bn_mont.c revision 337982 
1/* crypto/bn/bn_mont.c */
2/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
3 * All rights reserved.
4 *
5 * This package is an SSL implementation written
6 * by Eric Young (eay@cryptsoft.com).
7 * The implementation was written so as to conform with Netscapes SSL.
8 *
9 * This library is free for commercial and non-commercial use as long as
10 * the following conditions are aheared to.  The following conditions
11 * apply to all code found in this distribution, be it the RC4, RSA,
12 * lhash, DES, etc., code; not just the SSL code.  The SSL documentation
13 * included with this distribution is covered by the same copyright terms
14 * except that the holder is Tim Hudson (tjh@cryptsoft.com).
15 *
16 * Copyright remains Eric Young's, and as such any Copyright notices in
17 * the code are not to be removed.
18 * If this package is used in a product, Eric Young should be given attribution
19 * as the author of the parts of the library used.
20 * This can be in the form of a textual message at program startup or
21 * in documentation (online or textual) provided with the package.
22 *
23 * Redistribution and use in source and binary forms, with or without
24 * modification, are permitted provided that the following conditions
25 * are met:
26 * 1. Redistributions of source code must retain the copyright
27 *    notice, this list of conditions and the following disclaimer.
28 * 2. Redistributions in binary form must reproduce the above copyright
29 *    notice, this list of conditions and the following disclaimer in the
30 *    documentation and/or other materials provided with the distribution.
31 * 3. All advertising materials mentioning features or use of this software
32 *    must display the following acknowledgement:
33 *    "This product includes cryptographic software written by
34 *     Eric Young (eay@cryptsoft.com)"
35 *    The word 'cryptographic' can be left out if the rouines from the library
36 *    being used are not cryptographic related :-).
37 * 4. If you include any Windows specific code (or a derivative thereof) from
38 *    the apps directory (application code) you must include an acknowledgement:
39 *    "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
40 *
41 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
42 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
43 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
44 * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
45 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
46 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
47 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
48 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
49 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
50 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
51 * SUCH DAMAGE.
52 *
53 * The licence and distribution terms for any publically available version or
54 * derivative of this code cannot be changed.  i.e. this code cannot simply be
55 * copied and put under another distribution licence
56 * [including the GNU Public Licence.]
57 */
58/* ====================================================================
59 * Copyright (c) 1998-2018 The OpenSSL Project.  All rights reserved.
60 *
61 * Redistribution and use in source and binary forms, with or without
62 * modification, are permitted provided that the following conditions
63 * are met:
64 *
65 * 1. Redistributions of source code must retain the above copyright
66 *    notice, this list of conditions and the following disclaimer.
67 *
68 * 2. Redistributions in binary form must reproduce the above copyright
69 *    notice, this list of conditions and the following disclaimer in
70 *    the documentation and/or other materials provided with the
71 *    distribution.
72 *
73 * 3. All advertising materials mentioning features or use of this
74 *    software must display the following acknowledgment:
75 *    "This product includes software developed by the OpenSSL Project
76 *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
77 *
78 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
79 *    endorse or promote products derived from this software without
80 *    prior written permission. For written permission, please contact
81 *    openssl-core@openssl.org.
82 *
83 * 5. Products derived from this software may not be called "OpenSSL"
84 *    nor may "OpenSSL" appear in their names without prior written
85 *    permission of the OpenSSL Project.
86 *
87 * 6. Redistributions of any form whatsoever must retain the following
88 *    acknowledgment:
89 *    "This product includes software developed by the OpenSSL Project
90 *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
91 *
92 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
93 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
94 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
95 * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR
96 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
97 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
98 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
99 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
100 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
101 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
102 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
103 * OF THE POSSIBILITY OF SUCH DAMAGE.
104 * ====================================================================
105 *
106 * This product includes cryptographic software written by Eric Young
107 * (eay@cryptsoft.com).  This product includes software written by Tim
108 * Hudson (tjh@cryptsoft.com).
109 *
110 */
111
112/*
113 * Details about Montgomery multiplication algorithms can be found at
114 * http://security.ece.orst.edu/publications.html, e.g.
115 * http://security.ece.orst.edu/koc/papers/j37acmon.pdf and
116 * sections 3.8 and 4.2 in http://security.ece.orst.edu/koc/papers/r01rsasw.pdf
117 */
118
119#include <stdio.h>
120#include "cryptlib.h"
121#include "bn_lcl.h"
122
123#define MONT_WORD               /* use the faster word-based algorithm */
124
125#ifdef MONT_WORD
126static int bn_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont);
127#endif
128
129int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
130                          BN_MONT_CTX *mont, BN_CTX *ctx)
131{
132    int ret = bn_mul_mont_fixed_top(r, a, b, mont, ctx);
133
134    bn_correct_top(r);
135    bn_check_top(r);
136
137    return ret;
138}
139
140int bn_mul_mont_fixed_top(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
141                          BN_MONT_CTX *mont, BN_CTX *ctx)
142{
143    BIGNUM *tmp;
144    int ret = 0;
145#if defined(OPENSSL_BN_ASM_MONT) && defined(MONT_WORD)
146    int num = mont->N.top;
147
148    if (num > 1 && a->top == num && b->top == num) {
149        if (bn_wexpand(r, num) == NULL)
150            return (0);
151        if (bn_mul_mont(r->d, a->d, b->d, mont->N.d, mont->n0, num)) {
152            r->neg = a->neg ^ b->neg;
153            r->top = num;
154            r->flags |= BN_FLG_FIXED_TOP;
155            return 1;
156        }
157    }
158#endif
159
160    BN_CTX_start(ctx);
161    tmp = BN_CTX_get(ctx);
162    if (tmp == NULL)
163        goto err;
164
165    bn_check_top(tmp);
166    if (a == b) {
167        if (!BN_sqr(tmp, a, ctx))
168            goto err;
169    } else {
170        if (!BN_mul(tmp, a, b, ctx))
171            goto err;
172    }
173    /* reduce from aRR to aR */
174#ifdef MONT_WORD
175    if (!bn_from_montgomery_word(r, tmp, mont))
176        goto err;
177#else
178    if (!BN_from_montgomery(r, tmp, mont, ctx))
179        goto err;
180#endif
181    ret = 1;
182 err:
183    BN_CTX_end(ctx);
184    return (ret);
185}
186
187#ifdef MONT_WORD
188static int bn_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont)
189{
190    BIGNUM *n;
191    BN_ULONG *ap, *np, *rp, n0, v, carry;
192    int nl, max, i;
193
194    n = &(mont->N);
195    nl = n->top;
196    if (nl == 0) {
197        ret->top = 0;
198        return (1);
199    }
200
201    max = (2 * nl);             /* carry is stored separately */
202    if (bn_wexpand(r, max) == NULL)
203        return (0);
204
205    r->neg ^= n->neg;
206    np = n->d;
207    rp = r->d;
208
209    /* clear the top words of T */
210# if 1
211    for (i = r->top; i < max; i++) /* memset? XXX */
212        rp[i] = 0;
213# else
214    memset(&(rp[r->top]), 0, (max - r->top) * sizeof(BN_ULONG));
215# endif
216
217    r->top = max;
218    r->flags |= BN_FLG_FIXED_TOP;
219    n0 = mont->n0[0];
220
221    /*
222     * Add multiples of |n| to |r| until R = 2^(nl * BN_BITS2) divides it. On
223     * input, we had |r| < |n| * R, so now |r| < 2 * |n| * R. Note that |r|
224     * includes |carry| which is stored separately.
225     */
226    for (carry = 0, i = 0; i < nl; i++, rp++) {
227        v = bn_mul_add_words(rp, np, nl, (rp[0] * n0) & BN_MASK2);
228        v = (v + carry + rp[nl]) & BN_MASK2;
229        carry |= (v != rp[nl]);
230        carry &= (v <= rp[nl]);
231        rp[nl] = v;
232    }
233
234    if (bn_wexpand(ret, nl) == NULL)
235        return (0);
236    ret->top = nl;
237    ret->flags |= BN_FLG_FIXED_TOP;
238    ret->neg = r->neg;
239
240    rp = ret->d;
241
242    /*
243     * Shift |nl| words to divide by R. We have |ap| < 2 * |n|. Note that |ap|
244     * includes |carry| which is stored separately.
245     */
246    ap = &(r->d[nl]);
247
248    carry -= bn_sub_words(rp, ap, np, nl);
249    /*
250     * |carry| is -1 if |ap| - |np| underflowed or zero if it did not. Note
251     * |carry| cannot be 1. That would imply the subtraction did not fit in
252     * |nl| words, and we know at most one subtraction is needed.
253     */
254    for (i = 0; i < nl; i++) {
255        rp[i] = (carry & ap[i]) | (~carry & rp[i]);
256        ap[i] = 0;
257    }
258
259    return (1);
260}
261#endif                          /* MONT_WORD */
262
263int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
264                       BN_CTX *ctx)
265{
266    int retn = 0;
267#ifdef MONT_WORD
268    BIGNUM *t;
269
270    BN_CTX_start(ctx);
271    if ((t = BN_CTX_get(ctx)) && BN_copy(t, a)) {
272        retn = bn_from_montgomery_word(ret, t, mont);
273        bn_correct_top(ret);
274        bn_check_top(ret);
275    }
276    BN_CTX_end(ctx);
277#else                           /* !MONT_WORD */
278    BIGNUM *t1, *t2;
279
280    BN_CTX_start(ctx);
281    t1 = BN_CTX_get(ctx);
282    t2 = BN_CTX_get(ctx);
283    if (t1 == NULL || t2 == NULL)
284        goto err;
285
286    if (!BN_copy(t1, a))
287        goto err;
288    BN_mask_bits(t1, mont->ri);
289
290    if (!BN_mul(t2, t1, &mont->Ni, ctx))
291        goto err;
292    BN_mask_bits(t2, mont->ri);
293
294    if (!BN_mul(t1, t2, &mont->N, ctx))
295        goto err;
296    if (!BN_add(t2, a, t1))
297        goto err;
298    if (!BN_rshift(ret, t2, mont->ri))
299        goto err;
300
301    if (BN_ucmp(ret, &(mont->N)) >= 0) {
302        if (!BN_usub(ret, ret, &(mont->N)))
303            goto err;
304    }
305    retn = 1;
306    bn_check_top(ret);
307 err:
308    BN_CTX_end(ctx);
309#endif                          /* MONT_WORD */
310    return (retn);
311}
312
313int bn_to_mont_fixed_top(BIGNUM *r, const BIGNUM *a, BN_MONT_CTX *mont,
314                         BN_CTX *ctx)
315{
316    return bn_mul_mont_fixed_top(r, a, &(mont->RR), mont, ctx);
317}
318
319BN_MONT_CTX *BN_MONT_CTX_new(void)
320{
321    BN_MONT_CTX *ret;
322
323    if ((ret = (BN_MONT_CTX *)OPENSSL_malloc(sizeof(BN_MONT_CTX))) == NULL)
324        return (NULL);
325
326    BN_MONT_CTX_init(ret);
327    ret->flags = BN_FLG_MALLOCED;
328    return (ret);
329}
330
331void BN_MONT_CTX_init(BN_MONT_CTX *ctx)
332{
333    ctx->ri = 0;
334    BN_init(&(ctx->RR));
335    BN_init(&(ctx->N));
336    BN_init(&(ctx->Ni));
337    ctx->n0[0] = ctx->n0[1] = 0;
338    ctx->flags = 0;
339}
340
341void BN_MONT_CTX_free(BN_MONT_CTX *mont)
342{
343    if (mont == NULL)
344        return;
345
346    BN_clear_free(&(mont->RR));
347    BN_clear_free(&(mont->N));
348    BN_clear_free(&(mont->Ni));
349    if (mont->flags & BN_FLG_MALLOCED)
350        OPENSSL_free(mont);
351}
352
353int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx)
354{
355    int i, ret = 0;
356    BIGNUM *Ri, *R;
357
358    if (BN_is_zero(mod))
359        return 0;
360
361    BN_CTX_start(ctx);
362    if ((Ri = BN_CTX_get(ctx)) == NULL)
363        goto err;
364    R = &(mont->RR);            /* grab RR as a temp */
365    if (!BN_copy(&(mont->N), mod))
366        goto err;               /* Set N */
367    if (BN_get_flags(mod, BN_FLG_CONSTTIME) != 0)
368        BN_set_flags(&(mont->N), BN_FLG_CONSTTIME);
369    mont->N.neg = 0;
370
371#ifdef MONT_WORD
372    {
373        BIGNUM tmod;
374        BN_ULONG buf[2];
375
376        BN_init(&tmod);
377        tmod.d = buf;
378        tmod.dmax = 2;
379        tmod.neg = 0;
380
381        if (BN_get_flags(mod, BN_FLG_CONSTTIME) != 0)
382            BN_set_flags(&tmod, BN_FLG_CONSTTIME);
383
384        mont->ri = (BN_num_bits(mod) + (BN_BITS2 - 1)) / BN_BITS2 * BN_BITS2;
385
386# if defined(OPENSSL_BN_ASM_MONT) && (BN_BITS2<=32)
387        /*
388         * Only certain BN_BITS2<=32 platforms actually make use of n0[1],
389         * and we could use the #else case (with a shorter R value) for the
390         * others.  However, currently only the assembler files do know which
391         * is which.
392         */
393
394        BN_zero(R);
395        if (!(BN_set_bit(R, 2 * BN_BITS2)))
396            goto err;
397
398        tmod.top = 0;
399        if ((buf[0] = mod->d[0]))
400            tmod.top = 1;
401        if ((buf[1] = mod->top > 1 ? mod->d[1] : 0))
402            tmod.top = 2;
403
404        if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL)
405            goto err;
406        if (!BN_lshift(Ri, Ri, 2 * BN_BITS2))
407            goto err;           /* R*Ri */
408        if (!BN_is_zero(Ri)) {
409            if (!BN_sub_word(Ri, 1))
410                goto err;
411        } else {                /* if N mod word size == 1 */
412
413            if (bn_expand(Ri, (int)sizeof(BN_ULONG) * 2) == NULL)
414                goto err;
415            /* Ri-- (mod double word size) */
416            Ri->neg = 0;
417            Ri->d[0] = BN_MASK2;
418            Ri->d[1] = BN_MASK2;
419            Ri->top = 2;
420        }
421        if (!BN_div(Ri, NULL, Ri, &tmod, ctx))
422            goto err;
423        /*
424         * Ni = (R*Ri-1)/N, keep only couple of least significant words:
425         */
426        mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
427        mont->n0[1] = (Ri->top > 1) ? Ri->d[1] : 0;
428# else
429        BN_zero(R);
430        if (!(BN_set_bit(R, BN_BITS2)))
431            goto err;           /* R */
432
433        buf[0] = mod->d[0];     /* tmod = N mod word size */
434        buf[1] = 0;
435        tmod.top = buf[0] != 0 ? 1 : 0;
436        /* Ri = R^-1 mod N */
437        if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL)
438            goto err;
439        if (!BN_lshift(Ri, Ri, BN_BITS2))
440            goto err;           /* R*Ri */
441        if (!BN_is_zero(Ri)) {
442            if (!BN_sub_word(Ri, 1))
443                goto err;
444        } else {                /* if N mod word size == 1 */
445
446            if (!BN_set_word(Ri, BN_MASK2))
447                goto err;       /* Ri-- (mod word size) */
448        }
449        if (!BN_div(Ri, NULL, Ri, &tmod, ctx))
450            goto err;
451        /*
452         * Ni = (R*Ri-1)/N, keep only least significant word:
453         */
454        mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
455        mont->n0[1] = 0;
456# endif
457    }
458#else                           /* !MONT_WORD */
459    {                           /* bignum version */
460        mont->ri = BN_num_bits(&mont->N);
461        BN_zero(R);
462        if (!BN_set_bit(R, mont->ri))
463            goto err;           /* R = 2^ri */
464        /* Ri = R^-1 mod N */
465        if ((BN_mod_inverse(Ri, R, &mont->N, ctx)) == NULL)
466            goto err;
467        if (!BN_lshift(Ri, Ri, mont->ri))
468            goto err;           /* R*Ri */
469        if (!BN_sub_word(Ri, 1))
470            goto err;
471        /*
472         * Ni = (R*Ri-1) / N
473         */
474        if (!BN_div(&(mont->Ni), NULL, Ri, &mont->N, ctx))
475            goto err;
476    }
477#endif
478
479    /* setup RR for conversions */
480    BN_zero(&(mont->RR));
481    if (!BN_set_bit(&(mont->RR), mont->ri * 2))
482        goto err;
483    if (!BN_mod(&(mont->RR), &(mont->RR), &(mont->N), ctx))
484        goto err;
485
486    for (i = mont->RR.top, ret = mont->N.top; i < ret; i++)
487        mont->RR.d[i] = 0;
488    mont->RR.top = ret;
489    mont->RR.flags |= BN_FLG_FIXED_TOP;
490
491    ret = 1;
492 err:
493    BN_CTX_end(ctx);
494    return ret;
495}
496
497BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from)
498{
499    if (to == from)
500        return (to);
501
502    if (!BN_copy(&(to->RR), &(from->RR)))
503        return NULL;
504    if (!BN_copy(&(to->N), &(from->N)))
505        return NULL;
506    if (!BN_copy(&(to->Ni), &(from->Ni)))
507        return NULL;
508    to->ri = from->ri;
509    to->n0[0] = from->n0[0];
510    to->n0[1] = from->n0[1];
511    return (to);
512}
513
514BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock,
515                                    const BIGNUM *mod, BN_CTX *ctx)
516{
517    BN_MONT_CTX *ret;
518
519    CRYPTO_r_lock(lock);
520    ret = *pmont;
521    CRYPTO_r_unlock(lock);
522    if (ret)
523        return ret;
524
525    /*
526     * We don't want to serialise globally while doing our lazy-init math in
527     * BN_MONT_CTX_set. That punishes threads that are doing independent
528     * things. Instead, punish the case where more than one thread tries to
529     * lazy-init the same 'pmont', by having each do the lazy-init math work
530     * independently and only use the one from the thread that wins the race
531     * (the losers throw away the work they've done).
532     */
533    ret = BN_MONT_CTX_new();
534    if (!ret)
535        return NULL;
536    if (!BN_MONT_CTX_set(ret, mod, ctx)) {
537        BN_MONT_CTX_free(ret);
538        return NULL;
539    }
540
541    /* The locked compare-and-set, after the local work is done. */
542    CRYPTO_w_lock(lock);
543    if (*pmont) {
544        BN_MONT_CTX_free(ret);
545        ret = *pmont;
546    } else
547        *pmont = ret;
548    CRYPTO_w_unlock(lock);
549    return ret;
550}
551