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/*
* Copyright 2011-2018 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 <openssl/bn.h>
#include "bn_lcl.h"
/* X9.31 routines for prime derivation */
/*
* X9.31 prime derivation. This is used to generate the primes pi (p1, p2,
* q1, q2) from a parameter Xpi by checking successive odd integers.
*/
static int bn_x931_derive_pi(BIGNUM *pi, const BIGNUM *Xpi, BN_CTX *ctx,
BN_GENCB *cb)
{
int i = 0, is_prime;
if (!BN_copy(pi, Xpi))
return 0;
if (!BN_is_odd(pi) && !BN_add_word(pi, 1))
return 0;
for (;;) {
i++;
BN_GENCB_call(cb, 0, i);
/* NB 27 MR is specified in X9.31 */
is_prime = BN_is_prime_fasttest_ex(pi, 27, ctx, 1, cb);
if (is_prime < 0)
return 0;
if (is_prime)
break;
if (!BN_add_word(pi, 2))
return 0;
}
BN_GENCB_call(cb, 2, i);
return 1;
}
/*
* This is the main X9.31 prime derivation function. From parameters Xp1, Xp2
* and Xp derive the prime p. If the parameters p1 or p2 are not NULL they
* will be returned too: this is needed for testing.
*/
int BN_X931_derive_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
const BIGNUM *Xp, const BIGNUM *Xp1,
const BIGNUM *Xp2, const BIGNUM *e, BN_CTX *ctx,
BN_GENCB *cb)
{
int ret = 0;
BIGNUM *t, *p1p2, *pm1;
/* Only even e supported */
if (!BN_is_odd(e))
return 0;
BN_CTX_start(ctx);
if (p1 == NULL)
p1 = BN_CTX_get(ctx);
if (p2 == NULL)
p2 = BN_CTX_get(ctx);
t = BN_CTX_get(ctx);
p1p2 = BN_CTX_get(ctx);
pm1 = BN_CTX_get(ctx);
if (pm1 == NULL)
goto err;
if (!bn_x931_derive_pi(p1, Xp1, ctx, cb))
goto err;
if (!bn_x931_derive_pi(p2, Xp2, ctx, cb))
goto err;
if (!BN_mul(p1p2, p1, p2, ctx))
goto err;
/* First set p to value of Rp */
if (!BN_mod_inverse(p, p2, p1, ctx))
goto err;
if (!BN_mul(p, p, p2, ctx))
goto err;
if (!BN_mod_inverse(t, p1, p2, ctx))
goto err;
if (!BN_mul(t, t, p1, ctx))
goto err;
if (!BN_sub(p, p, t))
goto err;
if (p->neg && !BN_add(p, p, p1p2))
goto err;
/* p now equals Rp */
if (!BN_mod_sub(p, p, Xp, p1p2, ctx))
goto err;
if (!BN_add(p, p, Xp))
goto err;
/* p now equals Yp0 */
for (;;) {
int i = 1;
BN_GENCB_call(cb, 0, i++);
if (!BN_copy(pm1, p))
goto err;
if (!BN_sub_word(pm1, 1))
goto err;
if (!BN_gcd(t, pm1, e, ctx))
goto err;
if (BN_is_one(t)) {
/*
* X9.31 specifies 8 MR and 1 Lucas test or any prime test
* offering similar or better guarantees 50 MR is considerably
* better.
*/
int r = BN_is_prime_fasttest_ex(p, 50, ctx, 1, cb);
if (r < 0)
goto err;
if (r)
break;
}
if (!BN_add(p, p, p1p2))
goto err;
}
BN_GENCB_call(cb, 3, 0);
ret = 1;
err:
BN_CTX_end(ctx);
return ret;
}
/*
* Generate pair of parameters Xp, Xq for X9.31 prime generation. Note: nbits
* parameter is sum of number of bits in both.
*/
int BN_X931_generate_Xpq(BIGNUM *Xp, BIGNUM *Xq, int nbits, BN_CTX *ctx)
{
BIGNUM *t;
int i;
/*
* Number of bits for each prime is of the form 512+128s for s = 0, 1,
* ...
*/
if ((nbits < 1024) || (nbits & 0xff))
return 0;
nbits >>= 1;
/*
* The random value Xp must be between sqrt(2) * 2^(nbits-1) and 2^nbits
* - 1. By setting the top two bits we ensure that the lower bound is
* exceeded.
*/
if (!BN_priv_rand(Xp, nbits, BN_RAND_TOP_TWO, BN_RAND_BOTTOM_ANY))
goto err;
BN_CTX_start(ctx);
t = BN_CTX_get(ctx);
if (t == NULL)
goto err;
for (i = 0; i < 1000; i++) {
if (!BN_priv_rand(Xq, nbits, BN_RAND_TOP_TWO, BN_RAND_BOTTOM_ANY))
goto err;
/* Check that |Xp - Xq| > 2^(nbits - 100) */
if (!BN_sub(t, Xp, Xq))
goto err;
if (BN_num_bits(t) > (nbits - 100))
break;
}
BN_CTX_end(ctx);
if (i < 1000)
return 1;
return 0;
err:
BN_CTX_end(ctx);
return 0;
}
/*
* Generate primes using X9.31 algorithm. Of the values p, p1, p2, Xp1 and
* Xp2 only 'p' needs to be non-NULL. If any of the others are not NULL the
* relevant parameter will be stored in it. Due to the fact that |Xp - Xq| >
* 2^(nbits - 100) must be satisfied Xp and Xq are generated using the
* previous function and supplied as input.
*/
int BN_X931_generate_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
BIGNUM *Xp1, BIGNUM *Xp2,
const BIGNUM *Xp,
const BIGNUM *e, BN_CTX *ctx, BN_GENCB *cb)
{
int ret = 0;
BN_CTX_start(ctx);
if (Xp1 == NULL)
Xp1 = BN_CTX_get(ctx);
if (Xp2 == NULL)
Xp2 = BN_CTX_get(ctx);
if (Xp1 == NULL || Xp2 == NULL)
goto error;
if (!BN_priv_rand(Xp1, 101, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ANY))
goto error;
if (!BN_priv_rand(Xp2, 101, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ANY))
goto error;
if (!BN_X931_derive_prime_ex(p, p1, p2, Xp, Xp1, Xp2, e, ctx, cb))
goto error;
ret = 1;
error:
BN_CTX_end(ctx);
return ret;
}
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