| /* |
| * Copyright 1995-2018 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); |
| |
| 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); |
| 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 BN_is_word(a, primes[i]); |
| } |
| 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_priv_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; |
| } |
| |
| 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: |
| /* 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; |
| } |
