bn_mont.c revision 331638 
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    BIGNUM *tmp;
133    int ret = 0;
134#if defined(OPENSSL_BN_ASM_MONT) && defined(MONT_WORD)
135    int num = mont->N.top;
136
137    if (num > 1 && a->top == num && b->top == num) {
138        if (bn_wexpand(r, num) == NULL)
139            return (0);
140        if (bn_mul_mont(r->d, a->d, b->d, mont->N.d, mont->n0, num)) {
141            r->neg = a->neg ^ b->neg;
142            r->top = num;
143            bn_correct_top(r);
144            return (1);
145        }
146    }
147#endif
148
149    BN_CTX_start(ctx);
150    tmp = BN_CTX_get(ctx);
151    if (tmp == NULL)
152        goto err;
153
154    bn_check_top(tmp);
155    if (a == b) {
156        if (!BN_sqr(tmp, a, ctx))
157            goto err;
158    } else {
159        if (!BN_mul(tmp, a, b, ctx))
160            goto err;
161    }
162    /* reduce from aRR to aR */
163#ifdef MONT_WORD
164    if (!BN_from_montgomery_word(r, tmp, mont))
165        goto err;
166#else
167    if (!BN_from_montgomery(r, tmp, mont, ctx))
168        goto err;
169#endif
170    bn_check_top(r);
171    ret = 1;
172 err:
173    BN_CTX_end(ctx);
174    return (ret);
175}
176
177#ifdef MONT_WORD
178static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont)
179{
180    BIGNUM *n;
181    BN_ULONG *ap, *np, *rp, n0, v, carry;
182    int nl, max, i;
183
184    n = &(mont->N);
185    nl = n->top;
186    if (nl == 0) {
187        ret->top = 0;
188        return (1);
189    }
190
191    max = (2 * nl);             /* carry is stored separately */
192    if (bn_wexpand(r, max) == NULL)
193        return (0);
194
195    r->neg ^= n->neg;
196    np = n->d;
197    rp = r->d;
198
199    /* clear the top words of T */
200# if 1
201    for (i = r->top; i < max; i++) /* memset? XXX */
202        rp[i] = 0;
203# else
204    memset(&(rp[r->top]), 0, (max - r->top) * sizeof(BN_ULONG));
205# endif
206
207    r->top = max;
208    n0 = mont->n0[0];
209
210    /*
211     * Add multiples of |n| to |r| until R = 2^(nl * BN_BITS2) divides it. On
212     * input, we had |r| < |n| * R, so now |r| < 2 * |n| * R. Note that |r|
213     * includes |carry| which is stored separately.
214     */
215    for (carry = 0, i = 0; i < nl; i++, rp++) {
216        v = bn_mul_add_words(rp, np, nl, (rp[0] * n0) & BN_MASK2);
217        v = (v + carry + rp[nl]) & BN_MASK2;
218        carry |= (v != rp[nl]);
219        carry &= (v <= rp[nl]);
220        rp[nl] = v;
221    }
222
223    if (bn_wexpand(ret, nl) == NULL)
224        return (0);
225    ret->top = nl;
226    ret->neg = r->neg;
227
228    rp = ret->d;
229
230    /*
231     * Shift |nl| words to divide by R. We have |ap| < 2 * |n|. Note that |ap|
232     * includes |carry| which is stored separately.
233     */
234    ap = &(r->d[nl]);
235
236    /*
237     * |v| is one if |ap| - |np| underflowed or zero if it did not. Note |v|
238     * cannot be -1. That would imply the subtraction did not fit in |nl| words,
239     * and we know at most one subtraction is needed.
240     */
241    v = bn_sub_words(rp, ap, np, nl) - carry;
242    v = 0 - v;
243    for (i = 0; i < nl; i++) {
244        rp[i] = (v & ap[i]) | (~v & rp[i]);
245        ap[i] = 0;
246    }
247    bn_correct_top(r);
248    bn_correct_top(ret);
249    bn_check_top(ret);
250
251    return (1);
252}
253#endif                          /* MONT_WORD */
254
255int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
256                       BN_CTX *ctx)
257{
258    int retn = 0;
259#ifdef MONT_WORD
260    BIGNUM *t;
261
262    BN_CTX_start(ctx);
263    if ((t = BN_CTX_get(ctx)) && BN_copy(t, a))
264        retn = BN_from_montgomery_word(ret, t, mont);
265    BN_CTX_end(ctx);
266#else                           /* !MONT_WORD */
267    BIGNUM *t1, *t2;
268
269    BN_CTX_start(ctx);
270    t1 = BN_CTX_get(ctx);
271    t2 = BN_CTX_get(ctx);
272    if (t1 == NULL || t2 == NULL)
273        goto err;
274
275    if (!BN_copy(t1, a))
276        goto err;
277    BN_mask_bits(t1, mont->ri);
278
279    if (!BN_mul(t2, t1, &mont->Ni, ctx))
280        goto err;
281    BN_mask_bits(t2, mont->ri);
282
283    if (!BN_mul(t1, t2, &mont->N, ctx))
284        goto err;
285    if (!BN_add(t2, a, t1))
286        goto err;
287    if (!BN_rshift(ret, t2, mont->ri))
288        goto err;
289
290    if (BN_ucmp(ret, &(mont->N)) >= 0) {
291        if (!BN_usub(ret, ret, &(mont->N)))
292            goto err;
293    }
294    retn = 1;
295    bn_check_top(ret);
296 err:
297    BN_CTX_end(ctx);
298#endif                          /* MONT_WORD */
299    return (retn);
300}
301
302BN_MONT_CTX *BN_MONT_CTX_new(void)
303{
304    BN_MONT_CTX *ret;
305
306    if ((ret = (BN_MONT_CTX *)OPENSSL_malloc(sizeof(BN_MONT_CTX))) == NULL)
307        return (NULL);
308
309    BN_MONT_CTX_init(ret);
310    ret->flags = BN_FLG_MALLOCED;
311    return (ret);
312}
313
314void BN_MONT_CTX_init(BN_MONT_CTX *ctx)
315{
316    ctx->ri = 0;
317    BN_init(&(ctx->RR));
318    BN_init(&(ctx->N));
319    BN_init(&(ctx->Ni));
320    ctx->n0[0] = ctx->n0[1] = 0;
321    ctx->flags = 0;
322}
323
324void BN_MONT_CTX_free(BN_MONT_CTX *mont)
325{
326    if (mont == NULL)
327        return;
328
329    BN_clear_free(&(mont->RR));
330    BN_clear_free(&(mont->N));
331    BN_clear_free(&(mont->Ni));
332    if (mont->flags & BN_FLG_MALLOCED)
333        OPENSSL_free(mont);
334}
335
336int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx)
337{
338    int ret = 0;
339    BIGNUM *Ri, *R;
340
341    if (BN_is_zero(mod))
342        return 0;
343
344    BN_CTX_start(ctx);
345    if ((Ri = BN_CTX_get(ctx)) == NULL)
346        goto err;
347    R = &(mont->RR);            /* grab RR as a temp */
348    if (!BN_copy(&(mont->N), mod))
349        goto err;               /* Set N */
350    if (BN_get_flags(mod, BN_FLG_CONSTTIME) != 0)
351        BN_set_flags(&(mont->N), BN_FLG_CONSTTIME);
352    mont->N.neg = 0;
353
354#ifdef MONT_WORD
355    {
356        BIGNUM tmod;
357        BN_ULONG buf[2];
358
359        BN_init(&tmod);
360        tmod.d = buf;
361        tmod.dmax = 2;
362        tmod.neg = 0;
363
364        if (BN_get_flags(mod, BN_FLG_CONSTTIME) != 0)
365            BN_set_flags(&tmod, BN_FLG_CONSTTIME);
366
367        mont->ri = (BN_num_bits(mod) + (BN_BITS2 - 1)) / BN_BITS2 * BN_BITS2;
368
369# if defined(OPENSSL_BN_ASM_MONT) && (BN_BITS2<=32)
370        /*
371         * Only certain BN_BITS2<=32 platforms actually make use of n0[1],
372         * and we could use the #else case (with a shorter R value) for the
373         * others.  However, currently only the assembler files do know which
374         * is which.
375         */
376
377        BN_zero(R);
378        if (!(BN_set_bit(R, 2 * BN_BITS2)))
379            goto err;
380
381        tmod.top = 0;
382        if ((buf[0] = mod->d[0]))
383            tmod.top = 1;
384        if ((buf[1] = mod->top > 1 ? mod->d[1] : 0))
385            tmod.top = 2;
386
387        if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL)
388            goto err;
389        if (!BN_lshift(Ri, Ri, 2 * BN_BITS2))
390            goto err;           /* R*Ri */
391        if (!BN_is_zero(Ri)) {
392            if (!BN_sub_word(Ri, 1))
393                goto err;
394        } else {                /* if N mod word size == 1 */
395
396            if (bn_expand(Ri, (int)sizeof(BN_ULONG) * 2) == NULL)
397                goto err;
398            /* Ri-- (mod double word size) */
399            Ri->neg = 0;
400            Ri->d[0] = BN_MASK2;
401            Ri->d[1] = BN_MASK2;
402            Ri->top = 2;
403        }
404        if (!BN_div(Ri, NULL, Ri, &tmod, ctx))
405            goto err;
406        /*
407         * Ni = (R*Ri-1)/N, keep only couple of least significant words:
408         */
409        mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
410        mont->n0[1] = (Ri->top > 1) ? Ri->d[1] : 0;
411# else
412        BN_zero(R);
413        if (!(BN_set_bit(R, BN_BITS2)))
414            goto err;           /* R */
415
416        buf[0] = mod->d[0];     /* tmod = N mod word size */
417        buf[1] = 0;
418        tmod.top = buf[0] != 0 ? 1 : 0;
419        /* Ri = R^-1 mod N */
420        if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL)
421            goto err;
422        if (!BN_lshift(Ri, Ri, BN_BITS2))
423            goto err;           /* R*Ri */
424        if (!BN_is_zero(Ri)) {
425            if (!BN_sub_word(Ri, 1))
426                goto err;
427        } else {                /* if N mod word size == 1 */
428
429            if (!BN_set_word(Ri, BN_MASK2))
430                goto err;       /* Ri-- (mod word size) */
431        }
432        if (!BN_div(Ri, NULL, Ri, &tmod, ctx))
433            goto err;
434        /*
435         * Ni = (R*Ri-1)/N, keep only least significant word:
436         */
437        mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
438        mont->n0[1] = 0;
439# endif
440    }
441#else                           /* !MONT_WORD */
442    {                           /* bignum version */
443        mont->ri = BN_num_bits(&mont->N);
444        BN_zero(R);
445        if (!BN_set_bit(R, mont->ri))
446            goto err;           /* R = 2^ri */
447        /* Ri = R^-1 mod N */
448        if ((BN_mod_inverse(Ri, R, &mont->N, ctx)) == NULL)
449            goto err;
450        if (!BN_lshift(Ri, Ri, mont->ri))
451            goto err;           /* R*Ri */
452        if (!BN_sub_word(Ri, 1))
453            goto err;
454        /*
455         * Ni = (R*Ri-1) / N
456         */
457        if (!BN_div(&(mont->Ni), NULL, Ri, &mont->N, ctx))
458            goto err;
459    }
460#endif
461
462    /* setup RR for conversions */
463    BN_zero(&(mont->RR));
464    if (!BN_set_bit(&(mont->RR), mont->ri * 2))
465        goto err;
466    if (!BN_mod(&(mont->RR), &(mont->RR), &(mont->N), ctx))
467        goto err;
468
469    ret = 1;
470 err:
471    BN_CTX_end(ctx);
472    return ret;
473}
474
475BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from)
476{
477    if (to == from)
478        return (to);
479
480    if (!BN_copy(&(to->RR), &(from->RR)))
481        return NULL;
482    if (!BN_copy(&(to->N), &(from->N)))
483        return NULL;
484    if (!BN_copy(&(to->Ni), &(from->Ni)))
485        return NULL;
486    to->ri = from->ri;
487    to->n0[0] = from->n0[0];
488    to->n0[1] = from->n0[1];
489    return (to);
490}
491
492BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock,
493                                    const BIGNUM *mod, BN_CTX *ctx)
494{
495    BN_MONT_CTX *ret;
496
497    CRYPTO_r_lock(lock);
498    ret = *pmont;
499    CRYPTO_r_unlock(lock);
500    if (ret)
501        return ret;
502
503    /*
504     * We don't want to serialise globally while doing our lazy-init math in
505     * BN_MONT_CTX_set. That punishes threads that are doing independent
506     * things. Instead, punish the case where more than one thread tries to
507     * lazy-init the same 'pmont', by having each do the lazy-init math work
508     * independently and only use the one from the thread that wins the race
509     * (the losers throw away the work they've done).
510     */
511    ret = BN_MONT_CTX_new();
512    if (!ret)
513        return NULL;
514    if (!BN_MONT_CTX_set(ret, mod, ctx)) {
515        BN_MONT_CTX_free(ret);
516        return NULL;
517    }
518
519    /* The locked compare-and-set, after the local work is done. */
520    CRYPTO_w_lock(lock);
521    if (*pmont) {
522        BN_MONT_CTX_free(ret);
523        ret = *pmont;
524    } else
525        *pmont = ret;
526    CRYPTO_w_unlock(lock);
527    return ret;
528}
529