-/* crypto/bn/bn_prime.c */
-/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
- * All rights reserved.
+/*
+ * Copyright 1995-2019 The OpenSSL Project Authors. All Rights Reserved.
*
- * This package is an SSL implementation written
- * by Eric Young (eay@cryptsoft.com).
- * The implementation was written so as to conform with Netscapes SSL.
- *
- * This library is free for commercial and non-commercial use as long as
- * the following conditions are aheared to. The following conditions
- * apply to all code found in this distribution, be it the RC4, RSA,
- * lhash, DES, etc., code; not just the SSL code. The SSL documentation
- * included with this distribution is covered by the same copyright terms
- * except that the holder is Tim Hudson (tjh@cryptsoft.com).
- *
- * Copyright remains Eric Young's, and as such any Copyright notices in
- * the code are not to be removed.
- * If this package is used in a product, Eric Young should be given attribution
- * as the author of the parts of the library used.
- * This can be in the form of a textual message at program startup or
- * in documentation (online or textual) provided with the package.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- * 1. Redistributions of source code must retain the copyright
- * notice, this list of conditions and the following disclaimer.
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- * 3. All advertising materials mentioning features or use of this software
- * must display the following acknowledgement:
- * "This product includes cryptographic software written by
- * Eric Young (eay@cryptsoft.com)"
- * The word 'cryptographic' can be left out if the rouines from the library
- * being used are not cryptographic related :-).
- * 4. If you include any Windows specific code (or a derivative thereof) from
- * the apps directory (application code) you must include an acknowledgement:
- * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
- *
- * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- *
- * The licence and distribution terms for any publically available version or
- * derivative of this code cannot be changed. i.e. this code cannot simply be
- * copied and put under another distribution licence
- * [including the GNU Public Licence.]
+ * 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 "cryptlib.h"
+#include "internal/cryptlib.h"
#include "bn_lcl.h"
-#include <openssl/rand.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.
+/*
+ * 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 *a, BIGNUM *n, BN_CTX *ctx,BN_CTX *ctx2,
- BN_MONT_CTX *mont);
-static int probable_prime(BIGNUM *rnd, int bits);
-static int probable_prime_dh(BIGNUM *rnd, int bits,
- BIGNUM *add, BIGNUM *rem, BN_CTX *ctx);
+static int probable_prime(BIGNUM *rnd, int bits, prime_t *mods);
static int probable_prime_dh_safe(BIGNUM *rnd, int bits,
- BIGNUM *add, BIGNUM *rem, BN_CTX *ctx);
-
-BIGNUM *BN_generate_prime(BIGNUM *ret, int bits, int safe, BIGNUM *add,
- BIGNUM *rem, void (*callback)(int,int,void *), void *cb_arg)
- {
- BIGNUM *rnd=NULL;
- BIGNUM t;
- int found=0;
- int i,j,c1=0;
- BN_CTX *ctx;
- int checks = BN_prime_checks_size(bits);
-
- ctx=BN_CTX_new();
- if (ctx == NULL) goto err;
- if (ret == NULL)
- {
- if ((rnd=BN_new()) == NULL) goto err;
- }
- else
- rnd=ret;
- BN_init(&t);
-loop:
- /* make a random number and set the top and bottom bits */
- if (add == NULL)
- {
- if (!probable_prime(rnd,bits)) goto err;
- }
- else
- {
- if (safe)
- {
- if (!probable_prime_dh_safe(rnd,bits,add,rem,ctx))
- goto err;
- }
- else
- {
- if (!probable_prime_dh(rnd,bits,add,rem,ctx))
- goto err;
- }
- }
- /* if (BN_mod_word(rnd,(BN_ULONG)3) == 1) goto loop; */
- if (callback != NULL) callback(0,c1++,cb_arg);
-
- if (!safe)
- {
- i=BN_is_prime(rnd,checks,callback,ctx,cb_arg);
- 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,rnd)) goto err;
-
- for (i=0; i<checks; i++)
- {
- j=BN_is_prime(rnd,1,callback,ctx,cb_arg);
- if (j == -1) goto err;
- if (j == 0) goto loop;
-
- j=BN_is_prime(&t,1,callback,ctx,cb_arg);
- if (j == -1) goto err;
- if (j == 0) goto loop;
-
- if (callback != NULL) callback(2,c1-1,cb_arg);
- /* We have a safe prime test pass */
- }
- }
- /* we have a prime :-) */
- found = 1;
-err:
- if (!found && (ret == NULL) && (rnd != NULL)) BN_free(rnd);
- BN_free(&t);
- if (ctx != NULL) BN_CTX_free(ctx);
- return(found ? rnd : NULL);
- }
-
-int BN_is_prime(BIGNUM *a, int checks, void (*callback)(int,int,void *),
- BN_CTX *ctx_passed, void *cb_arg)
- {
- int i,j,c2=0,ret= -1;
- BIGNUM *check;
- BN_CTX *ctx=NULL,*ctx2=NULL;
- BN_MONT_CTX *mont=NULL;
-
- if (checks == BN_prime_checks)
- {
- int bits = BN_num_bits(a);
- checks = BN_prime_checks_size(bits);
- }
-
- if (!BN_is_odd(a))
- return(0);
- if (ctx_passed != NULL)
- ctx=ctx_passed;
- else
- if ((ctx=BN_CTX_new()) == NULL) goto err;
-
- if ((ctx2=BN_CTX_new()) == NULL) goto err;
- if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
-
- check= &(ctx->bn[ctx->tos++]);
-
- /* Setup the montgomery structure */
- if (!BN_MONT_CTX_set(mont,a,ctx2)) goto err;
-
- for (i=0; i<checks; i++)
- {
- if (!BN_pseudo_rand(check,BN_num_bits(a)-1,0,0)) goto err;
- j=witness(check,a,ctx,ctx2,mont);
- if (j == -1) goto err;
- if (j)
- {
- ret=0;
- goto err;
- }
- if (callback != NULL) callback(1,c2++,cb_arg);
- }
- ret=1;
-err:
- ctx->tos--;
- if ((ctx_passed == NULL) && (ctx != NULL))
- BN_CTX_free(ctx);
- if (ctx2 != NULL)
- BN_CTX_free(ctx2);
- if (mont != NULL) BN_MONT_CTX_free(mont);
-
- return(ret);
- }
-
-static int witness(BIGNUM *a, BIGNUM *n, BN_CTX *ctx, BN_CTX *ctx2,
- BN_MONT_CTX *mont)
- {
- int k,i,ret= -1,good;
- BIGNUM *d,*dd,*tmp,*d1,*d2,*n1;
- BIGNUM *mont_one,*mont_n1,*mont_a;
-
- d1= &(ctx->bn[ctx->tos]);
- d2= &(ctx->bn[ctx->tos+1]);
- n1= &(ctx->bn[ctx->tos+2]);
- ctx->tos+=3;
-
- mont_one= &(ctx2->bn[ctx2->tos]);
- mont_n1= &(ctx2->bn[ctx2->tos+1]);
- mont_a= &(ctx2->bn[ctx2->tos+2]);
- ctx2->tos+=3;
-
- d=d1;
- dd=d2;
- if (!BN_one(d)) goto err;
- if (!BN_sub(n1,n,d)) goto err; /* n1=n-1; */
- k=BN_num_bits(n1);
-
- if (!BN_to_montgomery(mont_one,BN_value_one(),mont,ctx2)) goto err;
- if (!BN_to_montgomery(mont_n1,n1,mont,ctx2)) goto err;
- if (!BN_to_montgomery(mont_a,a,mont,ctx2)) goto err;
-
- BN_copy(d,mont_one);
- for (i=k-1; i>=0; i--)
- {
- if ( (BN_cmp(d,mont_one) != 0) &&
- (BN_cmp(d,mont_n1) != 0))
- good=1;
- else
- good=0;
-
- BN_mod_mul_montgomery(dd,d,d,mont,ctx2);
-
- if (good && (BN_cmp(dd,mont_one) == 0))
- {
- ret=1;
- goto err;
- }
- if (BN_is_bit_set(n1,i))
- {
- BN_mod_mul_montgomery(d,dd,mont_a,mont,ctx2);
- }
- else
- {
- tmp=d;
- d=dd;
- dd=tmp;
- }
- }
- if (BN_cmp(d,mont_one) == 0)
- i=0;
- else i=1;
- ret=i;
-err:
- ctx->tos-=3;
- ctx2->tos-=3;
- return(ret);
- }
-
-static int probable_prime(BIGNUM *rnd, int bits)
- {
- int i;
- MS_STATIC BN_ULONG mods[NUMPRIMES];
- BN_ULONG delta,d;
-
-again:
- if (!BN_rand(rnd,bits,1,1)) return(0);
- /* we now have a random number 'rand' to test. */
- for (i=1; i<NUMPRIMES; i++)
- mods[i]=BN_mod_word(rnd,(BN_ULONG)primes[i]);
- delta=0;
- loop: 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)
- {
- d=delta;
- delta+=2;
- /* perhaps need to check for overflow of
- * delta (but delta can be upto 2^32)
- * 21-May-98 eay - added overflow check */
- if (delta < d) goto again;
- goto loop;
- }
- }
- if (!BN_add_word(rnd,delta)) return(0);
- return(1);
- }
-
-static int probable_prime_dh(BIGNUM *rnd, int bits, BIGNUM *add, BIGNUM *rem,
- BN_CTX *ctx)
- {
- int i,ret=0;
- BIGNUM *t1;
-
- t1= &(ctx->bn[ctx->tos++]);
-
- if (!BN_rand(rnd,bits,0,1)) 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 */
- if (BN_mod_word(rnd,(BN_ULONG)primes[i]) <= 1)
- {
- if (!BN_add(rnd,rnd,add)) goto err;
- goto loop;
- }
- }
- ret=1;
-err:
- ctx->tos--;
- return(ret);
- }
-
-static int probable_prime_dh_safe(BIGNUM *p, int bits, BIGNUM *padd,
- BIGNUM *rem, BN_CTX *ctx)
- {
- int i,ret=0;
- BIGNUM *t1,*qadd=NULL,*q=NULL;
-
- bits--;
- t1= &(ctx->bn[ctx->tos++]);
- q= &(ctx->bn[ctx->tos++]);
- qadd= &(ctx->bn[ctx->tos++]);
-
- if (!BN_rshift1(qadd,padd)) goto err;
-
- if (!BN_rand(q,bits,0,1)) 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) */
- if ( (BN_mod_word(p,(BN_ULONG)primes[i]) == 0) ||
- (BN_mod_word(q,(BN_ULONG)primes[i]) == 0))
- {
- if (!BN_add(p,p,padd)) goto err;
- if (!BN_add(q,q,qadd)) goto err;
- goto loop;
- }
- }
- ret=1;
-err:
- ctx->tos-=3;
- return(ret);
- }
-
-#if 0
-
-#define RECP_MUL_MOD
-
-static int witness(BIGNUM *a, BIGNUM *n, BN_CTX *ctx,
- BN_CTX *unused, BN_MONT_CTX *unused2)
- {
- int k,i,ret= -1;
- BIGNUM *d,*dd,*tmp;
- BIGNUM *d1,*d2,*x,*n1;
- BN_RECP_CTX recp;
-
- d1= &(ctx->bn[ctx->tos]);
- d2= &(ctx->bn[ctx->tos+1]);
- x= &(ctx->bn[ctx->tos+2]);
- n1= &(ctx->bn[ctx->tos+3]);
- ctx->tos+=4;
-
- d=d1;
- dd=d2;
- if (!BN_one(d)) goto err;
- if (!BN_sub(n1,n,d)) goto err; /* n1=n-1; */
- k=BN_num_bits(n1);
-
- /* i=BN_num_bits(n); */
-#ifdef RECP_MUL_MOD
- BN_RECP_CTX_init(&recp);
- if (BN_RECP_CTX_set(&recp,n,ctx) <= 0) goto err;
-#endif
+ const BIGNUM *add, const BIGNUM *rem,
+ BN_CTX *ctx);
- for (i=k-1; i>=0; i--)
- {
- if (BN_copy(x,d) == NULL) goto err;
-#ifndef RECP_MUL_MOD
- if (!BN_mod_mul(dd,d,d,n,ctx)) goto err;
-#else
- if (!BN_mod_mul_reciprocal(dd,d,d,&recp,ctx)) goto err;
-#endif
- if ( BN_is_one(dd) &&
- !BN_is_one(x) &&
- (BN_cmp(x,n1) != 0))
- {
- ret=1;
- goto err;
- }
- if (BN_is_bit_set(n1,i))
- {
-#ifndef RECP_MUL_MOD
- if (!BN_mod_mul(d,dd,a,n,ctx)) goto err;
+#if BN_BITS2 == 64
+# define BN_DEF(lo, hi) (BN_ULONG)hi<<32|lo
#else
- if (!BN_mod_mul_reciprocal(d,dd,a,&recp,ctx)) goto err;
+# define BN_DEF(lo, hi) lo, hi
#endif
- }
- else
- {
- tmp=d;
- d=dd;
- dd=tmp;
- }
- }
- if (BN_is_one(d))
- i=0;
- else i=1;
- ret=i;
+
+/*
+ * 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 */
+ 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 == NULL)
+ 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);
+ 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);
+}
+
+/* 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, status, ret = -1;
+ BN_CTX *ctx = NULL;
+
+ /* w must be bigger than 1 */
+ if (BN_cmp(w, BN_value_one()) <= 0)
+ return 0;
+
+ /* 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 (do_trial_division) {
+ for (i = 1; i < NUMPRIMES; i++) {
+ BN_ULONG mod = BN_mod_word(w, primes[i]);
+ if (mod == (BN_ULONG)-1)
+ return -1;
+ if (mod == 0)
+ return BN_is_word(w, primes[i]);
+ }
+ if (!BN_GENCB_call(cb, 1, -1))
+ return -1;
+ }
+ if (ctx_passed != NULL)
+ ctx = ctx_passed;
+ else if ((ctx = BN_CTX_new()) == NULL)
+ goto err;
+
+ ret = bn_miller_rabin_is_prime(w, checks, ctx, cb, 0, &status);
+ if (!ret)
+ goto err;
+ ret = (status == BN_PRIMETEST_PROBABLY_PRIME);
err:
- ctx->tos-=4;
-#ifdef RECP_MUL_MOD
- BN_RECP_CTX_free(&recp);
-#endif
- return(ret);
- }
-#endif
+ if (ctx_passed == NULL)
+ BN_CTX_free(ctx);
+ return ret;
+}
+
+/*
+ * 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;
+
+ /* 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;
+
+ /* (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 */
+ mont = BN_MONT_CTX_new();
+ if (mont == NULL || !BN_MONT_CTX_set(mont, w, ctx))
+ goto err;
+
+ if (iterations == BN_prime_checks)
+ iterations = BN_prime_checks_for_size(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(b, w3) || !BN_add_word(b, 2)) /* 1 < b < w-1 */
+ goto err;
+
+ 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:
+ 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 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:
+ /* 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 (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;
+}
projects / openssl.git / blobdiff