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 __RCSID("$MirOS: src/lib/libssl/src/crypto/bn/bn_mont.c,v 1.4 2014/06/05 13:26:37 tg Exp $");
124
125 #define MONT_WORD /* use the faster word-based algorithm */
126
BN_mod_mul_montgomery(BIGNUM * r,const BIGNUM * a,const BIGNUM * b,BN_MONT_CTX * mont,BN_CTX * ctx)127 int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
128 BN_MONT_CTX *mont, BN_CTX *ctx)
129 {
130 BIGNUM *tmp;
131 int ret=0;
132
133 BN_CTX_start(ctx);
134 tmp = BN_CTX_get(ctx);
135 if (tmp == NULL) goto err;
136
137 bn_check_top(tmp);
138 if (a == b)
139 {
140 if (!BN_sqr(tmp,a,ctx)) goto err;
141 }
142 else
143 {
144 if (!BN_mul(tmp,a,b,ctx)) goto err;
145 }
146 /* reduce from aRR to aR */
147 if (!BN_from_montgomery(r,tmp,mont,ctx)) goto err;
148 ret=1;
149 err:
150 BN_CTX_end(ctx);
151 return(ret);
152 }
153
BN_from_montgomery(BIGNUM * ret,const BIGNUM * a,BN_MONT_CTX * mont,BN_CTX * ctx)154 int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
155 BN_CTX *ctx)
156 {
157 int retn=0;
158
159 #ifdef MONT_WORD
160 BIGNUM *n,*r;
161 BN_ULONG *ap,*np,*rp,n0,v,*nrp;
162 int al,nl,max,i,x,ri;
163
164 BN_CTX_start(ctx);
165 if ((r = BN_CTX_get(ctx)) == NULL) goto err;
166
167 if (!BN_copy(r,a)) goto err;
168 n= &(mont->N);
169
170 ap=a->d;
171 /* mont->ri is the size of mont->N in bits (rounded up
172 to the word size) */
173 al=ri=mont->ri/BN_BITS2;
174
175 nl=n->top;
176 if ((al == 0) || (nl == 0)) { r->top=0; return(1); }
177
178 max=(nl+al+1); /* allow for overflow (no?) XXX */
179 if (bn_wexpand(r,max) == NULL) goto err;
180
181 r->neg=a->neg^n->neg;
182 np=n->d;
183 rp=r->d;
184 nrp= &(r->d[nl]);
185
186 /* clear the top words of T */
187 #if 1
188 for (i=r->top; i<max; i++) /* memset? XXX */
189 r->d[i]=0;
190 #else
191 memset(&(r->d[r->top]),0,(max-r->top)*sizeof(BN_ULONG));
192 #endif
193
194 r->top=max;
195 n0=mont->n0;
196
197 #ifdef BN_COUNT
198 fprintf(stderr,"word BN_from_montgomery %d * %d\n",nl,nl);
199 #endif
200 for (i=0; i<nl; i++)
201 {
202 #ifdef __TANDEM
203 {
204 long long t1;
205 long long t2;
206 long long t3;
207 t1 = rp[0] * (n0 & 0177777);
208 t2 = 037777600000l;
209 t2 = n0 & t2;
210 t3 = rp[0] & 0177777;
211 t2 = (t3 * t2) & BN_MASK2;
212 t1 = t1 + t2;
213 v=bn_mul_add_words(rp,np,nl,(BN_ULONG) t1);
214 }
215 #else
216 v=bn_mul_add_words(rp,np,nl,(rp[0]*n0)&BN_MASK2);
217 #endif
218 nrp++;
219 rp++;
220 if (((nrp[-1]+=v)&BN_MASK2) >= v)
221 continue;
222 else
223 {
224 if (((++nrp[0])&BN_MASK2) != 0) continue;
225 if (((++nrp[1])&BN_MASK2) != 0) continue;
226 for (x=2; (((++nrp[x])&BN_MASK2) == 0); x++) ;
227 }
228 }
229 bn_fix_top(r);
230
231 /* mont->ri will be a multiple of the word size and below code
232 * is kind of BN_rshift(ret,r,mont->ri) equivalent */
233 if (r->top <= ri)
234 {
235 ret->top=0;
236 retn=1;
237 goto err;
238 }
239 al=r->top-ri;
240
241 # define BRANCH_FREE 1
242 # if BRANCH_FREE
243 if (bn_wexpand(ret,ri) == NULL) goto err;
244 x=0-(((al-ri)>>(sizeof(al)*8-1))&1);
245 ret->top=x=(ri&~x)|(al&x); /* min(ri,al) */
246 ret->neg=r->neg;
247
248 rp=ret->d;
249 ap=&(r->d[ri]);
250
251 {
252 size_t m1,m2;
253
254 v=bn_sub_words(rp,ap,np,ri);
255 /* this ----------------^^ works even in al<ri case
256 * thanks to zealous zeroing of top of the vector in the
257 * beginning. */
258
259 /* if (al==ri && !v) || al>ri) nrp=rp; else nrp=ap; */
260 /* in other words if subtraction result is real, then
261 * trick unconditional memcpy below to perform in-place
262 * "refresh" instead of actual copy. */
263 m1=0-(size_t)(((al-ri)>>(sizeof(al)*8-1))&1); /* al<ri */
264 m2=0-(size_t)(((ri-al)>>(sizeof(al)*8-1))&1); /* al>ri */
265 m1|=m2; /* (al!=ri) */
266 m1|=(0-(size_t)v); /* (al!=ri || v) */
267 m1&=~m2; /* (al!=ri || v) && !al>ri */
268 nrp=(BN_ULONG *)(((size_t)rp&~m1)|((size_t)ap&m1));
269 }
270
271 /* 'i<ri' is chosen to eliminate dependency on input data, even
272 * though it results in redundant copy in al<ri case. */
273 for (i=0,ri-=4; i<ri; i+=4)
274 {
275 BN_ULONG t1,t2,t3,t4;
276
277 t1=nrp[i+0];
278 t2=nrp[i+1];
279 t3=nrp[i+2]; ap[i+0]=0;
280 t4=nrp[i+3]; ap[i+1]=0;
281 rp[i+0]=t1; ap[i+2]=0;
282 rp[i+1]=t2; ap[i+3]=0;
283 rp[i+2]=t3;
284 rp[i+3]=t4;
285 }
286 for (ri+=4; i<ri; i++)
287 rp[i]=nrp[i], ap[i]=0;
288 # else
289 if (bn_wexpand(ret,al) == NULL) goto err;
290 ret->top=al;
291 ret->neg=r->neg;
292
293 rp=ret->d;
294 ap=&(r->d[ri]);
295 al-=4;
296 for (i=0; i<al; i+=4)
297 {
298 BN_ULONG t1,t2,t3,t4;
299
300 t1=ap[i+0];
301 t2=ap[i+1];
302 t3=ap[i+2];
303 t4=ap[i+3];
304 rp[i+0]=t1;
305 rp[i+1]=t2;
306 rp[i+2]=t3;
307 rp[i+3]=t4;
308 }
309 al+=4;
310 for (; i<al; i++)
311 rp[i]=ap[i];
312 # endif
313 #else /* !MONT_WORD */
314 BIGNUM *t1,*t2;
315
316 BN_CTX_start(ctx);
317 t1 = BN_CTX_get(ctx);
318 t2 = BN_CTX_get(ctx);
319 if (t1 == NULL || t2 == NULL) goto err;
320
321 if (!BN_copy(t1,a)) goto err;
322 BN_mask_bits(t1,mont->ri);
323
324 if (!BN_mul(t2,t1,&mont->Ni,ctx)) goto err;
325 BN_mask_bits(t2,mont->ri);
326
327 if (!BN_mul(t1,t2,&mont->N,ctx)) goto err;
328 if (!BN_add(t2,a,t1)) goto err;
329 if (!BN_rshift(ret,t2,mont->ri)) goto err;
330 #endif /* MONT_WORD */
331
332 #if !defined(BRANCH_FREE) || BRANCH_FREE==0
333 if (BN_ucmp(ret, &(mont->N)) >= 0)
334 {
335 if (!BN_usub(ret,ret,&(mont->N))) goto err;
336 }
337 #endif
338 retn=1;
339 err:
340 BN_CTX_end(ctx);
341 return(retn);
342 }
343
BN_MONT_CTX_new(void)344 BN_MONT_CTX *BN_MONT_CTX_new(void)
345 {
346 BN_MONT_CTX *ret;
347
348 if ((ret=(BN_MONT_CTX *)OPENSSL_malloc(sizeof(BN_MONT_CTX))) == NULL)
349 return(NULL);
350
351 BN_MONT_CTX_init(ret);
352 ret->flags=BN_FLG_MALLOCED;
353 return(ret);
354 }
355
BN_MONT_CTX_init(BN_MONT_CTX * ctx)356 void BN_MONT_CTX_init(BN_MONT_CTX *ctx)
357 {
358 ctx->ri=0;
359 BN_init(&(ctx->RR));
360 BN_init(&(ctx->N));
361 BN_init(&(ctx->Ni));
362 ctx->flags=0;
363 }
364
BN_MONT_CTX_free(BN_MONT_CTX * mont)365 void BN_MONT_CTX_free(BN_MONT_CTX *mont)
366 {
367 if(mont == NULL)
368 return;
369
370 BN_free(&(mont->RR));
371 BN_free(&(mont->N));
372 BN_free(&(mont->Ni));
373 if (mont->flags & BN_FLG_MALLOCED)
374 OPENSSL_free(mont);
375 }
376
BN_MONT_CTX_set(BN_MONT_CTX * mont,const BIGNUM * mod,BN_CTX * ctx)377 int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx)
378 {
379 BIGNUM Ri,*R;
380
381 BN_init(&Ri);
382 R= &(mont->RR); /* grab RR as a temp */
383 if (!BN_copy(&(mont->N),mod)) goto err; /* Set N */
384 mont->N.neg = 0;
385
386 #ifdef MONT_WORD
387 {
388 BIGNUM tmod;
389 BN_ULONG buf[2];
390
391 mont->ri=(BN_num_bits(mod)+(BN_BITS2-1))/BN_BITS2*BN_BITS2;
392 if (!(BN_zero(R))) goto err;
393 if (!(BN_set_bit(R,BN_BITS2))) goto err; /* R */
394
395 buf[0]=mod->d[0]; /* tmod = N mod word size */
396 buf[1]=0;
397 tmod.d=buf;
398 tmod.top=1;
399 tmod.dmax=2;
400 tmod.neg=0;
401 /* Ri = R^-1 mod N*/
402 if ((BN_mod_inverse(&Ri,R,&tmod,ctx)) == NULL)
403 goto err;
404 if (!BN_lshift(&Ri,&Ri,BN_BITS2)) goto err; /* R*Ri */
405 if (!BN_is_zero(&Ri))
406 {
407 if (!BN_sub_word(&Ri,1)) goto err;
408 }
409 else /* if N mod word size == 1 */
410 {
411 if (!BN_set_word(&Ri,BN_MASK2)) goto err; /* Ri-- (mod word size) */
412 }
413 if (!BN_div(&Ri,NULL,&Ri,&tmod,ctx)) goto err;
414 /* Ni = (R*Ri-1)/N,
415 * keep only least significant word: */
416 mont->n0 = (Ri.top > 0) ? Ri.d[0] : 0;
417 BN_free(&Ri);
418 }
419 #else /* !MONT_WORD */
420 { /* bignum version */
421 mont->ri=BN_num_bits(&mont->N);
422 if (!BN_zero(R)) goto err;
423 if (!BN_set_bit(R,mont->ri)) goto err; /* R = 2^ri */
424 /* Ri = R^-1 mod N*/
425 if ((BN_mod_inverse(&Ri,R,&mont->N,ctx)) == NULL)
426 goto err;
427 if (!BN_lshift(&Ri,&Ri,mont->ri)) goto err; /* R*Ri */
428 if (!BN_sub_word(&Ri,1)) goto err;
429 /* Ni = (R*Ri-1) / N */
430 if (!BN_div(&(mont->Ni),NULL,&Ri,&mont->N,ctx)) goto err;
431 BN_free(&Ri);
432 }
433 #endif
434
435 /* setup RR for conversions */
436 if (!BN_zero(&(mont->RR))) goto err;
437 if (!BN_set_bit(&(mont->RR),mont->ri*2)) goto err;
438 if (!BN_mod(&(mont->RR),&(mont->RR),&(mont->N),ctx)) goto err;
439
440 return(1);
441 err:
442 return(0);
443 }
444
BN_MONT_CTX_copy(BN_MONT_CTX * to,BN_MONT_CTX * from)445 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from)
446 {
447 if (to == from) return(to);
448
449 if (!BN_copy(&(to->RR),&(from->RR))) return NULL;
450 if (!BN_copy(&(to->N),&(from->N))) return NULL;
451 if (!BN_copy(&(to->Ni),&(from->Ni))) return NULL;
452 to->ri=from->ri;
453 to->n0=from->n0;
454 return(to);
455 }
456
BN_MONT_CTX_set_locked(BN_MONT_CTX ** pmont,int lock,const BIGNUM * mod,BN_CTX * ctx)457 BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock,
458 const BIGNUM *mod, BN_CTX *ctx)
459 {
460 BN_MONT_CTX *ret;
461
462 CRYPTO_r_lock(lock);
463 ret = *pmont;
464 CRYPTO_r_unlock(lock);
465 if (ret)
466 return ret;
467
468 /* We don't want to serialise globally while doing our lazy-init math in
469 * BN_MONT_CTX_set. That punishes threads that are doing independent
470 * things. Instead, punish the case where more than one thread tries to
471 * lazy-init the same 'pmont', by having each do the lazy-init math work
472 * independently and only use the one from the thread that wins the race
473 * (the losers throw away the work they've done). */
474 ret = BN_MONT_CTX_new();
475 if (!ret)
476 return NULL;
477 if (!BN_MONT_CTX_set(ret, mod, ctx))
478 {
479 BN_MONT_CTX_free(ret);
480 return NULL;
481 }
482
483 /* The locked compare-and-set, after the local work is done. */
484 CRYPTO_w_lock(lock);
485 if (*pmont)
486 {
487 BN_MONT_CTX_free(ret);
488 ret = *pmont;
489 }
490 else
491 *pmont = ret;
492 CRYPTO_w_unlock(lock);
493 return ret;
494 }
495