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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/*
60 * Details about Montgomery multiplication algorithms can be found at
61 * http://security.ece.orst.edu/publications.html, e.g.
62 * http://security.ece.orst.edu/koc/papers/j37acmon.pdf and
63 * sections 3.8 and 4.2 in http://security.ece.orst.edu/koc/papers/r01rsasw.pdf
64 */
65
66#include <stdio.h>
67#include "cryptlib.h"
68#include "bn_lcl.h"
69
70#define MONT_WORD /* use the faster word-based algorithm */
71
72int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
73 BN_MONT_CTX *mont, BN_CTX *ctx)
74 {
75 BIGNUM *tmp;
76 int ret=0;
77
78 BN_CTX_start(ctx);
79 tmp = BN_CTX_get(ctx);
80 if (tmp == NULL) goto err;
81
82 bn_check_top(tmp);
83 if (a == b)
84 {
85 if (!BN_sqr(tmp,a,ctx)) goto err;
86 }
87 else
88 {
89 if (!BN_mul(tmp,a,b,ctx)) goto err;
90 }
91 /* reduce from aRR to aR */
92 if (!BN_from_montgomery(r,tmp,mont,ctx)) goto err;
93 ret=1;
94err:
95 BN_CTX_end(ctx);
96 return(ret);
97 }
98
99int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
100 BN_CTX *ctx)
101 {
102 int retn=0;
103
104#ifdef MONT_WORD
105 BIGNUM *n,*r;
106 BN_ULONG *ap,*np,*rp,n0,v,*nrp;
107 int al,nl,max,i,x,ri;
108
109 BN_CTX_start(ctx);
110 if ((r = BN_CTX_get(ctx)) == NULL) goto err;
111
112 if (!BN_copy(r,a)) goto err;
113 n= &(mont->N);
114
115 ap=a->d;
116 /* mont->ri is the size of mont->N in bits (rounded up
117 to the word size) */
118 al=ri=mont->ri/BN_BITS2;
119
120 nl=n->top;
121 if ((al == 0) || (nl == 0)) { r->top=0; return(1); }
122
123 max=(nl+al+1); /* allow for overflow (no?) XXX */
124 if (bn_wexpand(r,max) == NULL) goto err;
125
126 r->neg=a->neg^n->neg;
127 np=n->d;
128 rp=r->d;
129 nrp= &(r->d[nl]);
130
131 /* clear the top words of T */
132#if 1
133 for (i=r->top; i<max; i++) /* memset? XXX */
134 r->d[i]=0;
135#else
136 memset(&(r->d[r->top]),0,(max-r->top)*sizeof(BN_ULONG));
137#endif
138
139 r->top=max;
140 n0=mont->n0;
141
142#ifdef BN_COUNT
143 fprintf(stderr,"word BN_from_montgomery %d * %d\n",nl,nl);
144#endif
145 for (i=0; i<nl; i++)
146 {
147#ifdef __TANDEM
148 {
149 long long t1;
150 long long t2;
151 long long t3;
152 t1 = rp[0] * (n0 & 0177777);
153 t2 = 037777600000l;
154 t2 = n0 & t2;
155 t3 = rp[0] & 0177777;
156 t2 = (t3 * t2) & BN_MASK2;
157 t1 = t1 + t2;
158 v=bn_mul_add_words(rp,np,nl,(BN_ULONG) t1);
159 }
160#else
161 v=bn_mul_add_words(rp,np,nl,(rp[0]*n0)&BN_MASK2);
162#endif
163 nrp++;
164 rp++;
165 if (((nrp[-1]+=v)&BN_MASK2) >= v)
166 continue;
167 else
168 {
169 if (((++nrp[0])&BN_MASK2) != 0) continue;
170 if (((++nrp[1])&BN_MASK2) != 0) continue;
171 for (x=2; (((++nrp[x])&BN_MASK2) == 0); x++) ;
172 }
173 }
174 bn_fix_top(r);
175
176 /* mont->ri will be a multiple of the word size and below code
177 * is kind of BN_rshift(ret,r,mont->ri) equivalent */
178 if (r->top <= ri)
179 {
180 ret->top=0;
181 retn=1;
182 goto err;
183 }
184 al=r->top-ri;
185
186# define BRANCH_FREE 1
187# if BRANCH_FREE
188 if (bn_wexpand(ret,ri) == NULL) goto err;
189 x=0-(((al-ri)>>(sizeof(al)*8-1))&1);
190 ret->top=x=(ri&~x)|(al&x); /* min(ri,al) */
191 ret->neg=r->neg;
192
193 rp=ret->d;
194 ap=&(r->d[ri]);
195
196 {
197 size_t m1,m2;
198
199 v=bn_sub_words(rp,ap,np,ri);
200 /* this ----------------^^ works even in al<ri case
201 * thanks to zealous zeroing of top of the vector in the
202 * beginning. */
203
204 /* if (al==ri && !v) || al>ri) nrp=rp; else nrp=ap; */
205 /* in other words if subtraction result is real, then
206 * trick unconditional memcpy below to perform in-place
207 * "refresh" instead of actual copy. */
208 m1=0-(size_t)(((al-ri)>>(sizeof(al)*8-1))&1); /* al<ri */
209 m2=0-(size_t)(((ri-al)>>(sizeof(al)*8-1))&1); /* al>ri */
210 m1|=m2; /* (al!=ri) */
211 m1|=(0-(size_t)v); /* (al!=ri || v) */
212 m1&=~m2; /* (al!=ri || v) && !al>ri */
213 nrp=(BN_ULONG *)(((size_t)rp&~m1)|((size_t)ap&m1));
214 }
215
216 /* 'i<ri' is chosen to eliminate dependency on input data, even
217 * though it results in redundant copy in al<ri case. */
218 for (i=0,ri-=4; i<ri; i+=4)
219 {
220 BN_ULONG t1,t2,t3,t4;
221
222 t1=nrp[i+0];
223 t2=nrp[i+1];
224 t3=nrp[i+2]; ap[i+0]=0;
225 t4=nrp[i+3]; ap[i+1]=0;
226 rp[i+0]=t1; ap[i+2]=0;
227 rp[i+1]=t2; ap[i+3]=0;
228 rp[i+2]=t3;
229 rp[i+3]=t4;
230 }
231 for (ri+=4; i<ri; i++)
232 rp[i]=nrp[i], ap[i]=0;
233# else
234 if (bn_wexpand(ret,al) == NULL) goto err;
235 ret->top=al;
236 ret->neg=r->neg;
237
238 rp=ret->d;
239 ap=&(r->d[ri]);
240 al-=4;
241 for (i=0; i<al; i+=4)
242 {
243 BN_ULONG t1,t2,t3,t4;
244
245 t1=ap[i+0];
246 t2=ap[i+1];
247 t3=ap[i+2];
248 t4=ap[i+3];
249 rp[i+0]=t1;
250 rp[i+1]=t2;
251 rp[i+2]=t3;
252 rp[i+3]=t4;
253 }
254 al+=4;
255 for (; i<al; i++)
256 rp[i]=ap[i];
257# endif
258#else /* !MONT_WORD */
259 BIGNUM *t1,*t2;
260
261 BN_CTX_start(ctx);
262 t1 = BN_CTX_get(ctx);
263 t2 = BN_CTX_get(ctx);
264 if (t1 == NULL || t2 == NULL) goto err;
265
266 if (!BN_copy(t1,a)) goto err;
267 BN_mask_bits(t1,mont->ri);
268
269 if (!BN_mul(t2,t1,&mont->Ni,ctx)) goto err;
270 BN_mask_bits(t2,mont->ri);
271
272 if (!BN_mul(t1,t2,&mont->N,ctx)) goto err;
273 if (!BN_add(t2,a,t1)) goto err;
274 if (!BN_rshift(ret,t2,mont->ri)) goto err;
275#endif /* MONT_WORD */
276
277#if !defined(BRANCH_FREE) || BRANCH_FREE==0
278 if (BN_ucmp(ret, &(mont->N)) >= 0)
279 {
280 if (!BN_usub(ret,ret,&(mont->N))) goto err;
281 }
282#endif
283 retn=1;
284 err:
285 BN_CTX_end(ctx);
286 return(retn);
287 }
288
289BN_MONT_CTX *BN_MONT_CTX_new(void)
290 {
291 BN_MONT_CTX *ret;
292
293 if ((ret=(BN_MONT_CTX *)OPENSSL_malloc(sizeof(BN_MONT_CTX))) == NULL)
294 return(NULL);
295
296 BN_MONT_CTX_init(ret);
297 ret->flags=BN_FLG_MALLOCED;
298 return(ret);
299 }
300
301void BN_MONT_CTX_init(BN_MONT_CTX *ctx)
302 {
303 ctx->ri=0;
304 BN_init(&(ctx->RR));
305 BN_init(&(ctx->N));
306 BN_init(&(ctx->Ni));
307 ctx->flags=0;
308 }
309
310void BN_MONT_CTX_free(BN_MONT_CTX *mont)
311 {
312 if(mont == NULL)
313 return;
314
315 BN_free(&(mont->RR));
316 BN_free(&(mont->N));
317 BN_free(&(mont->Ni));
318 if (mont->flags & BN_FLG_MALLOCED)
319 OPENSSL_free(mont);
320 }
321
322int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx)
323 {
324 BIGNUM Ri,*R;
325
326 BN_init(&Ri);
327 R= &(mont->RR); /* grab RR as a temp */
328 if (!BN_copy(&(mont->N),mod)) goto err; /* Set N */
329 mont->N.neg = 0;
330
331#ifdef MONT_WORD
332 {
333 BIGNUM tmod;
334 BN_ULONG buf[2];
335
336 mont->ri=(BN_num_bits(mod)+(BN_BITS2-1))/BN_BITS2*BN_BITS2;
337 if (!(BN_zero(R))) goto err;
338 if (!(BN_set_bit(R,BN_BITS2))) goto err; /* R */
339
340 buf[0]=mod->d[0]; /* tmod = N mod word size */
341 buf[1]=0;
342 tmod.d=buf;
343 tmod.top=1;
344 tmod.dmax=2;
345 tmod.neg=0;
346 /* Ri = R^-1 mod N*/
347 if ((BN_mod_inverse(&Ri,R,&tmod,ctx)) == NULL)
348 goto err;
349 if (!BN_lshift(&Ri,&Ri,BN_BITS2)) goto err; /* R*Ri */
350 if (!BN_is_zero(&Ri))
351 {
352 if (!BN_sub_word(&Ri,1)) goto err;
353 }
354 else /* if N mod word size == 1 */
355 {
356 if (!BN_set_word(&Ri,BN_MASK2)) goto err; /* Ri-- (mod word size) */
357 }
358 if (!BN_div(&Ri,NULL,&Ri,&tmod,ctx)) goto err;
359 /* Ni = (R*Ri-1)/N,
360 * keep only least significant word: */
361 mont->n0 = (Ri.top > 0) ? Ri.d[0] : 0;
362 BN_free(&Ri);
363 }
364#else /* !MONT_WORD */
365 { /* bignum version */
366 mont->ri=BN_num_bits(&mont->N);
367 if (!BN_zero(R)) goto err;
368 if (!BN_set_bit(R,mont->ri)) goto err; /* R = 2^ri */
369 /* Ri = R^-1 mod N*/
370 if ((BN_mod_inverse(&Ri,R,&mont->N,ctx)) == NULL)
371 goto err;
372 if (!BN_lshift(&Ri,&Ri,mont->ri)) goto err; /* R*Ri */
373 if (!BN_sub_word(&Ri,1)) goto err;
374 /* Ni = (R*Ri-1) / N */
375 if (!BN_div(&(mont->Ni),NULL,&Ri,&mont->N,ctx)) goto err;
376 BN_free(&Ri);
377 }
378#endif
379
380 /* setup RR for conversions */
381 if (!BN_zero(&(mont->RR))) goto err;
382 if (!BN_set_bit(&(mont->RR),mont->ri*2)) goto err;
383 if (!BN_mod(&(mont->RR),&(mont->RR),&(mont->N),ctx)) goto err;
384
385 return(1);
386err:
387 return(0);
388 }
389
390BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from)
391 {
392 if (to == from) return(to);
393
394 if (!BN_copy(&(to->RR),&(from->RR))) return NULL;
395 if (!BN_copy(&(to->N),&(from->N))) return NULL;
396 if (!BN_copy(&(to->Ni),&(from->Ni))) return NULL;
397 to->ri=from->ri;
398 to->n0=from->n0;
399 return(to);
400 }
401
402BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock,
403 const BIGNUM *mod, BN_CTX *ctx)
404 {
405 if (*pmont)
406 return *pmont;
407 CRYPTO_w_lock(lock);
408 if (!*pmont)
409 {
410 *pmont = BN_MONT_CTX_new();
411 if (*pmont && !BN_MONT_CTX_set(*pmont, mod, ctx))
412 {
413 BN_MONT_CTX_free(*pmont);
414 *pmont = NULL;
415 }
416 }
417 CRYPTO_w_unlock(lock);
418 return *pmont;
419 }
420
421
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