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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, BIGNUM *a, BIGNUM *b,
73 BN_MONT_CTX *mont, BN_CTX *ctx)
74 {
75 BIGNUM *tmp,*tmp2;
76 int ret=0;
77
78 BN_CTX_start(ctx);
79 tmp = BN_CTX_get(ctx);
80 tmp2 = BN_CTX_get(ctx);
81 if (tmp == NULL || tmp2 == NULL) goto err;
82
83 bn_check_top(tmp);
84 bn_check_top(tmp2);
85
86 if (a == b)
87 {
88 if (!BN_sqr(tmp,a,ctx)) goto err;
89 }
90 else
91 {
92 if (!BN_mul(tmp,a,b,ctx)) goto err;
93 }
94 /* reduce from aRR to aR */
95 if (!BN_from_montgomery(r,tmp,mont,ctx)) goto err;
96 ret=1;
97err:
98 BN_CTX_end(ctx);
99 return(ret);
100 }
101
102int BN_from_montgomery(BIGNUM *ret, BIGNUM *a, BN_MONT_CTX *mont,
103 BN_CTX *ctx)
104 {
105 int retn=0;
106
107#ifdef MONT_WORD
108 BIGNUM *n,*r;
109 BN_ULONG *ap,*np,*rp,n0,v,*nrp;
110 int al,nl,max,i,x,ri;
111
112 BN_CTX_start(ctx);
113 if ((r = BN_CTX_get(ctx)) == NULL) goto err;
114
115 if (!BN_copy(r,a)) goto err;
116 n= &(mont->N);
117
118 ap=a->d;
119 /* mont->ri is the size of mont->N in bits (rounded up
120 to the word size) */
121 al=ri=mont->ri/BN_BITS2;
122
123 nl=n->top;
124 if ((al == 0) || (nl == 0)) { r->top=0; return(1); }
125
126 max=(nl+al+1); /* allow for overflow (no?) XXX */
127 if (bn_wexpand(r,max) == NULL) goto err;
128 if (bn_wexpand(ret,max) == NULL) goto err;
129
130 r->neg=a->neg^n->neg;
131 np=n->d;
132 rp=r->d;
133 nrp= &(r->d[nl]);
134
135 /* clear the top words of T */
136#if 1
137 for (i=r->top; i<max; i++) /* memset? XXX */
138 r->d[i]=0;
139#else
140 memset(&(r->d[r->top]),0,(max-r->top)*sizeof(BN_ULONG));
141#endif
142
143 r->top=max;
144 n0=mont->n0;
145
146#ifdef BN_COUNT
147 printf("word BN_from_montgomery %d * %d\n",nl,nl);
148#endif
149 for (i=0; i<nl; i++)
150 {
151#ifdef __TANDEM
152 {
153 long long t1;
154 long long t2;
155 long long t3;
156 t1 = rp[0] * (n0 & 0177777);
157 t2 = 037777600000l;
158 t2 = n0 & t2;
159 t3 = rp[0] & 0177777;
160 t2 = (t3 * t2) & BN_MASK2;
161 t1 = t1 + t2;
162 v=bn_mul_add_words(rp,np,nl,(BN_ULONG) t1);
163 }
164#else
165 v=bn_mul_add_words(rp,np,nl,(rp[0]*n0)&BN_MASK2);
166#endif
167 nrp++;
168 rp++;
169 if (((nrp[-1]+=v)&BN_MASK2) >= v)
170 continue;
171 else
172 {
173 if (((++nrp[0])&BN_MASK2) != 0) continue;
174 if (((++nrp[1])&BN_MASK2) != 0) continue;
175 for (x=2; (((++nrp[x])&BN_MASK2) == 0); x++) ;
176 }
177 }
178 bn_fix_top(r);
179
180 /* mont->ri will be a multiple of the word size */
181#if 0
182 BN_rshift(ret,r,mont->ri);
183#else
184 ret->neg = r->neg;
185 x=ri;
186 rp=ret->d;
187 ap= &(r->d[x]);
188 if (r->top < x)
189 al=0;
190 else
191 al=r->top-x;
192 ret->top=al;
193 al-=4;
194 for (i=0; i<al; i+=4)
195 {
196 BN_ULONG t1,t2,t3,t4;
197
198 t1=ap[i+0];
199 t2=ap[i+1];
200 t3=ap[i+2];
201 t4=ap[i+3];
202 rp[i+0]=t1;
203 rp[i+1]=t2;
204 rp[i+2]=t3;
205 rp[i+3]=t4;
206 }
207 al+=4;
208 for (; i<al; i++)
209 rp[i]=ap[i];
210#endif
211#else /* !MONT_WORD */
212 BIGNUM *t1,*t2;
213
214 BN_CTX_start(ctx);
215 t1 = BN_CTX_get(ctx);
216 t2 = BN_CTX_get(ctx);
217 if (t1 == NULL || t2 == NULL) goto err;
218
219 if (!BN_copy(t1,a)) goto err;
220 BN_mask_bits(t1,mont->ri);
221
222 if (!BN_mul(t2,t1,&mont->Ni,ctx)) goto err;
223 BN_mask_bits(t2,mont->ri);
224
225 if (!BN_mul(t1,t2,&mont->N,ctx)) goto err;
226 if (!BN_add(t2,a,t1)) goto err;
227 BN_rshift(ret,t2,mont->ri);
228#endif /* MONT_WORD */
229
230 if (BN_ucmp(ret, &(mont->N)) >= 0)
231 {
232 BN_usub(ret,ret,&(mont->N));
233 }
234 retn=1;
235 err:
236 BN_CTX_end(ctx);
237 return(retn);
238 }
239
240BN_MONT_CTX *BN_MONT_CTX_new(void)
241 {
242 BN_MONT_CTX *ret;
243
244 if ((ret=(BN_MONT_CTX *)OPENSSL_malloc(sizeof(BN_MONT_CTX))) == NULL)
245 return(NULL);
246
247 BN_MONT_CTX_init(ret);
248 ret->flags=BN_FLG_MALLOCED;
249 return(ret);
250 }
251
252void BN_MONT_CTX_init(BN_MONT_CTX *ctx)
253 {
254 ctx->ri=0;
255 BN_init(&(ctx->RR));
256 BN_init(&(ctx->N));
257 BN_init(&(ctx->Ni));
258 ctx->flags=0;
259 }
260
261void BN_MONT_CTX_free(BN_MONT_CTX *mont)
262 {
263 if(mont == NULL)
264 return;
265
266 BN_free(&(mont->RR));
267 BN_free(&(mont->N));
268 BN_free(&(mont->Ni));
269 if (mont->flags & BN_FLG_MALLOCED)
270 OPENSSL_free(mont);
271 }
272
273int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx)
274 {
275 BIGNUM Ri,*R;
276
277 BN_init(&Ri);
278 R= &(mont->RR); /* grab RR as a temp */
279 BN_copy(&(mont->N),mod); /* Set N */
280
281#ifdef MONT_WORD
282 {
283 BIGNUM tmod;
284 BN_ULONG buf[2];
285
286 mont->ri=(BN_num_bits(mod)+(BN_BITS2-1))/BN_BITS2*BN_BITS2;
287 BN_zero(R);
288 BN_set_bit(R,BN_BITS2); /* R */
289
290 buf[0]=mod->d[0]; /* tmod = N mod word size */
291 buf[1]=0;
292 tmod.d=buf;
293 tmod.top=1;
294 tmod.dmax=2;
295 tmod.neg=mod->neg;
296 /* Ri = R^-1 mod N*/
297 if ((BN_mod_inverse(&Ri,R,&tmod,ctx)) == NULL)
298 goto err;
299 BN_lshift(&Ri,&Ri,BN_BITS2); /* R*Ri */
300 if (!BN_is_zero(&Ri))
301 BN_sub_word(&Ri,1);
302 else /* if N mod word size == 1 */
303 BN_set_word(&Ri,BN_MASK2); /* Ri-- (mod word size) */
304 BN_div(&Ri,NULL,&Ri,&tmod,ctx); /* Ni = (R*Ri-1)/N,
305 * keep only least significant word: */
306 mont->n0=Ri.d[0];
307 BN_free(&Ri);
308 }
309#else /* !MONT_WORD */
310 { /* bignum version */
311 mont->ri=BN_num_bits(mod);
312 BN_zero(R);
313 BN_set_bit(R,mont->ri); /* R = 2^ri */
314 /* Ri = R^-1 mod N*/
315 if ((BN_mod_inverse(&Ri,R,mod,ctx)) == NULL)
316 goto err;
317 BN_lshift(&Ri,&Ri,mont->ri); /* R*Ri */
318 BN_sub_word(&Ri,1);
319 /* Ni = (R*Ri-1) / N */
320 BN_div(&(mont->Ni),NULL,&Ri,mod,ctx);
321 BN_free(&Ri);
322 }
323#endif
324
325 /* setup RR for conversions */
326 BN_zero(&(mont->RR));
327 BN_set_bit(&(mont->RR),mont->ri*2);
328 BN_mod(&(mont->RR),&(mont->RR),&(mont->N),ctx);
329
330 return(1);
331err:
332 return(0);
333 }
334
335BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from)
336 {
337 if (to == from) return(to);
338
339 BN_copy(&(to->RR),&(from->RR));
340 BN_copy(&(to->N),&(from->N));
341 BN_copy(&(to->Ni),&(from->Ni));
342 to->ri=from->ri;
343 to->n0=from->n0;
344 return(to);
345 }
346
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