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
BN_mod_mul_montgomery(BIGNUM * r,const BIGNUM * a,const BIGNUM * b,BN_MONT_CTX * mont,BN_CTX * ctx)72 int 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 bn_check_top(r);
94 ret=1;
95 err:
96 BN_CTX_end(ctx);
97 return(ret);
98 }
99
BN_from_montgomery(BIGNUM * ret,const BIGNUM * a,BN_MONT_CTX * mont,BN_CTX * ctx)100 int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
101 BN_CTX *ctx)
102 {
103 int retn=0;
104
105 #ifdef MONT_WORD
106 BIGNUM *n,*r;
107 BN_ULONG *ap,*np,*rp,n0,v,*nrp;
108 int al,nl,max,i,x,ri;
109
110 BN_CTX_start(ctx);
111 if ((r = BN_CTX_get(ctx)) == NULL) goto err;
112
113 if (!BN_copy(r,a)) goto err;
114 n= &(mont->N);
115
116 ap=a->d;
117 /* mont->ri is the size of mont->N in bits (rounded up
118 to the word size) */
119 al=ri=mont->ri/BN_BITS2;
120
121 nl=n->top;
122 if ((al == 0) || (nl == 0)) { r->top=0; return(1); }
123
124 max=(nl+al+1); /* allow for overflow (no?) XXX */
125 if (bn_wexpand(r,max) == NULL) goto err;
126
127 r->neg=a->neg^n->neg;
128 np=n->d;
129 rp=r->d;
130 nrp= &(r->d[nl]);
131
132 /* clear the top words of T */
133 #if 1
134 for (i=r->top; i<max; i++) /* memset? XXX */
135 r->d[i]=0;
136 #else
137 memset(&(r->d[r->top]),0,(max-r->top)*sizeof(BN_ULONG));
138 #endif
139
140 r->top=max;
141 n0=mont->n0;
142
143 #ifdef BN_COUNT
144 fprintf(stderr,"word BN_from_montgomery %d * %d\n",nl,nl);
145 #endif
146 for (i=0; i<nl; i++)
147 {
148 #ifdef __TANDEM
149 {
150 long long t1;
151 long long t2;
152 long long t3;
153 t1 = rp[0] * (n0 & 0177777);
154 t2 = 037777600000l;
155 t2 = n0 & t2;
156 t3 = rp[0] & 0177777;
157 t2 = (t3 * t2) & BN_MASK2;
158 t1 = t1 + t2;
159 v=bn_mul_add_words(rp,np,nl,(BN_ULONG) t1);
160 }
161 #else
162 v=bn_mul_add_words(rp,np,nl,(rp[0]*n0)&BN_MASK2);
163 #endif
164 nrp++;
165 rp++;
166 if (((nrp[-1]+=v)&BN_MASK2) >= v)
167 continue;
168 else
169 {
170 if (((++nrp[0])&BN_MASK2) != 0) continue;
171 if (((++nrp[1])&BN_MASK2) != 0) continue;
172 for (x=2; (((++nrp[x])&BN_MASK2) == 0); x++) ;
173 }
174 }
175 bn_correct_top(r);
176
177 /* mont->ri will be a multiple of the word size and below code
178 * is kind of BN_rshift(ret,r,mont->ri) equivalent */
179 if (r->top <= ri)
180 {
181 ret->top=0;
182 retn=1;
183 goto err;
184 }
185 al=r->top-ri;
186
187 # define BRANCH_FREE 1
188 # if BRANCH_FREE
189 if (bn_wexpand(ret,ri) == NULL) goto err;
190 x=0-(((al-ri)>>(sizeof(al)*8-1))&1);
191 ret->top=x=(ri&~x)|(al&x); /* min(ri,al) */
192 ret->neg=r->neg;
193
194 rp=ret->d;
195 ap=&(r->d[ri]);
196
197 {
198 size_t m1,m2;
199
200 v=bn_sub_words(rp,ap,np,ri);
201 /* this ----------------^^ works even in al<ri case
202 * thanks to zealous zeroing of top of the vector in the
203 * beginning. */
204
205 /* if (al==ri && !v) || al>ri) nrp=rp; else nrp=ap; */
206 /* in other words if subtraction result is real, then
207 * trick unconditional memcpy below to perform in-place
208 * "refresh" instead of actual copy. */
209 m1=0-(size_t)(((al-ri)>>(sizeof(al)*8-1))&1); /* al<ri */
210 m2=0-(size_t)(((ri-al)>>(sizeof(al)*8-1))&1); /* al>ri */
211 m1|=m2; /* (al!=ri) */
212 m1|=(0-(size_t)v); /* (al!=ri || v) */
213 m1&=~m2; /* (al!=ri || v) && !al>ri */
214 nrp=(BN_ULONG *)(((size_t)rp&~m1)|((size_t)ap&m1));
215 }
216
217 /* 'i<ri' is chosen to eliminate dependency on input data, even
218 * though it results in redundant copy in al<ri case. */
219 for (i=0,ri-=4; i<ri; i+=4)
220 {
221 BN_ULONG t1,t2,t3,t4;
222
223 t1=nrp[i+0];
224 t2=nrp[i+1];
225 t3=nrp[i+2]; ap[i+0]=0;
226 t4=nrp[i+3]; ap[i+1]=0;
227 rp[i+0]=t1; ap[i+2]=0;
228 rp[i+1]=t2; ap[i+3]=0;
229 rp[i+2]=t3;
230 rp[i+3]=t4;
231 }
232 for (ri+=4; i<ri; i++)
233 rp[i]=nrp[i], ap[i]=0;
234 # else
235 if (bn_wexpand(ret,al) == NULL) goto err;
236 ret->top=al;
237 ret->neg=r->neg;
238
239 rp=ret->d;
240 ap=&(r->d[ri]);
241 al-=4;
242 for (i=0; i<al; i+=4)
243 {
244 BN_ULONG t1,t2,t3,t4;
245
246 t1=ap[i+0];
247 t2=ap[i+1];
248 t3=ap[i+2];
249 t4=ap[i+3];
250 rp[i+0]=t1;
251 rp[i+1]=t2;
252 rp[i+2]=t3;
253 rp[i+3]=t4;
254 }
255 al+=4;
256 for (; i<al; i++)
257 rp[i]=ap[i];
258 # endif
259 #else /* !MONT_WORD */
260 BIGNUM *t1,*t2;
261
262 BN_CTX_start(ctx);
263 t1 = BN_CTX_get(ctx);
264 t2 = BN_CTX_get(ctx);
265 if (t1 == NULL || t2 == NULL) goto err;
266
267 if (!BN_copy(t1,a)) goto err;
268 BN_mask_bits(t1,mont->ri);
269
270 if (!BN_mul(t2,t1,&mont->Ni,ctx)) goto err;
271 BN_mask_bits(t2,mont->ri);
272
273 if (!BN_mul(t1,t2,&mont->N,ctx)) goto err;
274 if (!BN_add(t2,a,t1)) goto err;
275 if (!BN_rshift(ret,t2,mont->ri)) goto err;
276 #endif /* MONT_WORD */
277
278 #if !defined(BRANCH_FREE) || BRANCH_FREE==0
279 if (BN_ucmp(ret, &(mont->N)) >= 0)
280 {
281 if (!BN_usub(ret,ret,&(mont->N))) goto err;
282 }
283 #endif
284 retn=1;
285 bn_check_top(ret);
286 err:
287 BN_CTX_end(ctx);
288 return(retn);
289 }
290
BN_MONT_CTX_new(void)291 BN_MONT_CTX *BN_MONT_CTX_new(void)
292 {
293 BN_MONT_CTX *ret;
294
295 if ((ret=(BN_MONT_CTX *)OPENSSL_malloc(sizeof(BN_MONT_CTX))) == NULL)
296 return(NULL);
297
298 BN_MONT_CTX_init(ret);
299 ret->flags=BN_FLG_MALLOCED;
300 return(ret);
301 }
302
BN_MONT_CTX_init(BN_MONT_CTX * ctx)303 void BN_MONT_CTX_init(BN_MONT_CTX *ctx)
304 {
305 ctx->ri=0;
306 BN_init(&(ctx->RR));
307 BN_init(&(ctx->N));
308 BN_init(&(ctx->Ni));
309 ctx->flags=0;
310 }
311
BN_MONT_CTX_free(BN_MONT_CTX * mont)312 void BN_MONT_CTX_free(BN_MONT_CTX *mont)
313 {
314 if(mont == NULL)
315 return;
316
317 BN_free(&(mont->RR));
318 BN_free(&(mont->N));
319 BN_free(&(mont->Ni));
320 if (mont->flags & BN_FLG_MALLOCED)
321 OPENSSL_free(mont);
322 }
323
BN_MONT_CTX_set(BN_MONT_CTX * mont,const BIGNUM * mod,BN_CTX * ctx)324 int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx)
325 {
326 int ret = 0;
327 BIGNUM *Ri,*R;
328
329 BN_CTX_start(ctx);
330 if((Ri = BN_CTX_get(ctx)) == NULL) goto err;
331 R= &(mont->RR); /* grab RR as a temp */
332 if (!BN_copy(&(mont->N),mod)) goto err; /* Set N */
333 mont->N.neg = 0;
334
335 #ifdef MONT_WORD
336 {
337 BIGNUM tmod;
338 BN_ULONG buf[2];
339
340 mont->ri=(BN_num_bits(mod)+(BN_BITS2-1))/BN_BITS2*BN_BITS2;
341 BN_zero(R);
342 if (!(BN_set_bit(R,BN_BITS2))) goto err; /* R */
343
344 buf[0]=mod->d[0]; /* tmod = N mod word size */
345 buf[1]=0;
346 tmod.d=buf;
347 tmod.top = buf[0] != 0 ? 1 : 0;
348 tmod.dmax=2;
349 tmod.neg=0;
350 /* Ri = R^-1 mod N*/
351 if ((BN_mod_inverse(Ri,R,&tmod,ctx)) == NULL)
352 goto err;
353 if (!BN_lshift(Ri,Ri,BN_BITS2)) goto err; /* R*Ri */
354 if (!BN_is_zero(Ri))
355 {
356 if (!BN_sub_word(Ri,1)) goto err;
357 }
358 else /* if N mod word size == 1 */
359 {
360 if (!BN_set_word(Ri,BN_MASK2)) goto err; /* Ri-- (mod word size) */
361 }
362 if (!BN_div(Ri,NULL,Ri,&tmod,ctx)) goto err;
363 /* Ni = (R*Ri-1)/N,
364 * keep only least significant word: */
365 mont->n0 = (Ri->top > 0) ? Ri->d[0] : 0;
366 }
367 #else /* !MONT_WORD */
368 { /* bignum version */
369 mont->ri=BN_num_bits(&mont->N);
370 BN_zero(R);
371 if (!BN_set_bit(R,mont->ri)) goto err; /* R = 2^ri */
372 /* Ri = R^-1 mod N*/
373 if ((BN_mod_inverse(Ri,R,&mont->N,ctx)) == NULL)
374 goto err;
375 if (!BN_lshift(Ri,Ri,mont->ri)) goto err; /* R*Ri */
376 if (!BN_sub_word(Ri,1)) goto err;
377 /* Ni = (R*Ri-1) / N */
378 if (!BN_div(&(mont->Ni),NULL,Ri,&mont->N,ctx)) goto err;
379 }
380 #endif
381
382 /* setup RR for conversions */
383 BN_zero(&(mont->RR));
384 if (!BN_set_bit(&(mont->RR),mont->ri*2)) goto err;
385 if (!BN_mod(&(mont->RR),&(mont->RR),&(mont->N),ctx)) goto err;
386
387 ret = 1;
388 err:
389 BN_CTX_end(ctx);
390 return ret;
391 }
392
BN_MONT_CTX_copy(BN_MONT_CTX * to,BN_MONT_CTX * from)393 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from)
394 {
395 if (to == from) return(to);
396
397 if (!BN_copy(&(to->RR),&(from->RR))) return NULL;
398 if (!BN_copy(&(to->N),&(from->N))) return NULL;
399 if (!BN_copy(&(to->Ni),&(from->Ni))) return NULL;
400 to->ri=from->ri;
401 to->n0=from->n0;
402 return(to);
403 }
404
BN_MONT_CTX_set_locked(BN_MONT_CTX ** pmont,int lock,const BIGNUM * mod,BN_CTX * ctx)405 BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock,
406 const BIGNUM *mod, BN_CTX *ctx)
407 {
408 if (*pmont)
409 return *pmont;
410 CRYPTO_w_lock(lock);
411 if (!*pmont)
412 {
413 *pmont = BN_MONT_CTX_new();
414 if (*pmont && !BN_MONT_CTX_set(*pmont, mod, ctx))
415 {
416 BN_MONT_CTX_free(*pmont);
417 *pmont = NULL;
418 }
419 }
420 CRYPTO_w_unlock(lock);
421 return *pmont;
422 }
423