1 /* crypto/bn/bn_mont.c */
2 /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
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.
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).
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.
23 * Redistribution and use in source and binary forms, with or without
24 * modification, are permitted provided that the following conditions
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)"
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
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.]
60 * Details about Montgomery multiplication algorithms can be found at:
61 * http://www.ece.orst.edu/ISL/Publications.html
62 * http://www.ece.orst.edu/ISL/Koc/papers/j37acmon.pdf
71 int BN_mod_mul_montgomery(BIGNUM *r, BIGNUM *a, BIGNUM *b,
72 BN_MONT_CTX *mont, BN_CTX *ctx)
76 tmp= &(ctx->bn[ctx->tos]);
77 tmp2= &(ctx->bn[ctx->tos]);
86 bn_wexpand(tmp,a->top*2);
87 bn_wexpand(tmp2,a->top*4);
88 bn_sqr_recursive(tmp->d,a->d,a->top,tmp2->d);
90 if (tmp->d[tmp->top-1] == 0)
93 if (!BN_sqr(tmp,a,ctx)) goto err;
98 if (!BN_mul(tmp,a,b,ctx)) goto err;
100 /* reduce from aRR to aR */
101 if (!BN_from_montgomery(r,tmp,mont,ctx)) goto err;
108 int BN_from_montgomery(BIGNUM *ret, BIGNUM *a, BN_MONT_CTX *mont,
111 #ifdef BN_RECURSION_MONT
116 BN_ULONG *ap,*np,*rp,n0,v,*nrp;
117 int al,nl,max,i,x,ri;
120 r= &(ctx->bn[ctx->tos]);
122 if (!BN_copy(r,a)) goto err1;
126 /* mont->ri is the size of mont->N in bits/words */
127 al=ri=mont->ri/BN_BITS2;
130 if ((al == 0) || (nl == 0)) { r->top=0; return(1); }
132 max=(nl+al+1); /* allow for overflow (no?) XXX */
133 if (bn_wexpand(r,max) == NULL) goto err1;
134 if (bn_wexpand(ret,max) == NULL) goto err1;
136 r->neg=a->neg^n->neg;
141 /* clear the top words of T */
143 for (i=r->top; i<max; i++) /* memset? XXX */
146 memset(&(r->d[r->top]),0,(max-r->top)*sizeof(BN_ULONG));
153 printf("word BN_from_montgomery %d * %d\n",nl,nl);
157 v=bn_mul_add_words(rp,np,nl,(rp[0]*n0)&BN_MASK2);
160 if (((nrp[-1]+=v)&BN_MASK2) >= v)
164 if (((++nrp[0])&BN_MASK2) != 0) continue;
165 if (((++nrp[1])&BN_MASK2) != 0) continue;
166 for (x=2; (((++nrp[x])&BN_MASK2) == 0); x++) ;
171 /* mont->ri will be a multiple of the word size */
173 BN_rshift(ret,r,mont->ri);
184 for (i=0; i<al; i+=4)
186 BN_ULONG t1,t2,t3,t4;
202 if (BN_ucmp(ret, &(mont->N)) >= 0)
204 BN_usub(ret,ret,&(mont->N)); /* XXX */
210 #ifdef BN_RECURSION_MONT
211 else /* bignum version */
217 printf("number BN_from_montgomery\n");
220 t1= &(ctx->bn[ctx->tos]);
221 t2= &(ctx->bn[ctx->tos+1]);
222 t3= &(ctx->bn[ctx->tos+2]);
225 bn_wexpand(ret,i); /* perhaps only i*2 */
226 bn_wexpand(t1,i*4); /* perhaps only i*2 */
227 bn_wexpand(t2,i*2); /* perhaps only i */
229 bn_mul_low_recursive(t2->d,a->d,mont->Ni.d,i,t1->d);
232 BN_set_bit(t3,mont->N.top*BN_BITS2);
233 bn_sub_words(t3->d,t3->d,a->d,i);
234 bn_mul_high(ret->d,t2->d,mont->N.d,t3->d,i,t1->d);
236 /* hmm... if a is between i and 2*i, things are bad */
239 j=(int)(bn_add_words(ret->d,ret->d,&(a->d[i]),i));
240 if (j) /* overflow */
241 bn_sub_words(ret->d,ret->d,mont->N.d,i);
246 BN_add_word(ret,1); /* Always? */
247 else /* Very very rare */
249 for (i=1; i<mont->N.top-1; i++)
253 BN_add_word(ret,1); /* Always? */
259 if (BN_ucmp(ret,&(mont->N)) >= 0)
260 BN_usub(ret,ret,&(mont->N));
267 BN_MONT_CTX *BN_MONT_CTX_new(void)
271 if ((ret=(BN_MONT_CTX *)Malloc(sizeof(BN_MONT_CTX))) == NULL)
274 BN_MONT_CTX_init(ret);
275 ret->flags=BN_FLG_MALLOCED;
279 void BN_MONT_CTX_init(BN_MONT_CTX *ctx)
289 void BN_MONT_CTX_free(BN_MONT_CTX *mont)
294 BN_free(&(mont->RR));
296 BN_free(&(mont->Ni));
297 if (mont->flags & BN_FLG_MALLOCED)
301 int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx)
306 R= &(mont->RR); /* grab RR as a temp */
307 BN_copy(&(mont->N),mod); /* Set N */
309 #ifdef BN_RECURSION_MONT
310 if (mont->N.top < BN_MONT_CTX_SET_SIZE_WORD)
318 mont->ri=(BN_num_bits(mod)+(BN_BITS2-1))/BN_BITS2*BN_BITS2;
320 BN_set_bit(R,BN_BITS2);
321 /* I was bad, this modification of a passed variable was
322 * breaking the multithreaded stuff :-(
333 if ((BN_mod_inverse(&Ri,R,&tmod,ctx)) == NULL)
335 BN_lshift(&Ri,&Ri,BN_BITS2); /* R*Ri */
336 if (!BN_is_zero(&Ri))
341 BN_usub(&Ri,&Ri,BN_value_one()); /* R*Ri - 1 */
346 /* This is not common..., 1 in BN_MASK2,
347 * It happens when buf[0] was == 1. So for 8 bit,
348 * this is 1/256, 16bit, 1 in 2^16 etc.
350 BN_set_word(&Ri,BN_MASK2);
352 BN_div(&Ri,NULL,&Ri,&tmod,ctx);
357 #ifdef BN_RECURSION_MONT
361 mont->ri=(BN_num_bits(mod)+(BN_BITS2-1))/BN_BITS2*BN_BITS2;
364 BN_set_bit(R,mont->ri);
366 BN_lshift(R,BN_value_one(),mont->ri); /* R */
368 if ((BN_mod_inverse(&Ri,R,mod,ctx)) == NULL)
370 BN_lshift(&Ri,&Ri,mont->ri); /* R*Ri */
374 BN_usub(&Ri,&Ri,BN_value_one()); /* R*Ri - 1 */
376 BN_div(&(mont->Ni),NULL,&Ri,mod,ctx);
381 /* setup RR for conversions */
383 BN_zero(&(mont->RR));
384 BN_set_bit(&(mont->RR),mont->ri*2);
386 BN_lshift(mont->RR,BN_value_one(),mont->ri*2);
388 BN_mod(&(mont->RR),&(mont->RR),&(mont->N),ctx);
395 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from)
397 if (to == from) return(to);
399 BN_copy(&(to->RR),&(from->RR));
400 BN_copy(&(to->N),&(from->N));
401 BN_copy(&(to->Ni),&(from->Ni));
402 to->use_word=from->use_word;