res[32];
char *r, *r0;
gcry_mpi_print (GCRYMPI_FMT_USG, res, 32, NULL, mpi_k);
reverse_buffer (res, 32);
r0 = r = xmalloc (65);
if (!r0)
{
fail ("memory allocation for test %d", testno);
goto leave;
}
for (i=0; i < 32; i++, r += 2)
snprintf (r, 3, "%02x", res[i]);
if (strcmp (result_str, r0))
{
fail ("curv25519 failed for test %d: %s",
testno, "wrong value returned");
info (" expected: '%s'", result_str);
info (" got: '%s'", r0);
}
xfree (r0);
}
leave:
gcry_mpi_release (mpi_kk);
gcry_mpi_release (mpi_k);
gcry_mpi_point_release (P);
gcry_mpi_release (mpi_x);
xfree (buffer);
gcry_mpi_point_release (Q);
gcry_ctx_release (ctx);
}
