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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 w
ord 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 int got_write_lock = 0; | |
482 BN_MONT_CTX *ret; | |
483 | |
484 CRYPTO_r_lock(lock); | |
485 if (!*pmont) | |
486 { | |
487 CRYPTO_r_unlock(lock); | |
488 CRYPTO_w_lock(lock); | |
489 got_write_lock = 1; | |
490 | |
491 if (!*pmont) | |
492 { | |
493 ret = BN_MONT_CTX_new(); | |
494 if (ret && !BN_MONT_CTX_set(ret, mod, ctx)) | |
495 BN_MONT_CTX_free(ret); | |
496 else | |
497 *pmont = ret; | |
498 } | |
499 } | |
500 | |
501 ret = *pmont; | |
502 | |
503 if (got_write_lock) | |
504 CRYPTO_w_unlock(lock); | |
505 else | |
506 CRYPTO_r_unlock(lock); | |
507 | |
508 return ret; | |
509 } | |
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