bn_mont.c revision 325337 
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) 1998-2006 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# ifdef BN_COUNT
211    fprintf(stderr, "word BN_from_montgomery_word %d * %d\n", nl, nl);
212# endif
213    for (carry = 0, i = 0; i < nl; i++, rp++) {
214# ifdef __TANDEM
215        {
216            long long t1;
217            long long t2;
218            long long t3;
219            t1 = rp[0] * (n0 & 0177777);
220            t2 = 037777600000l;
221            t2 = n0 & t2;
222            t3 = rp[0] & 0177777;
223            t2 = (t3 * t2) & BN_MASK2;
224            t1 = t1 + t2;
225            v = bn_mul_add_words(rp, np, nl, (BN_ULONG)t1);
226        }
227# else
228        v = bn_mul_add_words(rp, np, nl, (rp[0] * n0) & BN_MASK2);
229# endif
230        v = (v + carry + rp[nl]) & BN_MASK2;
231        carry |= (v != rp[nl]);
232        carry &= (v <= rp[nl]);
233        rp[nl] = v;
234    }
235
236    if (bn_wexpand(ret, nl) == NULL)
237        return (0);
238    ret->top = nl;
239    ret->neg = r->neg;
240
241    rp = ret->d;
242    ap = &(r->d[nl]);
243
244# define BRANCH_FREE 1
245# if BRANCH_FREE
246    {
247        BN_ULONG *nrp;
248        size_t m;
249
250        v = bn_sub_words(rp, ap, np, nl) - carry;
251        /*
252         * if subtraction result is real, then trick unconditional memcpy
253         * below to perform in-place "refresh" instead of actual copy.
254         */
255        m = (0 - (size_t)v);
256        nrp =
257            (BN_ULONG *)(((PTR_SIZE_INT) rp & ~m) | ((PTR_SIZE_INT) ap & m));
258
259        for (i = 0, nl -= 4; i < nl; i += 4) {
260            BN_ULONG t1, t2, t3, t4;
261
262            t1 = nrp[i + 0];
263            t2 = nrp[i + 1];
264            t3 = nrp[i + 2];
265            ap[i + 0] = 0;
266            t4 = nrp[i + 3];
267            ap[i + 1] = 0;
268            rp[i + 0] = t1;
269            ap[i + 2] = 0;
270            rp[i + 1] = t2;
271            ap[i + 3] = 0;
272            rp[i + 2] = t3;
273            rp[i + 3] = t4;
274        }
275        for (nl += 4; i < nl; i++)
276            rp[i] = nrp[i], ap[i] = 0;
277    }
278# else
279    if (bn_sub_words(rp, ap, np, nl) - carry)
280        memcpy(rp, ap, nl * sizeof(BN_ULONG));
281# endif
282    bn_correct_top(r);
283    bn_correct_top(ret);
284    bn_check_top(ret);
285
286    return (1);
287}
288#endif                          /* MONT_WORD */
289
290int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
291                       BN_CTX *ctx)
292{
293    int retn = 0;
294#ifdef MONT_WORD
295    BIGNUM *t;
296
297    BN_CTX_start(ctx);
298    if ((t = BN_CTX_get(ctx)) && BN_copy(t, a))
299        retn = BN_from_montgomery_word(ret, t, mont);
300    BN_CTX_end(ctx);
301#else                           /* !MONT_WORD */
302    BIGNUM *t1, *t2;
303
304    BN_CTX_start(ctx);
305    t1 = BN_CTX_get(ctx);
306    t2 = BN_CTX_get(ctx);
307    if (t1 == NULL || t2 == NULL)
308        goto err;
309
310    if (!BN_copy(t1, a))
311        goto err;
312    BN_mask_bits(t1, mont->ri);
313
314    if (!BN_mul(t2, t1, &mont->Ni, ctx))
315        goto err;
316    BN_mask_bits(t2, mont->ri);
317
318    if (!BN_mul(t1, t2, &mont->N, ctx))
319        goto err;
320    if (!BN_add(t2, a, t1))
321        goto err;
322    if (!BN_rshift(ret, t2, mont->ri))
323        goto err;
324
325    if (BN_ucmp(ret, &(mont->N)) >= 0) {
326        if (!BN_usub(ret, ret, &(mont->N)))
327            goto err;
328    }
329    retn = 1;
330    bn_check_top(ret);
331 err:
332    BN_CTX_end(ctx);
333#endif                          /* MONT_WORD */
334    return (retn);
335}
336
337BN_MONT_CTX *BN_MONT_CTX_new(void)
338{
339    BN_MONT_CTX *ret;
340
341    if ((ret = (BN_MONT_CTX *)OPENSSL_malloc(sizeof(BN_MONT_CTX))) == NULL)
342        return (NULL);
343
344    BN_MONT_CTX_init(ret);
345    ret->flags = BN_FLG_MALLOCED;
346    return (ret);
347}
348
349void BN_MONT_CTX_init(BN_MONT_CTX *ctx)
350{
351    ctx->ri = 0;
352    BN_init(&(ctx->RR));
353    BN_init(&(ctx->N));
354    BN_init(&(ctx->Ni));
355    ctx->n0[0] = ctx->n0[1] = 0;
356    ctx->flags = 0;
357}
358
359void BN_MONT_CTX_free(BN_MONT_CTX *mont)
360{
361    if (mont == NULL)
362        return;
363
364    BN_clear_free(&(mont->RR));
365    BN_clear_free(&(mont->N));
366    BN_clear_free(&(mont->Ni));
367    if (mont->flags & BN_FLG_MALLOCED)
368        OPENSSL_free(mont);
369}
370
371int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx)
372{
373    int ret = 0;
374    BIGNUM *Ri, *R;
375
376    if (BN_is_zero(mod))
377        return 0;
378
379    BN_CTX_start(ctx);
380    if ((Ri = BN_CTX_get(ctx)) == NULL)
381        goto err;
382    R = &(mont->RR);            /* grab RR as a temp */
383    if (!BN_copy(&(mont->N), mod))
384        goto err;               /* Set N */
385    mont->N.neg = 0;
386
387#ifdef MONT_WORD
388    {
389        BIGNUM tmod;
390        BN_ULONG buf[2];
391
392        BN_init(&tmod);
393        tmod.d = buf;
394        tmod.dmax = 2;
395        tmod.neg = 0;
396
397        if (BN_get_flags(mod, BN_FLG_CONSTTIME) != 0)
398            BN_set_flags(&tmod, BN_FLG_CONSTTIME);
399
400        mont->ri = (BN_num_bits(mod) + (BN_BITS2 - 1)) / BN_BITS2 * BN_BITS2;
401
402# if defined(OPENSSL_BN_ASM_MONT) && (BN_BITS2<=32)
403        /*
404         * Only certain BN_BITS2<=32 platforms actually make use of n0[1],
405         * and we could use the #else case (with a shorter R value) for the
406         * others.  However, currently only the assembler files do know which
407         * is which.
408         */
409
410        BN_zero(R);
411        if (!(BN_set_bit(R, 2 * BN_BITS2)))
412            goto err;
413
414        tmod.top = 0;
415        if ((buf[0] = mod->d[0]))
416            tmod.top = 1;
417        if ((buf[1] = mod->top > 1 ? mod->d[1] : 0))
418            tmod.top = 2;
419
420        if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL)
421            goto err;
422        if (!BN_lshift(Ri, Ri, 2 * 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_expand(Ri, (int)sizeof(BN_ULONG) * 2) == NULL)
430                goto err;
431            /* Ri-- (mod double word size) */
432            Ri->neg = 0;
433            Ri->d[0] = BN_MASK2;
434            Ri->d[1] = BN_MASK2;
435            Ri->top = 2;
436        }
437        if (!BN_div(Ri, NULL, Ri, &tmod, ctx))
438            goto err;
439        /*
440         * Ni = (R*Ri-1)/N, keep only couple of least significant words:
441         */
442        mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
443        mont->n0[1] = (Ri->top > 1) ? Ri->d[1] : 0;
444# else
445        BN_zero(R);
446        if (!(BN_set_bit(R, BN_BITS2)))
447            goto err;           /* R */
448
449        buf[0] = mod->d[0];     /* tmod = N mod word size */
450        buf[1] = 0;
451        tmod.top = buf[0] != 0 ? 1 : 0;
452        /* Ri = R^-1 mod N */
453        if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL)
454            goto err;
455        if (!BN_lshift(Ri, Ri, BN_BITS2))
456            goto err;           /* R*Ri */
457        if (!BN_is_zero(Ri)) {
458            if (!BN_sub_word(Ri, 1))
459                goto err;
460        } else {                /* if N mod word size == 1 */
461
462            if (!BN_set_word(Ri, BN_MASK2))
463                goto err;       /* Ri-- (mod word size) */
464        }
465        if (!BN_div(Ri, NULL, Ri, &tmod, ctx))
466            goto err;
467        /*
468         * Ni = (R*Ri-1)/N, keep only least significant word:
469         */
470        mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
471        mont->n0[1] = 0;
472# endif
473    }
474#else                           /* !MONT_WORD */
475    {                           /* bignum version */
476        mont->ri = BN_num_bits(&mont->N);
477        BN_zero(R);
478        if (!BN_set_bit(R, mont->ri))
479            goto err;           /* R = 2^ri */
480        /* Ri = R^-1 mod N */
481        if ((BN_mod_inverse(Ri, R, &mont->N, ctx)) == NULL)
482            goto err;
483        if (!BN_lshift(Ri, Ri, mont->ri))
484            goto err;           /* R*Ri */
485        if (!BN_sub_word(Ri, 1))
486            goto err;
487        /*
488         * Ni = (R*Ri-1) / N
489         */
490        if (!BN_div(&(mont->Ni), NULL, Ri, &mont->N, ctx))
491            goto err;
492    }
493#endif
494
495    /* setup RR for conversions */
496    BN_zero(&(mont->RR));
497    if (!BN_set_bit(&(mont->RR), mont->ri * 2))
498        goto err;
499    if (!BN_mod(&(mont->RR), &(mont->RR), &(mont->N), ctx))
500        goto err;
501
502    ret = 1;
503 err:
504    BN_CTX_end(ctx);
505    return ret;
506}
507
508BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from)
509{
510    if (to == from)
511        return (to);
512
513    if (!BN_copy(&(to->RR), &(from->RR)))
514        return NULL;
515    if (!BN_copy(&(to->N), &(from->N)))
516        return NULL;
517    if (!BN_copy(&(to->Ni), &(from->Ni)))
518        return NULL;
519    to->ri = from->ri;
520    to->n0[0] = from->n0[0];
521    to->n0[1] = from->n0[1];
522    return (to);
523}
524
525BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock,
526                                    const BIGNUM *mod, BN_CTX *ctx)
527{
528    BN_MONT_CTX *ret;
529
530    CRYPTO_r_lock(lock);
531    ret = *pmont;
532    CRYPTO_r_unlock(lock);
533    if (ret)
534        return ret;
535
536    /*
537     * We don't want to serialise globally while doing our lazy-init math in
538     * BN_MONT_CTX_set. That punishes threads that are doing independent
539     * things. Instead, punish the case where more than one thread tries to
540     * lazy-init the same 'pmont', by having each do the lazy-init math work
541     * independently and only use the one from the thread that wins the race
542     * (the losers throw away the work they've done).
543     */
544    ret = BN_MONT_CTX_new();
545    if (!ret)
546        return NULL;
547    if (!BN_MONT_CTX_set(ret, mod, ctx)) {
548        BN_MONT_CTX_free(ret);
549        return NULL;
550    }
551
552    /* The locked compare-and-set, after the local work is done. */
553    CRYPTO_w_lock(lock);
554    if (*pmont) {
555        BN_MONT_CTX_free(ret);
556        ret = *pmont;
557    } else
558        *pmont = ret;
559    CRYPTO_w_unlock(lock);
560    return ret;
561}
562