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
126 static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont);
127 #endif
128
129 int 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 {
139 if (bn_wexpand(r,num) == NULL) return(0);
140 if (bn_mul_mont(r->d,a->d,b->d,mont->N.d,mont->n0,num))
141 {
142 r->neg = a->neg^b->neg;
143 r->top = num;
144 bn_correct_top(r);
145 return(1);
146 }
147 }
148 #endif
149
150 BN_CTX_start(ctx);
151 tmp = BN_CTX_get(ctx);
152 if (tmp == NULL) goto err;
153
154 bn_check_top(tmp);
155 if (a == b)
156 {
157 if (!BN_sqr(tmp,a,ctx)) goto err;
158 }
159 else
160 {
161 if (!BN_mul(tmp,a,b,ctx)) goto err;
162 }
163 /* reduce from aRR to aR */
164 #ifdef MONT_WORD
165 if (!BN_from_montgomery_word(r,tmp,mont)) goto err;
166 #else
167 if (!BN_from_montgomery(r,tmp,mont,ctx)) goto err;
168 #endif
169 bn_check_top(r);
170 ret=1;
171 err:
172 BN_CTX_end(ctx);
173 return(ret);
174 }
175
176 #ifdef MONT_WORD
177 static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont)
178 {
179 BIGNUM *n;
180 BN_ULONG *ap,*np,*rp,n0,v,carry;
181 int nl,max,i;
182
183 n= &(mont->N);
184 nl=n->top;
185 if (nl == 0) { ret->top=0; return(1); }
186
187 max=(2*nl); /* carry is stored separately */
188 if (bn_wexpand(r,max) == NULL) return(0);
189
190 r->neg^=n->neg;
191 np=n->d;
192 rp=r->d;
193
194 /* clear the top words of T */
195 #if 1
196 for (i=r->top; i<max; i++) /* memset? XXX */
197 rp[i]=0;
198 #else
199 memset(&(rp[r->top]),0,(max-r->top)*sizeof(BN_ULONG));
200 #endif
201
202 r->top=max;
203 n0=mont->n0[0];
204
205 #ifdef BN_COUNT
206 fprintf(stderr,"word BN_from_montgomery_word %d * %d\n",nl,nl);
207 #endif
208 for (carry=0, i=0; i<nl; i++, rp++)
209 {
210 #ifdef __TANDEM
211 {
212 long long t1;
213 long long t2;
214 long long t3;
215 t1 = rp[0] * (n0 & 0177777);
216 t2 = 037777600000l;
217 t2 = n0 & t2;
218 t3 = rp[0] & 0177777;
219 t2 = (t3 * t2) & BN_MASK2;
220 t1 = t1 + t2;
221 v=bn_mul_add_words(rp,np,nl,(BN_ULONG) t1);
222 }
223 #else
224 v=bn_mul_add_words(rp,np,nl,(rp[0]*n0)&BN_MASK2);
225 #endif
226 v = (v+carry+rp[nl])&BN_MASK2;
227 carry |= (v != rp[nl]);
228 carry &= (v <= rp[nl]);
229 rp[nl]=v;
230 }
231
232 if (bn_wexpand(ret,nl) == NULL) return(0);
233 ret->top=nl;
234 ret->neg=r->neg;
235
236 rp=ret->d;
237 ap=&(r->d[nl]);
238
239 #define BRANCH_FREE 1
240 #if BRANCH_FREE
241 {
242 BN_ULONG *nrp;
243 size_t m;
244
245 v=bn_sub_words(rp,ap,np,nl)-carry;
246 /* if subtraction result is real, then
247 * trick unconditional memcpy below to perform in-place
248 * "refresh" instead of actual copy. */
249 m=(0-(size_t)v);
250 nrp=(BN_ULONG *)(((PTR_SIZE_INT)rp&~m)|((PTR_SIZE_INT)ap&m));
251
252 for (i=0,nl-=4; i<nl; i+=4)
253 {
254 BN_ULONG t1,t2,t3,t4;
255
256 t1=nrp[i+0];
257 t2=nrp[i+1];
258 t3=nrp[i+2]; ap[i+0]=0;
259 t4=nrp[i+3]; ap[i+1]=0;
260 rp[i+0]=t1; ap[i+2]=0;
261 rp[i+1]=t2; ap[i+3]=0;
262 rp[i+2]=t3;
263 rp[i+3]=t4;
264 }
265 for (nl+=4; i<nl; i++)
266 rp[i]=nrp[i], ap[i]=0;
267 }
268 #else
269 if (bn_sub_words (rp,ap,np,nl)-carry)
270 memcpy(rp,ap,nl*sizeof(BN_ULONG));
271 #endif
272 bn_correct_top(r);
273 bn_correct_top(ret);
274 bn_check_top(ret);
275
276 return(1);
277 }
278 #endif /* MONT_WORD */
279
280 int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
281 BN_CTX *ctx)
282 {
283 int retn=0;
284 #ifdef MONT_WORD
285 BIGNUM *t;
286
287 BN_CTX_start(ctx);
288 if ((t = BN_CTX_get(ctx)) && BN_copy(t,a))
289 retn = BN_from_montgomery_word(ret,t,mont);
290 BN_CTX_end(ctx);
291 #else /* !MONT_WORD */
292 BIGNUM *t1,*t2;
293
294 BN_CTX_start(ctx);
295 t1 = BN_CTX_get(ctx);
296 t2 = BN_CTX_get(ctx);
297 if (t1 == NULL || t2 == NULL) goto err;
298
299 if (!BN_copy(t1,a)) goto err;
300 BN_mask_bits(t1,mont->ri);
301
302 if (!BN_mul(t2,t1,&mont->Ni,ctx)) goto err;
303 BN_mask_bits(t2,mont->ri);
304
305 if (!BN_mul(t1,t2,&mont->N,ctx)) goto err;
306 if (!BN_add(t2,a,t1)) goto err;
307 if (!BN_rshift(ret,t2,mont->ri)) goto err;
308
309 if (BN_ucmp(ret, &(mont->N)) >= 0)
310 {
311 if (!BN_usub(ret,ret,&(mont->N))) goto err;
312 }
313 retn=1;
314 bn_check_top(ret);
315 err:
316 BN_CTX_end(ctx);
317 #endif /* MONT_WORD */
318 return(retn);
319 }
320
321 BN_MONT_CTX *BN_MONT_CTX_new(void)
322 {
323 BN_MONT_CTX *ret;
324
325 if ((ret=(BN_MONT_CTX *)OPENSSL_malloc(sizeof(BN_MONT_CTX))) == NULL)
326 return(NULL);
327
328 BN_MONT_CTX_init(ret);
329 ret->flags=BN_FLG_MALLOCED;
330 return(ret);
331 }
332
333 void BN_MONT_CTX_init(BN_MONT_CTX *ctx)
334 {
335 ctx->ri=0;
336 BN_init(&(ctx->RR));
337 BN_init(&(ctx->N));
338 BN_init(&(ctx->Ni));
339 ctx->n0[0] = ctx->n0[1] = 0;
340 ctx->flags=0;
341 }
342
343 void BN_MONT_CTX_free(BN_MONT_CTX *mont)
344 {
345 if(mont == NULL)
346 return;
347
348 BN_free(&(mont->RR));
349 BN_free(&(mont->N));
350 BN_free(&(mont->Ni));
351 if (mont->flags & BN_FLG_MALLOCED)
352 OPENSSL_free(mont);
353 }
354
355 int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx)
356 {
357 int ret = 0;
358 BIGNUM *Ri,*R;
359
360 BN_CTX_start(ctx);
361 if((Ri = BN_CTX_get(ctx)) == NULL) goto err;
362 R= &(mont->RR); /* grab RR as a temp */
363 if (!BN_copy(&(mont->N),mod)) goto err; /* Set N */
364 mont->N.neg = 0;
365
366 #ifdef MONT_WORD
367 {
368 BIGNUM tmod;
369 BN_ULONG buf[2];
370
371 BN_init(&tmod);
372 tmod.d=buf;
373 tmod.dmax=2;
374 tmod.neg=0;
375
376 mont->ri=(BN_num_bits(mod)+(BN_BITS2-1))/BN_BITS2*BN_BITS2;
377
378 #if defined(OPENSSL_BN_ASM_MONT) && (BN_BITS2<=32)
379 /* Only certain BN_BITS2<=32 platforms actually make use of
380 * n0[1], and we could use the #else case (with a shorter R
381 * value) for the others. However, currently only the assembler
382 * files do know which is which. */
383
384 BN_zero(R);
385 if (!(BN_set_bit(R,2*BN_BITS2))) goto err;
386
387 tmod.top=0;
388 if ((buf[0] = mod->d[0])) tmod.top=1;
389 if ((buf[1] = mod->top>1 ? mod->d[1] : 0)) tmod.top=2;
390
391 if ((BN_mod_inverse(Ri,R,&tmod,ctx)) == NULL)
392 goto err;
393 if (!BN_lshift(Ri,Ri,2*BN_BITS2)) goto err; /* R*Ri */
394 if (!BN_is_zero(Ri))
395 {
396 if (!BN_sub_word(Ri,1)) goto err;
397 }
398 else /* if N mod word size == 1 */
399 {
400 if (bn_expand(Ri,(int)sizeof(BN_ULONG)*2) == NULL)
401 goto err;
402 /* Ri-- (mod double word size) */
403 Ri->neg=0;
404 Ri->d[0]=BN_MASK2;
405 Ri->d[1]=BN_MASK2;
406 Ri->top=2;
407 }
408 if (!BN_div(Ri,NULL,Ri,&tmod,ctx)) goto err;
409 /* Ni = (R*Ri-1)/N,
410 * keep only couple of least significant words: */
411 mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
412 mont->n0[1] = (Ri->top > 1) ? Ri->d[1] : 0;
413 #else
414 BN_zero(R);
415 if (!(BN_set_bit(R,BN_BITS2))) goto err; /* R */
416
417 buf[0]=mod->d[0]; /* tmod = N mod word size */
418 buf[1]=0;
419 tmod.top = buf[0] != 0 ? 1 : 0;
420 /* Ri = R^-1 mod N*/
421 if ((BN_mod_inverse(Ri,R,&tmod,ctx)) == NULL)
422 goto err;
423 if (!BN_lshift(Ri,Ri,BN_BITS2)) goto err; /* R*Ri */
424 if (!BN_is_zero(Ri))
425 {
426 if (!BN_sub_word(Ri,1)) goto err;
427 }
428 else /* if N mod word size == 1 */
429 {
430 if (!BN_set_word(Ri,BN_MASK2)) goto err; /* Ri-- (mod word size) */
431 }
432 if (!BN_div(Ri,NULL,Ri,&tmod,ctx)) goto err;
433 /* Ni = (R*Ri-1)/N,
434 * keep only least significant word: */
435 mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
436 mont->n0[1] = 0;
437 #endif
438 }
439 #else /* !MONT_WORD */
440 { /* bignum version */
441 mont->ri=BN_num_bits(&mont->N);
442 BN_zero(R);
443 if (!BN_set_bit(R,mont->ri)) goto err; /* R = 2^ri */
444 /* Ri = R^-1 mod N*/
445 if ((BN_mod_inverse(Ri,R,&mont->N,ctx)) == NULL)
446 goto err;
447 if (!BN_lshift(Ri,Ri,mont->ri)) goto err; /* R*Ri */
448 if (!BN_sub_word(Ri,1)) goto err;
449 /* Ni = (R*Ri-1) / N */
450 if (!BN_div(&(mont->Ni),NULL,Ri,&mont->N,ctx)) goto err;
451 }
452 #endif
453
454 /* setup RR for conversions */
455 BN_zero(&(mont->RR));
456 if (!BN_set_bit(&(mont->RR),mont->ri*2)) goto err;
457 if (!BN_mod(&(mont->RR),&(mont->RR),&(mont->N),ctx)) goto err;
458
459 ret = 1;
460 err:
461 BN_CTX_end(ctx);
462 return ret;
463 }
464
465 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from)
466 {
467 if (to == from) return(to);
468
469 if (!BN_copy(&(to->RR),&(from->RR))) return NULL;
470 if (!BN_copy(&(to->N),&(from->N))) return NULL;
471 if (!BN_copy(&(to->Ni),&(from->Ni))) return NULL;
472 to->ri=from->ri;
473 to->n0[0]=from->n0[0];
474 to->n0[1]=from->n0[1];
475 return(to);
476 }
477
478 BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock,
479 const BIGNUM *mod, BN_CTX *ctx)
480 {
481 BN_MONT_CTX *ret;
482
483 CRYPTO_r_lock(lock);
484 ret = *pmont;
485 CRYPTO_r_unlock(lock);
486 if (ret)
487 return ret;
488
489 /* We don't want to serialise globally while doing our lazy-init math in
490 * BN_MONT_CTX_set. That punishes threads that are doing independent
491 * things. Instead, punish the case where more than one thread tries to
492 * lazy-init the same 'pmont', by having each do the lazy-init math work
493 * independently and only use the one from the thread that wins the race
494 * (the losers throw away the work they've done). */
495 ret = BN_MONT_CTX_new();
496 if (!ret)
497 return NULL;
498 if (!BN_MONT_CTX_set(ret, mod, ctx))
499 {
500 BN_MONT_CTX_free(ret);
501 return NULL;
502 }
503
504 /* The locked compare-and-set, after the local work is done. */
505 CRYPTO_w_lock(lock);
506 if (*pmont)
507 {
508 BN_MONT_CTX_free(ret);
509 ret = *pmont;
510 }
511 else
512 *pmont = ret;
513 CRYPTO_w_unlock(lock);
514 return ret;
515 }