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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 #include <stdio.h>
73 #include <stdlib.h>
74 #include <string.h>
75
76 #include "e_os.h"
77
78 #include <openssl/bio.h>
79 #include <openssl/bn.h>
80 #include <openssl/rand.h>
81 #include <openssl/x509.h>
82 #include <openssl/err.h>
83
84 #include "../crypto/bn/bn_lcl.h"
85
86 const int num0 = 100; /* number of tests */
87 const int num1 = 50; /* additional tests for some functions */
88 const int num2 = 5; /* number of tests for slow functions */
89
90 int test_add(BIO *bp);
91 int test_sub(BIO *bp);
92 int test_lshift1(BIO *bp);
93 int test_lshift(BIO *bp, BN_CTX *ctx, BIGNUM *a_);
94 int test_rshift1(BIO *bp);
95 int test_rshift(BIO *bp, BN_CTX *ctx);
96 int test_div(BIO *bp, BN_CTX *ctx);
97 int test_div_word(BIO *bp);
98 int test_div_recp(BIO *bp, BN_CTX *ctx);
99 int test_mul(BIO *bp);
100 int test_sqr(BIO *bp, BN_CTX *ctx);
101 int test_mont(BIO *bp, BN_CTX *ctx);
102 int test_mod(BIO *bp, BN_CTX *ctx);
103 int test_mod_mul(BIO *bp, BN_CTX *ctx);
104 int test_mod_exp(BIO *bp, BN_CTX *ctx);
105 int test_mod_exp_mont_consttime(BIO *bp, BN_CTX *ctx);
106 int test_mod_exp_mont5(BIO *bp, BN_CTX *ctx);
107 int test_exp(BIO *bp, BN_CTX *ctx);
108 int test_gf2m_add(BIO *bp);
109 int test_gf2m_mod(BIO *bp);
110 int test_gf2m_mod_mul(BIO *bp, BN_CTX *ctx);
111 int test_gf2m_mod_sqr(BIO *bp, BN_CTX *ctx);
112 int test_gf2m_mod_inv(BIO *bp, BN_CTX *ctx);
113 int test_gf2m_mod_div(BIO *bp, BN_CTX *ctx);
114 int test_gf2m_mod_exp(BIO *bp, BN_CTX *ctx);
115 int test_gf2m_mod_sqrt(BIO *bp, BN_CTX *ctx);
116 int test_gf2m_mod_solve_quad(BIO *bp, BN_CTX *ctx);
117 int test_kron(BIO *bp, BN_CTX *ctx);
118 int test_sqrt(BIO *bp, BN_CTX *ctx);
119 int test_small_prime(BIO *bp, BN_CTX *ctx);
120 int test_probable_prime_coprime(BIO *bp, BN_CTX *ctx);
121 int rand_neg(void);
122 static int results = 0;
123
124 static unsigned char lst[] =
125 "\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
128 static const char rnd_seed[] =
129 "string to make the random number generator think it has entropy";
130
131 static void message(BIO *out, char *m)
132 {
133 fprintf(stderr, "test %s\n", m);
134 BIO_puts(out, "print \"test ");
135 BIO_puts(out, m);
136 BIO_puts(out, "\\n\"\n");
137 }
138
139 int main(int argc, char *argv[])
140 {
141 BN_CTX *ctx;
142 BIO *out;
143 char *outfile = NULL;
144
145 results = 0;
146
147 RAND_seed(rnd_seed, sizeof rnd_seed); /* or BN_generate_prime may fail */
148
149 argc--;
150 argv++;
151 while (argc >= 1) {
152 if (strcmp(*argv, "-results") == 0)
153 results = 1;
154 else if (strcmp(*argv, "-out") == 0) {
155 if (--argc < 1)
156 break;
157 outfile = *(++argv);
158 }
159 argc--;
160 argv++;
161 }
162
163 ctx = BN_CTX_new();
164 if (ctx == NULL)
165 EXIT(1);
166
167 out = BIO_new(BIO_s_file());
168 if (out == NULL)
169 EXIT(1);
170 if (outfile == NULL) {
171 BIO_set_fp(out, stdout, BIO_NOCLOSE | BIO_FP_TEXT);
172 } else {
173 if (!BIO_write_filename(out, outfile)) {
174 perror(outfile);
175 EXIT(1);
176 }
177 }
178
179 if (!results)
180 BIO_puts(out, "obase=16\nibase=16\n");
181
182 message(out, "BN_add");
183 if (!test_add(out))
184 goto err;
185 (void)BIO_flush(out);
186
187 message(out, "BN_sub");
188 if (!test_sub(out))
189 goto err;
190 (void)BIO_flush(out);
191
192 message(out, "BN_lshift1");
193 if (!test_lshift1(out))
194 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))
204 goto err;
205 (void)BIO_flush(out);
206
207 message(out, "BN_rshift1");
208 if (!test_rshift1(out))
209 goto err;
210 (void)BIO_flush(out);
211
212 message(out, "BN_rshift");
213 if (!test_rshift(out, ctx))
214 goto err;
215 (void)BIO_flush(out);
216
217 message(out, "BN_sqr");
218 if (!test_sqr(out, ctx))
219 goto err;
220 (void)BIO_flush(out);
221
222 message(out, "BN_mul");
223 if (!test_mul(out))
224 goto err;
225 (void)BIO_flush(out);
226
227 message(out, "BN_div");
228 if (!test_div(out, ctx))
229 goto err;
230 (void)BIO_flush(out);
231
232 message(out, "BN_div_word");
233 if (!test_div_word(out))
234 goto err;
235 (void)BIO_flush(out);
236
237 message(out, "BN_div_recp");
238 if (!test_div_recp(out, ctx))
239 goto err;
240 (void)BIO_flush(out);
241
242 message(out, "BN_mod");
243 if (!test_mod(out, ctx))
244 goto err;
245 (void)BIO_flush(out);
246
247 message(out, "BN_mod_mul");
248 if (!test_mod_mul(out, ctx))
249 goto err;
250 (void)BIO_flush(out);
251
252 message(out, "BN_mont");
253 if (!test_mont(out, ctx))
254 goto err;
255 (void)BIO_flush(out);
256
257 message(out, "BN_mod_exp");
258 if (!test_mod_exp(out, ctx))
259 goto err;
260 (void)BIO_flush(out);
261
262 message(out, "BN_mod_exp_mont_consttime");
263 if (!test_mod_exp_mont_consttime(out, ctx))
264 goto err;
265 if (!test_mod_exp_mont5(out, ctx))
266 goto err;
267 (void)BIO_flush(out);
268
269 message(out, "BN_exp");
270 if (!test_exp(out, ctx))
271 goto err;
272 (void)BIO_flush(out);
273
274 message(out, "BN_kronecker");
275 if (!test_kron(out, ctx))
276 goto err;
277 (void)BIO_flush(out);
278
279 message(out, "BN_mod_sqrt");
280 if (!test_sqrt(out, ctx))
281 goto err;
282 (void)BIO_flush(out);
283
284 message(out, "Small prime generation");
285 if (!test_small_prime(out, ctx))
286 goto err;
287 (void)BIO_flush(out);
288
289 #ifdef OPENSSL_SYS_WIN32
290 message(out, "Probable prime generation with coprimes disabled");
291 #else
292 message(out, "Probable prime generation with coprimes");
293 if (!test_probable_prime_coprime(out, ctx))
294 goto err;
295 #endif
296 (void)BIO_flush(out);
297
298 #ifndef OPENSSL_NO_EC2M
299 message(out, "BN_GF2m_add");
300 if (!test_gf2m_add(out))
301 goto err;
302 (void)BIO_flush(out);
303
304 message(out, "BN_GF2m_mod");
305 if (!test_gf2m_mod(out))
306 goto err;
307 (void)BIO_flush(out);
308
309 message(out, "BN_GF2m_mod_mul");
310 if (!test_gf2m_mod_mul(out, ctx))
311 goto err;
312 (void)BIO_flush(out);
313
314 message(out, "BN_GF2m_mod_sqr");
315 if (!test_gf2m_mod_sqr(out, ctx))
316 goto err;
317 (void)BIO_flush(out);
318
319 message(out, "BN_GF2m_mod_inv");
320 if (!test_gf2m_mod_inv(out, ctx))
321 goto err;
322 (void)BIO_flush(out);
323
324 message(out, "BN_GF2m_mod_div");
325 if (!test_gf2m_mod_div(out, ctx))
326 goto err;
327 (void)BIO_flush(out);
328
329 message(out, "BN_GF2m_mod_exp");
330 if (!test_gf2m_mod_exp(out, ctx))
331 goto err;
332 (void)BIO_flush(out);
333
334 message(out, "BN_GF2m_mod_sqrt");
335 if (!test_gf2m_mod_sqrt(out, ctx))
336 goto err;
337 (void)BIO_flush(out);
338
339 message(out, "BN_GF2m_mod_solve_quad");
340 if (!test_gf2m_mod_solve_quad(out, ctx))
341 goto err;
342 (void)BIO_flush(out);
343 #endif
344 BN_CTX_free(ctx);
345 BIO_free(out);
346
347 EXIT(0);
348 err:
349 BIO_puts(out, "1\n"); /* make sure the Perl script fed by bc
350 * notices the failure, see test_bn in
351 * test/Makefile.ssl */
352 (void)BIO_flush(out);
353 ERR_load_crypto_strings();
354 ERR_print_errors_fp(stderr);
355 EXIT(1);
356 }
357
358 int test_add(BIO *bp)
359 {
360 BIGNUM *a, *b, *c;
361 int i;
362
363 a = BN_new();
364 b = BN_new();
365 c = BN_new();
366
367 BN_bntest_rand(a, 512, 0, 0);
368 for (i = 0; i < num0; i++) {
369 BN_bntest_rand(b, 450 + i, 0, 0);
370 a->neg = rand_neg();
371 b->neg = rand_neg();
372 BN_add(c, a, b);
373 if (bp != NULL) {
374 if (!results) {
375 BN_print(bp, a);
376 BIO_puts(bp, " + ");
377 BN_print(bp, b);
378 BIO_puts(bp, " - ");
379 }
380 BN_print(bp, c);
381 BIO_puts(bp, "\n");
382 }
383 a->neg = !a->neg;
384 b->neg = !b->neg;
385 BN_add(c, c, b);
386 BN_add(c, c, a);
387 if (!BN_is_zero(c)) {
388 fprintf(stderr, "Add test failed!\n");
389 return 0;
390 }
391 }
392 BN_free(a);
393 BN_free(b);
394 BN_free(c);
395 return (1);
396 }
397
398 int test_sub(BIO *bp)
399 {
400 BIGNUM *a, *b, *c;
401 int i;
402
403 a = BN_new();
404 b = BN_new();
405 c = BN_new();
406
407 for (i = 0; i < num0 + num1; i++) {
408 if (i < num1) {
409 BN_bntest_rand(a, 512, 0, 0);
410 BN_copy(b, a);
411 if (BN_set_bit(a, i) == 0)
412 return (0);
413 BN_add_word(b, i);
414 } else {
415 BN_bntest_rand(b, 400 + i - num1, 0, 0);
416 a->neg = rand_neg();
417 b->neg = rand_neg();
418 }
419 BN_sub(c, a, b);
420 if (bp != NULL) {
421 if (!results) {
422 BN_print(bp, a);
423 BIO_puts(bp, " - ");
424 BN_print(bp, b);
425 BIO_puts(bp, " - ");
426 }
427 BN_print(bp, c);
428 BIO_puts(bp, "\n");
429 }
430 BN_add(c, c, b);
431 BN_sub(c, c, a);
432 if (!BN_is_zero(c)) {
433 fprintf(stderr, "Subtract test failed!\n");
434 return 0;
435 }
436 }
437 BN_free(a);
438 BN_free(b);
439 BN_free(c);
440 return (1);
441 }
442
443 int test_div(BIO *bp, BN_CTX *ctx)
444 {
445 BIGNUM *a, *b, *c, *d, *e;
446 int i;
447
448 a = BN_new();
449 b = BN_new();
450 c = BN_new();
451 d = BN_new();
452 e = BN_new();
453
454 BN_one(a);
455 BN_zero(b);
456
457 if (BN_div(d, c, a, b, ctx)) {
458 fprintf(stderr, "Division by zero succeeded!\n");
459 return 0;
460 }
461
462 for (i = 0; i < num0 + num1; i++) {
463 if (i < num1) {
464 BN_bntest_rand(a, 400, 0, 0);
465 BN_copy(b, a);
466 BN_lshift(a, a, i);
467 BN_add_word(a, i);
468 } else
469 BN_bntest_rand(b, 50 + 3 * (i - num1), 0, 0);
470 a->neg = rand_neg();
471 b->neg = rand_neg();
472 BN_div(d, c, a, b, ctx);
473 if (bp != NULL) {
474 if (!results) {
475 BN_print(bp, a);
476 BIO_puts(bp, " / ");
477 BN_print(bp, b);
478 BIO_puts(bp, " - ");
479 }
480 BN_print(bp, d);
481 BIO_puts(bp, "\n");
482
483 if (!results) {
484 BN_print(bp, a);
485 BIO_puts(bp, " % ");
486 BN_print(bp, b);
487 BIO_puts(bp, " - ");
488 }
489 BN_print(bp, c);
490 BIO_puts(bp, "\n");
491 }
492 BN_mul(e, d, b, ctx);
493 BN_add(d, e, c);
494 BN_sub(d, d, a);
495 if (!BN_is_zero(d)) {
496 fprintf(stderr, "Division test failed!\n");
497 return 0;
498 }
499 }
500 BN_free(a);
501 BN_free(b);
502 BN_free(c);
503 BN_free(d);
504 BN_free(e);
505 return (1);
506 }
507
508 static void print_word(BIO *bp, BN_ULONG w)
509 {
510 #ifdef SIXTY_FOUR_BIT
511 if (sizeof(w) > sizeof(unsigned long)) {
512 unsigned long h = (unsigned long)(w >> 32), l = (unsigned long)(w);
513
514 if (h)
515 BIO_printf(bp, "%lX%08lX", h, l);
516 else
517 BIO_printf(bp, "%lX", l);
518 return;
519 }
520 #endif
521 BIO_printf(bp, BN_HEX_FMT1, w);
522 }
523
524 int test_div_word(BIO *bp)
525 {
526 BIGNUM *a, *b;
527 BN_ULONG r, s;
528 int i;
529
530 a = BN_new();
531 b = BN_new();
532
533 for (i = 0; i < num0; i++) {
534 do {
535 BN_bntest_rand(a, 512, -1, 0);
536 BN_bntest_rand(b, BN_BITS2, -1, 0);
537 } while (BN_is_zero(b));
538
539 s = b->d[0];
540 BN_copy(b, a);
541 r = BN_div_word(b, s);
542
543 if (bp != NULL) {
544 if (!results) {
545 BN_print(bp, a);
546 BIO_puts(bp, " / ");
547 print_word(bp, s);
548 BIO_puts(bp, " - ");
549 }
550 BN_print(bp, b);
551 BIO_puts(bp, "\n");
552
553 if (!results) {
554 BN_print(bp, a);
555 BIO_puts(bp, " % ");
556 print_word(bp, s);
557 BIO_puts(bp, " - ");
558 }
559 print_word(bp, r);
560 BIO_puts(bp, "\n");
561 }
562 BN_mul_word(b, s);
563 BN_add_word(b, r);
564 BN_sub(b, a, b);
565 if (!BN_is_zero(b)) {
566 fprintf(stderr, "Division (word) test failed!\n");
567 return 0;
568 }
569 }
570 BN_free(a);
571 BN_free(b);
572 return (1);
573 }
574
575 int test_div_recp(BIO *bp, BN_CTX *ctx)
576 {
577 BIGNUM *a, *b, *c, *d, *e;
578 BN_RECP_CTX *recp;
579 int i;
580
581 recp = BN_RECP_CTX_new();
582 a = BN_new();
583 b = BN_new();
584 c = BN_new();
585 d = BN_new();
586 e = BN_new();
587
588 for (i = 0; i < num0 + num1; i++) {
589 if (i < num1) {
590 BN_bntest_rand(a, 400, 0, 0);
591 BN_copy(b, a);
592 BN_lshift(a, a, i);
593 BN_add_word(a, i);
594 } else
595 BN_bntest_rand(b, 50 + 3 * (i - num1), 0, 0);
596 a->neg = rand_neg();
597 b->neg = rand_neg();
598 BN_RECP_CTX_set(recp, b, ctx);
599 BN_div_recp(d, c, a, recp, ctx);
600 if (bp != NULL) {
601 if (!results) {
602 BN_print(bp, a);
603 BIO_puts(bp, " / ");
604 BN_print(bp, b);
605 BIO_puts(bp, " - ");
606 }
607 BN_print(bp, d);
608 BIO_puts(bp, "\n");
609
610 if (!results) {
611 BN_print(bp, a);
612 BIO_puts(bp, " % ");
613 BN_print(bp, b);
614 BIO_puts(bp, " - ");
615 }
616 BN_print(bp, c);
617 BIO_puts(bp, "\n");
618 }
619 BN_mul(e, d, b, ctx);
620 BN_add(d, e, c);
621 BN_sub(d, d, a);
622 if (!BN_is_zero(d)) {
623 fprintf(stderr, "Reciprocal division test failed!\n");
624 fprintf(stderr, "a=");
625 BN_print_fp(stderr, a);
626 fprintf(stderr, "\nb=");
627 BN_print_fp(stderr, b);
628 fprintf(stderr, "\n");
629 return 0;
630 }
631 }
632 BN_free(a);
633 BN_free(b);
634 BN_free(c);
635 BN_free(d);
636 BN_free(e);
637 BN_RECP_CTX_free(recp);
638 return (1);
639 }
640
641 int test_mul(BIO *bp)
642 {
643 BIGNUM *a, *b, *c, *d, *e;
644 int i;
645 BN_CTX *ctx;
646
647 ctx = BN_CTX_new();
648 if (ctx == NULL)
649 EXIT(1);
650
651 a = BN_new();
652 b = BN_new();
653 c = BN_new();
654 d = BN_new();
655 e = BN_new();
656
657 for (i = 0; i < num0 + num1; i++) {
658 if (i <= num1) {
659 BN_bntest_rand(a, 100, 0, 0);
660 BN_bntest_rand(b, 100, 0, 0);
661 } else
662 BN_bntest_rand(b, i - num1, 0, 0);
663 a->neg = rand_neg();
664 b->neg = rand_neg();
665 BN_mul(c, a, b, ctx);
666 if (bp != NULL) {
667 if (!results) {
668 BN_print(bp, a);
669 BIO_puts(bp, " * ");
670 BN_print(bp, b);
671 BIO_puts(bp, " - ");
672 }
673 BN_print(bp, c);
674 BIO_puts(bp, "\n");
675 }
676 BN_div(d, e, c, a, ctx);
677 BN_sub(d, d, b);
678 if (!BN_is_zero(d) || !BN_is_zero(e)) {
679 fprintf(stderr, "Multiplication test failed!\n");
680 return 0;
681 }
682 }
683 BN_free(a);
684 BN_free(b);
685 BN_free(c);
686 BN_free(d);
687 BN_free(e);
688 BN_CTX_free(ctx);
689 return (1);
690 }
691
692 int test_sqr(BIO *bp, BN_CTX *ctx)
693 {
694 BIGNUM *a, *c, *d, *e;
695 int i, ret = 0;
696
697 a = BN_new();
698 c = BN_new();
699 d = BN_new();
700 e = BN_new();
701 if (a == NULL || c == NULL || d == NULL || e == NULL) {
702 goto err;
703 }
704
705 for (i = 0; i < num0; i++) {
706 BN_bntest_rand(a, 40 + i * 10, 0, 0);
707 a->neg = rand_neg();
708 BN_sqr(c, a, ctx);
709 if (bp != NULL) {
710 if (!results) {
711 BN_print(bp, a);
712 BIO_puts(bp, " * ");
713 BN_print(bp, a);
714 BIO_puts(bp, " - ");
715 }
716 BN_print(bp, c);
717 BIO_puts(bp, "\n");
718 }
719 BN_div(d, e, c, a, ctx);
720 BN_sub(d, d, a);
721 if (!BN_is_zero(d) || !BN_is_zero(e)) {
722 fprintf(stderr, "Square test failed!\n");
723 goto err;
724 }
725 }
726
727 /* Regression test for a BN_sqr overflow bug. */
728 BN_hex2bn(&a,
729 "80000000000000008000000000000001"
730 "FFFFFFFFFFFFFFFE0000000000000000");
731 BN_sqr(c, a, ctx);
732 if (bp != NULL) {
733 if (!results) {
734 BN_print(bp, a);
735 BIO_puts(bp, " * ");
736 BN_print(bp, a);
737 BIO_puts(bp, " - ");
738 }
739 BN_print(bp, c);
740 BIO_puts(bp, "\n");
741 }
742 BN_mul(d, a, a, ctx);
743 if (BN_cmp(c, d)) {
744 fprintf(stderr, "Square test failed: BN_sqr and BN_mul produce "
745 "different results!\n");
746 goto err;
747 }
748
749 /* Regression test for a BN_sqr overflow bug. */
750 BN_hex2bn(&a,
751 "80000000000000000000000080000001"
752 "FFFFFFFE000000000000000000000000");
753 BN_sqr(c, a, ctx);
754 if (bp != NULL) {
755 if (!results) {
756 BN_print(bp, a);
757 BIO_puts(bp, " * ");
758 BN_print(bp, a);
759 BIO_puts(bp, " - ");
760 }
761 BN_print(bp, c);
762 BIO_puts(bp, "\n");
763 }
764 BN_mul(d, a, a, ctx);
765 if (BN_cmp(c, d)) {
766 fprintf(stderr, "Square test failed: BN_sqr and BN_mul produce "
767 "different results!\n");
768 goto err;
769 }
770 ret = 1;
771 err:
772 BN_free(a);
773 BN_free(c);
774 BN_free(d);
775 BN_free(e);
776 return ret;
777 }
778
779 int test_mont(BIO *bp, BN_CTX *ctx)
780 {
781 BIGNUM *a, *b, *c, *d, *A, *B;
782 BIGNUM *n;
783 int i;
784 BN_MONT_CTX *mont;
785
786 a = BN_new();
787 b = BN_new();
788 c = BN_new();
789 d = BN_new();
790 A = BN_new();
791 B = BN_new();
792 n = BN_new();
793
794 mont = BN_MONT_CTX_new();
795 if (mont == NULL)
796 return 0;
797
798 BN_zero(n);
799 if (BN_MONT_CTX_set(mont, n, ctx)) {
800 fprintf(stderr, "BN_MONT_CTX_set succeeded for zero modulus!\n");
801 return 0;
802 }
803
804 BN_set_word(n, 16);
805 if (BN_MONT_CTX_set(mont, n, ctx)) {
806 fprintf(stderr, "BN_MONT_CTX_set succeeded for even modulus!\n");
807 return 0;
808 }
809
810 BN_bntest_rand(a, 100, 0, 0);
811 BN_bntest_rand(b, 100, 0, 0);
812 for (i = 0; i < num2; i++) {
813 int bits = (200 * (i + 1)) / num2;
814
815 if (bits == 0)
816 continue;
817 BN_bntest_rand(n, bits, 0, 1);
818 BN_MONT_CTX_set(mont, n, ctx);
819
820 BN_nnmod(a, a, n, ctx);
821 BN_nnmod(b, b, n, ctx);
822
823 BN_to_montgomery(A, a, mont, ctx);
824 BN_to_montgomery(B, b, mont, ctx);
825
826 BN_mod_mul_montgomery(c, A, B, mont, ctx);
827 BN_from_montgomery(A, c, mont, ctx);
828 if (bp != NULL) {
829 if (!results) {
830 BN_print(bp, a);
831 BIO_puts(bp, " * ");
832 BN_print(bp, b);
833 BIO_puts(bp, " % ");
834 BN_print(bp, &mont->N);
835 BIO_puts(bp, " - ");
836 }
837 BN_print(bp, A);
838 BIO_puts(bp, "\n");
839 }
840 BN_mod_mul(d, a, b, n, ctx);
841 BN_sub(d, d, A);
842 if (!BN_is_zero(d)) {
843 fprintf(stderr, "Montgomery multiplication test failed!\n");
844 return 0;
845 }
846 }
847 BN_MONT_CTX_free(mont);
848 BN_free(a);
849 BN_free(b);
850 BN_free(c);
851 BN_free(d);
852 BN_free(A);
853 BN_free(B);
854 BN_free(n);
855 return (1);
856 }
857
858 int test_mod(BIO *bp, BN_CTX *ctx)
859 {
860 BIGNUM *a, *b, *c, *d, *e;
861 int i;
862
863 a = BN_new();
864 b = BN_new();
865 c = BN_new();
866 d = BN_new();
867 e = BN_new();
868
869 BN_bntest_rand(a, 1024, 0, 0);
870 for (i = 0; i < num0; i++) {
871 BN_bntest_rand(b, 450 + i * 10, 0, 0);
872 a->neg = rand_neg();
873 b->neg = rand_neg();
874 BN_mod(c, a, b, ctx);
875 if (bp != NULL) {
876 if (!results) {
877 BN_print(bp, a);
878 BIO_puts(bp, " % ");
879 BN_print(bp, b);
880 BIO_puts(bp, " - ");
881 }
882 BN_print(bp, c);
883 BIO_puts(bp, "\n");
884 }
885 BN_div(d, e, a, b, ctx);
886 BN_sub(e, e, c);
887 if (!BN_is_zero(e)) {
888 fprintf(stderr, "Modulo test failed!\n");
889 return 0;
890 }
891 }
892 BN_free(a);
893 BN_free(b);
894 BN_free(c);
895 BN_free(d);
896 BN_free(e);
897 return (1);
898 }
899
900 int test_mod_mul(BIO *bp, BN_CTX *ctx)
901 {
902 BIGNUM *a, *b, *c, *d, *e;
903 int i, j;
904
905 a = BN_new();
906 b = BN_new();
907 c = BN_new();
908 d = BN_new();
909 e = BN_new();
910
911 BN_one(a);
912 BN_one(b);
913 BN_zero(c);
914 if (BN_mod_mul(e, a, b, c, ctx)) {
915 fprintf(stderr, "BN_mod_mul with zero modulus succeeded!\n");
916 return 0;
917 }
918
919 for (j = 0; j < 3; j++) {
920 BN_bntest_rand(c, 1024, 0, 0);
921 for (i = 0; i < num0; i++) {
922 BN_bntest_rand(a, 475 + i * 10, 0, 0);
923 BN_bntest_rand(b, 425 + i * 11, 0, 0);
924 a->neg = rand_neg();
925 b->neg = rand_neg();
926 if (!BN_mod_mul(e, a, b, c, ctx)) {
927 unsigned long l;
928
929 while ((l = ERR_get_error()))
930 fprintf(stderr, "ERROR:%s\n", ERR_error_string(l, NULL));
931 EXIT(1);
932 }
933 if (bp != NULL) {
934 if (!results) {
935 BN_print(bp, a);
936 BIO_puts(bp, " * ");
937 BN_print(bp, b);
938 BIO_puts(bp, " % ");
939 BN_print(bp, c);
940 if ((a->neg ^ b->neg) && !BN_is_zero(e)) {
941 /*
942 * If (a*b) % c is negative, c must be added in order
943 * to obtain the normalized remainder (new with
944 * OpenSSL 0.9.7, previous versions of BN_mod_mul
945 * could generate negative results)
946 */
947 BIO_puts(bp, " + ");
948 BN_print(bp, c);
949 }
950 BIO_puts(bp, " - ");
951 }
952 BN_print(bp, e);
953 BIO_puts(bp, "\n");
954 }
955 BN_mul(d, a, b, ctx);
956 BN_sub(d, d, e);
957 BN_div(a, b, d, c, ctx);
958 if (!BN_is_zero(b)) {
959 fprintf(stderr, "Modulo multiply test failed!\n");
960 ERR_print_errors_fp(stderr);
961 return 0;
962 }
963 }
964 }
965 BN_free(a);
966 BN_free(b);
967 BN_free(c);
968 BN_free(d);
969 BN_free(e);
970 return (1);
971 }
972
973 int test_mod_exp(BIO *bp, BN_CTX *ctx)
974 {
975 BIGNUM *a, *b, *c, *d, *e;
976 int i;
977
978 a = BN_new();
979 b = BN_new();
980 c = BN_new();
981 d = BN_new();
982 e = BN_new();
983
984 BN_one(a);
985 BN_one(b);
986 BN_zero(c);
987 if (BN_mod_exp(d, a, b, c, ctx)) {
988 fprintf(stderr, "BN_mod_exp with zero modulus succeeded!\n");
989 return 0;
990 }
991
992 BN_bntest_rand(c, 30, 0, 1); /* must be odd for montgomery */
993 for (i = 0; i < num2; i++) {
994 BN_bntest_rand(a, 20 + i * 5, 0, 0);
995 BN_bntest_rand(b, 2 + i, 0, 0);
996
997 if (!BN_mod_exp(d, a, b, c, ctx))
998 return (0);
999
1000 if (bp != NULL) {
1001 if (!results) {
1002 BN_print(bp, a);
1003 BIO_puts(bp, " ^ ");
1004 BN_print(bp, b);
1005 BIO_puts(bp, " % ");
1006 BN_print(bp, c);
1007 BIO_puts(bp, " - ");
1008 }
1009 BN_print(bp, d);
1010 BIO_puts(bp, "\n");
1011 }
1012 BN_exp(e, a, b, ctx);
1013 BN_sub(e, e, d);
1014 BN_div(a, b, e, c, ctx);
1015 if (!BN_is_zero(b)) {
1016 fprintf(stderr, "Modulo exponentiation test failed!\n");
1017 return 0;
1018 }
1019 }
1020 BN_free(a);
1021 BN_free(b);
1022 BN_free(c);
1023 BN_free(d);
1024 BN_free(e);
1025 return (1);
1026 }
1027
1028 int test_mod_exp_mont_consttime(BIO *bp, BN_CTX *ctx)
1029 {
1030 BIGNUM *a, *b, *c, *d, *e;
1031 int i;
1032
1033 a = BN_new();
1034 b = BN_new();
1035 c = BN_new();
1036 d = BN_new();
1037 e = BN_new();
1038
1039 BN_one(a);
1040 BN_one(b);
1041 BN_zero(c);
1042 if (BN_mod_exp_mont_consttime(d, a, b, c, ctx, NULL)) {
1043 fprintf(stderr, "BN_mod_exp_mont_consttime with zero modulus "
1044 "succeeded\n");
1045 return 0;
1046 }
1047
1048 BN_set_word(c, 16);
1049 if (BN_mod_exp_mont_consttime(d, a, b, c, ctx, NULL)) {
1050 fprintf(stderr, "BN_mod_exp_mont_consttime with even modulus "
1051 "succeeded\n");
1052 return 0;
1053 }
1054
1055 BN_bntest_rand(c, 30, 0, 1); /* must be odd for montgomery */
1056 for (i = 0; i < num2; i++) {
1057 BN_bntest_rand(a, 20 + i * 5, 0, 0);
1058 BN_bntest_rand(b, 2 + i, 0, 0);
1059
1060 if (!BN_mod_exp_mont_consttime(d, a, b, c, ctx, NULL))
1061 return (00);
1062
1063 if (bp != NULL) {
1064 if (!results) {
1065 BN_print(bp, a);
1066 BIO_puts(bp, " ^ ");
1067 BN_print(bp, b);
1068 BIO_puts(bp, " % ");
1069 BN_print(bp, c);
1070 BIO_puts(bp, " - ");
1071 }
1072 BN_print(bp, d);
1073 BIO_puts(bp, "\n");
1074 }
1075 BN_exp(e, a, b, ctx);
1076 BN_sub(e, e, d);
1077 BN_div(a, b, e, c, ctx);
1078 if (!BN_is_zero(b)) {
1079 fprintf(stderr, "Modulo exponentiation test failed!\n");
1080 return 0;
1081 }
1082 }
1083 BN_free(a);
1084 BN_free(b);
1085 BN_free(c);
1086 BN_free(d);
1087 BN_free(e);
1088 return (1);
1089 }
1090
1091 /*
1092 * Test constant-time modular exponentiation with 1024-bit inputs, which on
1093 * x86_64 cause a different code branch to be taken.
1094 */
1095 int test_mod_exp_mont5(BIO *bp, BN_CTX *ctx)
1096 {
1097 BIGNUM *a, *p, *m, *d, *e;
1098 BN_MONT_CTX *mont;
1099
1100 a = BN_new();
1101 p = BN_new();
1102 m = BN_new();
1103 d = BN_new();
1104 e = BN_new();
1105 mont = BN_MONT_CTX_new();
1106
1107 BN_bntest_rand(m, 1024, 0, 1); /* must be odd for montgomery */
1108 /* Zero exponent */
1109 BN_bntest_rand(a, 1024, 0, 0);
1110 BN_zero(p);
1111 if (!BN_mod_exp_mont_consttime(d, a, p, m, ctx, NULL))
1112 return 0;
1113 if (!BN_is_one(d)) {
1114 fprintf(stderr, "Modular exponentiation test failed!\n");
1115 return 0;
1116 }
1117 /* Zero input */
1118 BN_bntest_rand(p, 1024, 0, 0);
1119 BN_zero(a);
1120 if (!BN_mod_exp_mont_consttime(d, a, p, m, ctx, NULL))
1121 return 0;
1122 if (!BN_is_zero(d)) {
1123 fprintf(stderr, "Modular exponentiation test failed!\n");
1124 return 0;
1125 }
1126 /*
1127 * Craft an input whose Montgomery representation is 1, i.e., shorter
1128 * than the modulus m, in order to test the const time precomputation
1129 * scattering/gathering.
1130 */
1131 BN_one(a);
1132 BN_MONT_CTX_set(mont, m, ctx);
1133 if (!BN_from_montgomery(e, a, mont, ctx))
1134 return 0;
1135 if (!BN_mod_exp_mont_consttime(d, e, p, m, ctx, NULL))
1136 return 0;
1137 if (!BN_mod_exp_simple(a, e, p, m, ctx))
1138 return 0;
1139 if (BN_cmp(a, d) != 0) {
1140 fprintf(stderr, "Modular exponentiation test failed!\n");
1141 return 0;
1142 }
1143 /* Finally, some regular test vectors. */
1144 BN_bntest_rand(e, 1024, 0, 0);
1145 if (!BN_mod_exp_mont_consttime(d, e, p, m, ctx, NULL))
1146 return 0;
1147 if (!BN_mod_exp_simple(a, e, p, m, ctx))
1148 return 0;
1149 if (BN_cmp(a, d) != 0) {
1150 fprintf(stderr, "Modular exponentiation test failed!\n");
1151 return 0;
1152 }
1153 BN_MONT_CTX_free(mont);
1154 BN_free(a);
1155 BN_free(p);
1156 BN_free(m);
1157 BN_free(d);
1158 BN_free(e);
1159 return (1);
1160 }
1161
1162 int test_exp(BIO *bp, BN_CTX *ctx)
1163 {
1164 BIGNUM *a, *b, *d, *e, *one;
1165 int i;
1166
1167 a = BN_new();
1168 b = BN_new();
1169 d = BN_new();
1170 e = BN_new();
1171 one = BN_new();
1172 BN_one(one);
1173
1174 for (i = 0; i < num2; i++) {
1175 BN_bntest_rand(a, 20 + i * 5, 0, 0);
1176 BN_bntest_rand(b, 2 + i, 0, 0);
1177
1178 if (BN_exp(d, a, b, ctx) <= 0)
1179 return (0);
1180
1181 if (bp != NULL) {
1182 if (!results) {
1183 BN_print(bp, a);
1184 BIO_puts(bp, " ^ ");
1185 BN_print(bp, b);
1186 BIO_puts(bp, " - ");
1187 }
1188 BN_print(bp, d);
1189 BIO_puts(bp, "\n");
1190 }
1191 BN_one(e);
1192 for (; !BN_is_zero(b); BN_sub(b, b, one))
1193 BN_mul(e, e, a, ctx);
1194 BN_sub(e, e, d);
1195 if (!BN_is_zero(e)) {
1196 fprintf(stderr, "Exponentiation test failed!\n");
1197 return 0;
1198 }
1199 }
1200 BN_free(a);
1201 BN_free(b);
1202 BN_free(d);
1203 BN_free(e);
1204 BN_free(one);
1205 return (1);
1206 }
1207
1208 #ifndef OPENSSL_NO_EC2M
1209 int test_gf2m_add(BIO *bp)
1210 {
1211 BIGNUM *a, *b, *c;
1212 int i, ret = 0;
1213
1214 a = BN_new();
1215 b = BN_new();
1216 c = BN_new();
1217
1218 for (i = 0; i < num0; i++) {
1219 BN_rand(a, 512, 0, 0);
1220 BN_copy(b, BN_value_one());
1221 a->neg = rand_neg();
1222 b->neg = rand_neg();
1223 BN_GF2m_add(c, a, b);
1224 /* Test that two added values have the correct parity. */
1225 if ((BN_is_odd(a) && BN_is_odd(c))
1226 || (!BN_is_odd(a) && !BN_is_odd(c))) {
1227 fprintf(stderr, "GF(2^m) addition test (a) failed!\n");
1228 goto err;
1229 }
1230 BN_GF2m_add(c, c, c);
1231 /* Test that c + c = 0. */
1232 if (!BN_is_zero(c)) {
1233 fprintf(stderr, "GF(2^m) addition test (b) failed!\n");
1234 goto err;
1235 }
1236 }
1237 ret = 1;
1238 err:
1239 BN_free(a);
1240 BN_free(b);
1241 BN_free(c);
1242 return ret;
1243 }
1244
1245 int test_gf2m_mod(BIO *bp)
1246 {
1247 BIGNUM *a, *b[2], *c, *d, *e;
1248 int i, j, ret = 0;
1249 int p0[] = { 163, 7, 6, 3, 0, -1 };
1250 int p1[] = { 193, 15, 0, -1 };
1251
1252 a = BN_new();
1253 b[0] = BN_new();
1254 b[1] = BN_new();
1255 c = BN_new();
1256 d = BN_new();
1257 e = 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 BN_bntest_rand(a, 1024, 0, 0);
1264 for (j = 0; j < 2; j++) {
1265 BN_GF2m_mod(c, a, b[j]);
1266 BN_GF2m_add(d, a, c);
1267 BN_GF2m_mod(e, d, b[j]);
1268 /* Test that a + (a mod p) mod p == 0. */
1269 if (!BN_is_zero(e)) {
1270 fprintf(stderr, "GF(2^m) modulo test failed!\n");
1271 goto err;
1272 }
1273 }
1274 }
1275 ret = 1;
1276 err:
1277 BN_free(a);
1278 BN_free(b[0]);
1279 BN_free(b[1]);
1280 BN_free(c);
1281 BN_free(d);
1282 BN_free(e);
1283 return ret;
1284 }
1285
1286 int test_gf2m_mod_mul(BIO *bp, BN_CTX *ctx)
1287 {
1288 BIGNUM *a, *b[2], *c, *d, *e, *f, *g, *h;
1289 int i, j, ret = 0;
1290 int p0[] = { 163, 7, 6, 3, 0, -1 };
1291 int p1[] = { 193, 15, 0, -1 };
1292
1293 a = BN_new();
1294 b[0] = BN_new();
1295 b[1] = BN_new();
1296 c = BN_new();
1297 d = BN_new();
1298 e = BN_new();
1299 f = BN_new();
1300 g = BN_new();
1301 h = BN_new();
1302
1303 BN_GF2m_arr2poly(p0, b[0]);
1304 BN_GF2m_arr2poly(p1, b[1]);
1305
1306 for (i = 0; i < num0; i++) {
1307 BN_bntest_rand(a, 1024, 0, 0);
1308 BN_bntest_rand(c, 1024, 0, 0);
1309 BN_bntest_rand(d, 1024, 0, 0);
1310 for (j = 0; j < 2; j++) {
1311 BN_GF2m_mod_mul(e, a, c, b[j], ctx);
1312 BN_GF2m_add(f, a, d);
1313 BN_GF2m_mod_mul(g, f, c, b[j], ctx);
1314 BN_GF2m_mod_mul(h, d, c, b[j], ctx);
1315 BN_GF2m_add(f, e, g);
1316 BN_GF2m_add(f, f, h);
1317 /* Test that (a+d)*c = a*c + d*c. */
1318 if (!BN_is_zero(f)) {
1319 fprintf(stderr,
1320 "GF(2^m) modular multiplication test failed!\n");
1321 goto err;
1322 }
1323 }
1324 }
1325 ret = 1;
1326 err:
1327 BN_free(a);
1328 BN_free(b[0]);
1329 BN_free(b[1]);
1330 BN_free(c);
1331 BN_free(d);
1332 BN_free(e);
1333 BN_free(f);
1334 BN_free(g);
1335 BN_free(h);
1336 return ret;
1337 }
1338
1339 int test_gf2m_mod_sqr(BIO *bp, BN_CTX *ctx)
1340 {
1341 BIGNUM *a, *b[2], *c, *d;
1342 int i, j, ret = 0;
1343 int p0[] = { 163, 7, 6, 3, 0, -1 };
1344 int p1[] = { 193, 15, 0, -1 };
1345
1346 a = BN_new();
1347 b[0] = BN_new();
1348 b[1] = BN_new();
1349 c = BN_new();
1350 d = BN_new();
1351
1352 BN_GF2m_arr2poly(p0, b[0]);
1353 BN_GF2m_arr2poly(p1, b[1]);
1354
1355 for (i = 0; i < num0; i++) {
1356 BN_bntest_rand(a, 1024, 0, 0);
1357 for (j = 0; j < 2; j++) {
1358 BN_GF2m_mod_sqr(c, a, b[j], ctx);
1359 BN_copy(d, a);
1360 BN_GF2m_mod_mul(d, a, d, b[j], ctx);
1361 BN_GF2m_add(d, c, d);
1362 /* Test that a*a = a^2. */
1363 if (!BN_is_zero(d)) {
1364 fprintf(stderr, "GF(2^m) modular squaring test failed!\n");
1365 goto err;
1366 }
1367 }
1368 }
1369 ret = 1;
1370 err:
1371 BN_free(a);
1372 BN_free(b[0]);
1373 BN_free(b[1]);
1374 BN_free(c);
1375 BN_free(d);
1376 return ret;
1377 }
1378
1379 int test_gf2m_mod_inv(BIO *bp, BN_CTX *ctx)
1380 {
1381 BIGNUM *a, *b[2], *c, *d;
1382 int i, j, ret = 0;
1383 int p0[] = { 163, 7, 6, 3, 0, -1 };
1384 int p1[] = { 193, 15, 0, -1 };
1385
1386 a = BN_new();
1387 b[0] = BN_new();
1388 b[1] = BN_new();
1389 c = BN_new();
1390 d = BN_new();
1391
1392 BN_GF2m_arr2poly(p0, b[0]);
1393 BN_GF2m_arr2poly(p1, b[1]);
1394
1395 for (i = 0; i < num0; i++) {
1396 BN_bntest_rand(a, 512, 0, 0);
1397 for (j = 0; j < 2; j++) {
1398 BN_GF2m_mod_inv(c, a, b[j], ctx);
1399 BN_GF2m_mod_mul(d, a, c, b[j], ctx);
1400 /* Test that ((1/a)*a) = 1. */
1401 if (!BN_is_one(d)) {
1402 fprintf(stderr, "GF(2^m) modular inversion test failed!\n");
1403 goto err;
1404 }
1405 }
1406 }
1407 ret = 1;
1408 err:
1409 BN_free(a);
1410 BN_free(b[0]);
1411 BN_free(b[1]);
1412 BN_free(c);
1413 BN_free(d);
1414 return ret;
1415 }
1416
1417 int test_gf2m_mod_div(BIO *bp, BN_CTX *ctx)
1418 {
1419 BIGNUM *a, *b[2], *c, *d, *e, *f;
1420 int i, j, ret = 0;
1421 int p0[] = { 163, 7, 6, 3, 0, -1 };
1422 int p1[] = { 193, 15, 0, -1 };
1423
1424 a = BN_new();
1425 b[0] = BN_new();
1426 b[1] = BN_new();
1427 c = BN_new();
1428 d = BN_new();
1429 e = BN_new();
1430 f = BN_new();
1431
1432 BN_GF2m_arr2poly(p0, b[0]);
1433 BN_GF2m_arr2poly(p1, b[1]);
1434
1435 for (i = 0; i < num0; i++) {
1436 BN_bntest_rand(a, 512, 0, 0);
1437 BN_bntest_rand(c, 512, 0, 0);
1438 for (j = 0; j < 2; j++) {
1439 BN_GF2m_mod_div(d, a, c, b[j], ctx);
1440 BN_GF2m_mod_mul(e, d, c, b[j], ctx);
1441 BN_GF2m_mod_div(f, a, e, b[j], ctx);
1442 /* Test that ((a/c)*c)/a = 1. */
1443 if (!BN_is_one(f)) {
1444 fprintf(stderr, "GF(2^m) modular division test failed!\n");
1445 goto err;
1446 }
1447 }
1448 }
1449 ret = 1;
1450 err:
1451 BN_free(a);
1452 BN_free(b[0]);
1453 BN_free(b[1]);
1454 BN_free(c);
1455 BN_free(d);
1456 BN_free(e);
1457 BN_free(f);
1458 return ret;
1459 }
1460
1461 int test_gf2m_mod_exp(BIO *bp, BN_CTX *ctx)
1462 {
1463 BIGNUM *a, *b[2], *c, *d, *e, *f;
1464 int i, j, ret = 0;
1465 int p0[] = { 163, 7, 6, 3, 0, -1 };
1466 int p1[] = { 193, 15, 0, -1 };
1467
1468 a = BN_new();
1469 b[0] = BN_new();
1470 b[1] = BN_new();
1471 c = BN_new();
1472 d = BN_new();
1473 e = BN_new();
1474 f = BN_new();
1475
1476 BN_GF2m_arr2poly(p0, b[0]);
1477 BN_GF2m_arr2poly(p1, b[1]);
1478
1479 for (i = 0; i < num0; i++) {
1480 BN_bntest_rand(a, 512, 0, 0);
1481 BN_bntest_rand(c, 512, 0, 0);
1482 BN_bntest_rand(d, 512, 0, 0);
1483 for (j = 0; j < 2; j++) {
1484 BN_GF2m_mod_exp(e, a, c, b[j], ctx);
1485 BN_GF2m_mod_exp(f, a, d, b[j], ctx);
1486 BN_GF2m_mod_mul(e, e, f, b[j], ctx);
1487 BN_add(f, c, d);
1488 BN_GF2m_mod_exp(f, a, f, b[j], ctx);
1489 BN_GF2m_add(f, e, f);
1490 /* Test that a^(c+d)=a^c*a^d. */
1491 if (!BN_is_zero(f)) {
1492 fprintf(stderr,
1493 "GF(2^m) modular exponentiation test failed!\n");
1494 goto err;
1495 }
1496 }
1497 }
1498 ret = 1;
1499 err:
1500 BN_free(a);
1501 BN_free(b[0]);
1502 BN_free(b[1]);
1503 BN_free(c);
1504 BN_free(d);
1505 BN_free(e);
1506 BN_free(f);
1507 return ret;
1508 }
1509
1510 int test_gf2m_mod_sqrt(BIO *bp, BN_CTX *ctx)
1511 {
1512 BIGNUM *a, *b[2], *c, *d, *e, *f;
1513 int i, j, ret = 0;
1514 int p0[] = { 163, 7, 6, 3, 0, -1 };
1515 int p1[] = { 193, 15, 0, -1 };
1516
1517 a = BN_new();
1518 b[0] = BN_new();
1519 b[1] = BN_new();
1520 c = BN_new();
1521 d = BN_new();
1522 e = BN_new();
1523 f = BN_new();
1524
1525 BN_GF2m_arr2poly(p0, b[0]);
1526 BN_GF2m_arr2poly(p1, b[1]);
1527
1528 for (i = 0; i < num0; i++) {
1529 BN_bntest_rand(a, 512, 0, 0);
1530 for (j = 0; j < 2; j++) {
1531 BN_GF2m_mod(c, a, b[j]);
1532 BN_GF2m_mod_sqrt(d, a, b[j], ctx);
1533 BN_GF2m_mod_sqr(e, d, b[j], ctx);
1534 BN_GF2m_add(f, c, e);
1535 /* Test that d^2 = a, where d = sqrt(a). */
1536 if (!BN_is_zero(f)) {
1537 fprintf(stderr, "GF(2^m) modular square root test failed!\n");
1538 goto err;
1539 }
1540 }
1541 }
1542 ret = 1;
1543 err:
1544 BN_free(a);
1545 BN_free(b[0]);
1546 BN_free(b[1]);
1547 BN_free(c);
1548 BN_free(d);
1549 BN_free(e);
1550 BN_free(f);
1551 return ret;
1552 }
1553
1554 int test_gf2m_mod_solve_quad(BIO *bp, BN_CTX *ctx)
1555 {
1556 BIGNUM *a, *b[2], *c, *d, *e;
1557 int i, j, s = 0, t, ret = 0;
1558 int p0[] = { 163, 7, 6, 3, 0, -1 };
1559 int p1[] = { 193, 15, 0, -1 };
1560
1561 a = BN_new();
1562 b[0] = BN_new();
1563 b[1] = BN_new();
1564 c = BN_new();
1565 d = BN_new();
1566 e = BN_new();
1567
1568 BN_GF2m_arr2poly(p0, b[0]);
1569 BN_GF2m_arr2poly(p1, b[1]);
1570
1571 for (i = 0; i < num0; i++) {
1572 BN_bntest_rand(a, 512, 0, 0);
1573 for (j = 0; j < 2; j++) {
1574 t = BN_GF2m_mod_solve_quad(c, a, b[j], ctx);
1575 if (t) {
1576 s++;
1577 BN_GF2m_mod_sqr(d, c, b[j], ctx);
1578 BN_GF2m_add(d, c, d);
1579 BN_GF2m_mod(e, a, b[j]);
1580 BN_GF2m_add(e, e, d);
1581 /*
1582 * Test that solution of quadratic c satisfies c^2 + c = a.
1583 */
1584 if (!BN_is_zero(e)) {
1585 fprintf(stderr,
1586 "GF(2^m) modular solve quadratic test failed!\n");
1587 goto err;
1588 }
1589
1590 }
1591 }
1592 }
1593 if (s == 0) {
1594 fprintf(stderr,
1595 "All %i tests of GF(2^m) modular solve quadratic resulted in no roots;\n",
1596 num0);
1597 fprintf(stderr,
1598 "this is very unlikely and probably indicates an error.\n");
1599 goto err;
1600 }
1601 ret = 1;
1602 err:
1603 BN_free(a);
1604 BN_free(b[0]);
1605 BN_free(b[1]);
1606 BN_free(c);
1607 BN_free(d);
1608 BN_free(e);
1609 return ret;
1610 }
1611 #endif
1612 static int genprime_cb(int p, int n, BN_GENCB *arg)
1613 {
1614 char c = '*';
1615
1616 if (p == 0)
1617 c = '.';
1618 if (p == 1)
1619 c = '+';
1620 if (p == 2)
1621 c = '*';
1622 if (p == 3)
1623 c = '\n';
1624 putc(c, stderr);
1625 fflush(stderr);
1626 return 1;
1627 }
1628
1629 int test_kron(BIO *bp, BN_CTX *ctx)
1630 {
1631 BN_GENCB cb;
1632 BIGNUM *a, *b, *r, *t;
1633 int i;
1634 int legendre, kronecker;
1635 int ret = 0;
1636
1637 a = BN_new();
1638 b = BN_new();
1639 r = BN_new();
1640 t = BN_new();
1641 if (a == NULL || b == NULL || r == NULL || t == NULL)
1642 goto err;
1643
1644 BN_GENCB_set(&cb, genprime_cb, NULL);
1645
1646 /*
1647 * We test BN_kronecker(a, b, ctx) just for b odd (Jacobi symbol). In
1648 * this case we know that if b is prime, then BN_kronecker(a, b, ctx) is
1649 * congruent to $a^{(b-1)/2}$, modulo $b$ (Legendre symbol). So we
1650 * generate a random prime b and compare these values for a number of
1651 * random a's. (That is, we run the Solovay-Strassen primality test to
1652 * confirm that b is prime, except that we don't want to test whether b
1653 * is prime but whether BN_kronecker works.)
1654 */
1655
1656 if (!BN_generate_prime_ex(b, 512, 0, NULL, NULL, &cb))
1657 goto err;
1658 b->neg = rand_neg();
1659 putc('\n', stderr);
1660
1661 for (i = 0; i < num0; i++) {
1662 if (!BN_bntest_rand(a, 512, 0, 0))
1663 goto err;
1664 a->neg = rand_neg();
1665
1666 /* t := (|b|-1)/2 (note that b is odd) */
1667 if (!BN_copy(t, b))
1668 goto err;
1669 t->neg = 0;
1670 if (!BN_sub_word(t, 1))
1671 goto err;
1672 if (!BN_rshift1(t, t))
1673 goto err;
1674 /* r := a^t mod b */
1675 b->neg = 0;
1676
1677 if (!BN_mod_exp_recp(r, a, t, b, ctx))
1678 goto err;
1679 b->neg = 1;
1680
1681 if (BN_is_word(r, 1))
1682 legendre = 1;
1683 else if (BN_is_zero(r))
1684 legendre = 0;
1685 else {
1686 if (!BN_add_word(r, 1))
1687 goto err;
1688 if (0 != BN_ucmp(r, b)) {
1689 fprintf(stderr, "Legendre symbol computation failed\n");
1690 goto err;
1691 }
1692 legendre = -1;
1693 }
1694
1695 kronecker = BN_kronecker(a, b, ctx);
1696 if (kronecker < -1)
1697 goto err;
1698 /* we actually need BN_kronecker(a, |b|) */
1699 if (a->neg && b->neg)
1700 kronecker = -kronecker;
1701
1702 if (legendre != kronecker) {
1703 fprintf(stderr, "legendre != kronecker; a = ");
1704 BN_print_fp(stderr, a);
1705 fprintf(stderr, ", b = ");
1706 BN_print_fp(stderr, b);
1707 fprintf(stderr, "\n");
1708 goto err;
1709 }
1710
1711 putc('.', stderr);
1712 fflush(stderr);
1713 }
1714
1715 putc('\n', stderr);
1716 fflush(stderr);
1717 ret = 1;
1718 err:
1719 BN_free(a);
1720 BN_free(b);
1721 BN_free(r);
1722 BN_free(t);
1723 return ret;
1724 }
1725
1726 int test_sqrt(BIO *bp, BN_CTX *ctx)
1727 {
1728 BN_GENCB cb;
1729 BIGNUM *a, *p, *r;
1730 int i, j;
1731 int ret = 0;
1732
1733 a = BN_new();
1734 p = BN_new();
1735 r = BN_new();
1736 if (a == NULL || p == NULL || r == NULL)
1737 goto err;
1738
1739 BN_GENCB_set(&cb, genprime_cb, NULL);
1740
1741 for (i = 0; i < 16; i++) {
1742 if (i < 8) {
1743 unsigned primes[8] = { 2, 3, 5, 7, 11, 13, 17, 19 };
1744
1745 if (!BN_set_word(p, primes[i]))
1746 goto err;
1747 } else {
1748 if (!BN_set_word(a, 32))
1749 goto err;
1750 if (!BN_set_word(r, 2 * i + 1))
1751 goto err;
1752
1753 if (!BN_generate_prime_ex(p, 256, 0, a, r, &cb))
1754 goto err;
1755 putc('\n', stderr);
1756 }
1757 p->neg = rand_neg();
1758
1759 for (j = 0; j < num2; j++) {
1760 /*
1761 * construct 'a' such that it is a square modulo p, but in
1762 * general not a proper square and not reduced modulo p
1763 */
1764 if (!BN_bntest_rand(r, 256, 0, 3))
1765 goto err;
1766 if (!BN_nnmod(r, r, p, ctx))
1767 goto err;
1768 if (!BN_mod_sqr(r, r, p, ctx))
1769 goto err;
1770 if (!BN_bntest_rand(a, 256, 0, 3))
1771 goto err;
1772 if (!BN_nnmod(a, a, p, ctx))
1773 goto err;
1774 if (!BN_mod_sqr(a, a, p, ctx))
1775 goto err;
1776 if (!BN_mul(a, a, r, ctx))
1777 goto err;
1778 if (rand_neg())
1779 if (!BN_sub(a, a, p))
1780 goto err;
1781
1782 if (!BN_mod_sqrt(r, a, p, ctx))
1783 goto err;
1784 if (!BN_mod_sqr(r, r, p, ctx))
1785 goto err;
1786
1787 if (!BN_nnmod(a, a, p, ctx))
1788 goto err;
1789
1790 if (BN_cmp(a, r) != 0) {
1791 fprintf(stderr, "BN_mod_sqrt failed: a = ");
1792 BN_print_fp(stderr, a);
1793 fprintf(stderr, ", r = ");
1794 BN_print_fp(stderr, r);
1795 fprintf(stderr, ", p = ");
1796 BN_print_fp(stderr, p);
1797 fprintf(stderr, "\n");
1798 goto err;
1799 }
1800
1801 putc('.', stderr);
1802 fflush(stderr);
1803 }
1804
1805 putc('\n', stderr);
1806 fflush(stderr);
1807 }
1808 ret = 1;
1809 err:
1810 BN_free(a);
1811 BN_free(p);
1812 BN_free(r);
1813 return ret;
1814 }
1815
1816 int test_small_prime(BIO *bp, BN_CTX *ctx)
1817 {
1818 static const int bits = 10;
1819 int ret = 0;
1820 BIGNUM *r;
1821
1822 r = BN_new();
1823 if (!BN_generate_prime_ex(r, bits, 0, NULL, NULL, NULL))
1824 goto err;
1825 if (BN_num_bits(r) != bits) {
1826 BIO_printf(bp, "Expected %d bit prime, got %d bit number\n", bits,
1827 BN_num_bits(r));
1828 goto err;
1829 }
1830
1831 ret = 1;
1832
1833 err:
1834 BN_clear_free(r);
1835 return ret;
1836 }
1837
1838 #ifndef OPENSSL_SYS_WIN32
1839 int test_probable_prime_coprime(BIO *bp, BN_CTX *ctx)
1840 {
1841 int i, j, ret = 0;
1842 BIGNUM *r;
1843 BN_ULONG primes[5] = { 2, 3, 5, 7, 11 };
1844
1845 r = BN_new();
1846
1847 for (i = 0; i < 1000; i++) {
1848 if (!bn_probable_prime_dh_coprime(r, 1024, ctx))
1849 goto err;
1850
1851 for (j = 0; j < 5; j++) {
1852 if (BN_mod_word(r, primes[j]) == 0) {
1853 BIO_printf(bp, "Number generated is not coprime to "
1854 BN_DEC_FMT1 ":\n", primes[j]);
1855 BN_print_fp(stdout, r);
1856 BIO_printf(bp, "\n");
1857 goto err;
1858 }
1859 }
1860 }
1861
1862 ret = 1;
1863
1864 err:
1865 BN_clear_free(r);
1866 return ret;
1867 }
1868 #endif
1869 int test_lshift(BIO *bp, BN_CTX *ctx, BIGNUM *a_)
1870 {
1871 BIGNUM *a, *b, *c, *d;
1872 int i;
1873
1874 b = BN_new();
1875 c = BN_new();
1876 d = BN_new();
1877 BN_one(c);
1878
1879 if (a_)
1880 a = a_;
1881 else {
1882 a = BN_new();
1883 BN_bntest_rand(a, 200, 0, 0);
1884 a->neg = rand_neg();
1885 }
1886 for (i = 0; i < num0; i++) {
1887 BN_lshift(b, a, i + 1);
1888 BN_add(c, c, c);
1889 if (bp != NULL) {
1890 if (!results) {
1891 BN_print(bp, a);
1892 BIO_puts(bp, " * ");
1893 BN_print(bp, c);
1894 BIO_puts(bp, " - ");
1895 }
1896 BN_print(bp, b);
1897 BIO_puts(bp, "\n");
1898 }
1899 BN_mul(d, a, c, ctx);
1900 BN_sub(d, d, b);
1901 if (!BN_is_zero(d)) {
1902 fprintf(stderr, "Left shift test failed!\n");
1903 fprintf(stderr, "a=");
1904 BN_print_fp(stderr, a);
1905 fprintf(stderr, "\nb=");
1906 BN_print_fp(stderr, b);
1907 fprintf(stderr, "\nc=");
1908 BN_print_fp(stderr, c);
1909 fprintf(stderr, "\nd=");
1910 BN_print_fp(stderr, d);
1911 fprintf(stderr, "\n");
1912 return 0;
1913 }
1914 }
1915 BN_free(a);
1916 BN_free(b);
1917 BN_free(c);
1918 BN_free(d);
1919 return (1);
1920 }
1921
1922 int test_lshift1(BIO *bp)
1923 {
1924 BIGNUM *a, *b, *c;
1925 int i;
1926
1927 a = BN_new();
1928 b = BN_new();
1929 c = BN_new();
1930
1931 BN_bntest_rand(a, 200, 0, 0);
1932 a->neg = rand_neg();
1933 for (i = 0; i < num0; i++) {
1934 BN_lshift1(b, a);
1935 if (bp != NULL) {
1936 if (!results) {
1937 BN_print(bp, a);
1938 BIO_puts(bp, " * 2");
1939 BIO_puts(bp, " - ");
1940 }
1941 BN_print(bp, b);
1942 BIO_puts(bp, "\n");
1943 }
1944 BN_add(c, a, a);
1945 BN_sub(a, b, c);
1946 if (!BN_is_zero(a)) {
1947 fprintf(stderr, "Left shift one test failed!\n");
1948 return 0;
1949 }
1950
1951 BN_copy(a, b);
1952 }
1953 BN_free(a);
1954 BN_free(b);
1955 BN_free(c);
1956 return (1);
1957 }
1958
1959 int test_rshift(BIO *bp, BN_CTX *ctx)
1960 {
1961 BIGNUM *a, *b, *c, *d, *e;
1962 int i;
1963
1964 a = BN_new();
1965 b = BN_new();
1966 c = BN_new();
1967 d = BN_new();
1968 e = BN_new();
1969 BN_one(c);
1970
1971 BN_bntest_rand(a, 200, 0, 0);
1972 a->neg = rand_neg();
1973 for (i = 0; i < num0; i++) {
1974 BN_rshift(b, a, i + 1);
1975 BN_add(c, c, c);
1976 if (bp != NULL) {
1977 if (!results) {
1978 BN_print(bp, a);
1979 BIO_puts(bp, " / ");
1980 BN_print(bp, c);
1981 BIO_puts(bp, " - ");
1982 }
1983 BN_print(bp, b);
1984 BIO_puts(bp, "\n");
1985 }
1986 BN_div(d, e, a, c, ctx);
1987 BN_sub(d, d, b);
1988 if (!BN_is_zero(d)) {
1989 fprintf(stderr, "Right shift test failed!\n");
1990 return 0;
1991 }
1992 }
1993 BN_free(a);
1994 BN_free(b);
1995 BN_free(c);
1996 BN_free(d);
1997 BN_free(e);
1998 return (1);
1999 }
2000
2001 int test_rshift1(BIO *bp)
2002 {
2003 BIGNUM *a, *b, *c;
2004 int i;
2005
2006 a = BN_new();
2007 b = BN_new();
2008 c = BN_new();
2009
2010 BN_bntest_rand(a, 200, 0, 0);
2011 a->neg = rand_neg();
2012 for (i = 0; i < num0; i++) {
2013 BN_rshift1(b, a);
2014 if (bp != NULL) {
2015 if (!results) {
2016 BN_print(bp, a);
2017 BIO_puts(bp, " / 2");
2018 BIO_puts(bp, " - ");
2019 }
2020 BN_print(bp, b);
2021 BIO_puts(bp, "\n");
2022 }
2023 BN_sub(c, a, b);
2024 BN_sub(c, c, b);
2025 if (!BN_is_zero(c) && !BN_abs_is_word(c, 1)) {
2026 fprintf(stderr, "Right shift one test failed!\n");
2027 return 0;
2028 }
2029 BN_copy(a, b);
2030 }
2031 BN_free(a);
2032 BN_free(b);
2033 BN_free(c);
2034 return (1);
2035 }
2036
2037 int rand_neg(void)
2038 {
2039 static unsigned int neg = 0;
2040 static int sign[8] = { 0, 0, 0, 1, 1, 0, 1, 1 };
2041
2042 return (sign[(neg++) % 8]);
2043 }
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