Coverage Report

Created: 2024-11-21 06:47

/src/openssl/crypto/bn/bn_mont.c
Line
Count
Source (jump to first uncovered line)
1
/*
2
 * Copyright 1995-2024 The OpenSSL Project Authors. All Rights Reserved.
3
 *
4
 * Licensed under the Apache License 2.0 (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
8
 */
9
10
/*
11
 * Details about Montgomery multiplication algorithms can be found at
12
 * http://security.ece.orst.edu/publications.html, e.g.
13
 * http://security.ece.orst.edu/koc/papers/j37acmon.pdf and
14
 * sections 3.8 and 4.2 in http://security.ece.orst.edu/koc/papers/r01rsasw.pdf
15
 */
16
17
#include "internal/cryptlib.h"
18
#include "bn_local.h"
19
20
#define MONT_WORD               /* use the faster word-based algorithm */
21
22
#ifdef MONT_WORD
23
static int bn_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont);
24
#endif
25
26
int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
27
                          BN_MONT_CTX *mont, BN_CTX *ctx)
28
2.34M
{
29
2.34M
    int ret = bn_mul_mont_fixed_top(r, a, b, mont, ctx);
30
31
2.34M
    bn_correct_top(r);
32
2.34M
    bn_check_top(r);
33
34
2.34M
    return ret;
35
2.34M
}
36
37
int bn_mul_mont_fixed_top(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
38
                          BN_MONT_CTX *mont, BN_CTX *ctx)
39
68.6M
{
40
68.6M
    BIGNUM *tmp;
41
68.6M
    int ret = 0;
42
68.6M
    int num = mont->N.top;
43
44
68.6M
#if defined(OPENSSL_BN_ASM_MONT) && defined(MONT_WORD)
45
68.6M
    if (num > 1 && num <= BN_SOFT_LIMIT && a->top == num && b->top == num) {
46
67.1M
        if (bn_wexpand(r, num) == NULL)
47
0
            return 0;
48
67.1M
        if (bn_mul_mont(r->d, a->d, b->d, mont->N.d, mont->n0, num)) {
49
67.1M
            r->neg = a->neg ^ b->neg;
50
67.1M
            r->top = num;
51
67.1M
            r->flags |= BN_FLG_FIXED_TOP;
52
67.1M
            return 1;
53
67.1M
        }
54
67.1M
    }
55
1.49M
#endif
56
57
1.49M
    if ((a->top + b->top) > 2 * num)
58
0
        return 0;
59
60
1.49M
    BN_CTX_start(ctx);
61
1.49M
    tmp = BN_CTX_get(ctx);
62
1.49M
    if (tmp == NULL)
63
0
        goto err;
64
65
1.49M
    bn_check_top(tmp);
66
1.49M
    if (a == b) {
67
1.12M
        if (!bn_sqr_fixed_top(tmp, a, ctx))
68
0
            goto err;
69
1.12M
    } else {
70
366k
        if (!bn_mul_fixed_top(tmp, a, b, ctx))
71
0
            goto err;
72
366k
    }
73
    /* reduce from aRR to aR */
74
1.49M
#ifdef MONT_WORD
75
1.49M
    if (!bn_from_montgomery_word(r, tmp, mont))
76
0
        goto err;
77
#else
78
    if (!BN_from_montgomery(r, tmp, mont, ctx))
79
        goto err;
80
#endif
81
1.49M
    ret = 1;
82
1.49M
 err:
83
1.49M
    BN_CTX_end(ctx);
84
1.49M
    return ret;
85
1.49M
}
86
87
#ifdef MONT_WORD
88
static int bn_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont)
89
1.55M
{
90
1.55M
    BIGNUM *n;
91
1.55M
    BN_ULONG *ap, *np, *rp, n0, v, carry;
92
1.55M
    int nl, max, i;
93
1.55M
    unsigned int rtop;
94
95
1.55M
    n = &(mont->N);
96
1.55M
    nl = n->top;
97
1.55M
    if (nl == 0) {
98
0
        ret->top = 0;
99
0
        return 1;
100
0
    }
101
102
1.55M
    max = (2 * nl);             /* carry is stored separately */
103
1.55M
    if (bn_wexpand(r, max) == NULL)
104
0
        return 0;
105
106
1.55M
    r->neg ^= n->neg;
107
1.55M
    np = n->d;
108
1.55M
    rp = r->d;
109
110
    /* clear the top words of T */
111
21.2M
    for (rtop = r->top, i = 0; i < max; i++) {
112
19.7M
        v = (BN_ULONG)0 - ((i - rtop) >> (8 * sizeof(rtop) - 1));
113
19.7M
        rp[i] &= v;
114
19.7M
    }
115
116
1.55M
    r->top = max;
117
1.55M
    r->flags |= BN_FLG_FIXED_TOP;
118
1.55M
    n0 = mont->n0[0];
119
120
    /*
121
     * Add multiples of |n| to |r| until R = 2^(nl * BN_BITS2) divides it. On
122
     * input, we had |r| < |n| * R, so now |r| < 2 * |n| * R. Note that |r|
123
     * includes |carry| which is stored separately.
124
     */
125
11.4M
    for (carry = 0, i = 0; i < nl; i++, rp++) {
126
9.85M
        v = bn_mul_add_words(rp, np, nl, (rp[0] * n0) & BN_MASK2);
127
9.85M
        v = (v + carry + rp[nl]) & BN_MASK2;
128
9.85M
        carry |= (v != rp[nl]);
129
9.85M
        carry &= (v <= rp[nl]);
130
9.85M
        rp[nl] = v;
131
9.85M
    }
132
133
1.55M
    if (bn_wexpand(ret, nl) == NULL)
134
0
        return 0;
135
1.55M
    ret->top = nl;
136
1.55M
    ret->flags |= BN_FLG_FIXED_TOP;
137
1.55M
    ret->neg = r->neg;
138
139
1.55M
    rp = ret->d;
140
141
    /*
142
     * Shift |nl| words to divide by R. We have |ap| < 2 * |n|. Note that |ap|
143
     * includes |carry| which is stored separately.
144
     */
145
1.55M
    ap = &(r->d[nl]);
146
147
1.55M
    carry -= bn_sub_words(rp, ap, np, nl);
148
    /*
149
     * |carry| is -1 if |ap| - |np| underflowed or zero if it did not. Note
150
     * |carry| cannot be 1. That would imply the subtraction did not fit in
151
     * |nl| words, and we know at most one subtraction is needed.
152
     */
153
11.4M
    for (i = 0; i < nl; i++) {
154
9.85M
        rp[i] = (carry & ap[i]) | (~carry & rp[i]);
155
9.85M
        ap[i] = 0;
156
9.85M
    }
157
158
1.55M
    return 1;
159
1.55M
}
160
#endif                          /* MONT_WORD */
161
162
int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
163
                       BN_CTX *ctx)
164
61.1k
{
165
61.1k
    int retn;
166
167
61.1k
    retn = bn_from_mont_fixed_top(ret, a, mont, ctx);
168
61.1k
    bn_correct_top(ret);
169
61.1k
    bn_check_top(ret);
170
171
61.1k
    return retn;
172
61.1k
}
173
174
int bn_from_mont_fixed_top(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
175
                           BN_CTX *ctx)
176
61.1k
{
177
61.1k
    int retn = 0;
178
61.1k
#ifdef MONT_WORD
179
61.1k
    BIGNUM *t;
180
181
61.1k
    BN_CTX_start(ctx);
182
61.1k
    if ((t = BN_CTX_get(ctx)) && BN_copy(t, a)) {
183
61.1k
        retn = bn_from_montgomery_word(ret, t, mont);
184
61.1k
    }
185
61.1k
    BN_CTX_end(ctx);
186
#else                           /* !MONT_WORD */
187
    BIGNUM *t1, *t2;
188
189
    BN_CTX_start(ctx);
190
    t1 = BN_CTX_get(ctx);
191
    t2 = BN_CTX_get(ctx);
192
    if (t2 == NULL)
193
        goto err;
194
195
    if (!BN_copy(t1, a))
196
        goto err;
197
    BN_mask_bits(t1, mont->ri);
198
199
    if (!BN_mul(t2, t1, &mont->Ni, ctx))
200
        goto err;
201
    BN_mask_bits(t2, mont->ri);
202
203
    if (!BN_mul(t1, t2, &mont->N, ctx))
204
        goto err;
205
    if (!BN_add(t2, a, t1))
206
        goto err;
207
    if (!BN_rshift(ret, t2, mont->ri))
208
        goto err;
209
210
    if (BN_ucmp(ret, &(mont->N)) >= 0) {
211
        if (!BN_usub(ret, ret, &(mont->N)))
212
            goto err;
213
    }
214
    retn = 1;
215
    bn_check_top(ret);
216
 err:
217
    BN_CTX_end(ctx);
218
#endif                          /* MONT_WORD */
219
61.1k
    return retn;
220
61.1k
}
221
222
int bn_to_mont_fixed_top(BIGNUM *r, const BIGNUM *a, BN_MONT_CTX *mont,
223
                         BN_CTX *ctx)
224
108k
{
225
108k
    return bn_mul_mont_fixed_top(r, a, &(mont->RR), mont, ctx);
226
108k
}
227
228
BN_MONT_CTX *BN_MONT_CTX_new(void)
229
15.9k
{
230
15.9k
    BN_MONT_CTX *ret;
231
232
15.9k
    if ((ret = OPENSSL_malloc(sizeof(*ret))) == NULL)
233
0
        return NULL;
234
235
15.9k
    BN_MONT_CTX_init(ret);
236
15.9k
    ret->flags = BN_FLG_MALLOCED;
237
15.9k
    return ret;
238
15.9k
}
239
240
void BN_MONT_CTX_init(BN_MONT_CTX *ctx)
241
10.6k
{
242
10.6k
    ctx->ri = 0;
243
10.6k
    bn_init(&ctx->RR);
244
10.6k
    bn_init(&ctx->N);
245
10.6k
    bn_init(&ctx->Ni);
246
10.6k
    ctx->n0[0] = ctx->n0[1] = 0;
247
10.6k
    ctx->flags = 0;
248
10.6k
}
249
250
void BN_MONT_CTX_free(BN_MONT_CTX *mont)
251
11.6k
{
252
11.6k
    if (mont == NULL)
253
1.01k
        return;
254
10.6k
    BN_clear_free(&mont->RR);
255
10.6k
    BN_clear_free(&mont->N);
256
10.6k
    BN_clear_free(&mont->Ni);
257
10.6k
    if (mont->flags & BN_FLG_MALLOCED)
258
10.6k
        OPENSSL_free(mont);
259
10.6k
}
260
261
int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx)
262
10.6k
{
263
10.6k
    int i, ret = 0;
264
10.6k
    BIGNUM *Ri, *R;
265
266
10.6k
    if (BN_is_zero(mod))
267
57
        return 0;
268
269
10.5k
    BN_CTX_start(ctx);
270
10.5k
    if ((Ri = BN_CTX_get(ctx)) == NULL)
271
0
        goto err;
272
10.5k
    R = &(mont->RR);            /* grab RR as a temp */
273
10.5k
    if (!BN_copy(&(mont->N), mod))
274
0
        goto err;               /* Set N */
275
10.5k
    if (BN_get_flags(mod, BN_FLG_CONSTTIME) != 0)
276
835
        BN_set_flags(&(mont->N), BN_FLG_CONSTTIME);
277
10.5k
    mont->N.neg = 0;
278
279
10.5k
#ifdef MONT_WORD
280
10.5k
    {
281
10.5k
        BIGNUM tmod;
282
10.5k
        BN_ULONG buf[2];
283
284
10.5k
        bn_init(&tmod);
285
10.5k
        tmod.d = buf;
286
10.5k
        tmod.dmax = 2;
287
10.5k
        tmod.neg = 0;
288
289
10.5k
        if (BN_get_flags(mod, BN_FLG_CONSTTIME) != 0)
290
835
            BN_set_flags(&tmod, BN_FLG_CONSTTIME);
291
292
10.5k
        mont->ri = (BN_num_bits(mod) + (BN_BITS2 - 1)) / BN_BITS2 * BN_BITS2;
293
294
# if defined(OPENSSL_BN_ASM_MONT) && (BN_BITS2<=32)
295
        /*
296
         * Only certain BN_BITS2<=32 platforms actually make use of n0[1],
297
         * and we could use the #else case (with a shorter R value) for the
298
         * others.  However, currently only the assembler files do know which
299
         * is which.
300
         */
301
302
        BN_zero(R);
303
        if (!(BN_set_bit(R, 2 * BN_BITS2)))
304
            goto err;
305
306
        tmod.top = 0;
307
        if ((buf[0] = mod->d[0]))
308
            tmod.top = 1;
309
        if ((buf[1] = mod->top > 1 ? mod->d[1] : 0))
310
            tmod.top = 2;
311
312
        if (BN_is_one(&tmod))
313
            BN_zero(Ri);
314
        else if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL)
315
            goto err;
316
        if (!BN_lshift(Ri, Ri, 2 * BN_BITS2))
317
            goto err;           /* R*Ri */
318
        if (!BN_is_zero(Ri)) {
319
            if (!BN_sub_word(Ri, 1))
320
                goto err;
321
        } else {                /* if N mod word size == 1 */
322
323
            if (bn_expand(Ri, (int)sizeof(BN_ULONG) * 2) == NULL)
324
                goto err;
325
            /* Ri-- (mod double word size) */
326
            Ri->neg = 0;
327
            Ri->d[0] = BN_MASK2;
328
            Ri->d[1] = BN_MASK2;
329
            Ri->top = 2;
330
        }
331
        if (!BN_div(Ri, NULL, Ri, &tmod, ctx))
332
            goto err;
333
        /*
334
         * Ni = (R*Ri-1)/N, keep only couple of least significant words:
335
         */
336
        mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
337
        mont->n0[1] = (Ri->top > 1) ? Ri->d[1] : 0;
338
# else
339
10.5k
        BN_zero(R);
340
10.5k
        if (!(BN_set_bit(R, BN_BITS2)))
341
0
            goto err;           /* R */
342
343
10.5k
        buf[0] = mod->d[0];     /* tmod = N mod word size */
344
10.5k
        buf[1] = 0;
345
10.5k
        tmod.top = buf[0] != 0 ? 1 : 0;
346
        /* Ri = R^-1 mod N */
347
10.5k
        if (BN_is_one(&tmod))
348
283
            BN_zero(Ri);
349
10.2k
        else if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL)
350
2.18k
            goto err;
351
8.37k
        if (!BN_lshift(Ri, Ri, BN_BITS2))
352
0
            goto err;           /* R*Ri */
353
8.37k
        if (!BN_is_zero(Ri)) {
354
8.08k
            if (!BN_sub_word(Ri, 1))
355
0
                goto err;
356
8.08k
        } else {                /* if N mod word size == 1 */
357
358
283
            if (!BN_set_word(Ri, BN_MASK2))
359
0
                goto err;       /* Ri-- (mod word size) */
360
283
        }
361
8.37k
        if (!BN_div(Ri, NULL, Ri, &tmod, ctx))
362
0
            goto err;
363
        /*
364
         * Ni = (R*Ri-1)/N, keep only least significant word:
365
         */
366
8.37k
        mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
367
8.37k
        mont->n0[1] = 0;
368
8.37k
# endif
369
8.37k
    }
370
#else                           /* !MONT_WORD */
371
    {                           /* bignum version */
372
        mont->ri = BN_num_bits(&mont->N);
373
        BN_zero(R);
374
        if (!BN_set_bit(R, mont->ri))
375
            goto err;           /* R = 2^ri */
376
        /* Ri = R^-1 mod N */
377
        if ((BN_mod_inverse(Ri, R, &mont->N, ctx)) == NULL)
378
            goto err;
379
        if (!BN_lshift(Ri, Ri, mont->ri))
380
            goto err;           /* R*Ri */
381
        if (!BN_sub_word(Ri, 1))
382
            goto err;
383
        /*
384
         * Ni = (R*Ri-1) / N
385
         */
386
        if (!BN_div(&(mont->Ni), NULL, Ri, &mont->N, ctx))
387
            goto err;
388
    }
389
#endif
390
391
    /* setup RR for conversions */
392
8.37k
    BN_zero(&(mont->RR));
393
8.37k
    if (!BN_set_bit(&(mont->RR), mont->ri * 2))
394
0
        goto err;
395
8.37k
    if (!BN_mod(&(mont->RR), &(mont->RR), &(mont->N), ctx))
396
0
        goto err;
397
398
9.40k
    for (i = mont->RR.top, ret = mont->N.top; i < ret; i++)
399
1.02k
        mont->RR.d[i] = 0;
400
8.37k
    mont->RR.top = ret;
401
8.37k
    mont->RR.flags |= BN_FLG_FIXED_TOP;
402
403
8.37k
    ret = 1;
404
10.5k
 err:
405
10.5k
    BN_CTX_end(ctx);
406
10.5k
    return ret;
407
8.37k
}
408
409
BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from)
410
0
{
411
0
    if (to == from)
412
0
        return to;
413
414
0
    if (!BN_copy(&(to->RR), &(from->RR)))
415
0
        return NULL;
416
0
    if (!BN_copy(&(to->N), &(from->N)))
417
0
        return NULL;
418
0
    if (!BN_copy(&(to->Ni), &(from->Ni)))
419
0
        return NULL;
420
0
    to->ri = from->ri;
421
0
    to->n0[0] = from->n0[0];
422
0
    to->n0[1] = from->n0[1];
423
0
    return to;
424
0
}
425
426
BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, CRYPTO_RWLOCK *lock,
427
                                    const BIGNUM *mod, BN_CTX *ctx)
428
161
{
429
161
    BN_MONT_CTX *ret;
430
431
161
    if (!CRYPTO_THREAD_read_lock(lock))
432
0
        return NULL;
433
161
    ret = *pmont;
434
161
    CRYPTO_THREAD_unlock(lock);
435
161
    if (ret)
436
0
        return ret;
437
438
    /*
439
     * We don't want to serialize globally while doing our lazy-init math in
440
     * BN_MONT_CTX_set. That punishes threads that are doing independent
441
     * things. Instead, punish the case where more than one thread tries to
442
     * lazy-init the same 'pmont', by having each do the lazy-init math work
443
     * independently and only use the one from the thread that wins the race
444
     * (the losers throw away the work they've done).
445
     */
446
161
    ret = BN_MONT_CTX_new();
447
161
    if (ret == NULL)
448
0
        return NULL;
449
161
    if (!BN_MONT_CTX_set(ret, mod, ctx)) {
450
88
        BN_MONT_CTX_free(ret);
451
88
        return NULL;
452
88
    }
453
454
    /* The locked compare-and-set, after the local work is done. */
455
73
    if (!CRYPTO_THREAD_write_lock(lock)) {
456
0
        BN_MONT_CTX_free(ret);
457
0
        return NULL;
458
0
    }
459
460
73
    if (*pmont) {
461
0
        BN_MONT_CTX_free(ret);
462
0
        ret = *pmont;
463
0
    } else
464
73
        *pmont = ret;
465
73
    CRYPTO_THREAD_unlock(lock);
466
73
    return ret;
467
73
}
468
469
int ossl_bn_mont_ctx_set(BN_MONT_CTX *ctx, const BIGNUM *modulus, int ri, const unsigned char *rr,
470
                         size_t rrlen, uint32_t nlo, uint32_t nhi)
471
0
{
472
0
    if (BN_copy(&ctx->N, modulus) == NULL)
473
0
        return 0;
474
0
    if (BN_bin2bn(rr, rrlen, &ctx->RR) == NULL)
475
0
        return 0;
476
0
    ctx->ri = ri;
477
#if (BN_BITS2 <= 32) && defined(OPENSSL_BN_ASM_MONT)
478
    ctx->n0[0] = nlo;
479
    ctx->n0[1] = nhi;
480
#elif BN_BITS2 <= 32
481
    ctx->n0[0] = nlo;
482
    ctx->n0[1] = 0;
483
#else
484
0
    ctx->n0[0] = ((BN_ULONG)nhi << 32)| nlo;
485
0
    ctx->n0[1] = 0;
486
0
#endif
487
488
0
    return 1;
489
0
}
490
491
int ossl_bn_mont_ctx_eq(const BN_MONT_CTX *m1, const BN_MONT_CTX *m2)
492
0
{
493
0
    if (m1->ri != m2->ri)
494
0
        return 0;
495
0
    if (BN_cmp(&m1->RR, &m2->RR) != 0)
496
0
        return 0;
497
0
    if (m1->flags != m2->flags)
498
0
        return 0;
499
0
#ifdef MONT_WORD
500
0
    if (m1->n0[0] != m2->n0[0])
501
0
        return 0;
502
0
    if (m1->n0[1] != m2->n0[1])
503
0
        return 0;
504
#else
505
    if (BN_cmp(&m1->Ni, &m2->Ni) != 0)
506
        return 0;
507
#endif
508
0
    return 1;
509
0
}