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diff --git a/src/lib/libcrypto/bn/bn_prime.c b/src/lib/libcrypto/bn/bn_prime.c
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1/* crypto/bn/bn_prime.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#include <stdio.h>
60#include <time.h>
61#include "cryptlib.h"
62#include "bn_lcl.h"
63#include "rand.h"
64
65/* The quick seive algorithm approach to weeding out primes is
66 * Philip Zimmermann's, as implemented in PGP. I have had a read of
67 * his comments and implemented my own version.
68 */
69#include "bn_prime.h"
70
71#ifndef NOPROTO
72static int witness(BIGNUM *a, BIGNUM *n, BN_CTX *ctx,BN_CTX *ctx2,
73 BN_MONT_CTX *mont);
74static int probable_prime(BIGNUM *rnd, int bits);
75static int probable_prime_dh(BIGNUM *rnd, int bits,
76 BIGNUM *add, BIGNUM *rem, BN_CTX *ctx);
77static int probable_prime_dh_strong(BIGNUM *rnd, int bits,
78 BIGNUM *add, BIGNUM *rem, BN_CTX *ctx);
79#else
80static int witness();
81static int probable_prime();
82static int probable_prime_dh();
83static int probable_prime_dh_strong();
84#endif
85
86BIGNUM *BN_generate_prime(bits,strong,add,rem,callback,cb_arg)
87int bits;
88int strong;
89BIGNUM *add;
90BIGNUM *rem;
91void (*callback)(P_I_I_P);
92char *cb_arg;
93 {
94 BIGNUM *rnd=NULL;
95 BIGNUM *ret=NULL;
96 BIGNUM *t=NULL;
97 int i,j,c1=0;
98 BN_CTX *ctx;
99
100 ctx=BN_CTX_new();
101 if (ctx == NULL) goto err;
102 if ((rnd=BN_new()) == NULL) goto err;
103 if (strong)
104 if ((t=BN_new()) == NULL) goto err;
105loop:
106 /* make a random number and set the top and bottom bits */
107 if (add == NULL)
108 {
109 if (!probable_prime(rnd,bits)) goto err;
110 }
111 else
112 {
113 if (strong)
114 {
115 if (!probable_prime_dh_strong(rnd,bits,add,rem,ctx))
116 goto err;
117 }
118 else
119 {
120 if (!probable_prime_dh(rnd,bits,add,rem,ctx))
121 goto err;
122 }
123 }
124 /* if (BN_mod_word(rnd,(BN_ULONG)3) == 1) goto loop; */
125 if (callback != NULL) callback(0,c1++,cb_arg);
126
127 if (!strong)
128 {
129 i=BN_is_prime(rnd,BN_prime_checks,callback,ctx,cb_arg);
130 if (i == -1) goto err;
131 if (i == 0) goto loop;
132 }
133 else
134 {
135 /* for a strong prime generation,
136 * check that (p-1)/2 is prime.
137 * Since a prime is odd, We just
138 * need to divide by 2 */
139 if (!BN_rshift1(t,rnd)) goto err;
140
141 for (i=0; i<BN_prime_checks; i++)
142 {
143 j=BN_is_prime(rnd,1,callback,ctx,cb_arg);
144 if (j == -1) goto err;
145 if (j == 0) goto loop;
146
147 j=BN_is_prime(t,1,callback,ctx,cb_arg);
148 if (j == -1) goto err;
149 if (j == 0) goto loop;
150
151 if (callback != NULL) callback(2,c1-1,cb_arg);
152 /* We have a strong prime test pass */
153 }
154 }
155 /* we have a prime :-) */
156 ret=rnd;
157err:
158 if ((ret == NULL) && (rnd != NULL)) BN_free(rnd);
159 if (t != NULL) BN_free(t);
160 if (ctx != NULL) BN_CTX_free(ctx);
161 return(ret);
162 }
163
164int BN_is_prime(a,checks,callback,ctx_passed,cb_arg)
165BIGNUM *a;
166int checks;
167void (*callback)(P_I_I_P);
168BN_CTX *ctx_passed;
169char *cb_arg;
170 {
171 int i,j,c2=0,ret= -1;
172 BIGNUM *check;
173 BN_CTX *ctx=NULL,*ctx2=NULL;
174 BN_MONT_CTX *mont=NULL;
175
176 if (!BN_is_odd(a))
177 return(0);
178 if (ctx_passed != NULL)
179 ctx=ctx_passed;
180 else
181 if ((ctx=BN_CTX_new()) == NULL) goto err;
182
183 if ((ctx2=BN_CTX_new()) == NULL) goto err;
184 if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
185
186 check=ctx->bn[ctx->tos++];
187
188 /* Setup the montgomery structure */
189 if (!BN_MONT_CTX_set(mont,a,ctx2)) goto err;
190
191 for (i=0; i<checks; i++)
192 {
193 if (!BN_rand(check,BN_num_bits(a)-1,0,0)) goto err;
194 j=witness(check,a,ctx,ctx2,mont);
195 if (j == -1) goto err;
196 if (j)
197 {
198 ret=0;
199 goto err;
200 }
201 if (callback != NULL) callback(1,c2++,cb_arg);
202 }
203 ret=1;
204err:
205 ctx->tos--;
206 if ((ctx_passed == NULL) && (ctx != NULL))
207 BN_CTX_free(ctx);
208 if (ctx2 != NULL)
209 BN_CTX_free(ctx2);
210 if (mont != NULL) BN_MONT_CTX_free(mont);
211
212 return(ret);
213 }
214
215#define RECP_MUL_MOD
216
217static int witness(a,n,ctx,ctx2,mont)
218BIGNUM *a;
219BIGNUM *n;
220BN_CTX *ctx,*ctx2;
221BN_MONT_CTX *mont;
222 {
223 int k,i,ret= -1,good;
224 BIGNUM *d,*dd,*tmp,*d1,*d2,*n1;
225 BIGNUM *mont_one,*mont_n1,*mont_a;
226
227 d1=ctx->bn[ctx->tos];
228 d2=ctx->bn[ctx->tos+1];
229 n1=ctx->bn[ctx->tos+2];
230 ctx->tos+=3;
231
232 mont_one=ctx2->bn[ctx2->tos];
233 mont_n1=ctx2->bn[ctx2->tos+1];
234 mont_a=ctx2->bn[ctx2->tos+2];
235 ctx2->tos+=3;
236
237 d=d1;
238 dd=d2;
239 if (!BN_one(d)) goto err;
240 if (!BN_sub(n1,n,d)) goto err; /* n1=n-1; */
241 k=BN_num_bits(n1);
242
243 if (!BN_to_montgomery(mont_one,BN_value_one(),mont,ctx2)) goto err;
244 if (!BN_to_montgomery(mont_n1,n1,mont,ctx2)) goto err;
245 if (!BN_to_montgomery(mont_a,a,mont,ctx2)) goto err;
246
247 BN_copy(d,mont_one);
248 for (i=k-1; i>=0; i--)
249 {
250 if ( (BN_cmp(d,mont_one) != 0) &&
251 (BN_cmp(d,mont_n1) != 0))
252 good=1;
253 else
254 good=0;
255
256 BN_mod_mul_montgomery(dd,d,d,mont,ctx2);
257
258 if (good && (BN_cmp(dd,mont_one) == 0))
259 {
260 ret=1;
261 goto err;
262 }
263 if (BN_is_bit_set(n1,i))
264 {
265 BN_mod_mul_montgomery(d,dd,mont_a,mont,ctx2);
266 }
267 else
268 {
269 tmp=d;
270 d=dd;
271 dd=tmp;
272 }
273 }
274 if (BN_cmp(d,mont_one) == 0)
275 i=0;
276 else i=1;
277 ret=i;
278err:
279 ctx->tos-=3;
280 ctx2->tos-=3;
281 return(ret);
282 }
283
284static int probable_prime(rnd, bits)
285BIGNUM *rnd;
286int bits;
287 {
288 int i;
289 MS_STATIC BN_ULONG mods[NUMPRIMES];
290 BN_ULONG delta;
291
292 if (!BN_rand(rnd,bits,1,1)) return(0);
293 /* we now have a random number 'rand' to test. */
294 for (i=1; i<NUMPRIMES; i++)
295 mods[i]=BN_mod_word(rnd,(BN_ULONG)primes[i]);
296 delta=0;
297 loop: for (i=1; i<NUMPRIMES; i++)
298 {
299 /* check that rnd is not a prime and also
300 * that gcd(rnd-1,primes) == 1 (except for 2) */
301 if (((mods[i]+delta)%primes[i]) <= 1)
302 {
303 delta+=2;
304 /* perhaps need to check for overflow of
305 * delta (but delta can be upto 2^32) */
306 goto loop;
307 }
308 }
309 if (!BN_add_word(rnd,delta)) return(0);
310 return(1);
311 }
312
313static int probable_prime_dh(rnd, bits, add, rem,ctx)
314BIGNUM *rnd;
315int bits;
316BIGNUM *add;
317BIGNUM *rem;
318BN_CTX *ctx;
319 {
320 int i,ret=0;
321 BIGNUM *t1;
322
323 t1=ctx->bn[ctx->tos++];
324
325 if (!BN_rand(rnd,bits,0,1)) goto err;
326
327 /* we need ((rnd-rem) % add) == 0 */
328
329 if (!BN_mod(t1,rnd,add,ctx)) goto err;
330 if (!BN_sub(rnd,rnd,t1)) goto err;
331 if (rem == NULL)
332 { if (!BN_add_word(rnd,1)) goto err; }
333 else
334 { if (!BN_add(rnd,rnd,rem)) goto err; }
335
336 /* we now have a random number 'rand' to test. */
337
338 loop: for (i=1; i<NUMPRIMES; i++)
339 {
340 /* check that rnd is a prime */
341 if (BN_mod_word(rnd,(BN_LONG)primes[i]) <= 1)
342 {
343 if (!BN_add(rnd,rnd,add)) goto err;
344 goto loop;
345 }
346 }
347 ret=1;
348err:
349 ctx->tos--;
350 return(ret);
351 }
352
353static int probable_prime_dh_strong(p, bits, padd, rem,ctx)
354BIGNUM *p;
355int bits;
356BIGNUM *padd;
357BIGNUM *rem;
358BN_CTX *ctx;
359 {
360 int i,ret=0;
361 BIGNUM *t1,*qadd=NULL,*q=NULL;
362
363 bits--;
364 t1=ctx->bn[ctx->tos++];
365 q=ctx->bn[ctx->tos++];
366 qadd=ctx->bn[ctx->tos++];
367
368 if (!BN_rshift1(qadd,padd)) goto err;
369
370 if (!BN_rand(q,bits,0,1)) goto err;
371
372 /* we need ((rnd-rem) % add) == 0 */
373 if (!BN_mod(t1,q,qadd,ctx)) goto err;
374 if (!BN_sub(q,q,t1)) goto err;
375 if (rem == NULL)
376 { if (!BN_add_word(q,1)) goto err; }
377 else
378 {
379 if (!BN_rshift1(t1,rem)) goto err;
380 if (!BN_add(q,q,t1)) goto err;
381 }
382
383 /* we now have a random number 'rand' to test. */
384 if (!BN_lshift1(p,q)) goto err;
385 if (!BN_add_word(p,1)) goto err;
386
387 loop: for (i=1; i<NUMPRIMES; i++)
388 {
389 /* check that p and q are prime */
390 /* check that for p and q
391 * gcd(p-1,primes) == 1 (except for 2) */
392 if ( (BN_mod_word(p,(BN_LONG)primes[i]) == 0) ||
393 (BN_mod_word(q,(BN_LONG)primes[i]) == 0))
394 {
395 if (!BN_add(p,p,padd)) goto err;
396 if (!BN_add(q,q,qadd)) goto err;
397 goto loop;
398 }
399 }
400 ret=1;
401err:
402 ctx->tos-=3;
403 return(ret);
404 }
405
406#if 0
407static int witness(a, n,ctx)
408BIGNUM *a;
409BIGNUM *n;
410BN_CTX *ctx;
411 {
412 int k,i,nb,ret= -1;
413 BIGNUM *d,*dd,*tmp;
414 BIGNUM *d1,*d2,*x,*n1,*inv;
415
416 d1=ctx->bn[ctx->tos];
417 d2=ctx->bn[ctx->tos+1];
418 x=ctx->bn[ctx->tos+2];
419 n1=ctx->bn[ctx->tos+3];
420 inv=ctx->bn[ctx->tos+4];
421 ctx->tos+=5;
422
423 d=d1;
424 dd=d2;
425 if (!BN_one(d)) goto err;
426 if (!BN_sub(n1,n,d)) goto err; /* n1=n-1; */
427 k=BN_num_bits(n1);
428
429 /* i=BN_num_bits(n); */
430#ifdef RECP_MUL_MOD
431 nb=BN_reciprocal(inv,n,ctx); /**/
432 if (nb == -1) goto err;
433#endif
434
435 for (i=k-1; i>=0; i--)
436 {
437 if (BN_copy(x,d) == NULL) goto err;
438#ifndef RECP_MUL_MOD
439 if (!BN_mod_mul(dd,d,d,n,ctx)) goto err;
440#else
441 if (!BN_mod_mul_reciprocal(dd,d,d,n,inv,nb,ctx)) goto err;
442#endif
443 if ( BN_is_one(dd) &&
444 !BN_is_one(x) &&
445 (BN_cmp(x,n1) != 0))
446 {
447 ret=1;
448 goto err;
449 }
450 if (BN_is_bit_set(n1,i))
451 {
452#ifndef RECP_MUL_MOD
453 if (!BN_mod_mul(d,dd,a,n,ctx)) goto err;
454#else
455 if (!BN_mod_mul_reciprocal(d,dd,a,n,inv,nb,ctx)) goto err;
456#endif
457 }
458 else
459 {
460 tmp=d;
461 d=dd;
462 dd=tmp;
463 }
464 }
465 if (BN_is_one(d))
466 i=0;
467 else i=1;
468 ret=i;
469err:
470 ctx->tos-=5;
471 return(ret);
472 }
473#endif