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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://www.ece.orst.edu/ISL/Publications.html
62 * http://www.ece.orst.edu/ISL/Koc/papers/j37acmon.pdf
63 */
64
65#include <stdio.h>
66#include "cryptlib.h"
67#include "bn_lcl.h"
68
69#define MONT_WORD
70
71int BN_mod_mul_montgomery(BIGNUM *r, BIGNUM *a, BIGNUM *b,
72 BN_MONT_CTX *mont, BN_CTX *ctx)
73 {
74 BIGNUM *tmp,*tmp2;
75
76 tmp= &(ctx->bn[ctx->tos]);
77 tmp2= &(ctx->bn[ctx->tos]);
78 ctx->tos+=2;
79
80 bn_check_top(tmp);
81 bn_check_top(tmp2);
82
83 if (a == b)
84 {
85#if 0
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);
89 tmp->top=a->top*2;
90 if (tmp->d[tmp->top-1] == 0)
91 tmp->top--;
92#else
93 if (!BN_sqr(tmp,a,ctx)) goto err;
94#endif
95 }
96 else
97 {
98 if (!BN_mul(tmp,a,b,ctx)) goto err;
99 }
100 /* reduce from aRR to aR */
101 if (!BN_from_montgomery(r,tmp,mont,ctx)) goto err;
102 ctx->tos-=2;
103 return(1);
104err:
105 return(0);
106 }
107
108int BN_from_montgomery(BIGNUM *ret, BIGNUM *a, BN_MONT_CTX *mont,
109 BN_CTX *ctx)
110 {
111#ifdef BN_RECURSION_MONT
112 if (mont->use_word)
113#endif
114 {
115 BIGNUM *n,*r;
116 BN_ULONG *ap,*np,*rp,n0,v,*nrp;
117 int al,nl,max,i,x,ri;
118 int retn=0;
119
120 r= &(ctx->bn[ctx->tos]);
121
122 if (!BN_copy(r,a)) goto err1;
123 n= &(mont->N);
124
125 ap=a->d;
126 /* mont->ri is the size of mont->N in bits/words */
127 al=ri=mont->ri/BN_BITS2;
128
129 nl=n->top;
130 if ((al == 0) || (nl == 0)) { r->top=0; return(1); }
131
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;
135
136 r->neg=a->neg^n->neg;
137 np=n->d;
138 rp=r->d;
139 nrp= &(r->d[nl]);
140
141 /* clear the top words of T */
142#if 1
143 for (i=r->top; i<max; i++) /* memset? XXX */
144 r->d[i]=0;
145#else
146 memset(&(r->d[r->top]),0,(max-r->top)*sizeof(BN_ULONG));
147#endif
148
149 r->top=max;
150 n0=mont->n0;
151
152#ifdef BN_COUNT
153printf("word BN_from_montgomery %d * %d\n",nl,nl);
154#endif
155 for (i=0; i<nl; i++)
156 {
157 v=bn_mul_add_words(rp,np,nl,(rp[0]*n0)&BN_MASK2);
158 nrp++;
159 rp++;
160 if (((nrp[-1]+=v)&BN_MASK2) >= v)
161 continue;
162 else
163 {
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++) ;
167 }
168 }
169 bn_fix_top(r);
170
171 /* mont->ri will be a multiple of the word size */
172#if 0
173 BN_rshift(ret,r,mont->ri);
174#else
175 x=ri;
176 rp=ret->d;
177 ap= &(r->d[x]);
178 if (r->top < x)
179 al=0;
180 else
181 al=r->top-x;
182 ret->top=al;
183 al-=4;
184 for (i=0; i<al; i+=4)
185 {
186 BN_ULONG t1,t2,t3,t4;
187
188 t1=ap[i+0];
189 t2=ap[i+1];
190 t3=ap[i+2];
191 t4=ap[i+3];
192 rp[i+0]=t1;
193 rp[i+1]=t2;
194 rp[i+2]=t3;
195 rp[i+3]=t4;
196 }
197 al+=4;
198 for (; i<al; i++)
199 rp[i]=ap[i];
200#endif
201
202 if (BN_ucmp(ret, &(mont->N)) >= 0)
203 {
204 BN_usub(ret,ret,&(mont->N)); /* XXX */
205 }
206 retn=1;
207err1:
208 return(retn);
209 }
210#ifdef BN_RECURSION_MONT
211 else /* bignum version */
212 {
213 BIGNUM *t1,*t2,*t3;
214 int j,i;
215
216#ifdef BN_COUNT
217printf("number BN_from_montgomery\n");
218#endif
219
220 t1= &(ctx->bn[ctx->tos]);
221 t2= &(ctx->bn[ctx->tos+1]);
222 t3= &(ctx->bn[ctx->tos+2]);
223
224 i=mont->Ni.top;
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 */
228
229 bn_mul_low_recursive(t2->d,a->d,mont->Ni.d,i,t1->d);
230
231 BN_zero(t3);
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);
235
236 /* hmm... if a is between i and 2*i, things are bad */
237 if (a->top > i)
238 {
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);
242 }
243 ret->top=i;
244 bn_fix_top(ret);
245 if (a->d[0])
246 BN_add_word(ret,1); /* Always? */
247 else /* Very very rare */
248 {
249 for (i=1; i<mont->N.top-1; i++)
250 {
251 if (a->d[i])
252 {
253 BN_add_word(ret,1); /* Always? */
254 break;
255 }
256 }
257 }
258
259 if (BN_ucmp(ret,&(mont->N)) >= 0)
260 BN_usub(ret,ret,&(mont->N));
261
262 return(1);
263 }
264#endif
265 }
266
267BN_MONT_CTX *BN_MONT_CTX_new(void)
268 {
269 BN_MONT_CTX *ret;
270
271 if ((ret=(BN_MONT_CTX *)Malloc(sizeof(BN_MONT_CTX))) == NULL)
272 return(NULL);
273
274 BN_MONT_CTX_init(ret);
275 ret->flags=BN_FLG_MALLOCED;
276 return(ret);
277 }
278
279void BN_MONT_CTX_init(BN_MONT_CTX *ctx)
280 {
281 ctx->use_word=0;
282 ctx->ri=0;
283 BN_init(&(ctx->RR));
284 BN_init(&(ctx->N));
285 BN_init(&(ctx->Ni));
286 ctx->flags=0;
287 }
288
289void BN_MONT_CTX_free(BN_MONT_CTX *mont)
290 {
291 if(mont == NULL)
292 return;
293
294 BN_free(&(mont->RR));
295 BN_free(&(mont->N));
296 BN_free(&(mont->Ni));
297 if (mont->flags & BN_FLG_MALLOCED)
298 Free(mont);
299 }
300
301int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx)
302 {
303 BIGNUM Ri,*R;
304
305 BN_init(&Ri);
306 R= &(mont->RR); /* grab RR as a temp */
307 BN_copy(&(mont->N),mod); /* Set N */
308
309#ifdef BN_RECURSION_MONT
310 if (mont->N.top < BN_MONT_CTX_SET_SIZE_WORD)
311#endif
312 {
313 BIGNUM tmod;
314 BN_ULONG buf[2];
315
316 mont->use_word=1;
317
318 mont->ri=(BN_num_bits(mod)+(BN_BITS2-1))/BN_BITS2*BN_BITS2;
319 BN_zero(R);
320 BN_set_bit(R,BN_BITS2);
321 /* I was bad, this modification of a passed variable was
322 * breaking the multithreaded stuff :-(
323 * z=mod->top;
324 * mod->top=1; */
325
326 buf[0]=mod->d[0];
327 buf[1]=0;
328 tmod.d=buf;
329 tmod.top=1;
330 tmod.max=mod->max;
331 tmod.neg=mod->neg;
332
333 if ((BN_mod_inverse(&Ri,R,&tmod,ctx)) == NULL)
334 goto err;
335 BN_lshift(&Ri,&Ri,BN_BITS2); /* R*Ri */
336 if (!BN_is_zero(&Ri))
337 {
338#if 1
339 BN_sub_word(&Ri,1);
340#else
341 BN_usub(&Ri,&Ri,BN_value_one()); /* R*Ri - 1 */
342#endif
343 }
344 else
345 {
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.
349 */
350 BN_set_word(&Ri,BN_MASK2);
351 }
352 BN_div(&Ri,NULL,&Ri,&tmod,ctx);
353 mont->n0=Ri.d[0];
354 BN_free(&Ri);
355 /* mod->top=z; */
356 }
357#ifdef BN_RECURSION_MONT
358 else
359 {
360 mont->use_word=0;
361 mont->ri=(BN_num_bits(mod)+(BN_BITS2-1))/BN_BITS2*BN_BITS2;
362#if 1
363 BN_zero(R);
364 BN_set_bit(R,mont->ri);
365#else
366 BN_lshift(R,BN_value_one(),mont->ri); /* R */
367#endif
368 if ((BN_mod_inverse(&Ri,R,mod,ctx)) == NULL)
369 goto err;
370 BN_lshift(&Ri,&Ri,mont->ri); /* R*Ri */
371#if 1
372 BN_sub_word(&Ri,1);
373#else
374 BN_usub(&Ri,&Ri,BN_value_one()); /* R*Ri - 1 */
375#endif
376 BN_div(&(mont->Ni),NULL,&Ri,mod,ctx);
377 BN_free(&Ri);
378 }
379#endif
380
381 /* setup RR for conversions */
382#if 1
383 BN_zero(&(mont->RR));
384 BN_set_bit(&(mont->RR),mont->ri*2);
385#else
386 BN_lshift(mont->RR,BN_value_one(),mont->ri*2);
387#endif
388 BN_mod(&(mont->RR),&(mont->RR),&(mont->N),ctx);
389
390 return(1);
391err:
392 return(0);
393 }
394
395BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from)
396 {
397 if (to == from) return(to);
398
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;
403 to->ri=from->ri;
404 to->n0=from->n0;
405 return(to);
406 }
407
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