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1/* crypto/bn/bntest.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 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
60 *
61 * Portions of the attached software ("Contribution") are developed by
62 * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
63 *
64 * The Contribution is licensed pursuant to the Eric Young open source
65 * license provided above.
66 *
67 * The binary polynomial arithmetic software is originally written by
68 * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
69 *
70 */
71
72/* Until the key-gen callbacks are modified to use newer prototypes, we allow
73 * deprecated functions for openssl-internal code */
74#ifdef OPENSSL_NO_DEPRECATED
75#undef OPENSSL_NO_DEPRECATED
76#endif
77
78#include <stdio.h>
79#include <stdlib.h>
80#include <string.h>
81
82#include "e_os.h"
83
84#include <openssl/bio.h>
85#include <openssl/bn.h>
86#include <openssl/rand.h>
87#include <openssl/x509.h>
88#include <openssl/err.h>
89
90const int num0 = 100; /* number of tests */
91const int num1 = 50; /* additional tests for some functions */
92const int num2 = 5; /* number of tests for slow functions */
93
94int test_add(BIO *bp);
95int test_sub(BIO *bp);
96int test_lshift1(BIO *bp);
97int test_lshift(BIO *bp,BN_CTX *ctx,BIGNUM *a_);
98int test_rshift1(BIO *bp);
99int test_rshift(BIO *bp,BN_CTX *ctx);
100int test_div(BIO *bp,BN_CTX *ctx);
101int test_div_word(BIO *bp);
102int test_div_recp(BIO *bp,BN_CTX *ctx);
103int test_mul(BIO *bp);
104int test_sqr(BIO *bp,BN_CTX *ctx);
105int test_mont(BIO *bp,BN_CTX *ctx);
106int test_mod(BIO *bp,BN_CTX *ctx);
107int test_mod_mul(BIO *bp,BN_CTX *ctx);
108int test_mod_exp(BIO *bp,BN_CTX *ctx);
109int test_mod_exp_mont_consttime(BIO *bp,BN_CTX *ctx);
110int test_exp(BIO *bp,BN_CTX *ctx);
111int test_gf2m_add(BIO *bp);
112int test_gf2m_mod(BIO *bp);
113int test_gf2m_mod_mul(BIO *bp,BN_CTX *ctx);
114int test_gf2m_mod_sqr(BIO *bp,BN_CTX *ctx);
115int test_gf2m_mod_inv(BIO *bp,BN_CTX *ctx);
116int test_gf2m_mod_div(BIO *bp,BN_CTX *ctx);
117int test_gf2m_mod_exp(BIO *bp,BN_CTX *ctx);
118int test_gf2m_mod_sqrt(BIO *bp,BN_CTX *ctx);
119int test_gf2m_mod_solve_quad(BIO *bp,BN_CTX *ctx);
120int test_kron(BIO *bp,BN_CTX *ctx);
121int test_sqrt(BIO *bp,BN_CTX *ctx);
122int rand_neg(void);
123static int results=0;
124
125static unsigned char lst[]="\xC6\x4F\x43\x04\x2A\xEA\xCA\x6E\x58\x36\x80\x5B\xE8\xC9"
126"\x9B\x04\x5D\x48\x36\xC2\xFD\x16\xC9\x64\xF0";
127
128static const char rnd_seed[] = "string to make the random number generator think it has entropy";
129
130static void message(BIO *out, char *m)
131 {
132 fprintf(stderr, "test %s\n", m);
133 BIO_puts(out, "print \"test ");
134 BIO_puts(out, m);
135 BIO_puts(out, "\\n\"\n");
136 }
137
138int main(int argc, char *argv[])
139 {
140 BN_CTX *ctx;
141 BIO *out;
142 char *outfile=NULL;
143
144 results = 0;
145
146 RAND_seed(rnd_seed, sizeof rnd_seed); /* or BN_generate_prime may fail */
147
148 argc--;
149 argv++;
150 while (argc >= 1)
151 {
152 if (strcmp(*argv,"-results") == 0)
153 results=1;
154 else if (strcmp(*argv,"-out") == 0)
155 {
156 if (--argc < 1) break;
157 outfile= *(++argv);
158 }
159 argc--;
160 argv++;
161 }
162
163
164 ctx=BN_CTX_new();
165 if (ctx == NULL) EXIT(1);
166
167 out=BIO_new(BIO_s_file());
168 if (out == NULL) EXIT(1);
169 if (outfile == NULL)
170 {
171 BIO_set_fp(out,stdout,BIO_NOCLOSE);
172 }
173 else
174 {
175 if (!BIO_write_filename(out,outfile))
176 {
177 perror(outfile);
178 EXIT(1);
179 }
180 }
181
182 if (!results)
183 BIO_puts(out,"obase=16\nibase=16\n");
184
185 message(out,"BN_add");
186 if (!test_add(out)) goto err;
187 (void)BIO_flush(out);
188
189 message(out,"BN_sub");
190 if (!test_sub(out)) goto err;
191 (void)BIO_flush(out);
192
193 message(out,"BN_lshift1");
194 if (!test_lshift1(out)) goto err;
195 (void)BIO_flush(out);
196
197 message(out,"BN_lshift (fixed)");
198 if (!test_lshift(out,ctx,BN_bin2bn(lst,sizeof(lst)-1,NULL)))
199 goto err;
200 (void)BIO_flush(out);
201
202 message(out,"BN_lshift");
203 if (!test_lshift(out,ctx,NULL)) goto err;
204 (void)BIO_flush(out);
205
206 message(out,"BN_rshift1");
207 if (!test_rshift1(out)) goto err;
208 (void)BIO_flush(out);
209
210 message(out,"BN_rshift");
211 if (!test_rshift(out,ctx)) goto err;
212 (void)BIO_flush(out);
213
214 message(out,"BN_sqr");
215 if (!test_sqr(out,ctx)) goto err;
216 (void)BIO_flush(out);
217
218 message(out,"BN_mul");
219 if (!test_mul(out)) goto err;
220 (void)BIO_flush(out);
221
222 message(out,"BN_div");
223 if (!test_div(out,ctx)) goto err;
224 (void)BIO_flush(out);
225
226 message(out,"BN_div_word");
227 if (!test_div_word(out)) goto err;
228 (void)BIO_flush(out);
229
230 message(out,"BN_div_recp");
231 if (!test_div_recp(out,ctx)) goto err;
232 (void)BIO_flush(out);
233
234 message(out,"BN_mod");
235 if (!test_mod(out,ctx)) goto err;
236 (void)BIO_flush(out);
237
238 message(out,"BN_mod_mul");
239 if (!test_mod_mul(out,ctx)) goto err;
240 (void)BIO_flush(out);
241
242 message(out,"BN_mont");
243 if (!test_mont(out,ctx)) goto err;
244 (void)BIO_flush(out);
245
246 message(out,"BN_mod_exp");
247 if (!test_mod_exp(out,ctx)) goto err;
248 (void)BIO_flush(out);
249
250 message(out,"BN_mod_exp_mont_consttime");
251 if (!test_mod_exp_mont_consttime(out,ctx)) goto err;
252 (void)BIO_flush(out);
253
254 message(out,"BN_exp");
255 if (!test_exp(out,ctx)) goto err;
256 (void)BIO_flush(out);
257
258 message(out,"BN_kronecker");
259 if (!test_kron(out,ctx)) goto err;
260 (void)BIO_flush(out);
261
262 message(out,"BN_mod_sqrt");
263 if (!test_sqrt(out,ctx)) goto err;
264 (void)BIO_flush(out);
265
266 message(out,"BN_GF2m_add");
267 if (!test_gf2m_add(out)) goto err;
268 (void)BIO_flush(out);
269
270 message(out,"BN_GF2m_mod");
271 if (!test_gf2m_mod(out)) goto err;
272 (void)BIO_flush(out);
273
274 message(out,"BN_GF2m_mod_mul");
275 if (!test_gf2m_mod_mul(out,ctx)) goto err;
276 (void)BIO_flush(out);
277
278 message(out,"BN_GF2m_mod_sqr");
279 if (!test_gf2m_mod_sqr(out,ctx)) goto err;
280 (void)BIO_flush(out);
281
282 message(out,"BN_GF2m_mod_inv");
283 if (!test_gf2m_mod_inv(out,ctx)) goto err;
284 (void)BIO_flush(out);
285
286 message(out,"BN_GF2m_mod_div");
287 if (!test_gf2m_mod_div(out,ctx)) goto err;
288 (void)BIO_flush(out);
289
290 message(out,"BN_GF2m_mod_exp");
291 if (!test_gf2m_mod_exp(out,ctx)) goto err;
292 (void)BIO_flush(out);
293
294 message(out,"BN_GF2m_mod_sqrt");
295 if (!test_gf2m_mod_sqrt(out,ctx)) goto err;
296 (void)BIO_flush(out);
297
298 message(out,"BN_GF2m_mod_solve_quad");
299 if (!test_gf2m_mod_solve_quad(out,ctx)) goto err;
300 (void)BIO_flush(out);
301
302 BN_CTX_free(ctx);
303 BIO_free(out);
304
305/**/
306 EXIT(0);
307err:
308 BIO_puts(out,"1\n"); /* make sure the Perl script fed by bc notices
309 * the failure, see test_bn in test/Makefile.ssl*/
310 (void)BIO_flush(out);
311 ERR_load_crypto_strings();
312 ERR_print_errors_fp(stderr);
313 EXIT(1);
314 return(1);
315 }
316
317int test_add(BIO *bp)
318 {
319 BIGNUM a,b,c;
320 int i;
321
322 BN_init(&a);
323 BN_init(&b);
324 BN_init(&c);
325
326 BN_bntest_rand(&a,512,0,0);
327 for (i=0; i<num0; i++)
328 {
329 BN_bntest_rand(&b,450+i,0,0);
330 a.neg=rand_neg();
331 b.neg=rand_neg();
332 BN_add(&c,&a,&b);
333 if (bp != NULL)
334 {
335 if (!results)
336 {
337 BN_print(bp,&a);
338 BIO_puts(bp," + ");
339 BN_print(bp,&b);
340 BIO_puts(bp," - ");
341 }
342 BN_print(bp,&c);
343 BIO_puts(bp,"\n");
344 }
345 a.neg=!a.neg;
346 b.neg=!b.neg;
347 BN_add(&c,&c,&b);
348 BN_add(&c,&c,&a);
349 if(!BN_is_zero(&c))
350 {
351 fprintf(stderr,"Add test failed!\n");
352 return 0;
353 }
354 }
355 BN_free(&a);
356 BN_free(&b);
357 BN_free(&c);
358 return(1);
359 }
360
361int test_sub(BIO *bp)
362 {
363 BIGNUM a,b,c;
364 int i;
365
366 BN_init(&a);
367 BN_init(&b);
368 BN_init(&c);
369
370 for (i=0; i<num0+num1; i++)
371 {
372 if (i < num1)
373 {
374 BN_bntest_rand(&a,512,0,0);
375 BN_copy(&b,&a);
376 if (BN_set_bit(&a,i)==0) return(0);
377 BN_add_word(&b,i);
378 }
379 else
380 {
381 BN_bntest_rand(&b,400+i-num1,0,0);
382 a.neg=rand_neg();
383 b.neg=rand_neg();
384 }
385 BN_sub(&c,&a,&b);
386 if (bp != NULL)
387 {
388 if (!results)
389 {
390 BN_print(bp,&a);
391 BIO_puts(bp," - ");
392 BN_print(bp,&b);
393 BIO_puts(bp," - ");
394 }
395 BN_print(bp,&c);
396 BIO_puts(bp,"\n");
397 }
398 BN_add(&c,&c,&b);
399 BN_sub(&c,&c,&a);
400 if(!BN_is_zero(&c))
401 {
402 fprintf(stderr,"Subtract test failed!\n");
403 return 0;
404 }
405 }
406 BN_free(&a);
407 BN_free(&b);
408 BN_free(&c);
409 return(1);
410 }
411
412int test_div(BIO *bp, BN_CTX *ctx)
413 {
414 BIGNUM a,b,c,d,e;
415 int i;
416
417 BN_init(&a);
418 BN_init(&b);
419 BN_init(&c);
420 BN_init(&d);
421 BN_init(&e);
422
423 for (i=0; i<num0+num1; i++)
424 {
425 if (i < num1)
426 {
427 BN_bntest_rand(&a,400,0,0);
428 BN_copy(&b,&a);
429 BN_lshift(&a,&a,i);
430 BN_add_word(&a,i);
431 }
432 else
433 BN_bntest_rand(&b,50+3*(i-num1),0,0);
434 a.neg=rand_neg();
435 b.neg=rand_neg();
436 BN_div(&d,&c,&a,&b,ctx);
437 if (bp != NULL)
438 {
439 if (!results)
440 {
441 BN_print(bp,&a);
442 BIO_puts(bp," / ");
443 BN_print(bp,&b);
444 BIO_puts(bp," - ");
445 }
446 BN_print(bp,&d);
447 BIO_puts(bp,"\n");
448
449 if (!results)
450 {
451 BN_print(bp,&a);
452 BIO_puts(bp," % ");
453 BN_print(bp,&b);
454 BIO_puts(bp," - ");
455 }
456 BN_print(bp,&c);
457 BIO_puts(bp,"\n");
458 }
459 BN_mul(&e,&d,&b,ctx);
460 BN_add(&d,&e,&c);
461 BN_sub(&d,&d,&a);
462 if(!BN_is_zero(&d))
463 {
464 fprintf(stderr,"Division test failed!\n");
465 return 0;
466 }
467 }
468 BN_free(&a);
469 BN_free(&b);
470 BN_free(&c);
471 BN_free(&d);
472 BN_free(&e);
473 return(1);
474 }
475
476static void print_word(BIO *bp,BN_ULONG w)
477 {
478#ifdef SIXTY_FOUR_BIT
479 if (sizeof(w) > sizeof(unsigned long))
480 {
481 unsigned long h=(unsigned long)(w>>32),
482 l=(unsigned long)(w);
483
484 if (h) BIO_printf(bp,"%lX%08lX",h,l);
485 else BIO_printf(bp,"%lX",l);
486 return;
487 }
488#endif
489 BIO_printf(bp,BN_HEX_FMT1,w);
490 }
491
492int test_div_word(BIO *bp)
493 {
494 BIGNUM a,b;
495 BN_ULONG r,s;
496 int i;
497
498 BN_init(&a);
499 BN_init(&b);
500
501 for (i=0; i<num0; i++)
502 {
503 do {
504 BN_bntest_rand(&a,512,-1,0);
505 BN_bntest_rand(&b,BN_BITS2,-1,0);
506 s = b.d[0];
507 } while (!s);
508
509 BN_copy(&b, &a);
510 r = BN_div_word(&b, s);
511
512 if (bp != NULL)
513 {
514 if (!results)
515 {
516 BN_print(bp,&a);
517 BIO_puts(bp," / ");
518 print_word(bp,s);
519 BIO_puts(bp," - ");
520 }
521 BN_print(bp,&b);
522 BIO_puts(bp,"\n");
523
524 if (!results)
525 {
526 BN_print(bp,&a);
527 BIO_puts(bp," % ");
528 print_word(bp,s);
529 BIO_puts(bp," - ");
530 }
531 print_word(bp,r);
532 BIO_puts(bp,"\n");
533 }
534 BN_mul_word(&b,s);
535 BN_add_word(&b,r);
536 BN_sub(&b,&a,&b);
537 if(!BN_is_zero(&b))
538 {
539 fprintf(stderr,"Division (word) test failed!\n");
540 return 0;
541 }
542 }
543 BN_free(&a);
544 BN_free(&b);
545 return(1);
546 }
547
548int test_div_recp(BIO *bp, BN_CTX *ctx)
549 {
550 BIGNUM a,b,c,d,e;
551 BN_RECP_CTX recp;
552 int i;
553
554 BN_RECP_CTX_init(&recp);
555 BN_init(&a);
556 BN_init(&b);
557 BN_init(&c);
558 BN_init(&d);
559 BN_init(&e);
560
561 for (i=0; i<num0+num1; i++)
562 {
563 if (i < num1)
564 {
565 BN_bntest_rand(&a,400,0,0);
566 BN_copy(&b,&a);
567 BN_lshift(&a,&a,i);
568 BN_add_word(&a,i);
569 }
570 else
571 BN_bntest_rand(&b,50+3*(i-num1),0,0);
572 a.neg=rand_neg();
573 b.neg=rand_neg();
574 BN_RECP_CTX_set(&recp,&b,ctx);
575 BN_div_recp(&d,&c,&a,&recp,ctx);
576 if (bp != NULL)
577 {
578 if (!results)
579 {
580 BN_print(bp,&a);
581 BIO_puts(bp," / ");
582 BN_print(bp,&b);
583 BIO_puts(bp," - ");
584 }
585 BN_print(bp,&d);
586 BIO_puts(bp,"\n");
587
588 if (!results)
589 {
590 BN_print(bp,&a);
591 BIO_puts(bp," % ");
592 BN_print(bp,&b);
593 BIO_puts(bp," - ");
594 }
595 BN_print(bp,&c);
596 BIO_puts(bp,"\n");
597 }
598 BN_mul(&e,&d,&b,ctx);
599 BN_add(&d,&e,&c);
600 BN_sub(&d,&d,&a);
601 if(!BN_is_zero(&d))
602 {
603 fprintf(stderr,"Reciprocal division test failed!\n");
604 fprintf(stderr,"a=");
605 BN_print_fp(stderr,&a);
606 fprintf(stderr,"\nb=");
607 BN_print_fp(stderr,&b);
608 fprintf(stderr,"\n");
609 return 0;
610 }
611 }
612 BN_free(&a);
613 BN_free(&b);
614 BN_free(&c);
615 BN_free(&d);
616 BN_free(&e);
617 BN_RECP_CTX_free(&recp);
618 return(1);
619 }
620
621int test_mul(BIO *bp)
622 {
623 BIGNUM a,b,c,d,e;
624 int i;
625 BN_CTX *ctx;
626
627 ctx = BN_CTX_new();
628 if (ctx == NULL) EXIT(1);
629
630 BN_init(&a);
631 BN_init(&b);
632 BN_init(&c);
633 BN_init(&d);
634 BN_init(&e);
635
636 for (i=0; i<num0+num1; i++)
637 {
638 if (i <= num1)
639 {
640 BN_bntest_rand(&a,100,0,0);
641 BN_bntest_rand(&b,100,0,0);
642 }
643 else
644 BN_bntest_rand(&b,i-num1,0,0);
645 a.neg=rand_neg();
646 b.neg=rand_neg();
647 BN_mul(&c,&a,&b,ctx);
648 if (bp != NULL)
649 {
650 if (!results)
651 {
652 BN_print(bp,&a);
653 BIO_puts(bp," * ");
654 BN_print(bp,&b);
655 BIO_puts(bp," - ");
656 }
657 BN_print(bp,&c);
658 BIO_puts(bp,"\n");
659 }
660 BN_div(&d,&e,&c,&a,ctx);
661 BN_sub(&d,&d,&b);
662 if(!BN_is_zero(&d) || !BN_is_zero(&e))
663 {
664 fprintf(stderr,"Multiplication test failed!\n");
665 return 0;
666 }
667 }
668 BN_free(&a);
669 BN_free(&b);
670 BN_free(&c);
671 BN_free(&d);
672 BN_free(&e);
673 BN_CTX_free(ctx);
674 return(1);
675 }
676
677int test_sqr(BIO *bp, BN_CTX *ctx)
678 {
679 BIGNUM a,c,d,e;
680 int i;
681
682 BN_init(&a);
683 BN_init(&c);
684 BN_init(&d);
685 BN_init(&e);
686
687 for (i=0; i<num0; i++)
688 {
689 BN_bntest_rand(&a,40+i*10,0,0);
690 a.neg=rand_neg();
691 BN_sqr(&c,&a,ctx);
692 if (bp != NULL)
693 {
694 if (!results)
695 {
696 BN_print(bp,&a);
697 BIO_puts(bp," * ");
698 BN_print(bp,&a);
699 BIO_puts(bp," - ");
700 }
701 BN_print(bp,&c);
702 BIO_puts(bp,"\n");
703 }
704 BN_div(&d,&e,&c,&a,ctx);
705 BN_sub(&d,&d,&a);
706 if(!BN_is_zero(&d) || !BN_is_zero(&e))
707 {
708 fprintf(stderr,"Square test failed!\n");
709 return 0;
710 }
711 }
712 BN_free(&a);
713 BN_free(&c);
714 BN_free(&d);
715 BN_free(&e);
716 return(1);
717 }
718
719int test_mont(BIO *bp, BN_CTX *ctx)
720 {
721 BIGNUM a,b,c,d,A,B;
722 BIGNUM n;
723 int i;
724 BN_MONT_CTX *mont;
725
726 BN_init(&a);
727 BN_init(&b);
728 BN_init(&c);
729 BN_init(&d);
730 BN_init(&A);
731 BN_init(&B);
732 BN_init(&n);
733
734 mont=BN_MONT_CTX_new();
735 if (mont == NULL)
736 return 0;
737
738 BN_bntest_rand(&a,100,0,0); /**/
739 BN_bntest_rand(&b,100,0,0); /**/
740 for (i=0; i<num2; i++)
741 {
742 int bits = (200*(i+1))/num2;
743
744 if (bits == 0)
745 continue;
746 BN_bntest_rand(&n,bits,0,1);
747 BN_MONT_CTX_set(mont,&n,ctx);
748
749 BN_nnmod(&a,&a,&n,ctx);
750 BN_nnmod(&b,&b,&n,ctx);
751
752 BN_to_montgomery(&A,&a,mont,ctx);
753 BN_to_montgomery(&B,&b,mont,ctx);
754
755 BN_mod_mul_montgomery(&c,&A,&B,mont,ctx);/**/
756 BN_from_montgomery(&A,&c,mont,ctx);/**/
757 if (bp != NULL)
758 {
759 if (!results)
760 {
761#ifdef undef
762fprintf(stderr,"%d * %d %% %d\n",
763BN_num_bits(&a),
764BN_num_bits(&b),
765BN_num_bits(mont->N));
766#endif
767 BN_print(bp,&a);
768 BIO_puts(bp," * ");
769 BN_print(bp,&b);
770 BIO_puts(bp," % ");
771 BN_print(bp,&(mont->N));
772 BIO_puts(bp," - ");
773 }
774 BN_print(bp,&A);
775 BIO_puts(bp,"\n");
776 }
777 BN_mod_mul(&d,&a,&b,&n,ctx);
778 BN_sub(&d,&d,&A);
779 if(!BN_is_zero(&d))
780 {
781 fprintf(stderr,"Montgomery multiplication test failed!\n");
782 return 0;
783 }
784 }
785 BN_MONT_CTX_free(mont);
786 BN_free(&a);
787 BN_free(&b);
788 BN_free(&c);
789 BN_free(&d);
790 BN_free(&A);
791 BN_free(&B);
792 BN_free(&n);
793 return(1);
794 }
795
796int test_mod(BIO *bp, BN_CTX *ctx)
797 {
798 BIGNUM *a,*b,*c,*d,*e;
799 int i;
800
801 a=BN_new();
802 b=BN_new();
803 c=BN_new();
804 d=BN_new();
805 e=BN_new();
806
807 BN_bntest_rand(a,1024,0,0); /**/
808 for (i=0; i<num0; i++)
809 {
810 BN_bntest_rand(b,450+i*10,0,0); /**/
811 a->neg=rand_neg();
812 b->neg=rand_neg();
813 BN_mod(c,a,b,ctx);/**/
814 if (bp != NULL)
815 {
816 if (!results)
817 {
818 BN_print(bp,a);
819 BIO_puts(bp," % ");
820 BN_print(bp,b);
821 BIO_puts(bp," - ");
822 }
823 BN_print(bp,c);
824 BIO_puts(bp,"\n");
825 }
826 BN_div(d,e,a,b,ctx);
827 BN_sub(e,e,c);
828 if(!BN_is_zero(e))
829 {
830 fprintf(stderr,"Modulo test failed!\n");
831 return 0;
832 }
833 }
834 BN_free(a);
835 BN_free(b);
836 BN_free(c);
837 BN_free(d);
838 BN_free(e);
839 return(1);
840 }
841
842int test_mod_mul(BIO *bp, BN_CTX *ctx)
843 {
844 BIGNUM *a,*b,*c,*d,*e;
845 int i,j;
846
847 a=BN_new();
848 b=BN_new();
849 c=BN_new();
850 d=BN_new();
851 e=BN_new();
852
853 for (j=0; j<3; j++) {
854 BN_bntest_rand(c,1024,0,0); /**/
855 for (i=0; i<num0; i++)
856 {
857 BN_bntest_rand(a,475+i*10,0,0); /**/
858 BN_bntest_rand(b,425+i*11,0,0); /**/
859 a->neg=rand_neg();
860 b->neg=rand_neg();
861 if (!BN_mod_mul(e,a,b,c,ctx))
862 {
863 unsigned long l;
864
865 while ((l=ERR_get_error()))
866 fprintf(stderr,"ERROR:%s\n",
867 ERR_error_string(l,NULL));
868 EXIT(1);
869 }
870 if (bp != NULL)
871 {
872 if (!results)
873 {
874 BN_print(bp,a);
875 BIO_puts(bp," * ");
876 BN_print(bp,b);
877 BIO_puts(bp," % ");
878 BN_print(bp,c);
879 if ((a->neg ^ b->neg) && !BN_is_zero(e))
880 {
881 /* If (a*b) % c is negative, c must be added
882 * in order to obtain the normalized remainder
883 * (new with OpenSSL 0.9.7, previous versions of
884 * BN_mod_mul could generate negative results)
885 */
886 BIO_puts(bp," + ");
887 BN_print(bp,c);
888 }
889 BIO_puts(bp," - ");
890 }
891 BN_print(bp,e);
892 BIO_puts(bp,"\n");
893 }
894 BN_mul(d,a,b,ctx);
895 BN_sub(d,d,e);
896 BN_div(a,b,d,c,ctx);
897 if(!BN_is_zero(b))
898 {
899 fprintf(stderr,"Modulo multiply test failed!\n");
900 ERR_print_errors_fp(stderr);
901 return 0;
902 }
903 }
904 }
905 BN_free(a);
906 BN_free(b);
907 BN_free(c);
908 BN_free(d);
909 BN_free(e);
910 return(1);
911 }
912
913int test_mod_exp(BIO *bp, BN_CTX *ctx)
914 {
915 BIGNUM *a,*b,*c,*d,*e;
916 int i;
917
918 a=BN_new();
919 b=BN_new();
920 c=BN_new();
921 d=BN_new();
922 e=BN_new();
923
924 BN_bntest_rand(c,30,0,1); /* must be odd for montgomery */
925 for (i=0; i<num2; i++)
926 {
927 BN_bntest_rand(a,20+i*5,0,0); /**/
928 BN_bntest_rand(b,2+i,0,0); /**/
929
930 if (!BN_mod_exp(d,a,b,c,ctx))
931 return(0);
932
933 if (bp != NULL)
934 {
935 if (!results)
936 {
937 BN_print(bp,a);
938 BIO_puts(bp," ^ ");
939 BN_print(bp,b);
940 BIO_puts(bp," % ");
941 BN_print(bp,c);
942 BIO_puts(bp," - ");
943 }
944 BN_print(bp,d);
945 BIO_puts(bp,"\n");
946 }
947 BN_exp(e,a,b,ctx);
948 BN_sub(e,e,d);
949 BN_div(a,b,e,c,ctx);
950 if(!BN_is_zero(b))
951 {
952 fprintf(stderr,"Modulo exponentiation test failed!\n");
953 return 0;
954 }
955 }
956 BN_free(a);
957 BN_free(b);
958 BN_free(c);
959 BN_free(d);
960 BN_free(e);
961 return(1);
962 }
963
964int test_mod_exp_mont_consttime(BIO *bp, BN_CTX *ctx)
965 {
966 BIGNUM *a,*b,*c,*d,*e;
967 int i;
968
969 a=BN_new();
970 b=BN_new();
971 c=BN_new();
972 d=BN_new();
973 e=BN_new();
974
975 BN_bntest_rand(c,30,0,1); /* must be odd for montgomery */
976 for (i=0; i<num2; i++)
977 {
978 BN_bntest_rand(a,20+i*5,0,0); /**/
979 BN_bntest_rand(b,2+i,0,0); /**/
980
981 if (!BN_mod_exp_mont_consttime(d,a,b,c,ctx,NULL))
982 return(00);
983
984 if (bp != NULL)
985 {
986 if (!results)
987 {
988 BN_print(bp,a);
989 BIO_puts(bp," ^ ");
990 BN_print(bp,b);
991 BIO_puts(bp," % ");
992 BN_print(bp,c);
993 BIO_puts(bp," - ");
994 }
995 BN_print(bp,d);
996 BIO_puts(bp,"\n");
997 }
998 BN_exp(e,a,b,ctx);
999 BN_sub(e,e,d);
1000 BN_div(a,b,e,c,ctx);
1001 if(!BN_is_zero(b))
1002 {
1003 fprintf(stderr,"Modulo exponentiation test failed!\n");
1004 return 0;
1005 }
1006 }
1007 BN_free(a);
1008 BN_free(b);
1009 BN_free(c);
1010 BN_free(d);
1011 BN_free(e);
1012 return(1);
1013 }
1014
1015int test_exp(BIO *bp, BN_CTX *ctx)
1016 {
1017 BIGNUM *a,*b,*d,*e,*one;
1018 int i;
1019
1020 a=BN_new();
1021 b=BN_new();
1022 d=BN_new();
1023 e=BN_new();
1024 one=BN_new();
1025 BN_one(one);
1026
1027 for (i=0; i<num2; i++)
1028 {
1029 BN_bntest_rand(a,20+i*5,0,0); /**/
1030 BN_bntest_rand(b,2+i,0,0); /**/
1031
1032 if (BN_exp(d,a,b,ctx) <= 0)
1033 return(0);
1034
1035 if (bp != NULL)
1036 {
1037 if (!results)
1038 {
1039 BN_print(bp,a);
1040 BIO_puts(bp," ^ ");
1041 BN_print(bp,b);
1042 BIO_puts(bp," - ");
1043 }
1044 BN_print(bp,d);
1045 BIO_puts(bp,"\n");
1046 }
1047 BN_one(e);
1048 for( ; !BN_is_zero(b) ; BN_sub(b,b,one))
1049 BN_mul(e,e,a,ctx);
1050 BN_sub(e,e,d);
1051 if(!BN_is_zero(e))
1052 {
1053 fprintf(stderr,"Exponentiation test failed!\n");
1054 return 0;
1055 }
1056 }
1057 BN_free(a);
1058 BN_free(b);
1059 BN_free(d);
1060 BN_free(e);
1061 BN_free(one);
1062 return(1);
1063 }
1064
1065int test_gf2m_add(BIO *bp)
1066 {
1067 BIGNUM a,b,c;
1068 int i, ret = 0;
1069
1070 BN_init(&a);
1071 BN_init(&b);
1072 BN_init(&c);
1073
1074 for (i=0; i<num0; i++)
1075 {
1076 BN_rand(&a,512,0,0);
1077 BN_copy(&b, BN_value_one());
1078 a.neg=rand_neg();
1079 b.neg=rand_neg();
1080 BN_GF2m_add(&c,&a,&b);
1081#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1082 if (bp != NULL)
1083 {
1084 if (!results)
1085 {
1086 BN_print(bp,&a);
1087 BIO_puts(bp," ^ ");
1088 BN_print(bp,&b);
1089 BIO_puts(bp," = ");
1090 }
1091 BN_print(bp,&c);
1092 BIO_puts(bp,"\n");
1093 }
1094#endif
1095 /* Test that two added values have the correct parity. */
1096 if((BN_is_odd(&a) && BN_is_odd(&c)) || (!BN_is_odd(&a) && !BN_is_odd(&c)))
1097 {
1098 fprintf(stderr,"GF(2^m) addition test (a) failed!\n");
1099 goto err;
1100 }
1101 BN_GF2m_add(&c,&c,&c);
1102 /* Test that c + c = 0. */
1103 if(!BN_is_zero(&c))
1104 {
1105 fprintf(stderr,"GF(2^m) addition test (b) failed!\n");
1106 goto err;
1107 }
1108 }
1109 ret = 1;
1110 err:
1111 BN_free(&a);
1112 BN_free(&b);
1113 BN_free(&c);
1114 return ret;
1115 }
1116
1117int test_gf2m_mod(BIO *bp)
1118 {
1119 BIGNUM *a,*b[2],*c,*d,*e;
1120 int i, j, ret = 0;
1121 int p0[] = {163,7,6,3,0,-1};
1122 int p1[] = {193,15,0,-1};
1123
1124 a=BN_new();
1125 b[0]=BN_new();
1126 b[1]=BN_new();
1127 c=BN_new();
1128 d=BN_new();
1129 e=BN_new();
1130
1131 BN_GF2m_arr2poly(p0, b[0]);
1132 BN_GF2m_arr2poly(p1, b[1]);
1133
1134 for (i=0; i<num0; i++)
1135 {
1136 BN_bntest_rand(a, 1024, 0, 0);
1137 for (j=0; j < 2; j++)
1138 {
1139 BN_GF2m_mod(c, a, b[j]);
1140#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1141 if (bp != NULL)
1142 {
1143 if (!results)
1144 {
1145 BN_print(bp,a);
1146 BIO_puts(bp," % ");
1147 BN_print(bp,b[j]);
1148 BIO_puts(bp," - ");
1149 BN_print(bp,c);
1150 BIO_puts(bp,"\n");
1151 }
1152 }
1153#endif
1154 BN_GF2m_add(d, a, c);
1155 BN_GF2m_mod(e, d, b[j]);
1156 /* Test that a + (a mod p) mod p == 0. */
1157 if(!BN_is_zero(e))
1158 {
1159 fprintf(stderr,"GF(2^m) modulo test failed!\n");
1160 goto err;
1161 }
1162 }
1163 }
1164 ret = 1;
1165 err:
1166 BN_free(a);
1167 BN_free(b[0]);
1168 BN_free(b[1]);
1169 BN_free(c);
1170 BN_free(d);
1171 BN_free(e);
1172 return ret;
1173 }
1174
1175int test_gf2m_mod_mul(BIO *bp,BN_CTX *ctx)
1176 {
1177 BIGNUM *a,*b[2],*c,*d,*e,*f,*g,*h;
1178 int i, j, ret = 0;
1179 int p0[] = {163,7,6,3,0,-1};
1180 int p1[] = {193,15,0,-1};
1181
1182 a=BN_new();
1183 b[0]=BN_new();
1184 b[1]=BN_new();
1185 c=BN_new();
1186 d=BN_new();
1187 e=BN_new();
1188 f=BN_new();
1189 g=BN_new();
1190 h=BN_new();
1191
1192 BN_GF2m_arr2poly(p0, b[0]);
1193 BN_GF2m_arr2poly(p1, b[1]);
1194
1195 for (i=0; i<num0; i++)
1196 {
1197 BN_bntest_rand(a, 1024, 0, 0);
1198 BN_bntest_rand(c, 1024, 0, 0);
1199 BN_bntest_rand(d, 1024, 0, 0);
1200 for (j=0; j < 2; j++)
1201 {
1202 BN_GF2m_mod_mul(e, a, c, b[j], ctx);
1203#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1204 if (bp != NULL)
1205 {
1206 if (!results)
1207 {
1208 BN_print(bp,a);
1209 BIO_puts(bp," * ");
1210 BN_print(bp,c);
1211 BIO_puts(bp," % ");
1212 BN_print(bp,b[j]);
1213 BIO_puts(bp," - ");
1214 BN_print(bp,e);
1215 BIO_puts(bp,"\n");
1216 }
1217 }
1218#endif
1219 BN_GF2m_add(f, a, d);
1220 BN_GF2m_mod_mul(g, f, c, b[j], ctx);
1221 BN_GF2m_mod_mul(h, d, c, b[j], ctx);
1222 BN_GF2m_add(f, e, g);
1223 BN_GF2m_add(f, f, h);
1224 /* Test that (a+d)*c = a*c + d*c. */
1225 if(!BN_is_zero(f))
1226 {
1227 fprintf(stderr,"GF(2^m) modular multiplication test failed!\n");
1228 goto err;
1229 }
1230 }
1231 }
1232 ret = 1;
1233 err:
1234 BN_free(a);
1235 BN_free(b[0]);
1236 BN_free(b[1]);
1237 BN_free(c);
1238 BN_free(d);
1239 BN_free(e);
1240 BN_free(f);
1241 BN_free(g);
1242 BN_free(h);
1243 return ret;
1244 }
1245
1246int test_gf2m_mod_sqr(BIO *bp,BN_CTX *ctx)
1247 {
1248 BIGNUM *a,*b[2],*c,*d;
1249 int i, j, ret = 0;
1250 int p0[] = {163,7,6,3,0,-1};
1251 int p1[] = {193,15,0,-1};
1252
1253 a=BN_new();
1254 b[0]=BN_new();
1255 b[1]=BN_new();
1256 c=BN_new();
1257 d=BN_new();
1258
1259 BN_GF2m_arr2poly(p0, b[0]);
1260 BN_GF2m_arr2poly(p1, b[1]);
1261
1262 for (i=0; i<num0; i++)
1263 {
1264 BN_bntest_rand(a, 1024, 0, 0);
1265 for (j=0; j < 2; j++)
1266 {
1267 BN_GF2m_mod_sqr(c, a, b[j], ctx);
1268 BN_copy(d, a);
1269 BN_GF2m_mod_mul(d, a, d, b[j], ctx);
1270#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1271 if (bp != NULL)
1272 {
1273 if (!results)
1274 {
1275 BN_print(bp,a);
1276 BIO_puts(bp," ^ 2 % ");
1277 BN_print(bp,b[j]);
1278 BIO_puts(bp, " = ");
1279 BN_print(bp,c);
1280 BIO_puts(bp,"; a * a = ");
1281 BN_print(bp,d);
1282 BIO_puts(bp,"\n");
1283 }
1284 }
1285#endif
1286 BN_GF2m_add(d, c, d);
1287 /* Test that a*a = a^2. */
1288 if(!BN_is_zero(d))
1289 {
1290 fprintf(stderr,"GF(2^m) modular squaring test failed!\n");
1291 goto err;
1292 }
1293 }
1294 }
1295 ret = 1;
1296 err:
1297 BN_free(a);
1298 BN_free(b[0]);
1299 BN_free(b[1]);
1300 BN_free(c);
1301 BN_free(d);
1302 return ret;
1303 }
1304
1305int test_gf2m_mod_inv(BIO *bp,BN_CTX *ctx)
1306 {
1307 BIGNUM *a,*b[2],*c,*d;
1308 int i, j, ret = 0;
1309 int p0[] = {163,7,6,3,0,-1};
1310 int p1[] = {193,15,0,-1};
1311
1312 a=BN_new();
1313 b[0]=BN_new();
1314 b[1]=BN_new();
1315 c=BN_new();
1316 d=BN_new();
1317
1318 BN_GF2m_arr2poly(p0, b[0]);
1319 BN_GF2m_arr2poly(p1, b[1]);
1320
1321 for (i=0; i<num0; i++)
1322 {
1323 BN_bntest_rand(a, 512, 0, 0);
1324 for (j=0; j < 2; j++)
1325 {
1326 BN_GF2m_mod_inv(c, a, b[j], ctx);
1327 BN_GF2m_mod_mul(d, a, c, b[j], ctx);
1328#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1329 if (bp != NULL)
1330 {
1331 if (!results)
1332 {
1333 BN_print(bp,a);
1334 BIO_puts(bp, " * ");
1335 BN_print(bp,c);
1336 BIO_puts(bp," - 1 % ");
1337 BN_print(bp,b[j]);
1338 BIO_puts(bp,"\n");
1339 }
1340 }
1341#endif
1342 /* Test that ((1/a)*a) = 1. */
1343 if(!BN_is_one(d))
1344 {
1345 fprintf(stderr,"GF(2^m) modular inversion test failed!\n");
1346 goto err;
1347 }
1348 }
1349 }
1350 ret = 1;
1351 err:
1352 BN_free(a);
1353 BN_free(b[0]);
1354 BN_free(b[1]);
1355 BN_free(c);
1356 BN_free(d);
1357 return ret;
1358 }
1359
1360int test_gf2m_mod_div(BIO *bp,BN_CTX *ctx)
1361 {
1362 BIGNUM *a,*b[2],*c,*d,*e,*f;
1363 int i, j, ret = 0;
1364 int p0[] = {163,7,6,3,0,-1};
1365 int p1[] = {193,15,0,-1};
1366
1367 a=BN_new();
1368 b[0]=BN_new();
1369 b[1]=BN_new();
1370 c=BN_new();
1371 d=BN_new();
1372 e=BN_new();
1373 f=BN_new();
1374
1375 BN_GF2m_arr2poly(p0, b[0]);
1376 BN_GF2m_arr2poly(p1, b[1]);
1377
1378 for (i=0; i<num0; i++)
1379 {
1380 BN_bntest_rand(a, 512, 0, 0);
1381 BN_bntest_rand(c, 512, 0, 0);
1382 for (j=0; j < 2; j++)
1383 {
1384 BN_GF2m_mod_div(d, a, c, b[j], ctx);
1385 BN_GF2m_mod_mul(e, d, c, b[j], ctx);
1386 BN_GF2m_mod_div(f, a, e, b[j], ctx);
1387#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1388 if (bp != NULL)
1389 {
1390 if (!results)
1391 {
1392 BN_print(bp,a);
1393 BIO_puts(bp, " = ");
1394 BN_print(bp,c);
1395 BIO_puts(bp," * ");
1396 BN_print(bp,d);
1397 BIO_puts(bp, " % ");
1398 BN_print(bp,b[j]);
1399 BIO_puts(bp,"\n");
1400 }
1401 }
1402#endif
1403 /* Test that ((a/c)*c)/a = 1. */
1404 if(!BN_is_one(f))
1405 {
1406 fprintf(stderr,"GF(2^m) modular division test failed!\n");
1407 goto err;
1408 }
1409 }
1410 }
1411 ret = 1;
1412 err:
1413 BN_free(a);
1414 BN_free(b[0]);
1415 BN_free(b[1]);
1416 BN_free(c);
1417 BN_free(d);
1418 BN_free(e);
1419 BN_free(f);
1420 return ret;
1421 }
1422
1423int test_gf2m_mod_exp(BIO *bp,BN_CTX *ctx)
1424 {
1425 BIGNUM *a,*b[2],*c,*d,*e,*f;
1426 int i, j, ret = 0;
1427 int p0[] = {163,7,6,3,0,-1};
1428 int p1[] = {193,15,0,-1};
1429
1430 a=BN_new();
1431 b[0]=BN_new();
1432 b[1]=BN_new();
1433 c=BN_new();
1434 d=BN_new();
1435 e=BN_new();
1436 f=BN_new();
1437
1438 BN_GF2m_arr2poly(p0, b[0]);
1439 BN_GF2m_arr2poly(p1, b[1]);
1440
1441 for (i=0; i<num0; i++)
1442 {
1443 BN_bntest_rand(a, 512, 0, 0);
1444 BN_bntest_rand(c, 512, 0, 0);
1445 BN_bntest_rand(d, 512, 0, 0);
1446 for (j=0; j < 2; j++)
1447 {
1448 BN_GF2m_mod_exp(e, a, c, b[j], ctx);
1449 BN_GF2m_mod_exp(f, a, d, b[j], ctx);
1450 BN_GF2m_mod_mul(e, e, f, b[j], ctx);
1451 BN_add(f, c, d);
1452 BN_GF2m_mod_exp(f, a, f, b[j], ctx);
1453#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1454 if (bp != NULL)
1455 {
1456 if (!results)
1457 {
1458 BN_print(bp,a);
1459 BIO_puts(bp, " ^ (");
1460 BN_print(bp,c);
1461 BIO_puts(bp," + ");
1462 BN_print(bp,d);
1463 BIO_puts(bp, ") = ");
1464 BN_print(bp,e);
1465 BIO_puts(bp, "; - ");
1466 BN_print(bp,f);
1467 BIO_puts(bp, " % ");
1468 BN_print(bp,b[j]);
1469 BIO_puts(bp,"\n");
1470 }
1471 }
1472#endif
1473 BN_GF2m_add(f, e, f);
1474 /* Test that a^(c+d)=a^c*a^d. */
1475 if(!BN_is_zero(f))
1476 {
1477 fprintf(stderr,"GF(2^m) modular exponentiation test failed!\n");
1478 goto err;
1479 }
1480 }
1481 }
1482 ret = 1;
1483 err:
1484 BN_free(a);
1485 BN_free(b[0]);
1486 BN_free(b[1]);
1487 BN_free(c);
1488 BN_free(d);
1489 BN_free(e);
1490 BN_free(f);
1491 return ret;
1492 }
1493
1494int test_gf2m_mod_sqrt(BIO *bp,BN_CTX *ctx)
1495 {
1496 BIGNUM *a,*b[2],*c,*d,*e,*f;
1497 int i, j, ret = 0;
1498 int p0[] = {163,7,6,3,0,-1};
1499 int p1[] = {193,15,0,-1};
1500
1501 a=BN_new();
1502 b[0]=BN_new();
1503 b[1]=BN_new();
1504 c=BN_new();
1505 d=BN_new();
1506 e=BN_new();
1507 f=BN_new();
1508
1509 BN_GF2m_arr2poly(p0, b[0]);
1510 BN_GF2m_arr2poly(p1, b[1]);
1511
1512 for (i=0; i<num0; i++)
1513 {
1514 BN_bntest_rand(a, 512, 0, 0);
1515 for (j=0; j < 2; j++)
1516 {
1517 BN_GF2m_mod(c, a, b[j]);
1518 BN_GF2m_mod_sqrt(d, a, b[j], ctx);
1519 BN_GF2m_mod_sqr(e, d, b[j], ctx);
1520#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1521 if (bp != NULL)
1522 {
1523 if (!results)
1524 {
1525 BN_print(bp,d);
1526 BIO_puts(bp, " ^ 2 - ");
1527 BN_print(bp,a);
1528 BIO_puts(bp,"\n");
1529 }
1530 }
1531#endif
1532 BN_GF2m_add(f, c, e);
1533 /* Test that d^2 = a, where d = sqrt(a). */
1534 if(!BN_is_zero(f))
1535 {
1536 fprintf(stderr,"GF(2^m) modular square root test failed!\n");
1537 goto err;
1538 }
1539 }
1540 }
1541 ret = 1;
1542 err:
1543 BN_free(a);
1544 BN_free(b[0]);
1545 BN_free(b[1]);
1546 BN_free(c);
1547 BN_free(d);
1548 BN_free(e);
1549 BN_free(f);
1550 return ret;
1551 }
1552
1553int test_gf2m_mod_solve_quad(BIO *bp,BN_CTX *ctx)
1554 {
1555 BIGNUM *a,*b[2],*c,*d,*e;
1556 int i, j, s = 0, t, ret = 0;
1557 int p0[] = {163,7,6,3,0,-1};
1558 int p1[] = {193,15,0,-1};
1559
1560 a=BN_new();
1561 b[0]=BN_new();
1562 b[1]=BN_new();
1563 c=BN_new();
1564 d=BN_new();
1565 e=BN_new();
1566
1567 BN_GF2m_arr2poly(p0, b[0]);
1568 BN_GF2m_arr2poly(p1, b[1]);
1569
1570 for (i=0; i<num0; i++)
1571 {
1572 BN_bntest_rand(a, 512, 0, 0);
1573 for (j=0; j < 2; j++)
1574 {
1575 t = BN_GF2m_mod_solve_quad(c, a, b[j], ctx);
1576 if (t)
1577 {
1578 s++;
1579 BN_GF2m_mod_sqr(d, c, b[j], ctx);
1580 BN_GF2m_add(d, c, d);
1581 BN_GF2m_mod(e, a, b[j]);
1582#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1583 if (bp != NULL)
1584 {
1585 if (!results)
1586 {
1587 BN_print(bp,c);
1588 BIO_puts(bp, " is root of z^2 + z = ");
1589 BN_print(bp,a);
1590 BIO_puts(bp, " % ");
1591 BN_print(bp,b[j]);
1592 BIO_puts(bp, "\n");
1593 }
1594 }
1595#endif
1596 BN_GF2m_add(e, e, d);
1597 /* Test that solution of quadratic c satisfies c^2 + c = a. */
1598 if(!BN_is_zero(e))
1599 {
1600 fprintf(stderr,"GF(2^m) modular solve quadratic test failed!\n");
1601 goto err;
1602 }
1603
1604 }
1605 else
1606 {
1607#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1608 if (bp != NULL)
1609 {
1610 if (!results)
1611 {
1612 BIO_puts(bp, "There are no roots of z^2 + z = ");
1613 BN_print(bp,a);
1614 BIO_puts(bp, " % ");
1615 BN_print(bp,b[j]);
1616 BIO_puts(bp, "\n");
1617 }
1618 }
1619#endif
1620 }
1621 }
1622 }
1623 if (s == 0)
1624 {
1625 fprintf(stderr,"All %i tests of GF(2^m) modular solve quadratic resulted in no roots;\n", num0);
1626 fprintf(stderr,"this is very unlikely and probably indicates an error.\n");
1627 goto err;
1628 }
1629 ret = 1;
1630 err:
1631 BN_free(a);
1632 BN_free(b[0]);
1633 BN_free(b[1]);
1634 BN_free(c);
1635 BN_free(d);
1636 BN_free(e);
1637 return ret;
1638 }
1639
1640static int genprime_cb(int p, int n, BN_GENCB *arg)
1641 {
1642 char c='*';
1643
1644 if (p == 0) c='.';
1645 if (p == 1) c='+';
1646 if (p == 2) c='*';
1647 if (p == 3) c='\n';
1648 putc(c, stderr);
1649 fflush(stderr);
1650 return 1;
1651 }
1652
1653int test_kron(BIO *bp, BN_CTX *ctx)
1654 {
1655 BN_GENCB cb;
1656 BIGNUM *a,*b,*r,*t;
1657 int i;
1658 int legendre, kronecker;
1659 int ret = 0;
1660
1661 a = BN_new();
1662 b = BN_new();
1663 r = BN_new();
1664 t = BN_new();
1665 if (a == NULL || b == NULL || r == NULL || t == NULL) goto err;
1666
1667 BN_GENCB_set(&cb, genprime_cb, NULL);
1668
1669 /* We test BN_kronecker(a, b, ctx) just for b odd (Jacobi symbol).
1670 * In this case we know that if b is prime, then BN_kronecker(a, b, ctx)
1671 * is congruent to $a^{(b-1)/2}$, modulo $b$ (Legendre symbol).
1672 * So we generate a random prime b and compare these values
1673 * for a number of random a's. (That is, we run the Solovay-Strassen
1674 * primality test to confirm that b is prime, except that we
1675 * don't want to test whether b is prime but whether BN_kronecker
1676 * works.) */
1677
1678 if (!BN_generate_prime_ex(b, 512, 0, NULL, NULL, &cb)) goto err;
1679 b->neg = rand_neg();
1680 putc('\n', stderr);
1681
1682 for (i = 0; i < num0; i++)
1683 {
1684 if (!BN_bntest_rand(a, 512, 0, 0)) goto err;
1685 a->neg = rand_neg();
1686
1687 /* t := (|b|-1)/2 (note that b is odd) */
1688 if (!BN_copy(t, b)) goto err;
1689 t->neg = 0;
1690 if (!BN_sub_word(t, 1)) goto err;
1691 if (!BN_rshift1(t, t)) goto err;
1692 /* r := a^t mod b */
1693 b->neg=0;
1694
1695 if (!BN_mod_exp_recp(r, a, t, b, ctx)) goto err;
1696 b->neg=1;
1697
1698 if (BN_is_word(r, 1))
1699 legendre = 1;
1700 else if (BN_is_zero(r))
1701 legendre = 0;
1702 else
1703 {
1704 if (!BN_add_word(r, 1)) goto err;
1705 if (0 != BN_ucmp(r, b))
1706 {
1707 fprintf(stderr, "Legendre symbol computation failed\n");
1708 goto err;
1709 }
1710 legendre = -1;
1711 }
1712
1713 kronecker = BN_kronecker(a, b, ctx);
1714 if (kronecker < -1) goto err;
1715 /* we actually need BN_kronecker(a, |b|) */
1716 if (a->neg && b->neg)
1717 kronecker = -kronecker;
1718
1719 if (legendre != kronecker)
1720 {
1721 fprintf(stderr, "legendre != kronecker; a = ");
1722 BN_print_fp(stderr, a);
1723 fprintf(stderr, ", b = ");
1724 BN_print_fp(stderr, b);
1725 fprintf(stderr, "\n");
1726 goto err;
1727 }
1728
1729 putc('.', stderr);
1730 fflush(stderr);
1731 }
1732
1733 putc('\n', stderr);
1734 fflush(stderr);
1735 ret = 1;
1736 err:
1737 if (a != NULL) BN_free(a);
1738 if (b != NULL) BN_free(b);
1739 if (r != NULL) BN_free(r);
1740 if (t != NULL) BN_free(t);
1741 return ret;
1742 }
1743
1744int test_sqrt(BIO *bp, BN_CTX *ctx)
1745 {
1746 BN_GENCB cb;
1747 BIGNUM *a,*p,*r;
1748 int i, j;
1749 int ret = 0;
1750
1751 a = BN_new();
1752 p = BN_new();
1753 r = BN_new();
1754 if (a == NULL || p == NULL || r == NULL) goto err;
1755
1756 BN_GENCB_set(&cb, genprime_cb, NULL);
1757
1758 for (i = 0; i < 16; i++)
1759 {
1760 if (i < 8)
1761 {
1762 unsigned primes[8] = { 2, 3, 5, 7, 11, 13, 17, 19 };
1763
1764 if (!BN_set_word(p, primes[i])) goto err;
1765 }
1766 else
1767 {
1768 if (!BN_set_word(a, 32)) goto err;
1769 if (!BN_set_word(r, 2*i + 1)) goto err;
1770
1771 if (!BN_generate_prime_ex(p, 256, 0, a, r, &cb)) goto err;
1772 putc('\n', stderr);
1773 }
1774 p->neg = rand_neg();
1775
1776 for (j = 0; j < num2; j++)
1777 {
1778 /* construct 'a' such that it is a square modulo p,
1779 * but in general not a proper square and not reduced modulo p */
1780 if (!BN_bntest_rand(r, 256, 0, 3)) goto err;
1781 if (!BN_nnmod(r, r, p, ctx)) goto err;
1782 if (!BN_mod_sqr(r, r, p, ctx)) goto err;
1783 if (!BN_bntest_rand(a, 256, 0, 3)) goto err;
1784 if (!BN_nnmod(a, a, p, ctx)) goto err;
1785 if (!BN_mod_sqr(a, a, p, ctx)) goto err;
1786 if (!BN_mul(a, a, r, ctx)) goto err;
1787 if (rand_neg())
1788 if (!BN_sub(a, a, p)) goto err;
1789
1790 if (!BN_mod_sqrt(r, a, p, ctx)) goto err;
1791 if (!BN_mod_sqr(r, r, p, ctx)) goto err;
1792
1793 if (!BN_nnmod(a, a, p, ctx)) goto err;
1794
1795 if (BN_cmp(a, r) != 0)
1796 {
1797 fprintf(stderr, "BN_mod_sqrt failed: a = ");
1798 BN_print_fp(stderr, a);
1799 fprintf(stderr, ", r = ");
1800 BN_print_fp(stderr, r);
1801 fprintf(stderr, ", p = ");
1802 BN_print_fp(stderr, p);
1803 fprintf(stderr, "\n");
1804 goto err;
1805 }
1806
1807 putc('.', stderr);
1808 fflush(stderr);
1809 }
1810
1811 putc('\n', stderr);
1812 fflush(stderr);
1813 }
1814 ret = 1;
1815 err:
1816 if (a != NULL) BN_free(a);
1817 if (p != NULL) BN_free(p);
1818 if (r != NULL) BN_free(r);
1819 return ret;
1820 }
1821
1822int test_lshift(BIO *bp,BN_CTX *ctx,BIGNUM *a_)
1823 {
1824 BIGNUM *a,*b,*c,*d;
1825 int i;
1826
1827 b=BN_new();
1828 c=BN_new();
1829 d=BN_new();
1830 BN_one(c);
1831
1832 if(a_)
1833 a=a_;
1834 else
1835 {
1836 a=BN_new();
1837 BN_bntest_rand(a,200,0,0); /**/
1838 a->neg=rand_neg();
1839 }
1840 for (i=0; i<num0; i++)
1841 {
1842 BN_lshift(b,a,i+1);
1843 BN_add(c,c,c);
1844 if (bp != NULL)
1845 {
1846 if (!results)
1847 {
1848 BN_print(bp,a);
1849 BIO_puts(bp," * ");
1850 BN_print(bp,c);
1851 BIO_puts(bp," - ");
1852 }
1853 BN_print(bp,b);
1854 BIO_puts(bp,"\n");
1855 }
1856 BN_mul(d,a,c,ctx);
1857 BN_sub(d,d,b);
1858 if(!BN_is_zero(d))
1859 {
1860 fprintf(stderr,"Left shift test failed!\n");
1861 fprintf(stderr,"a=");
1862 BN_print_fp(stderr,a);
1863 fprintf(stderr,"\nb=");
1864 BN_print_fp(stderr,b);
1865 fprintf(stderr,"\nc=");
1866 BN_print_fp(stderr,c);
1867 fprintf(stderr,"\nd=");
1868 BN_print_fp(stderr,d);
1869 fprintf(stderr,"\n");
1870 return 0;
1871 }
1872 }
1873 BN_free(a);
1874 BN_free(b);
1875 BN_free(c);
1876 BN_free(d);
1877 return(1);
1878 }
1879
1880int test_lshift1(BIO *bp)
1881 {
1882 BIGNUM *a,*b,*c;
1883 int i;
1884
1885 a=BN_new();
1886 b=BN_new();
1887 c=BN_new();
1888
1889 BN_bntest_rand(a,200,0,0); /**/
1890 a->neg=rand_neg();
1891 for (i=0; i<num0; i++)
1892 {
1893 BN_lshift1(b,a);
1894 if (bp != NULL)
1895 {
1896 if (!results)
1897 {
1898 BN_print(bp,a);
1899 BIO_puts(bp," * 2");
1900 BIO_puts(bp," - ");
1901 }
1902 BN_print(bp,b);
1903 BIO_puts(bp,"\n");
1904 }
1905 BN_add(c,a,a);
1906 BN_sub(a,b,c);
1907 if(!BN_is_zero(a))
1908 {
1909 fprintf(stderr,"Left shift one test failed!\n");
1910 return 0;
1911 }
1912
1913 BN_copy(a,b);
1914 }
1915 BN_free(a);
1916 BN_free(b);
1917 BN_free(c);
1918 return(1);
1919 }
1920
1921int test_rshift(BIO *bp,BN_CTX *ctx)
1922 {
1923 BIGNUM *a,*b,*c,*d,*e;
1924 int i;
1925
1926 a=BN_new();
1927 b=BN_new();
1928 c=BN_new();
1929 d=BN_new();
1930 e=BN_new();
1931 BN_one(c);
1932
1933 BN_bntest_rand(a,200,0,0); /**/
1934 a->neg=rand_neg();
1935 for (i=0; i<num0; i++)
1936 {
1937 BN_rshift(b,a,i+1);
1938 BN_add(c,c,c);
1939 if (bp != NULL)
1940 {
1941 if (!results)
1942 {
1943 BN_print(bp,a);
1944 BIO_puts(bp," / ");
1945 BN_print(bp,c);
1946 BIO_puts(bp," - ");
1947 }
1948 BN_print(bp,b);
1949 BIO_puts(bp,"\n");
1950 }
1951 BN_div(d,e,a,c,ctx);
1952 BN_sub(d,d,b);
1953 if(!BN_is_zero(d))
1954 {
1955 fprintf(stderr,"Right shift test failed!\n");
1956 return 0;
1957 }
1958 }
1959 BN_free(a);
1960 BN_free(b);
1961 BN_free(c);
1962 BN_free(d);
1963 BN_free(e);
1964 return(1);
1965 }
1966
1967int test_rshift1(BIO *bp)
1968 {
1969 BIGNUM *a,*b,*c;
1970 int i;
1971
1972 a=BN_new();
1973 b=BN_new();
1974 c=BN_new();
1975
1976 BN_bntest_rand(a,200,0,0); /**/
1977 a->neg=rand_neg();
1978 for (i=0; i<num0; i++)
1979 {
1980 BN_rshift1(b,a);
1981 if (bp != NULL)
1982 {
1983 if (!results)
1984 {
1985 BN_print(bp,a);
1986 BIO_puts(bp," / 2");
1987 BIO_puts(bp," - ");
1988 }
1989 BN_print(bp,b);
1990 BIO_puts(bp,"\n");
1991 }
1992 BN_sub(c,a,b);
1993 BN_sub(c,c,b);
1994 if(!BN_is_zero(c) && !BN_abs_is_word(c, 1))
1995 {
1996 fprintf(stderr,"Right shift one test failed!\n");
1997 return 0;
1998 }
1999 BN_copy(a,b);
2000 }
2001 BN_free(a);
2002 BN_free(b);
2003 BN_free(c);
2004 return(1);
2005 }
2006
2007int rand_neg(void)
2008 {
2009 static unsigned int neg=0;
2010 static int sign[8]={0,0,0,1,1,0,1,1};
2011
2012 return(sign[(neg++)%8]);
2013 }
generated by cgit v1.2.3-55-g6feb (git 2.39.1) at 2025-04-27 00:48:57 +0000