/*
* WARNING: do not edit!
* Generated by crypto/bn/bn_prime.pl
* Copyright 1995-2016 The OpenSSL Project Authors. All Rights Reserved.
*
* Licensed under the OpenSSL license (the "License"). You may not use
* this file except in compliance with the License. You can obtain a copy
* in the file LICENSE in the source distribution or at
* https://www.openssl.org/source/license.html
*/
#include <stdio.h>
#include <time.h>
#include "internal/cryptlib.h"
#include "bn_lcl.h"
/*
* The quick sieve algorithm approach to weeding out primes is Philip
* Zimmermann's, as implemented in PGP. I have had a read of his comments
* and implemented my own version.
*/
#include "bn_prime.h"
static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
const BIGNUM *a1_odd, int k, BN_CTX *ctx,
BN_MONT_CTX *mont);
static int probable_prime(BIGNUM *rnd, int bits, prime_t *mods);
static int probable_prime_dh_safe(BIGNUM *rnd, int bits,
const BIGNUM *add, const BIGNUM *rem,
BN_CTX *ctx);
static const int prime_offsets[480] = {
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, 169, 173, 179, 181, 191, 193, 197, 199, 211, 221, 223, 227, 229,
233, 239, 241, 247, 251, 257, 263, 269, 271, 277, 281, 283, 289, 293,
299, 307, 311, 313, 317, 323, 331, 337, 347, 349, 353, 359, 361, 367,
373, 377, 379, 383, 389, 391, 397, 401, 403, 409, 419, 421, 431, 433,
437, 439, 443, 449, 457, 461, 463, 467, 479, 481, 487, 491, 493, 499,
503, 509, 521, 523, 527, 529, 533, 541, 547, 551, 557, 559, 563, 569,
571, 577, 587, 589, 593, 599, 601, 607, 611, 613, 617, 619, 629, 631,
641, 643, 647, 653, 659, 661, 667, 673, 677, 683, 689, 691, 697, 701,
703, 709, 713, 719, 727, 731, 733, 739, 743, 751, 757, 761, 767, 769,
773, 779, 787, 793, 797, 799, 809, 811, 817, 821, 823, 827, 829, 839,
841, 851, 853, 857, 859, 863, 871, 877, 881, 883, 887, 893, 899, 901,
907, 911, 919, 923, 929, 937, 941, 943, 947, 949, 953, 961, 967, 971,
977, 983, 989, 991, 997, 1003, 1007, 1009, 1013, 1019, 1021, 1027, 1031,
1033, 1037, 1039, 1049, 1051, 1061, 1063, 1069, 1073, 1079, 1081, 1087,
1091, 1093, 1097, 1103, 1109, 1117, 1121, 1123, 1129, 1139, 1147, 1151,
1153, 1157, 1159, 1163, 1171, 1181, 1187, 1189, 1193, 1201, 1207, 1213,
1217, 1219, 1223, 1229, 1231, 1237, 1241, 1247, 1249, 1259, 1261, 1271,
1273, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1313, 1319,
1321, 1327, 1333, 1339, 1343, 1349, 1357, 1361, 1363, 1367, 1369, 1373,
1381, 1387, 1391, 1399, 1403, 1409, 1411, 1417, 1423, 1427, 1429, 1433,
1439, 1447, 1451, 1453, 1457, 1459, 1469, 1471, 1481, 1483, 1487, 1489,
1493, 1499, 1501, 1511, 1513, 1517, 1523, 1531, 1537, 1541, 1543, 1549,
1553, 1559, 1567, 1571, 1577, 1579, 1583, 1591, 1597, 1601, 1607, 1609,
1613, 1619, 1621, 1627, 1633, 1637, 1643, 1649, 1651, 1657, 1663, 1667,
1669, 1679, 1681, 1691, 1693, 1697, 1699, 1703, 1709, 1711, 1717, 1721,
1723, 1733, 1739, 1741, 1747, 1751, 1753, 1759, 1763, 1769, 1777, 1781,
1783, 1787, 1789, 1801, 1807, 1811, 1817, 1819, 1823, 1829, 1831, 1843,
1847, 1849, 1853, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1891, 1901,
1907, 1909, 1913, 1919, 1921, 1927, 1931, 1933, 1937, 1943, 1949, 1951,
1957, 1961, 1963, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017,
2021, 2027, 2029, 2033, 2039, 2041, 2047, 2053, 2059, 2063, 2069, 2071,
2077, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2117, 2119, 2129, 2131,
2137, 2141, 2143, 2147, 2153, 2159, 2161, 2171, 2173, 2179, 2183, 2197,
2201, 2203, 2207, 2209, 2213, 2221, 2227, 2231, 2237, 2239, 2243, 2249,
2251, 2257, 2263, 2267, 2269, 2273, 2279, 2281, 2287, 2291, 2293, 2297,
2309, 2311
};
static const int prime_offset_count = 480;
static const int prime_multiplier = 2310;
static const int prime_multiplier_bits = 11; /* 2^|prime_multiplier_bits| <=
* |prime_multiplier| */
static const int first_prime_index = 5;
int BN_GENCB_call(BN_GENCB *cb, int a, int b)
{
/* No callback means continue */
if (!cb)
return 1;
switch (cb->ver) {
case 1:
/* Deprecated-style callbacks */
if (!cb->cb.cb_1)
return 1;
cb->cb.cb_1(a, b, cb->arg);
return 1;
case 2:
/* New-style callbacks */
return cb->cb.cb_2(a, b, cb);
default:
break;
}
/* Unrecognised callback type */
return 0;
}
int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe,
const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb)
{
BIGNUM *t;
int found = 0;
int i, j, c1 = 0;
BN_CTX *ctx = NULL;
prime_t *mods = NULL;
int checks = BN_prime_checks_for_size(bits);
if (bits < 2) {
/* There are no prime numbers this small. */
BNerr(BN_F_BN_GENERATE_PRIME_EX, BN_R_BITS_TOO_SMALL);
return 0;
} else if (bits == 2 && safe) {
/* The smallest safe prime (7) is three bits. */
BNerr(BN_F_BN_GENERATE_PRIME_EX, BN_R_BITS_TOO_SMALL);
return 0;
}
mods = OPENSSL_zalloc(sizeof(*mods) * NUMPRIMES);
if (mods == NULL)
goto err;
ctx = BN_CTX_new();
if (ctx == NULL)
goto err;
BN_CTX_start(ctx);
t = BN_CTX_get(ctx);
if (!t)
goto err;
loop:
/* make a random number and set the top and bottom bits */
if (add == NULL) {
if (!probable_prime(ret, bits, mods))
goto err;
} else {
if (safe) {
if (!probable_prime_dh_safe(ret, bits, add, rem, ctx))
goto err;
} else {
if (!bn_probable_prime_dh(ret, bits, add, rem, ctx))
goto err;
}
}
if (!BN_GENCB_call(cb, 0, c1++))
/* aborted */
goto err;
if (!safe) {
i = BN_is_prime_fasttest_ex(ret, checks, ctx, 0, cb);
if (i == -1)
goto err;
if (i == 0)
goto loop;
} else {
/*
* for "safe prime" generation, check that (p-1)/2 is prime. Since a
* prime is odd, We just need to divide by 2
*/
if (!BN_rshift1(t, ret))
goto err;
for (i = 0; i < checks; i++) {
j = BN_is_prime_fasttest_ex(ret, 1, ctx, 0, cb);
if (j == -1)
goto err;
if (j == 0)
goto loop;
j = BN_is_prime_fasttest_ex(t, 1, ctx, 0, cb);
if (j == -1)
goto err;
if (j == 0)
goto loop;
if (!BN_GENCB_call(cb, 2, c1 - 1))
goto err;
/* We have a safe prime test pass */
}
}
/* we have a prime :-) */
found = 1;
err:
OPENSSL_free(mods);
if (ctx != NULL)
BN_CTX_end(ctx);
BN_CTX_free(ctx);
bn_check_top(ret);
return found;
}
int BN_is_prime_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed,
BN_GENCB *cb)
{
return BN_is_prime_fasttest_ex(a, checks, ctx_passed, 0, cb);
}
int BN_is_prime_fasttest_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed,
int do_trial_division, BN_GENCB *cb)
{
int i, j, ret = -1;
int k;
BN_CTX *ctx = NULL;
BIGNUM *A1, *A1_odd, *check; /* taken from ctx */
BN_MONT_CTX *mont = NULL;
if (BN_cmp(a, BN_value_one()) <= 0)
return 0;
if (checks == BN_prime_checks)
checks = BN_prime_checks_for_size(BN_num_bits(a));
/* first look for small factors */
if (!BN_is_odd(a))
/* a is even => a is prime if and only if a == 2 */
return BN_is_word(a, 2);
if (do_trial_division) {
for (i = 1; i < NUMPRIMES; i++) {
BN_ULONG mod = BN_mod_word(a, primes[i]);
if (mod == (BN_ULONG)-1)
goto err;
if (mod == 0)
return 0;
}
if (!BN_GENCB_call(cb, 1, -1))
goto err;
}
if (ctx_passed != NULL)
ctx = ctx_passed;
else if ((ctx = BN_CTX_new()) == NULL)
goto err;
BN_CTX_start(ctx);
A1 = BN_CTX_get(ctx);
A1_odd = BN_CTX_get(ctx);
check = BN_CTX_get(ctx);
if (check == NULL)
goto err;
/* compute A1 := a - 1 */
if (!BN_copy(A1, a))
goto err;
if (!BN_sub_word(A1, 1))
goto err;
if (BN_is_zero(A1)) {
ret = 0;
goto err;
}
/* write A1 as A1_odd * 2^k */
k = 1;
while (!BN_is_bit_set(A1, k))
k++;
if (!BN_rshift(A1_odd, A1, k))
goto err;
/* Montgomery setup for computations mod a */
mont = BN_MONT_CTX_new();
if (mont == NULL)
goto err;
if (!BN_MONT_CTX_set(mont, a, ctx))
goto err;
for (i = 0; i < checks; i++) {
if (!BN_pseudo_rand_range(check, A1))
goto err;
if (!BN_add_word(check, 1))
goto err;
/* now 1 <= check < a */
j = witness(check, a, A1, A1_odd, k, ctx, mont);
if (j == -1)
goto err;
if (j) {
ret = 0;
goto err;
}
if (!BN_GENCB_call(cb, 1, i))
goto err;
}
ret = 1;
err:
if (ctx != NULL) {
BN_CTX_end(ctx);
if (ctx_passed == NULL)
BN_CTX_free(ctx);
}
BN_MONT_CTX_free(mont);
return (ret);
}
int bn_probable_prime_dh_retry(BIGNUM *rnd, int bits, BN_CTX *ctx)
{
int i;
int ret = 0;
loop:
if (!BN_rand(rnd, bits, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ODD))
goto err;
/* we now have a random number 'rand' to test. */
for (i = 1; i < NUMPRIMES; i++) {
/* check that rnd is a prime */
BN_ULONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]);
if (mod == (BN_ULONG)-1)
goto err;
if (mod <= 1) {
goto loop;
}
}
ret = 1;
err:
bn_check_top(rnd);
return (ret);
}
int bn_probable_prime_dh_coprime(BIGNUM *rnd, int bits, BN_CTX *ctx)
{
int i;
BIGNUM *offset_index;
BIGNUM *offset_count;
int ret = 0;
OPENSSL_assert(bits > prime_multiplier_bits);
BN_CTX_start(ctx);
if ((offset_index = BN_CTX_get(ctx)) == NULL)
goto err;
if ((offset_count = BN_CTX_get(ctx)) == NULL)
goto err;
if (!BN_add_word(offset_count, prime_offset_count))
goto err;
loop:
if (!BN_rand(rnd, bits - prime_multiplier_bits,
BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ODD))
goto err;
if (BN_is_bit_set(rnd, bits))
goto loop;
if (!BN_rand_range(offset_index, offset_count))
goto err;
if (!BN_mul_word(rnd, prime_multiplier)
|| !BN_add_word(rnd, prime_offsets[BN_get_word(offset_index)]))
goto err;
/* we now have a random number 'rand' to test. */
/* skip coprimes */
for (i = first_prime_index; i < NUMPRIMES; i++) {
/* check that rnd is a prime */
BN_ULONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]);
if (mod == (BN_ULONG)-1)
goto err;
if (mod <= 1)
goto loop;
}
ret = 1;
err:
BN_CTX_end(ctx);
bn_check_top(rnd);
return ret;
}
static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
const BIGNUM *a1_odd, int k, BN_CTX *ctx,
BN_MONT_CTX *mont)
{
if (!BN_mod_exp_mont(w, w, a1_odd, a, ctx, mont)) /* w := w^a1_odd mod a */
return -1;
if (BN_is_one(w))
return 0; /* probably prime */
if (BN_cmp(w, a1) == 0)
return 0; /* w == -1 (mod a), 'a' is probably prime */
while (--k) {
if (!BN_mod_mul(w, w, w, a, ctx)) /* w := w^2 mod a */
return -1;
if (BN_is_one(w))
return 1; /* 'a' is composite, otherwise a previous 'w'
* would have been == -1 (mod 'a') */
if (BN_cmp(w, a1) == 0)
return 0; /* w == -1 (mod a), 'a' is probably prime */
}
/*
* If we get here, 'w' is the (a-1)/2-th power of the original 'w', and
* it is neither -1 nor +1 -- so 'a' cannot be prime
*/
bn_check_top(w);
return 1;
}
static int probable_prime(BIGNUM *rnd, int bits, prime_t *mods)
{
int i;
BN_ULONG delta;
BN_ULONG maxdelta = BN_MASK2 - primes[NUMPRIMES - 1];
char is_single_word = bits <= BN_BITS2;
again:
if (!BN_rand(rnd, bits, BN_RAND_TOP_TWO, BN_RAND_BOTTOM_ODD))
return (0);
/* we now have a random number 'rnd' to test. */
for (i = 1; i < NUMPRIMES; i++) {
BN_ULONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]);
if (mod == (BN_ULONG)-1)
return 0;
mods[i] = (prime_t) mod;
}
/*
* If bits is so small that it fits into a single word then we
* additionally don't want to exceed that many bits.
*/
if (is_single_word) {
BN_ULONG size_limit;
if (bits == BN_BITS2) {
/*
* Shifting by this much has undefined behaviour so we do it a
* different way
*/
size_limit = ~((BN_ULONG)0) - BN_get_word(rnd);
} else {
size_limit = (((BN_ULONG)1) << bits) - BN_get_word(rnd) - 1;
}
if (size_limit < maxdelta)
maxdelta = size_limit;
}
delta = 0;
loop:
if (is_single_word) {
BN_ULONG rnd_word = BN_get_word(rnd);
/*-
* In the case that the candidate prime is a single word then
* we check that:
* 1) It's greater than primes[i] because we shouldn't reject
* 3 as being a prime number because it's a multiple of
* three.
* 2) That it's not a multiple of a known prime. We don't
* check that rnd-1 is also coprime to all the known
* primes because there aren't many small primes where
* that's true.
*/
for (i = 1; i < NUMPRIMES && primes[i] < rnd_word; i++) {
if ((mods[i] + delta) % primes[i] == 0) {
delta += 2;
if (delta > maxdelta)
goto again;
goto loop;
}
}
} else {
for (i = 1; i < NUMPRIMES; i++) {
/*
* check that rnd is not a prime and also that gcd(rnd-1,primes)
* == 1 (except for 2)
*/
if (((mods[i] + delta) % primes[i]) <= 1) {
delta += 2;
if (delta > maxdelta)
goto again;
goto loop;
}
}
}
if (!BN_add_word(rnd, delta))
return (0);
if (BN_num_bits(rnd) != bits)
goto again;
bn_check_top(rnd);
return (1);
}
int bn_probable_prime_dh(BIGNUM *rnd, int bits,
const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx)
{
int i, ret = 0;
BIGNUM *t1;
BN_CTX_start(ctx);
if ((t1 = BN_CTX_get(ctx)) == NULL)
goto err;
if (!BN_rand(rnd, bits, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ODD))
goto err;
/* we need ((rnd-rem) % add) == 0 */
if (!BN_mod(t1, rnd, add, ctx))
goto err;
if (!BN_sub(rnd, rnd, t1))
goto err;
if (rem == NULL) {
if (!BN_add_word(rnd, 1))
goto err;
} else {
if (!BN_add(rnd, rnd, rem))
goto err;
}
/* we now have a random number 'rand' to test. */
loop:
for (i = 1; i < NUMPRIMES; i++) {
/* check that rnd is a prime */
BN_ULONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]);
if (mod == (BN_ULONG)-1)
goto err;
if (mod <= 1) {
if (!BN_add(rnd, rnd, add))
goto err;
goto loop;
}
}
ret = 1;
err:
BN_CTX_end(ctx);
bn_check_top(rnd);
return (ret);
}
static int probable_prime_dh_safe(BIGNUM *p, int bits, const BIGNUM *padd,
const BIGNUM *rem, BN_CTX *ctx)
{
int i, ret = 0;
BIGNUM *t1, *qadd, *q;
bits--;
BN_CTX_start(ctx);
t1 = BN_CTX_get(ctx);
q = BN_CTX_get(ctx);
qadd = BN_CTX_get(ctx);
if (qadd == NULL)
goto err;
if (!BN_rshift1(qadd, padd))
goto err;
if (!BN_rand(q, bits, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ODD))
goto err;
/* we need ((rnd-rem) % add) == 0 */
if (!BN_mod(t1, q, qadd, ctx))
goto err;
if (!BN_sub(q, q, t1))
goto err;
if (rem == NULL) {
if (!BN_add_word(q, 1))
goto err;
} else {
if (!BN_rshift1(t1, rem))
goto err;
if (!BN_add(q, q, t1))
goto err;
}
/* we now have a random number 'rand' to test. */
if (!BN_lshift1(p, q))
goto err;
if (!BN_add_word(p, 1))
goto err;
loop:
for (i = 1; i < NUMPRIMES; i++) {
/* check that p and q are prime */
/*
* check that for p and q gcd(p-1,primes) == 1 (except for 2)
*/
BN_ULONG pmod = BN_mod_word(p, (BN_ULONG)primes[i]);
BN_ULONG qmod = BN_mod_word(q, (BN_ULONG)primes[i]);
if (pmod == (BN_ULONG)-1 || qmod == (BN_ULONG)-1)
goto err;
if (pmod == 0 || qmod == 0) {
if (!BN_add(p, p, padd))
goto err;
if (!BN_add(q, q, qadd))
goto err;
goto loop;
}
}
ret = 1;
err:
BN_CTX_end(ctx);
bn_check_top(p);
return (ret);
}
