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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 if (bn_wexpand(ret,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_fix_top(r);
176
177 /* mont->ri will be a multiple of the word size */
178#if 0
179 BN_rshift(ret,r,mont->ri);
180#else
181 ret->neg = r->neg;
182 x=ri;
183 rp=ret->d;
184 ap= &(r->d[x]);
185 if (r->top < x)
186 al=0;
187 else
188 al=r->top-x;
189 ret->top=al;
190 al-=4;
191 for (i=0; i<al; i+=4)
192 {
193 BN_ULONG t1,t2,t3,t4;
194
195 t1=ap[i+0];
196 t2=ap[i+1];
197 t3=ap[i+2];
198 t4=ap[i+3];
199 rp[i+0]=t1;
200 rp[i+1]=t2;
201 rp[i+2]=t3;
202 rp[i+3]=t4;
203 }
204 al+=4;
205 for (; i<al; i++)
206 rp[i]=ap[i];
207#endif
208#else /* !MONT_WORD */
209 BIGNUM *t1,*t2;
210
211 BN_CTX_start(ctx);
212 t1 = BN_CTX_get(ctx);
213 t2 = BN_CTX_get(ctx);
214 if (t1 == NULL || t2 == NULL) goto err;
215
216 if (!BN_copy(t1,a)) goto err;
217 BN_mask_bits(t1,mont->ri);
218
219 if (!BN_mul(t2,t1,&mont->Ni,ctx)) goto err;
220 BN_mask_bits(t2,mont->ri);
221
222 if (!BN_mul(t1,t2,&mont->N,ctx)) goto err;
223 if (!BN_add(t2,a,t1)) goto err;
224 if (!BN_rshift(ret,t2,mont->ri)) goto err;
225#endif /* MONT_WORD */
226
227 if (BN_ucmp(ret, &(mont->N)) >= 0)
228 {
229 if (!BN_usub(ret,ret,&(mont->N))) goto err;
230 }
231 retn=1;
232 err:
233 BN_CTX_end(ctx);
234 return(retn);
235 }
236
237BN_MONT_CTX *BN_MONT_CTX_new(void)
238 {
239 BN_MONT_CTX *ret;
240
241 if ((ret=(BN_MONT_CTX *)OPENSSL_malloc(sizeof(BN_MONT_CTX))) == NULL)
242 return(NULL);
243
244 BN_MONT_CTX_init(ret);
245 ret->flags=BN_FLG_MALLOCED;
246 return(ret);
247 }
248
249void BN_MONT_CTX_init(BN_MONT_CTX *ctx)
250 {
251 ctx->ri=0;
252 BN_init(&(ctx->RR));
253 BN_init(&(ctx->N));
254 BN_init(&(ctx->Ni));
255 ctx->flags=0;
256 }
257
258void BN_MONT_CTX_free(BN_MONT_CTX *mont)
259 {
260 if(mont == NULL)
261 return;
262
263 BN_free(&(mont->RR));
264 BN_free(&(mont->N));
265 BN_free(&(mont->Ni));
266 if (mont->flags & BN_FLG_MALLOCED)
267 OPENSSL_free(mont);
268 }
269
270int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx)
271 {
272 BIGNUM Ri,*R;
273
274 BN_init(&Ri);
275 R= &(mont->RR); /* grab RR as a temp */
276 if (!BN_copy(&(mont->N),mod)) goto err; /* Set N */
277 mont->N.neg = 0;
278
279#ifdef MONT_WORD
280 {
281 BIGNUM tmod;
282 BN_ULONG buf[2];
283
284 mont->ri=(BN_num_bits(mod)+(BN_BITS2-1))/BN_BITS2*BN_BITS2;
285 if (!(BN_zero(R))) goto err;
286 if (!(BN_set_bit(R,BN_BITS2))) goto err; /* R */
287
288 buf[0]=mod->d[0]; /* tmod = N mod word size */
289 buf[1]=0;
290 tmod.d=buf;
291 tmod.top=1;
292 tmod.dmax=2;
293 tmod.neg=0;
294 /* Ri = R^-1 mod N*/
295 if ((BN_mod_inverse(&Ri,R,&tmod,ctx)) == NULL)
296 goto err;
297 if (!BN_lshift(&Ri,&Ri,BN_BITS2)) goto err; /* R*Ri */
298 if (!BN_is_zero(&Ri))
299 {
300 if (!BN_sub_word(&Ri,1)) goto err;
301 }
302 else /* if N mod word size == 1 */
303 {
304 if (!BN_set_word(&Ri,BN_MASK2)) goto err; /* Ri-- (mod word size) */
305 }
306 if (!BN_div(&Ri,NULL,&Ri,&tmod,ctx)) goto err;
307 /* Ni = (R*Ri-1)/N,
308 * keep only least significant word: */
309 mont->n0 = (Ri.top > 0) ? Ri.d[0] : 0;
310 BN_free(&Ri);
311 }
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 */
317 /* Ri = R^-1 mod N*/
318 if ((BN_mod_inverse(&Ri,R,&mont->N,ctx)) == NULL)
319 goto err;
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;
324 BN_free(&Ri);
325 }
326#endif
327
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;
332
333 return(1);
334err:
335 return(0);
336 }
337
338BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from)
339 {
340 if (to == from) return(to);
341
342 if (!BN_copy(&(to->RR),&(from->RR))) return NULL;
343 if (!BN_copy(&(to->N),&(from->N))) return NULL;
344 if (!BN_copy(&(to->Ni),&(from->Ni))) return NULL;
345 to->ri=from->ri;
346 to->n0=from->n0;
347 return(to);
348 }
349
350BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock,
351 const BIGNUM *mod, BN_CTX *ctx)
352 {
353 if (*pmont)
354 return *pmont;
355 CRYPTO_w_lock(lock);
356 if (!*pmont)
357 {
358 *pmont = BN_MONT_CTX_new();
359 if (*pmont && !BN_MONT_CTX_set(*pmont, mod, ctx))
360 {
361 BN_MONT_CTX_free(*pmont);
362 *pmont = NULL;
363 }
364 }
365 CRYPTO_w_unlock(lock);
366 return *pmont;
367 }
368
369
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