/*
- * WARNING: do not edit!
- * Generated by crypto/bn/bn_prime.pl
- * Copyright 1995-2016 The OpenSSL Project Authors. All Rights Reserved.
+ * Copyright 1995-2021 The OpenSSL Project Authors. All Rights Reserved.
*
- * Licensed under the OpenSSL license (the "License"). You may not use
+ * Licensed under the Apache License 2.0 (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"
+#include "bn_local.h"
/*
* The quick sieve algorithm approach to weeding out primes is Philip
*/
#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 int probable_prime(BIGNUM *rnd, int bits, int safe, prime_t *mods,
+ BN_CTX *ctx);
+static int probable_prime_dh(BIGNUM *rnd, int bits, int safe, prime_t *mods,
+ const BIGNUM *add, const BIGNUM *rem,
+ BN_CTX *ctx);
+static int bn_is_prime_int(const BIGNUM *w, int checks, BN_CTX *ctx,
+ int do_trial_division, BN_GENCB *cb);
+
+#define square(x) ((BN_ULONG)(x) * (BN_ULONG)(x))
+
+#if BN_BITS2 == 64
+# define BN_DEF(lo, hi) (BN_ULONG)hi<<32|lo
+#else
+# define BN_DEF(lo, hi) lo, hi
+#endif
+
+/*
+ * See SP800 89 5.3.3 (Step f)
+ * The product of the set of primes ranging from 3 to 751
+ * Generated using process in test/bn_internal_test.c test_bn_small_factors().
+ * This includes 751 (which is not currently included in SP 800-89).
+ */
+static const BN_ULONG small_prime_factors[] = {
+ BN_DEF(0x3ef4e3e1, 0xc4309333), BN_DEF(0xcd2d655f, 0x71161eb6),
+ BN_DEF(0x0bf94862, 0x95e2238c), BN_DEF(0x24f7912b, 0x3eb233d3),
+ BN_DEF(0xbf26c483, 0x6b55514b), BN_DEF(0x5a144871, 0x0a84d817),
+ BN_DEF(0x9b82210a, 0x77d12fee), BN_DEF(0x97f050b3, 0xdb5b93c2),
+ BN_DEF(0x4d6c026b, 0x4acad6b9), BN_DEF(0x54aec893, 0xeb7751f3),
+ BN_DEF(0x36bc85c4, 0xdba53368), BN_DEF(0x7f5ec78e, 0xd85a1b28),
+ BN_DEF(0x6b322244, 0x2eb072d8), BN_DEF(0x5e2b3aea, 0xbba51112),
+ BN_DEF(0x0e2486bf, 0x36ed1a6c), BN_DEF(0xec0c5727, 0x5f270460),
+ (BN_ULONG)0x000017b1
+};
+
+#define BN_SMALL_PRIME_FACTORS_TOP OSSL_NELEM(small_prime_factors)
+static const BIGNUM _bignum_small_prime_factors = {
+ (BN_ULONG *)small_prime_factors,
+ BN_SMALL_PRIME_FACTORS_TOP,
+ BN_SMALL_PRIME_FACTORS_TOP,
+ 0,
+ BN_FLG_STATIC_DATA
+};
+
+const BIGNUM *ossl_bn_get0_small_factors(void)
+{
+ return &_bignum_small_prime_factors;
+}
+
+/*
+ * Calculate the number of trial divisions that gives the best speed in
+ * combination with Miller-Rabin prime test, based on the sized of the prime.
+ */
+static int calc_trial_divisions(int bits)
+{
+ if (bits <= 512)
+ return 64;
+ else if (bits <= 1024)
+ return 128;
+ else if (bits <= 2048)
+ return 384;
+ else if (bits <= 4096)
+ return 1024;
+ return NUMPRIMES;
+}
+
+/*
+ * Use a minimum of 64 rounds of Miller-Rabin, which should give a false
+ * positive rate of 2^-128. If the size of the prime is larger than 2048
+ * the user probably wants a higher security level than 128, so switch
+ * to 128 rounds giving a false positive rate of 2^-256.
+ * Returns the number of rounds.
+ */
+static int bn_mr_min_checks(int bits)
+{
+ if (bits > 2048)
+ return 128;
+ return 64;
+}
int BN_GENCB_call(BN_GENCB *cb, int a, int b)
{
return 0;
}
-int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe,
- const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb)
+int BN_generate_prime_ex2(BIGNUM *ret, int bits, int safe,
+ const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb,
+ BN_CTX *ctx)
{
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);
+ int checks = bn_mr_min_checks(bits);
if (bits < 2) {
/* There are no prime numbers this small. */
- BNerr(BN_F_BN_GENERATE_PRIME_EX, BN_R_BITS_TOO_SMALL);
+ ERR_raise(ERR_LIB_BN, 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);
+ } else if (add == NULL && safe && bits < 6 && bits != 3) {
+ /*
+ * The smallest safe prime (7) is three bits.
+ * But the following two safe primes with less than 6 bits (11, 23)
+ * are unreachable for BN_rand with BN_RAND_TOP_TWO.
+ */
+ ERR_raise(ERR_LIB_BN, BN_R_BITS_TOO_SMALL);
return 0;
}
mods = OPENSSL_zalloc(sizeof(*mods) * NUMPRIMES);
if (mods == NULL)
- goto err;
+ return 0;
- ctx = BN_CTX_new();
- if (ctx == NULL)
- goto err;
BN_CTX_start(ctx);
t = BN_CTX_get(ctx);
- if (!t)
+ if (t == NULL)
goto err;
loop:
/* make a random number and set the top and bottom bits */
if (add == NULL) {
- if (!probable_prime(ret, bits, mods))
+ if (!probable_prime(ret, bits, safe, mods, ctx))
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 (!probable_prime_dh(ret, bits, safe, mods, add, rem, ctx))
+ goto err;
}
if (!BN_GENCB_call(cb, 0, c1++))
goto err;
if (!safe) {
- i = BN_is_prime_fasttest_ex(ret, checks, ctx, 0, cb);
+ i = bn_is_prime_int(ret, checks, ctx, 0, cb);
if (i == -1)
goto err;
if (i == 0)
goto err;
for (i = 0; i < checks; i++) {
- j = BN_is_prime_fasttest_ex(ret, 1, ctx, 0, cb);
+ j = bn_is_prime_int(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);
+ j = bn_is_prime_int(t, 1, ctx, 0, cb);
if (j == -1)
goto err;
if (j == 0)
found = 1;
err:
OPENSSL_free(mods);
- if (ctx != NULL)
- BN_CTX_end(ctx);
- BN_CTX_free(ctx);
+ BN_CTX_end(ctx);
bn_check_top(ret);
return found;
}
+#ifndef FIPS_MODULE
+int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe,
+ const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb)
+{
+ BN_CTX *ctx = BN_CTX_new();
+ int retval;
+
+ if (ctx == NULL)
+ return 0;
+
+ retval = BN_generate_prime_ex2(ret, bits, safe, add, rem, cb, ctx);
+
+ BN_CTX_free(ctx);
+ return retval;
+}
+#endif
+
+#ifndef OPENSSL_NO_DEPRECATED_3_0
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);
+ return ossl_bn_check_prime(a, checks, ctx_passed, 0, cb);
}
-int BN_is_prime_fasttest_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed,
+int BN_is_prime_fasttest_ex(const BIGNUM *w, int checks, BN_CTX *ctx,
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;
- const BIGNUM *A = NULL;
+ return ossl_bn_check_prime(w, checks, ctx, do_trial_division, cb);
+}
+#endif
+
+/* Wrapper around bn_is_prime_int that sets the minimum number of checks */
+int ossl_bn_check_prime(const BIGNUM *w, int checks, BN_CTX *ctx,
+ int do_trial_division, BN_GENCB *cb)
+{
+ int min_checks = bn_mr_min_checks(BN_num_bits(w));
+
+ if (checks < min_checks)
+ checks = min_checks;
- if (BN_cmp(a, BN_value_one()) <= 0)
+ return bn_is_prime_int(w, checks, ctx, do_trial_division, cb);
+}
+
+/*
+ * Use this only for key generation.
+ * It always uses trial division. The number of checks
+ * (MR rounds) passed in is used without being clamped to a minimum value.
+ */
+int ossl_bn_check_generated_prime(const BIGNUM *w, int checks, BN_CTX *ctx,
+ BN_GENCB *cb)
+{
+ return bn_is_prime_int(w, checks, ctx, 1, cb);
+}
+
+int BN_check_prime(const BIGNUM *p, BN_CTX *ctx, BN_GENCB *cb)
+{
+ return ossl_bn_check_prime(p, 0, ctx, 1, cb);
+}
+
+/*
+ * Tests that |w| is probably prime
+ * See FIPS 186-4 C.3.1 Miller Rabin Probabilistic Primality Test.
+ *
+ * Returns 0 when composite, 1 when probable prime, -1 on error.
+ */
+static int bn_is_prime_int(const BIGNUM *w, int checks, BN_CTX *ctx,
+ int do_trial_division, BN_GENCB *cb)
+{
+ int i, status, ret = -1;
+#ifndef FIPS_MODULE
+ BN_CTX *ctxlocal = NULL;
+#else
+
+ if (ctx == NULL)
+ return -1;
+#endif
+
+ /* w must be bigger than 1 */
+ if (BN_cmp(w, BN_value_one()) <= 0)
return 0;
- if (checks == BN_prime_checks)
- checks = BN_prime_checks_for_size(BN_num_bits(a));
+ /* w must be odd */
+ if (BN_is_odd(w)) {
+ /* Take care of the really small prime 3 */
+ if (BN_is_word(w, 3))
+ return 1;
+ } else {
+ /* 2 is the only even prime */
+ return BN_is_word(w, 2);
+ }
/* 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]);
+ int trial_divisions = calc_trial_divisions(BN_num_bits(w));
+
+ for (i = 1; i < trial_divisions; i++) {
+ BN_ULONG mod = BN_mod_word(w, primes[i]);
if (mod == (BN_ULONG)-1)
- goto err;
+ return -1;
if (mod == 0)
- return 0;
+ return BN_is_word(w, primes[i]);
}
if (!BN_GENCB_call(cb, 1, -1))
- goto err;
+ return -1;
}
-
- if (ctx_passed != NULL)
- ctx = ctx_passed;
- else if ((ctx = BN_CTX_new()) == NULL)
+#ifndef FIPS_MODULE
+ if (ctx == NULL && (ctxlocal = ctx = BN_CTX_new()) == NULL)
goto err;
- BN_CTX_start(ctx);
+#endif
- /* A := abs(a) */
- if (a->neg) {
- BIGNUM *t;
- if ((t = BN_CTX_get(ctx)) == NULL)
- goto err;
- if (BN_copy(t, a) == NULL)
- goto err;
- t->neg = 0;
- A = t;
- } else
- A = a;
- A1 = BN_CTX_get(ctx);
- A1_odd = BN_CTX_get(ctx);
- check = BN_CTX_get(ctx);
- if (check == NULL)
+ if (!ossl_bn_miller_rabin_is_prime(w, checks, ctx, cb, 0, &status)) {
+ ret = -1;
goto err;
+ }
+ ret = (status == BN_PRIMETEST_PROBABLY_PRIME);
+err:
+#ifndef FIPS_MODULE
+ BN_CTX_free(ctxlocal);
+#endif
+ return ret;
+}
- /* compute A1 := A - 1 */
- if (!BN_copy(A1, A))
- goto err;
- if (!BN_sub_word(A1, 1))
+/*
+ * Refer to FIPS 186-4 C.3.2 Enhanced Miller-Rabin Probabilistic Primality Test.
+ * OR C.3.1 Miller-Rabin Probabilistic Primality Test (if enhanced is zero).
+ * The Step numbers listed in the code refer to the enhanced case.
+ *
+ * if enhanced is set, then status returns one of the following:
+ * BN_PRIMETEST_PROBABLY_PRIME
+ * BN_PRIMETEST_COMPOSITE_WITH_FACTOR
+ * BN_PRIMETEST_COMPOSITE_NOT_POWER_OF_PRIME
+ * if enhanced is zero, then status returns either
+ * BN_PRIMETEST_PROBABLY_PRIME or
+ * BN_PRIMETEST_COMPOSITE
+ *
+ * returns 0 if there was an error, otherwise it returns 1.
+ */
+int ossl_bn_miller_rabin_is_prime(const BIGNUM *w, int iterations, BN_CTX *ctx,
+ BN_GENCB *cb, int enhanced, int *status)
+{
+ int i, j, a, ret = 0;
+ BIGNUM *g, *w1, *w3, *x, *m, *z, *b;
+ BN_MONT_CTX *mont = NULL;
+
+ /* w must be odd */
+ if (!BN_is_odd(w))
+ return 0;
+
+ BN_CTX_start(ctx);
+ g = BN_CTX_get(ctx);
+ w1 = BN_CTX_get(ctx);
+ w3 = BN_CTX_get(ctx);
+ x = BN_CTX_get(ctx);
+ m = BN_CTX_get(ctx);
+ z = BN_CTX_get(ctx);
+ b = BN_CTX_get(ctx);
+
+ if (!(b != NULL
+ /* w1 := w - 1 */
+ && BN_copy(w1, w)
+ && BN_sub_word(w1, 1)
+ /* w3 := w - 3 */
+ && BN_copy(w3, w)
+ && BN_sub_word(w3, 3)))
goto err;
- if (BN_is_zero(A1)) {
- ret = 0;
+
+ /* check w is larger than 3, otherwise the random b will be too small */
+ if (BN_is_zero(w3) || BN_is_negative(w3))
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))
+ /* (Step 1) Calculate largest integer 'a' such that 2^a divides w-1 */
+ a = 1;
+ while (!BN_is_bit_set(w1, a))
+ a++;
+ /* (Step 2) m = (w-1) / 2^a */
+ if (!BN_rshift(m, w1, a))
goto err;
- /* Montgomery setup for computations mod A */
+ /* Montgomery setup for computations mod a */
mont = BN_MONT_CTX_new();
- if (mont == NULL)
- goto err;
- if (!BN_MONT_CTX_set(mont, A, ctx))
+ if (mont == NULL || !BN_MONT_CTX_set(mont, w, ctx))
goto err;
- for (i = 0; i < checks; i++) {
- if (!BN_pseudo_rand_range(check, A1))
- goto err;
- if (!BN_add_word(check, 1))
+ if (iterations == 0)
+ iterations = bn_mr_min_checks(BN_num_bits(w));
+
+ /* (Step 4) */
+ for (i = 0; i < iterations; ++i) {
+ /* (Step 4.1) obtain a Random string of bits b where 1 < b < w-1 */
+ if (!BN_priv_rand_range_ex(b, w3, 0, ctx)
+ || !BN_add_word(b, 2)) /* 1 < b < w-1 */
goto err;
- /* now 1 <= check < A */
- j = witness(check, A, A1, A1_odd, k, ctx, mont);
- if (j == -1)
+ if (enhanced) {
+ /* (Step 4.3) */
+ if (!BN_gcd(g, b, w, ctx))
+ goto err;
+ /* (Step 4.4) */
+ if (!BN_is_one(g)) {
+ *status = BN_PRIMETEST_COMPOSITE_WITH_FACTOR;
+ ret = 1;
+ goto err;
+ }
+ }
+ /* (Step 4.5) z = b^m mod w */
+ if (!BN_mod_exp_mont(z, b, m, w, ctx, mont))
+ goto err;
+ /* (Step 4.6) if (z = 1 or z = w-1) */
+ if (BN_is_one(z) || BN_cmp(z, w1) == 0)
+ goto outer_loop;
+ /* (Step 4.7) for j = 1 to a-1 */
+ for (j = 1; j < a ; ++j) {
+ /* (Step 4.7.1 - 4.7.2) x = z. z = x^2 mod w */
+ if (!BN_copy(x, z) || !BN_mod_mul(z, x, x, w, ctx))
+ goto err;
+ /* (Step 4.7.3) */
+ if (BN_cmp(z, w1) == 0)
+ goto outer_loop;
+ /* (Step 4.7.4) */
+ if (BN_is_one(z))
+ goto composite;
+ }
+ /* At this point z = b^((w-1)/2) mod w */
+ /* (Steps 4.8 - 4.9) x = z, z = x^2 mod w */
+ if (!BN_copy(x, z) || !BN_mod_mul(z, x, x, w, ctx))
goto err;
- if (j) {
- ret = 0;
+ /* (Step 4.10) */
+ if (BN_is_one(z))
+ goto composite;
+ /* (Step 4.11) x = b^(w-1) mod w */
+ if (!BN_copy(x, z))
goto err;
+composite:
+ if (enhanced) {
+ /* (Step 4.1.2) g = GCD(x-1, w) */
+ if (!BN_sub_word(x, 1) || !BN_gcd(g, x, w, ctx))
+ goto err;
+ /* (Steps 4.1.3 - 4.1.4) */
+ if (BN_is_one(g))
+ *status = BN_PRIMETEST_COMPOSITE_NOT_POWER_OF_PRIME;
+ else
+ *status = BN_PRIMETEST_COMPOSITE_WITH_FACTOR;
+ } else {
+ *status = BN_PRIMETEST_COMPOSITE;
}
+ ret = 1;
+ goto err;
+outer_loop: ;
+ /* (Step 4.1.5) */
if (!BN_GENCB_call(cb, 1, i))
goto err;
}
+ /* (Step 5) */
+ *status = BN_PRIMETEST_PROBABLY_PRIME;
ret = 1;
- err:
- if (ctx != NULL) {
- BN_CTX_end(ctx);
- if (ctx_passed == NULL)
- BN_CTX_free(ctx);
- }
+err:
+ BN_clear(g);
+ BN_clear(w1);
+ BN_clear(w3);
+ BN_clear(x);
+ BN_clear(m);
+ BN_clear(z);
+ BN_clear(b);
+ BN_CTX_end(ctx);
BN_MONT_CTX_free(mont);
-
- 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;
+ return ret;
}
-static int probable_prime(BIGNUM *rnd, int bits, prime_t *mods)
+/*
+ * Generate a random number of |bits| bits that is probably prime by sieving.
+ * If |safe| != 0, it generates a safe prime.
+ * |mods| is a preallocated array that gets reused when called again.
+ *
+ * The probably prime is saved in |rnd|.
+ *
+ * Returns 1 on success and 0 on error.
+ */
+static int probable_prime(BIGNUM *rnd, int bits, int safe, prime_t *mods,
+ BN_CTX *ctx)
{
int i;
BN_ULONG delta;
- BN_ULONG maxdelta = BN_MASK2 - primes[NUMPRIMES - 1];
- char is_single_word = bits <= BN_BITS2;
+ int trial_divisions = calc_trial_divisions(bits);
+ BN_ULONG maxdelta = BN_MASK2 - primes[trial_divisions - 1];
again:
- if (!BN_rand(rnd, bits, BN_RAND_TOP_TWO, BN_RAND_BOTTOM_ODD))
- return (0);
+ if (!BN_priv_rand_ex(rnd, bits, BN_RAND_TOP_TWO, BN_RAND_BOTTOM_ODD, 0,
+ ctx))
+ return 0;
+ if (safe && !BN_set_bit(rnd, 1))
+ return 0;
/* we now have a random number 'rnd' to test. */
- for (i = 1; i < NUMPRIMES; i++) {
+ for (i = 1; i < trial_divisions; 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 < trial_divisions; i++) {
+ /*
+ * check that rnd is a prime and also that
+ * gcd(rnd-1,primes) == 1 (except for 2)
+ * do the second check only if we are interested in safe primes
+ * in the case that the candidate prime is a single word then
+ * we check only the primes up to sqrt(rnd)
*/
- 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 (bits <= 31 && delta <= 0x7fffffff
+ && square(primes[i]) > BN_get_word(rnd) + delta)
+ break;
+ if (safe ? (mods[i] + delta) % primes[i] <= 1
+ : (mods[i] + delta) % primes[i] == 0) {
+ delta += safe ? 4 : 2;
+ if (delta > maxdelta)
+ goto again;
+ goto loop;
}
}
if (!BN_add_word(rnd, delta))
- return (0);
+ return 0;
if (BN_num_bits(rnd) != bits)
goto again;
bn_check_top(rnd);
- return (1);
+ return 1;
}
-int bn_probable_prime_dh(BIGNUM *rnd, int bits,
- const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx)
+/*
+ * Generate a random number |rnd| of |bits| bits that is probably prime
+ * and satisfies |rnd| % |add| == |rem| by sieving.
+ * If |safe| != 0, it generates a safe prime.
+ * |mods| is a preallocated array that gets reused when called again.
+ *
+ * Returns 1 on success and 0 on error.
+ */
+static int probable_prime_dh(BIGNUM *rnd, int bits, int safe, prime_t *mods,
+ const BIGNUM *add, const BIGNUM *rem,
+ BN_CTX *ctx)
{
int i, ret = 0;
BIGNUM *t1;
+ BN_ULONG delta;
+ int trial_divisions = calc_trial_divisions(bits);
+ BN_ULONG maxdelta = BN_MASK2 - primes[trial_divisions - 1];
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))
+ if (maxdelta > BN_MASK2 - BN_get_word(add))
+ maxdelta = BN_MASK2 - BN_get_word(add);
+
+ again:
+ if (!BN_rand_ex(rnd, bits, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ODD, 0, ctx))
goto err;
/* we need ((rnd-rem) % add) == 0 */
if (!BN_sub(rnd, rnd, t1))
goto err;
if (rem == NULL) {
- if (!BN_add_word(rnd, 1))
+ if (!BN_add_word(rnd, safe ? 3u : 1u))
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)
+ if (BN_num_bits(rnd) < bits
+ || BN_get_word(rnd) < (safe ? 5u : 3u)) {
+ if (!BN_add(rnd, rnd, add))
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))
+ /* we now have a random number 'rnd' to test. */
+ for (i = 1; i < trial_divisions; i++) {
+ BN_ULONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]);
+ if (mod == (BN_ULONG)-1)
goto err;
+ mods[i] = (prime_t) mod;
}
-
- /* we now have a random number 'rand' to test. */
- if (!BN_lshift1(p, q))
- goto err;
- if (!BN_add_word(p, 1))
- goto err;
-
+ delta = 0;
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;
+ for (i = 1; i < trial_divisions; i++) {
+ /* check that rnd is a prime */
+ if (bits <= 31 && delta <= 0x7fffffff
+ && square(primes[i]) > BN_get_word(rnd) + delta)
+ break;
+ /* rnd mod p == 1 implies q = (rnd-1)/2 is divisible by p */
+ if (safe ? (mods[i] + delta) % primes[i] <= 1
+ : (mods[i] + delta) % primes[i] == 0) {
+ delta += BN_get_word(add);
+ if (delta > maxdelta)
+ goto again;
goto loop;
}
}
+ if (!BN_add_word(rnd, delta))
+ goto err;
ret = 1;
err:
BN_CTX_end(ctx);
- bn_check_top(p);
- return (ret);
+ bn_check_top(rnd);
+ return ret;
}
projects / openssl.git / blobdiff