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://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
70 #define MONT_WORD /* use the faster word-based algorithm */
72 int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
73 BN_MONT_CTX *mont, BN_CTX *ctx)
79 tmp = BN_CTX_get(ctx);
80 if (tmp == NULL) goto err;
85 if (!BN_sqr(tmp,a,ctx)) goto err;
89 if (!BN_mul(tmp,a,b,ctx)) goto err;
91 /* reduce from aRR to aR */
92 if (!BN_from_montgomery(r,tmp,mont,ctx)) goto err;
99 int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
106 BN_ULONG *ap,*np,*rp,n0,v,*nrp;
107 int al,nl,max,i,x,ri;
110 if ((r = BN_CTX_get(ctx)) == NULL) goto err;
112 if (!BN_copy(r,a)) goto err;
116 /* mont->ri is the size of mont->N in bits (rounded up
118 al=ri=mont->ri/BN_BITS2;
121 if ((al == 0) || (nl == 0)) { r->top=0; return(1); }
123 max=(nl+al+1); /* allow for overflow (no?) XXX */
124 if (bn_wexpand(r,max) == NULL) goto err;
125 if (bn_wexpand(ret,max) == NULL) goto err;
127 r->neg=a->neg^n->neg;
132 /* clear the top words of T */
134 for (i=r->top; i<max; i++) /* memset? XXX */
137 memset(&(r->d[r->top]),0,(max-r->top)*sizeof(BN_ULONG));
144 fprintf(stderr,"word BN_from_montgomery %d * %d\n",nl,nl);
153 t1 = rp[0] * (n0 & 0177777);
156 t3 = rp[0] & 0177777;
157 t2 = (t3 * t2) & BN_MASK2;
159 v=bn_mul_add_words(rp,np,nl,(BN_ULONG) t1);
162 v=bn_mul_add_words(rp,np,nl,(rp[0]*n0)&BN_MASK2);
166 if (((nrp[-1]+=v)&BN_MASK2) >= v)
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++) ;
177 /* mont->ri will be a multiple of the word size */
179 BN_rshift(ret,r,mont->ri);
191 for (i=0; i<al; i+=4)
193 BN_ULONG t1,t2,t3,t4;
208 #else /* !MONT_WORD */
212 t1 = BN_CTX_get(ctx);
213 t2 = BN_CTX_get(ctx);
214 if (t1 == NULL || t2 == NULL) goto err;
216 if (!BN_copy(t1,a)) goto err;
217 BN_mask_bits(t1,mont->ri);
219 if (!BN_mul(t2,t1,&mont->Ni,ctx)) goto err;
220 BN_mask_bits(t2,mont->ri);
222 if (!BN_mul(t1,t2,&mont->N,ctx)) goto err;
223 if (!BN_add(t2,a,t1)) goto err;
224 BN_rshift(ret,t2,mont->ri);
225 #endif /* MONT_WORD */
227 if (BN_ucmp(ret, &(mont->N)) >= 0)
229 if (!BN_usub(ret,ret,&(mont->N))) goto err;
237 BN_MONT_CTX *BN_MONT_CTX_new(void)
241 if ((ret=(BN_MONT_CTX *)OPENSSL_malloc(sizeof(BN_MONT_CTX))) == NULL)
244 BN_MONT_CTX_init(ret);
245 ret->flags=BN_FLG_MALLOCED;
249 void BN_MONT_CTX_init(BN_MONT_CTX *ctx)
258 void BN_MONT_CTX_free(BN_MONT_CTX *mont)
263 BN_free(&(mont->RR));
265 BN_free(&(mont->Ni));
266 if (mont->flags & BN_FLG_MALLOCED)
270 int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx)
275 R= &(mont->RR); /* grab RR as a temp */
276 BN_copy(&(mont->N),mod); /* Set N */
284 mont->ri=(BN_num_bits(mod)+(BN_BITS2-1))/BN_BITS2*BN_BITS2;
286 BN_set_bit(R,BN_BITS2); /* R */
288 buf[0]=mod->d[0]; /* tmod = N mod word size */
295 if ((BN_mod_inverse(&Ri,R,&tmod,ctx)) == NULL)
297 if (!BN_lshift(&Ri,&Ri,BN_BITS2)) goto err; /* R*Ri */
298 if (!BN_is_zero(&Ri))
300 if (!BN_sub_word(&Ri,1)) goto err;
302 else /* if N mod word size == 1 */
304 if (!BN_set_word(&Ri,BN_MASK2)) goto err; /* Ri-- (mod word size) */
306 if (!BN_div(&Ri,NULL,&Ri,&tmod,ctx)) goto err;
308 * keep only least significant word: */
309 mont->n0 = (Ri.top > 0) ? Ri.d[0] : 0;
312 #else /* !MONT_WORD */
313 { /* bignum version */
314 mont->ri=BN_num_bits(&mont->N);
315 if (!BN_zero(R)) goto err;
316 if (!BN_set_bit(R,mont->ri)) goto err; /* R = 2^ri */
318 if ((BN_mod_inverse(&Ri,R,&mont->N,ctx)) == NULL)
320 if (!BN_lshift(&Ri,&Ri,mont->ri)) goto err; /* R*Ri */
321 if (!BN_sub_word(&Ri,1)) goto err;
322 /* Ni = (R*Ri-1) / N */
323 if (!BN_div(&(mont->Ni),NULL,&Ri,&mont->N,ctx)) goto err;
328 /* setup RR for conversions */
329 if (!BN_zero(&(mont->RR))) goto err;
330 if (!BN_set_bit(&(mont->RR),mont->ri*2)) goto err;
331 if (!BN_mod(&(mont->RR),&(mont->RR),&(mont->N),ctx)) goto err;
338 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from)
340 if (to == from) return(to);
342 BN_copy(&(to->RR),&(from->RR));
343 BN_copy(&(to->N),&(from->N));
344 BN_copy(&(to->Ni),&(from->Ni));