aboutsummaryrefslogtreecommitdiffstats
path: root/crypto/bn/bn_prime.c
blob: d0cf3779fa50d8fc7a1079002f82925edaf1ba22 (plain) (blame)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
/*
 * Copyright 1995-2020 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;
}