/*
- * WARNING: do not edit!
- * Generated by crypto/bn/bn_prime.pl
- * Copyright 1995-2016 The OpenSSL Project Authors. All Rights Reserved.
+ * Copyright 1995-2019 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 "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);
+#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 *bn_get0_small_factors(void)
+{
+ return &_bignum_small_prime_factors;
+}
+
int BN_GENCB_call(BN_GENCB *cb, int a, int b)
{
/* No callback means continue */
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 */
found = 1;
err:
OPENSSL_free(mods);
- if (ctx != NULL)
- BN_CTX_end(ctx);
+ BN_CTX_end(ctx);
BN_CTX_free(ctx);
bn_check_top(ret);
return found;
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,
+/* See FIPS 186-4 C.3.1 Miller Rabin Probabilistic Primality Test. */
+int BN_is_prime_fasttest_ex(const BIGNUM *w, int checks, BN_CTX *ctx_passed,
int do_trial_division, BN_GENCB *cb)
{
- int i, j, ret = -1;
- int k;
+ int i, status, ret = -1;
BN_CTX *ctx = NULL;
- BIGNUM *A1, *A1_odd, *check; /* taken from ctx */
- BN_MONT_CTX *mont = NULL;
- const BIGNUM *A = NULL;
- if (BN_cmp(a, BN_value_one()) <= 0)
+ /* 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]);
+ BN_ULONG mod = BN_mod_word(w, primes[i]);
if (mod == (BN_ULONG)-1)
- goto err;
+ return -1;
if (mod == 0)
- return BN_is_word(a, primes[i]);
+ 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)
goto err;
- BN_CTX_start(ctx);
- /* 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)
+ ret = bn_miller_rabin_is_prime(w, checks, ctx, cb, 0, &status);
+ if (!ret)
goto err;
+ ret = (status == BN_PRIMETEST_PROBABLY_PRIME);
+err:
+ if (ctx_passed == NULL)
+ BN_CTX_free(ctx);
+ 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 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))
- goto err;
- /* now 1 <= check < A */
+ if (iterations == BN_prime_checks)
+ iterations = BN_prime_checks_for_size(BN_num_bits(w));
- j = witness(check, A, A1, A1_odd, k, ctx, mont);
- if (j == -1)
+ /* (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(b, w3) || !BN_add_word(b, 2)) /* 1 < b < w-1 */
goto err;
- if (j) {
- ret = 0;
+
+ 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;
}
if (!BN_GENCB_call(cb, 1, i))
goto err;
+ /* 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;
+ /* (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) */
}
+ /* (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)
char is_single_word = bits <= BN_BITS2;
again:
- if (!BN_rand(rnd, bits, BN_RAND_TOP_TWO, BN_RAND_BOTTOM_ODD))
- return (0);
+ /* TODO: Not all primes are private */
+ if (!BN_priv_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 (!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,
err:
BN_CTX_end(ctx);
bn_check_top(rnd);
- return (ret);
+ return ret;
}
static int probable_prime_dh_safe(BIGNUM *p, int bits, const BIGNUM *padd,
err:
BN_CTX_end(ctx);
bn_check_top(p);
- return (ret);
+ return ret;
}
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