[thirdparty/openssl.git] / crypto / bn / bn_prime.c

/*
 * Copyright 1995-2019 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_local.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, int safe, prime_t *mods);
static int probable_prime_dh(BIGNUM *rnd, int bits, int safe, prime_t *mods,
                             const BIGNUM *add, const BIGNUM *rem,
                             BN_CTX *ctx);

#define square(x) ((BN_ULONG)(x) * (BN_ULONG)(x))

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 (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.
         */
        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, safe, mods))
            goto err;
    } else {
        if (!probable_prime_dh(ret, bits, safe, mods, 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);
}

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, *A3, *check; /* taken from ctx */
    BN_MONT_CTX *mont = NULL;

    /* Take care of the really small primes 2 & 3 */
    if (BN_is_word(a, 2) || BN_is_word(a, 3))
        return 1;

    /* Check odd and bigger than 1 */
    if (!BN_is_odd(a) || 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 (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);
    A3 = 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) || !BN_sub_word(A1, 1))
        goto err;
    /* compute A3 := a - 3 */
    if (!BN_copy(A3, a) || !BN_sub_word(A3, 3))
        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++) {
        /* 1 < check < a-1 */
        if (!BN_priv_rand_range(check, A3) || !BN_add_word(check, 2))
            goto err;

        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, int safe, prime_t *mods)
{
    int i;
    BN_ULONG delta;
    BN_ULONG maxdelta = BN_MASK2 - primes[NUMPRIMES - 1];

 again:
    /* TODO: Not all primes are private */
    if (!BN_priv_rand(rnd, bits, BN_RAND_TOP_TWO, BN_RAND_BOTTOM_ODD))
        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++) {
        BN_ULONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]);
        if (mod == (BN_ULONG)-1)
            return 0;
        mods[i] = (prime_t) mod;
    }
    delta = 0;
 loop:
    for (i = 1; i < NUMPRIMES; 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)
         */
        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;
    if (BN_num_bits(rnd) != bits)
        goto again;
    bn_check_top(rnd);
    return 1;
}

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;
    BN_ULONG maxdelta = BN_MASK2 - primes[NUMPRIMES - 1];

    BN_CTX_start(ctx);
    if ((t1 = BN_CTX_get(ctx)) == NULL)
        goto err;

    if (maxdelta > BN_MASK2 - BN_get_word(add))
        maxdelta = BN_MASK2 - BN_get_word(add);

 again:
    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, safe ? 3u : 1u))
            goto err;
    } else {
        if (!BN_add(rnd, rnd, rem))
            goto err;
    }

    if (BN_num_bits(rnd) < bits
            || BN_get_word(rnd) < (safe ? 5u : 3u)) {
        if (!BN_add(rnd, rnd, add))
            goto err;
    }

    /* 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)
            goto err;
        mods[i] = (prime_t) mod;
    }
    delta = 0;
 loop:
    for (i = 1; i < NUMPRIMES; 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(rnd);
    return ret;
}
Commit	Line	Data
4f22f405	1	/*
35fd9953	2	* Copyright 1995-2019 The OpenSSL Project Authors. All Rights Reserved.
4f22f405 RS	3	*
	4	* Licensed under the OpenSSL license (the "License"). You may not use
	5	* this file except in compliance with the License. You can obtain a copy
	6	* in the file LICENSE in the source distribution or at
	7	* https://www.openssl.org/source/license.html
bfe30e4d	8	*/
d02b48c6 RE	9
	10	#include <stdio.h>
	11	#include <time.h>
b39fc560	12	#include "internal/cryptlib.h"
b5acbf91	13	#include "bn_local.h"
d02b48c6	14
0f113f3e MC	15	/*
	16	* The quick sieve algorithm approach to weeding out primes is Philip
	17	* Zimmermann's, as implemented in PGP. I have had a read of his comments
	18	* and implemented my own version.
d02b48c6 RE	19	*/
	20	#include "bn_prime.h"
	21
7999c65c	22	static int witness(BIGNUM w, const BIGNUM a, const BIGNUM *a1,
0f113f3e MC	23	const BIGNUM a1_odd, int k, BN_CTX ctx,
0f113f3e MC	24	BN_MONT_CTX *mont);
7eccef21	25	static int probable_prime(BIGNUM rnd, int bits, int safe, prime_t mods);
0032bfea BE	26	static int probable_prime_dh(BIGNUM rnd, int bits, int safe, prime_t mods,
	27	const BIGNUM add, const BIGNUM rem,
	28	BN_CTX *ctx);
eb952088	29
7eccef21 BE	30	#define square(x) ((BN_ULONG)(x) * (BN_ULONG)(x))
7eccef21 BE	31
e9224c71	32	int BN_GENCB_call(BN_GENCB *cb, int a, int b)
0f113f3e MC	33	{
	34	/* No callback means continue */
	35	if (!cb)
	36	return 1;
	37	switch (cb->ver) {
	38	case 1:
	39	/* Deprecated-style callbacks */
	40	if (!cb->cb.cb_1)
	41	return 1;
	42	cb->cb.cb_1(a, b, cb->arg);
	43	return 1;
	44	case 2:
	45	/* New-style callbacks */
	46	return cb->cb.cb_2(a, b, cb);
	47	default:
	48	break;
	49	}
	50	/* Unrecognised callback type */
	51	return 0;
	52	}
e9224c71 GT	53
e9224c71 GT	54	int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe,
0f113f3e MC	55	const BIGNUM add, const BIGNUM rem, BN_GENCB *cb)
	56	{
	57	BIGNUM *t;
	58	int found = 0;
	59	int i, j, c1 = 0;
8e704858 RS	60	BN_CTX *ctx = NULL;
8e704858 RS	61	prime_t *mods = NULL;
0f113f3e MC	62	int checks = BN_prime_checks_for_size(bits);
	63
	64	if (bits < 2) {
	65	/* There are no prime numbers this small. */
	66	BNerr(BN_F_BN_GENERATE_PRIME_EX, BN_R_BITS_TOO_SMALL);
	67	return 0;
9fd44200 BE	68	} else if (add == NULL && safe && bits < 6 && bits != 3) {
	69	/*
	70	* The smallest safe prime (7) is three bits.
	71	* But the following two safe primes with less than 6 bits (11, 23)
	72	* are unreachable for BN_rand with BN_RAND_TOP_TWO.
	73	*/
0f113f3e MC	74	BNerr(BN_F_BN_GENERATE_PRIME_EX, BN_R_BITS_TOO_SMALL);
	75	return 0;
	76	}
	77
d71eb667 MC	78	mods = OPENSSL_zalloc(sizeof(mods) NUMPRIMES);
	79	if (mods == NULL)
	80	goto err;
	81
0f113f3e MC	82	ctx = BN_CTX_new();
	83	if (ctx == NULL)
	84	goto err;
	85	BN_CTX_start(ctx);
	86	t = BN_CTX_get(ctx);
e8e55976	87	if (t == NULL)
0f113f3e MC	88	goto err;
	89	loop:
	90	/* make a random number and set the top and bottom bits */
	91	if (add == NULL) {
7eccef21	92	if (!probable_prime(ret, bits, safe, mods))
0f113f3e MC	93	goto err;
0f113f3e MC	94	} else {
0032bfea BE	95	if (!probable_prime_dh(ret, bits, safe, mods, add, rem, ctx))
0032bfea BE	96	goto err;
0f113f3e	97	}
d70a5627	98
0f113f3e MC	99	if (!BN_GENCB_call(cb, 0, c1++))
	100	/* aborted */
	101	goto err;
	102
	103	if (!safe) {
	104	i = BN_is_prime_fasttest_ex(ret, checks, ctx, 0, cb);
	105	if (i == -1)
	106	goto err;
	107	if (i == 0)
	108	goto loop;
	109	} else {
	110	/*
	111	* for "safe prime" generation, check that (p-1)/2 is prime. Since a
	112	* prime is odd, We just need to divide by 2
	113	*/
	114	if (!BN_rshift1(t, ret))
	115	goto err;
	116
	117	for (i = 0; i < checks; i++) {
	118	j = BN_is_prime_fasttest_ex(ret, 1, ctx, 0, cb);
	119	if (j == -1)
	120	goto err;
	121	if (j == 0)
	122	goto loop;
	123
	124	j = BN_is_prime_fasttest_ex(t, 1, ctx, 0, cb);
	125	if (j == -1)
	126	goto err;
	127	if (j == 0)
	128	goto loop;
	129
	130	if (!BN_GENCB_call(cb, 2, c1 - 1))
	131	goto err;
	132	/* We have a safe prime test pass */
	133	}
	134	}
	135	/* we have a prime :-) */
	136	found = 1;
	137	err:
8e704858	138	OPENSSL_free(mods);
c8a9fa69	139	BN_CTX_end(ctx);
23a1d5e9	140	BN_CTX_free(ctx);
0f113f3e MC	141	bn_check_top(ret);
	142	return found;
	143	}
	144
	145	int BN_is_prime_ex(const BIGNUM a, int checks, BN_CTX ctx_passed,
	146	BN_GENCB *cb)
	147	{
	148	return BN_is_prime_fasttest_ex(a, checks, ctx_passed, 0, cb);
	149	}
e74231ed	150
e9224c71	151	int BN_is_prime_fasttest_ex(const BIGNUM a, int checks, BN_CTX ctx_passed,
0f113f3e MC	152	int do_trial_division, BN_GENCB *cb)
	153	{
	154	int i, j, ret = -1;
	155	int k;
	156	BN_CTX *ctx = NULL;
7d79d13a	157	BIGNUM A1, A1_odd, A3, check; /* taken from ctx */
0f113f3e	158	BN_MONT_CTX *mont = NULL;
0f113f3e	159
7d79d13a SL	160	/* Take care of the really small primes 2 & 3 */
	161	if (BN_is_word(a, 2) \|\| BN_is_word(a, 3))
	162	return 1;
	163
	164	/* Check odd and bigger than 1 */
	165	if (!BN_is_odd(a) \|\| BN_cmp(a, BN_value_one()) <= 0)
0f113f3e MC	166	return 0;
	167
	168	if (checks == BN_prime_checks)
	169	checks = BN_prime_checks_for_size(BN_num_bits(a));
	170
	171	/* first look for small factors */
0f113f3e	172	if (do_trial_division) {
d70a5627 DB	173	for (i = 1; i < NUMPRIMES; i++) {
	174	BN_ULONG mod = BN_mod_word(a, primes[i]);
	175	if (mod == (BN_ULONG)-1)
	176	goto err;
	177	if (mod == 0)
6e64c560	178	return BN_is_word(a, primes[i]);
d70a5627	179	}
0f113f3e MC	180	if (!BN_GENCB_call(cb, 1, -1))
	181	goto err;
	182	}
	183
	184	if (ctx_passed != NULL)
	185	ctx = ctx_passed;
	186	else if ((ctx = BN_CTX_new()) == NULL)
	187	goto err;
	188	BN_CTX_start(ctx);
	189
0f113f3e	190	A1 = BN_CTX_get(ctx);
7d79d13a	191	A3 = BN_CTX_get(ctx);
0f113f3e MC	192	A1_odd = BN_CTX_get(ctx);
	193	check = BN_CTX_get(ctx);
	194	if (check == NULL)
	195	goto err;
	196
8b24f942	197	/* compute A1 := a - 1 */
7d79d13a	198	if (!BN_copy(A1, a) \|\| !BN_sub_word(A1, 1))
0f113f3e	199	goto err;
7d79d13a SL	200	/* compute A3 := a - 3 */
7d79d13a SL	201	if (!BN_copy(A3, a) \|\| !BN_sub_word(A3, 3))
0f113f3e	202	goto err;
0f113f3e MC	203
	204	/* write A1 as A1_odd * 2^k */
	205	k = 1;
	206	while (!BN_is_bit_set(A1, k))
	207	k++;
	208	if (!BN_rshift(A1_odd, A1, k))
	209	goto err;
	210
8b24f942	211	/* Montgomery setup for computations mod a */
0f113f3e MC	212	mont = BN_MONT_CTX_new();
	213	if (mont == NULL)
	214	goto err;
8b24f942	215	if (!BN_MONT_CTX_set(mont, a, ctx))
0f113f3e MC	216	goto err;
	217
	218	for (i = 0; i < checks; i++) {
7d79d13a SL	219	/* 1 < check < a-1 */
7d79d13a SL	220	if (!BN_priv_rand_range(check, A3) \|\| !BN_add_word(check, 2))
0f113f3e	221	goto err;
0f113f3e	222
8b24f942	223	j = witness(check, a, A1, A1_odd, k, ctx, mont);
0f113f3e MC	224	if (j == -1)
	225	goto err;
	226	if (j) {
	227	ret = 0;
	228	goto err;
	229	}
	230	if (!BN_GENCB_call(cb, 1, i))
	231	goto err;
	232	}
	233	ret = 1;
	234	err:
	235	if (ctx != NULL) {
	236	BN_CTX_end(ctx);
	237	if (ctx_passed == NULL)
	238	BN_CTX_free(ctx);
	239	}
23a1d5e9	240	BN_MONT_CTX_free(mont);
0f113f3e	241
26a7d938	242	return ret;
0f113f3e	243	}
a87030a1	244
7999c65c	245	static int witness(BIGNUM w, const BIGNUM a, const BIGNUM *a1,
0f113f3e MC	246	const BIGNUM a1_odd, int k, BN_CTX ctx,
	247	BN_MONT_CTX *mont)
	248	{
	249	if (!BN_mod_exp_mont(w, w, a1_odd, a, ctx, mont)) /* w := w^a1_odd mod a */
	250	return -1;
	251	if (BN_is_one(w))
	252	return 0; /* probably prime */
	253	if (BN_cmp(w, a1) == 0)
	254	return 0; /* w == -1 (mod a), 'a' is probably prime */
	255	while (--k) {
	256	if (!BN_mod_mul(w, w, w, a, ctx)) /* w := w^2 mod a */
	257	return -1;
	258	if (BN_is_one(w))
	259	return 1; /* 'a' is composite, otherwise a previous 'w'
	260	* would have been == -1 (mod 'a') */
	261	if (BN_cmp(w, a1) == 0)
	262	return 0; /* w == -1 (mod a), 'a' is probably prime */
	263	}
	264	/*
	265	* If we get here, 'w' is the (a-1)/2-th power of the original 'w', and
	266	* it is neither -1 nor +1 -- so 'a' cannot be prime
	267	*/
	268	bn_check_top(w);
	269	return 1;
	270	}
d02b48c6	271
7eccef21	272	static int probable_prime(BIGNUM rnd, int bits, int safe, prime_t mods)
0f113f3e MC	273	{
0f113f3e MC	274	int i;
0f113f3e MC	275	BN_ULONG delta;
0f113f3e MC	276	BN_ULONG maxdelta = BN_MASK2 - primes[NUMPRIMES - 1];
0f113f3e MC	277
0f113f3e MC	278	again:
4cffafe9	279	/* TODO: Not all primes are private */
ddc6a5c8	280	if (!BN_priv_rand(rnd, bits, BN_RAND_TOP_TWO, BN_RAND_BOTTOM_ODD))
26a7d938	281	return 0;
7eccef21 BE	282	if (safe && !BN_set_bit(rnd, 1))
7eccef21 BE	283	return 0;
0f113f3e	284	/* we now have a random number 'rnd' to test. */
d70a5627 DB	285	for (i = 1; i < NUMPRIMES; i++) {
	286	BN_ULONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]);
	287	if (mod == (BN_ULONG)-1)
	288	return 0;
	289	mods[i] = (prime_t) mod;
	290	}
0f113f3e MC	291	delta = 0;
0f113f3e MC	292	loop:
7eccef21 BE	293	for (i = 1; i < NUMPRIMES; i++) {
	294	/*
	295	* check that rnd is a prime and also that
	296	* gcd(rnd-1,primes) == 1 (except for 2)
	297	* do the second check only if we are interested in safe primes
	298	* in the case that the candidate prime is a single word then
	299	* we check only the primes up to sqrt(rnd)
50e735f9	300	*/
7eccef21 BE	301	if (bits <= 31 && delta <= 0x7fffffff
	302	&& square(primes[i]) > BN_get_word(rnd) + delta)
	303	break;
	304	if (safe ? (mods[i] + delta) % primes[i] <= 1
	305	: (mods[i] + delta) % primes[i] == 0) {
	306	delta += safe ? 4 : 2;
	307	if (delta > maxdelta)
	308	goto again;
	309	goto loop;
0f113f3e MC	310	}
	311	}
	312	if (!BN_add_word(rnd, delta))
26a7d938	313	return 0;
0f113f3e MC	314	if (BN_num_bits(rnd) != bits)
	315	goto again;
	316	bn_check_top(rnd);
208fb891	317	return 1;
0f113f3e	318	}
d02b48c6	319
0032bfea BE	320	static int probable_prime_dh(BIGNUM rnd, int bits, int safe, prime_t mods,
	321	const BIGNUM add, const BIGNUM rem,
	322	BN_CTX *ctx)
0f113f3e MC	323	{
	324	int i, ret = 0;
	325	BIGNUM *t1;
0032bfea BE	326	BN_ULONG delta;
0032bfea BE	327	BN_ULONG maxdelta = BN_MASK2 - primes[NUMPRIMES - 1];
0f113f3e MC	328
	329	BN_CTX_start(ctx);
	330	if ((t1 = BN_CTX_get(ctx)) == NULL)
	331	goto err;
	332
0032bfea BE	333	if (maxdelta > BN_MASK2 - BN_get_word(add))
	334	maxdelta = BN_MASK2 - BN_get_word(add);
	335
	336	again:
4cffafe9	337	if (!BN_rand(rnd, bits, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ODD))
0f113f3e MC	338	goto err;
	339
	340	/* we need ((rnd-rem) % add) == 0 */
	341
	342	if (!BN_mod(t1, rnd, add, ctx))
	343	goto err;
	344	if (!BN_sub(rnd, rnd, t1))
	345	goto err;
	346	if (rem == NULL) {
0032bfea	347	if (!BN_add_word(rnd, safe ? 3u : 1u))
0f113f3e MC	348	goto err;
	349	} else {
	350	if (!BN_add(rnd, rnd, rem))
	351	goto err;
	352	}
	353
0032bfea BE	354	if (BN_num_bits(rnd) < bits
	355	\|\| BN_get_word(rnd) < (safe ? 5u : 3u)) {
	356	if (!BN_add(rnd, rnd, add))
	357	goto err;
	358	}
0f113f3e	359
0032bfea	360	/* we now have a random number 'rnd' to test. */
0f113f3e	361	for (i = 1; i < NUMPRIMES; i++) {
d70a5627 DB	362	BN_ULONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]);
	363	if (mod == (BN_ULONG)-1)
	364	goto err;
0032bfea	365	mods[i] = (prime_t) mod;
0f113f3e	366	}
0032bfea	367	delta = 0;
0f113f3e MC	368	loop:
0f113f3e MC	369	for (i = 1; i < NUMPRIMES; i++) {
0032bfea BE	370	/* check that rnd is a prime */
	371	if (bits <= 31 && delta <= 0x7fffffff
	372	&& square(primes[i]) > BN_get_word(rnd) + delta)
	373	break;
	374	/* rnd mod p == 1 implies q = (rnd-1)/2 is divisible by p */
	375	if (safe ? (mods[i] + delta) % primes[i] <= 1
	376	: (mods[i] + delta) % primes[i] == 0) {
	377	delta += BN_get_word(add);
	378	if (delta > maxdelta)
	379	goto again;
0f113f3e MC	380	goto loop;
	381	}
	382	}
0032bfea BE	383	if (!BN_add_word(rnd, delta))
0032bfea BE	384	goto err;
0f113f3e MC	385	ret = 1;
	386
	387	err:
	388	BN_CTX_end(ctx);
0032bfea	389	bn_check_top(rnd);
26a7d938	390	return ret;
0f113f3e	391	}