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OpenSSL: update to 1.0.1m
[tomato.git] / release / src / router / openssl / crypto / bn / bntest.c
blob06662c58b32f3c7eb22706a0d6effd80c97f1c73
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 /*
73 * Until the key-gen callbacks are modified to use newer prototypes, we allow
74 * deprecated functions for openssl-internal code
75 */
76 #ifdef OPENSSL_NO_DEPRECATED
77 # undef OPENSSL_NO_DEPRECATED
78 #endif
79
80 #include <stdio.h>
81 #include <stdlib.h>
82 #include <string.h>
83
84 #include "e_os.h"
85
86 #include <openssl/bio.h>
87 #include <openssl/bn.h>
88 #include <openssl/rand.h>
89 #include <openssl/x509.h>
90 #include <openssl/err.h>
91
92 const int num0 = 100; /* number of tests */
93 const int num1 = 50; /* additional tests for some functions */
94 const int num2 = 5; /* number of tests for slow functions */
95
96 int test_add(BIO *bp);
97 int test_sub(BIO *bp);
98 int test_lshift1(BIO *bp);
99 int test_lshift(BIO *bp, BN_CTX *ctx, BIGNUM *a_);
100 int test_rshift1(BIO *bp);
101 int test_rshift(BIO *bp, BN_CTX *ctx);
102 int test_div(BIO *bp, BN_CTX *ctx);
103 int test_div_word(BIO *bp);
104 int test_div_recp(BIO *bp, BN_CTX *ctx);
105 int test_mul(BIO *bp);
106 int test_sqr(BIO *bp, BN_CTX *ctx);
107 int test_mont(BIO *bp, BN_CTX *ctx);
108 int test_mod(BIO *bp, BN_CTX *ctx);
109 int test_mod_mul(BIO *bp, BN_CTX *ctx);
110 int test_mod_exp(BIO *bp, BN_CTX *ctx);
111 int test_mod_exp_mont_consttime(BIO *bp, BN_CTX *ctx);
112 int test_mod_exp_mont5(BIO *bp, BN_CTX *ctx);
113 int test_exp(BIO *bp, BN_CTX *ctx);
114 int test_gf2m_add(BIO *bp);
115 int test_gf2m_mod(BIO *bp);
116 int test_gf2m_mod_mul(BIO *bp, BN_CTX *ctx);
117 int test_gf2m_mod_sqr(BIO *bp, BN_CTX *ctx);
118 int test_gf2m_mod_inv(BIO *bp, BN_CTX *ctx);
119 int test_gf2m_mod_div(BIO *bp, BN_CTX *ctx);
120 int test_gf2m_mod_exp(BIO *bp, BN_CTX *ctx);
121 int test_gf2m_mod_sqrt(BIO *bp, BN_CTX *ctx);
122 int test_gf2m_mod_solve_quad(BIO *bp, BN_CTX *ctx);
123 int test_kron(BIO *bp, BN_CTX *ctx);
124 int test_sqrt(BIO *bp, BN_CTX *ctx);
125 int rand_neg(void);
126 static int results = 0;
127
128 static unsigned char lst[] =
129 "\xC6\x4F\x43\x04\x2A\xEA\xCA\x6E\x58\x36\x80\x5B\xE8\xC9"
130 "\x9B\x04\x5D\x48\x36\xC2\xFD\x16\xC9\x64\xF0";
131
132 static const char rnd_seed[] =
133 "string to make the random number generator think it has entropy";
134
135 static void message(BIO *out, char *m)
136 {
137 fprintf(stderr, "test %s\n", m);
138 BIO_puts(out, "print \"test ");
139 BIO_puts(out, m);
140 BIO_puts(out, "\\n\"\n");
141 }
142
143 int main(int argc, char *argv[])
144 {
145 BN_CTX *ctx;
146 BIO *out;
147 char *outfile = NULL;
148
149 results = 0;
150
151 RAND_seed(rnd_seed, sizeof rnd_seed); /* or BN_generate_prime may fail */
152
153 argc--;
154 argv++;
155 while (argc >= 1) {
156 if (strcmp(*argv, "-results") == 0)
157 results = 1;
158 else if (strcmp(*argv, "-out") == 0) {
159 if (--argc < 1)
160 break;
161 outfile = *(++argv);
162 }
163 argc--;
164 argv++;
165 }
166
167 ctx = BN_CTX_new();
168 if (ctx == NULL)
169 EXIT(1);
170
171 out = BIO_new(BIO_s_file());
172 if (out == NULL)
173 EXIT(1);
174 if (outfile == NULL) {
175 BIO_set_fp(out, stdout, BIO_NOCLOSE);
176 } else {
177 if (!BIO_write_filename(out, outfile)) {
178 perror(outfile);
179 EXIT(1);
180 }
181 }
182
183 if (!results)
184 BIO_puts(out, "obase=16\nibase=16\n");
185
186 message(out, "BN_add");
187 if (!test_add(out))
188 goto err;
189 (void)BIO_flush(out);
190
191 message(out, "BN_sub");
192 if (!test_sub(out))
193 goto err;
194 (void)BIO_flush(out);
195
196 message(out, "BN_lshift1");
197 if (!test_lshift1(out))
198 goto err;
199 (void)BIO_flush(out);
200
201 message(out, "BN_lshift (fixed)");
202 if (!test_lshift(out, ctx, BN_bin2bn(lst, sizeof(lst) - 1, NULL)))
203 goto err;
204 (void)BIO_flush(out);
205
206 message(out, "BN_lshift");
207 if (!test_lshift(out, ctx, NULL))
208 goto err;
209 (void)BIO_flush(out);
210
211 message(out, "BN_rshift1");
212 if (!test_rshift1(out))
213 goto err;
214 (void)BIO_flush(out);
215
216 message(out, "BN_rshift");
217 if (!test_rshift(out, ctx))
218 goto err;
219 (void)BIO_flush(out);
220
221 message(out, "BN_sqr");
222 if (!test_sqr(out, ctx))
223 goto err;
224 (void)BIO_flush(out);
225
226 message(out, "BN_mul");
227 if (!test_mul(out))
228 goto err;
229 (void)BIO_flush(out);
230
231 message(out, "BN_div");
232 if (!test_div(out, ctx))
233 goto err;
234 (void)BIO_flush(out);
235
236 message(out, "BN_div_word");
237 if (!test_div_word(out))
238 goto err;
239 (void)BIO_flush(out);
240
241 message(out, "BN_div_recp");
242 if (!test_div_recp(out, ctx))
243 goto err;
244 (void)BIO_flush(out);
245
246 message(out, "BN_mod");
247 if (!test_mod(out, ctx))
248 goto err;
249 (void)BIO_flush(out);
250
251 message(out, "BN_mod_mul");
252 if (!test_mod_mul(out, ctx))
253 goto err;
254 (void)BIO_flush(out);
255
256 message(out, "BN_mont");
257 if (!test_mont(out, ctx))
258 goto err;
259 (void)BIO_flush(out);
260
261 message(out, "BN_mod_exp");
262 if (!test_mod_exp(out, ctx))
263 goto err;
264 (void)BIO_flush(out);
265
266 message(out, "BN_mod_exp_mont_consttime");
267 if (!test_mod_exp_mont_consttime(out, ctx))
268 goto err;
269 if (!test_mod_exp_mont5(out, ctx))
270 goto err;
271 (void)BIO_flush(out);
272
273 message(out, "BN_exp");
274 if (!test_exp(out, ctx))
275 goto err;
276 (void)BIO_flush(out);
277
278 message(out, "BN_kronecker");
279 if (!test_kron(out, ctx))
280 goto err;
281 (void)BIO_flush(out);
282
283 message(out, "BN_mod_sqrt");
284 if (!test_sqrt(out, ctx))
285 goto err;
286 (void)BIO_flush(out);
287 #ifndef OPENSSL_NO_EC2M
288 message(out, "BN_GF2m_add");
289 if (!test_gf2m_add(out))
290 goto err;
291 (void)BIO_flush(out);
292
293 message(out, "BN_GF2m_mod");
294 if (!test_gf2m_mod(out))
295 goto err;
296 (void)BIO_flush(out);
297
298 message(out, "BN_GF2m_mod_mul");
299 if (!test_gf2m_mod_mul(out, ctx))
300 goto err;
301 (void)BIO_flush(out);
302
303 message(out, "BN_GF2m_mod_sqr");
304 if (!test_gf2m_mod_sqr(out, ctx))
305 goto err;
306 (void)BIO_flush(out);
307
308 message(out, "BN_GF2m_mod_inv");
309 if (!test_gf2m_mod_inv(out, ctx))
310 goto err;
311 (void)BIO_flush(out);
312
313 message(out, "BN_GF2m_mod_div");
314 if (!test_gf2m_mod_div(out, ctx))
315 goto err;
316 (void)BIO_flush(out);
317
318 message(out, "BN_GF2m_mod_exp");
319 if (!test_gf2m_mod_exp(out, ctx))
320 goto err;
321 (void)BIO_flush(out);
322
323 message(out, "BN_GF2m_mod_sqrt");
324 if (!test_gf2m_mod_sqrt(out, ctx))
325 goto err;
326 (void)BIO_flush(out);
327
328 message(out, "BN_GF2m_mod_solve_quad");
329 if (!test_gf2m_mod_solve_quad(out, ctx))
330 goto err;
331 (void)BIO_flush(out);
332 #endif
333 BN_CTX_free(ctx);
334 BIO_free(out);
335
336 EXIT(0);
337 err:
338 BIO_puts(out, "1\n"); /* make sure the Perl script fed by bc
339 * notices the failure, see test_bn in
340 * test/Makefile.ssl */
341 (void)BIO_flush(out);
342 ERR_load_crypto_strings();
343 ERR_print_errors_fp(stderr);
344 EXIT(1);
345 return (1);
346 }
347
348 int test_add(BIO *bp)
349 {
350 BIGNUM a, b, c;
351 int i;
352
353 BN_init(&a);
354 BN_init(&b);
355 BN_init(&c);
356
357 BN_bntest_rand(&a, 512, 0, 0);
358 for (i = 0; i < num0; i++) {
359 BN_bntest_rand(&b, 450 + i, 0, 0);
360 a.neg = rand_neg();
361 b.neg = rand_neg();
362 BN_add(&c, &a, &b);
363 if (bp != NULL) {
364 if (!results) {
365 BN_print(bp, &a);
366 BIO_puts(bp, " + ");
367 BN_print(bp, &b);
368 BIO_puts(bp, " - ");
369 }
370 BN_print(bp, &c);
371 BIO_puts(bp, "\n");
372 }
373 a.neg = !a.neg;
374 b.neg = !b.neg;
375 BN_add(&c, &c, &b);
376 BN_add(&c, &c, &a);
377 if (!BN_is_zero(&c)) {
378 fprintf(stderr, "Add test failed!\n");
379 return 0;
380 }
381 }
382 BN_free(&a);
383 BN_free(&b);
384 BN_free(&c);
385 return (1);
386 }
387
388 int test_sub(BIO *bp)
389 {
390 BIGNUM a, b, c;
391 int i;
392
393 BN_init(&a);
394 BN_init(&b);
395 BN_init(&c);
396
397 for (i = 0; i < num0 + num1; i++) {
398 if (i < num1) {
399 BN_bntest_rand(&a, 512, 0, 0);
400 BN_copy(&b, &a);
401 if (BN_set_bit(&a, i) == 0)
402 return (0);
403 BN_add_word(&b, i);
404 } else {
405 BN_bntest_rand(&b, 400 + i - num1, 0, 0);
406 a.neg = rand_neg();
407 b.neg = rand_neg();
408 }
409 BN_sub(&c, &a, &b);
410 if (bp != NULL) {
411 if (!results) {
412 BN_print(bp, &a);
413 BIO_puts(bp, " - ");
414 BN_print(bp, &b);
415 BIO_puts(bp, " - ");
416 }
417 BN_print(bp, &c);
418 BIO_puts(bp, "\n");
419 }
420 BN_add(&c, &c, &b);
421 BN_sub(&c, &c, &a);
422 if (!BN_is_zero(&c)) {
423 fprintf(stderr, "Subtract test failed!\n");
424 return 0;
425 }
426 }
427 BN_free(&a);
428 BN_free(&b);
429 BN_free(&c);
430 return (1);
431 }
432
433 int test_div(BIO *bp, BN_CTX *ctx)
434 {
435 BIGNUM a, b, c, d, e;
436 int i;
437
438 BN_init(&a);
439 BN_init(&b);
440 BN_init(&c);
441 BN_init(&d);
442 BN_init(&e);
443
444 for (i = 0; i < num0 + num1; i++) {
445 if (i < num1) {
446 BN_bntest_rand(&a, 400, 0, 0);
447 BN_copy(&b, &a);
448 BN_lshift(&a, &a, i);
449 BN_add_word(&a, i);
450 } else
451 BN_bntest_rand(&b, 50 + 3 * (i - num1), 0, 0);
452 a.neg = rand_neg();
453 b.neg = rand_neg();
454 BN_div(&d, &c, &a, &b, ctx);
455 if (bp != NULL) {
456 if (!results) {
457 BN_print(bp, &a);
458 BIO_puts(bp, " / ");
459 BN_print(bp, &b);
460 BIO_puts(bp, " - ");
461 }
462 BN_print(bp, &d);
463 BIO_puts(bp, "\n");
464
465 if (!results) {
466 BN_print(bp, &a);
467 BIO_puts(bp, " % ");
468 BN_print(bp, &b);
469 BIO_puts(bp, " - ");
470 }
471 BN_print(bp, &c);
472 BIO_puts(bp, "\n");
473 }
474 BN_mul(&e, &d, &b, ctx);
475 BN_add(&d, &e, &c);
476 BN_sub(&d, &d, &a);
477 if (!BN_is_zero(&d)) {
478 fprintf(stderr, "Division test failed!\n");
479 return 0;
480 }
481 }
482 BN_free(&a);
483 BN_free(&b);
484 BN_free(&c);
485 BN_free(&d);
486 BN_free(&e);
487 return (1);
488 }
489
490 static void print_word(BIO *bp, BN_ULONG w)
491 {
492 #ifdef SIXTY_FOUR_BIT
493 if (sizeof(w) > sizeof(unsigned long)) {
494 unsigned long h = (unsigned long)(w >> 32), l = (unsigned long)(w);
495
496 if (h)
497 BIO_printf(bp, "%lX%08lX", h, l);
498 else
499 BIO_printf(bp, "%lX", l);
500 return;
501 }
502 #endif
503 BIO_printf(bp, BN_HEX_FMT1, w);
504 }
505
506 int test_div_word(BIO *bp)
507 {
508 BIGNUM a, b;
509 BN_ULONG r, s;
510 int i;
511
512 BN_init(&a);
513 BN_init(&b);
514
515 for (i = 0; i < num0; i++) {
516 do {
517 BN_bntest_rand(&a, 512, -1, 0);
518 BN_bntest_rand(&b, BN_BITS2, -1, 0);
519 s = b.d[0];
520 } while (!s);
521
522 BN_copy(&b, &a);
523 r = BN_div_word(&b, s);
524
525 if (bp != NULL) {
526 if (!results) {
527 BN_print(bp, &a);
528 BIO_puts(bp, " / ");
529 print_word(bp, s);
530 BIO_puts(bp, " - ");
531 }
532 BN_print(bp, &b);
533 BIO_puts(bp, "\n");
534
535 if (!results) {
536 BN_print(bp, &a);
537 BIO_puts(bp, " % ");
538 print_word(bp, s);
539 BIO_puts(bp, " - ");
540 }
541 print_word(bp, r);
542 BIO_puts(bp, "\n");
543 }
544 BN_mul_word(&b, s);
545 BN_add_word(&b, r);
546 BN_sub(&b, &a, &b);
547 if (!BN_is_zero(&b)) {
548 fprintf(stderr, "Division (word) test failed!\n");
549 return 0;
550 }
551 }
552 BN_free(&a);
553 BN_free(&b);
554 return (1);
555 }
556
557 int test_div_recp(BIO *bp, BN_CTX *ctx)
558 {
559 BIGNUM a, b, c, d, e;
560 BN_RECP_CTX recp;
561 int i;
562
563 BN_RECP_CTX_init(&recp);
564 BN_init(&a);
565 BN_init(&b);
566 BN_init(&c);
567 BN_init(&d);
568 BN_init(&e);
569
570 for (i = 0; i < num0 + num1; i++) {
571 if (i < num1) {
572 BN_bntest_rand(&a, 400, 0, 0);
573 BN_copy(&b, &a);
574 BN_lshift(&a, &a, i);
575 BN_add_word(&a, i);
576 } else
577 BN_bntest_rand(&b, 50 + 3 * (i - num1), 0, 0);
578 a.neg = rand_neg();
579 b.neg = rand_neg();
580 BN_RECP_CTX_set(&recp, &b, ctx);
581 BN_div_recp(&d, &c, &a, &recp, ctx);
582 if (bp != NULL) {
583 if (!results) {
584 BN_print(bp, &a);
585 BIO_puts(bp, " / ");
586 BN_print(bp, &b);
587 BIO_puts(bp, " - ");
588 }
589 BN_print(bp, &d);
590 BIO_puts(bp, "\n");
591
592 if (!results) {
593 BN_print(bp, &a);
594 BIO_puts(bp, " % ");
595 BN_print(bp, &b);
596 BIO_puts(bp, " - ");
597 }
598 BN_print(bp, &c);
599 BIO_puts(bp, "\n");
600 }
601 BN_mul(&e, &d, &b, ctx);
602 BN_add(&d, &e, &c);
603 BN_sub(&d, &d, &a);
604 if (!BN_is_zero(&d)) {
605 fprintf(stderr, "Reciprocal division test failed!\n");
606 fprintf(stderr, "a=");
607 BN_print_fp(stderr, &a);
608 fprintf(stderr, "\nb=");
609 BN_print_fp(stderr, &b);
610 fprintf(stderr, "\n");
611 return 0;
612 }
613 }
614 BN_free(&a);
615 BN_free(&b);
616 BN_free(&c);
617 BN_free(&d);
618 BN_free(&e);
619 BN_RECP_CTX_free(&recp);
620 return (1);
621 }
622
623 int test_mul(BIO *bp)
624 {
625 BIGNUM a, b, c, d, e;
626 int i;
627 BN_CTX *ctx;
628
629 ctx = BN_CTX_new();
630 if (ctx == NULL)
631 EXIT(1);
632
633 BN_init(&a);
634 BN_init(&b);
635 BN_init(&c);
636 BN_init(&d);
637 BN_init(&e);
638
639 for (i = 0; i < num0 + num1; i++) {
640 if (i <= num1) {
641 BN_bntest_rand(&a, 100, 0, 0);
642 BN_bntest_rand(&b, 100, 0, 0);
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 if (!results) {
650 BN_print(bp, &a);
651 BIO_puts(bp, " * ");
652 BN_print(bp, &b);
653 BIO_puts(bp, " - ");
654 }
655 BN_print(bp, &c);
656 BIO_puts(bp, "\n");
657 }
658 BN_div(&d, &e, &c, &a, ctx);
659 BN_sub(&d, &d, &b);
660 if (!BN_is_zero(&d) || !BN_is_zero(&e)) {
661 fprintf(stderr, "Multiplication test failed!\n");
662 return 0;
663 }
664 }
665 BN_free(&a);
666 BN_free(&b);
667 BN_free(&c);
668 BN_free(&d);
669 BN_free(&e);
670 BN_CTX_free(ctx);
671 return (1);
672 }
673
674 int test_sqr(BIO *bp, BN_CTX *ctx)
675 {
676 BIGNUM *a, *c, *d, *e;
677 int i, ret = 0;
678
679 a = BN_new();
680 c = BN_new();
681 d = BN_new();
682 e = BN_new();
683 if (a == NULL || c == NULL || d == NULL || e == NULL) {
684 goto err;
685 }
686
687 for (i = 0; i < num0; i++) {
688 BN_bntest_rand(a, 40 + i * 10, 0, 0);
689 a->neg = rand_neg();
690 BN_sqr(c, a, ctx);
691 if (bp != NULL) {
692 if (!results) {
693 BN_print(bp, a);
694 BIO_puts(bp, " * ");
695 BN_print(bp, a);
696 BIO_puts(bp, " - ");
697 }
698 BN_print(bp, c);
699 BIO_puts(bp, "\n");
700 }
701 BN_div(d, e, c, a, ctx);
702 BN_sub(d, d, a);
703 if (!BN_is_zero(d) || !BN_is_zero(e)) {
704 fprintf(stderr, "Square test failed!\n");
705 goto err;
706 }
707 }
708
709 /* Regression test for a BN_sqr overflow bug. */
710 BN_hex2bn(&a,
711 "80000000000000008000000000000001"
712 "FFFFFFFFFFFFFFFE0000000000000000");
713 BN_sqr(c, a, ctx);
714 if (bp != NULL) {
715 if (!results) {
716 BN_print(bp, a);
717 BIO_puts(bp, " * ");
718 BN_print(bp, a);
719 BIO_puts(bp, " - ");
720 }
721 BN_print(bp, c);
722 BIO_puts(bp, "\n");
723 }
724 BN_mul(d, a, a, ctx);
725 if (BN_cmp(c, d)) {
726 fprintf(stderr, "Square test failed: BN_sqr and BN_mul produce "
727 "different results!\n");
728 goto err;
729 }
730
731 /* Regression test for a BN_sqr overflow bug. */
732 BN_hex2bn(&a,
733 "80000000000000000000000080000001"
734 "FFFFFFFE000000000000000000000000");
735 BN_sqr(c, a, ctx);
736 if (bp != NULL) {
737 if (!results) {
738 BN_print(bp, a);
739 BIO_puts(bp, " * ");
740 BN_print(bp, a);
741 BIO_puts(bp, " - ");
742 }
743 BN_print(bp, c);
744 BIO_puts(bp, "\n");
745 }
746 BN_mul(d, a, a, ctx);
747 if (BN_cmp(c, d)) {
748 fprintf(stderr, "Square test failed: BN_sqr and BN_mul produce "
749 "different results!\n");
750 goto err;
751 }
752 ret = 1;
753 err:
754 if (a != NULL)
755 BN_free(a);
756 if (c != NULL)
757 BN_free(c);
758 if (d != NULL)
759 BN_free(d);
760 if (e != NULL)
761 BN_free(e);
762 return ret;
763 }
764
765 int test_mont(BIO *bp, BN_CTX *ctx)
766 {
767 BIGNUM a, b, c, d, A, B;
768 BIGNUM n;
769 int i;
770 BN_MONT_CTX *mont;
771
772 BN_init(&a);
773 BN_init(&b);
774 BN_init(&c);
775 BN_init(&d);
776 BN_init(&A);
777 BN_init(&B);
778 BN_init(&n);
779
780 mont = BN_MONT_CTX_new();
781 if (mont == NULL)
782 return 0;
783
784 BN_bntest_rand(&a, 100, 0, 0);
785 BN_bntest_rand(&b, 100, 0, 0);
786 for (i = 0; i < num2; i++) {
787 int bits = (200 * (i + 1)) / num2;
788
789 if (bits == 0)
790 continue;
791 BN_bntest_rand(&n, bits, 0, 1);
792 BN_MONT_CTX_set(mont, &n, ctx);
793
794 BN_nnmod(&a, &a, &n, ctx);
795 BN_nnmod(&b, &b, &n, ctx);
796
797 BN_to_montgomery(&A, &a, mont, ctx);
798 BN_to_montgomery(&B, &b, mont, ctx);
799
800 BN_mod_mul_montgomery(&c, &A, &B, mont, ctx);
801 BN_from_montgomery(&A, &c, mont, ctx);
802 if (bp != NULL) {
803 if (!results) {
804 #ifdef undef
805 fprintf(stderr, "%d * %d %% %d\n",
806 BN_num_bits(&a),
807 BN_num_bits(&b), BN_num_bits(mont->N));
808 #endif
809 BN_print(bp, &a);
810 BIO_puts(bp, " * ");
811 BN_print(bp, &b);
812 BIO_puts(bp, " % ");
813 BN_print(bp, &(mont->N));
814 BIO_puts(bp, " - ");
815 }
816 BN_print(bp, &A);
817 BIO_puts(bp, "\n");
818 }
819 BN_mod_mul(&d, &a, &b, &n, ctx);
820 BN_sub(&d, &d, &A);
821 if (!BN_is_zero(&d)) {
822 fprintf(stderr, "Montgomery multiplication test failed!\n");
823 return 0;
824 }
825 }
826 BN_MONT_CTX_free(mont);
827 BN_free(&a);
828 BN_free(&b);
829 BN_free(&c);
830 BN_free(&d);
831 BN_free(&A);
832 BN_free(&B);
833 BN_free(&n);
834 return (1);
835 }
836
837 int test_mod(BIO *bp, BN_CTX *ctx)
838 {
839 BIGNUM *a, *b, *c, *d, *e;
840 int i;
841
842 a = BN_new();
843 b = BN_new();
844 c = BN_new();
845 d = BN_new();
846 e = BN_new();
847
848 BN_bntest_rand(a, 1024, 0, 0);
849 for (i = 0; i < num0; i++) {
850 BN_bntest_rand(b, 450 + i * 10, 0, 0);
851 a->neg = rand_neg();
852 b->neg = rand_neg();
853 BN_mod(c, a, b, ctx);
854 if (bp != NULL) {
855 if (!results) {
856 BN_print(bp, a);
857 BIO_puts(bp, " % ");
858 BN_print(bp, b);
859 BIO_puts(bp, " - ");
860 }
861 BN_print(bp, c);
862 BIO_puts(bp, "\n");
863 }
864 BN_div(d, e, a, b, ctx);
865 BN_sub(e, e, c);
866 if (!BN_is_zero(e)) {
867 fprintf(stderr, "Modulo test failed!\n");
868 return 0;
869 }
870 }
871 BN_free(a);
872 BN_free(b);
873 BN_free(c);
874 BN_free(d);
875 BN_free(e);
876 return (1);
877 }
878
879 int test_mod_mul(BIO *bp, BN_CTX *ctx)
880 {
881 BIGNUM *a, *b, *c, *d, *e;
882 int i, j;
883
884 a = BN_new();
885 b = BN_new();
886 c = BN_new();
887 d = BN_new();
888 e = BN_new();
889
890 for (j = 0; j < 3; j++) {
891 BN_bntest_rand(c, 1024, 0, 0);
892 for (i = 0; i < num0; i++) {
893 BN_bntest_rand(a, 475 + i * 10, 0, 0);
894 BN_bntest_rand(b, 425 + i * 11, 0, 0);
895 a->neg = rand_neg();
896 b->neg = rand_neg();
897 if (!BN_mod_mul(e, a, b, c, ctx)) {
898 unsigned long l;
899
900 while ((l = ERR_get_error()))
901 fprintf(stderr, "ERROR:%s\n", ERR_error_string(l, NULL));
902 EXIT(1);
903 }
904 if (bp != NULL) {
905 if (!results) {
906 BN_print(bp, a);
907 BIO_puts(bp, " * ");
908 BN_print(bp, b);
909 BIO_puts(bp, " % ");
910 BN_print(bp, c);
911 if ((a->neg ^ b->neg) && !BN_is_zero(e)) {
912 /*
913 * If (a*b) % c is negative, c must be added in order
914 * to obtain the normalized remainder (new with
915 * OpenSSL 0.9.7, previous versions of BN_mod_mul
916 * could generate negative results)
917 */
918 BIO_puts(bp, " + ");
919 BN_print(bp, c);
920 }
921 BIO_puts(bp, " - ");
922 }
923 BN_print(bp, e);
924 BIO_puts(bp, "\n");
925 }
926 BN_mul(d, a, b, ctx);
927 BN_sub(d, d, e);
928 BN_div(a, b, d, c, ctx);
929 if (!BN_is_zero(b)) {
930 fprintf(stderr, "Modulo multiply test failed!\n");
931 ERR_print_errors_fp(stderr);
932 return 0;
933 }
934 }
935 }
936 BN_free(a);
937 BN_free(b);
938 BN_free(c);
939 BN_free(d);
940 BN_free(e);
941 return (1);
942 }
943
944 int test_mod_exp(BIO *bp, BN_CTX *ctx)
945 {
946 BIGNUM *a, *b, *c, *d, *e;
947 int i;
948
949 a = BN_new();
950 b = BN_new();
951 c = BN_new();
952 d = BN_new();
953 e = BN_new();
954
955 BN_bntest_rand(c, 30, 0, 1); /* must be odd for montgomery */
956 for (i = 0; i < num2; i++) {
957 BN_bntest_rand(a, 20 + i * 5, 0, 0);
958 BN_bntest_rand(b, 2 + i, 0, 0);
959
960 if (!BN_mod_exp(d, a, b, c, ctx))
961 return (0);
962
963 if (bp != NULL) {
964 if (!results) {
965 BN_print(bp, a);
966 BIO_puts(bp, " ^ ");
967 BN_print(bp, b);
968 BIO_puts(bp, " % ");
969 BN_print(bp, c);
970 BIO_puts(bp, " - ");
971 }
972 BN_print(bp, d);
973 BIO_puts(bp, "\n");
974 }
975 BN_exp(e, a, b, ctx);
976 BN_sub(e, e, d);
977 BN_div(a, b, e, c, ctx);
978 if (!BN_is_zero(b)) {
979 fprintf(stderr, "Modulo exponentiation test failed!\n");
980 return 0;
981 }
982 }
983 BN_free(a);
984 BN_free(b);
985 BN_free(c);
986 BN_free(d);
987 BN_free(e);
988 return (1);
989 }
990
991 int test_mod_exp_mont_consttime(BIO *bp, BN_CTX *ctx)
992 {
993 BIGNUM *a, *b, *c, *d, *e;
994 int i;
995
996 a = BN_new();
997 b = BN_new();
998 c = BN_new();
999 d = BN_new();
1000 e = BN_new();
1001
1002 BN_bntest_rand(c, 30, 0, 1); /* must be odd for montgomery */
1003 for (i = 0; i < num2; i++) {
1004 BN_bntest_rand(a, 20 + i * 5, 0, 0);
1005 BN_bntest_rand(b, 2 + i, 0, 0);
1006
1007 if (!BN_mod_exp_mont_consttime(d, a, b, c, ctx, NULL))
1008 return (00);
1009
1010 if (bp != NULL) {
1011 if (!results) {
1012 BN_print(bp, a);
1013 BIO_puts(bp, " ^ ");
1014 BN_print(bp, b);
1015 BIO_puts(bp, " % ");
1016 BN_print(bp, c);
1017 BIO_puts(bp, " - ");
1018 }
1019 BN_print(bp, d);
1020 BIO_puts(bp, "\n");
1021 }
1022 BN_exp(e, a, b, ctx);
1023 BN_sub(e, e, d);
1024 BN_div(a, b, e, c, ctx);
1025 if (!BN_is_zero(b)) {
1026 fprintf(stderr, "Modulo exponentiation test failed!\n");
1027 return 0;
1028 }
1029 }
1030 BN_free(a);
1031 BN_free(b);
1032 BN_free(c);
1033 BN_free(d);
1034 BN_free(e);
1035 return (1);
1036 }
1037
1038 /*
1039 * Test constant-time modular exponentiation with 1024-bit inputs, which on
1040 * x86_64 cause a different code branch to be taken.
1041 */
1042 int test_mod_exp_mont5(BIO *bp, BN_CTX *ctx)
1043 {
1044 BIGNUM *a, *p, *m, *d, *e;
1045
1046 BN_MONT_CTX *mont;
1047
1048 a = BN_new();
1049 p = BN_new();
1050 m = BN_new();
1051 d = BN_new();
1052 e = BN_new();
1053
1054 mont = BN_MONT_CTX_new();
1055
1056 BN_bntest_rand(m, 1024, 0, 1); /* must be odd for montgomery */
1057 /* Zero exponent */
1058 BN_bntest_rand(a, 1024, 0, 0);
1059 BN_zero(p);
1060 if (!BN_mod_exp_mont_consttime(d, a, p, m, ctx, NULL))
1061 return 0;
1062 if (!BN_is_one(d)) {
1063 fprintf(stderr, "Modular exponentiation test failed!\n");
1064 return 0;
1065 }
1066 /* Zero input */
1067 BN_bntest_rand(p, 1024, 0, 0);
1068 BN_zero(a);
1069 if (!BN_mod_exp_mont_consttime(d, a, p, m, ctx, NULL))
1070 return 0;
1071 if (!BN_is_zero(d)) {
1072 fprintf(stderr, "Modular exponentiation test failed!\n");
1073 return 0;
1074 }
1075 /*
1076 * Craft an input whose Montgomery representation is 1, i.e., shorter
1077 * than the modulus m, in order to test the const time precomputation
1078 * scattering/gathering.
1079 */
1080 BN_one(a);
1081 BN_MONT_CTX_set(mont, m, ctx);
1082 if (!BN_from_montgomery(e, a, mont, ctx))
1083 return 0;
1084 if (!BN_mod_exp_mont_consttime(d, e, p, m, ctx, NULL))
1085 return 0;
1086 if (!BN_mod_exp_simple(a, e, p, m, ctx))
1087 return 0;
1088 if (BN_cmp(a, d) != 0) {
1089 fprintf(stderr, "Modular exponentiation test failed!\n");
1090 return 0;
1091 }
1092 /* Finally, some regular test vectors. */
1093 BN_bntest_rand(e, 1024, 0, 0);
1094 if (!BN_mod_exp_mont_consttime(d, e, p, m, ctx, NULL))
1095 return 0;
1096 if (!BN_mod_exp_simple(a, e, p, m, ctx))
1097 return 0;
1098 if (BN_cmp(a, d) != 0) {
1099 fprintf(stderr, "Modular exponentiation test failed!\n");
1100 return 0;
1101 }
1102 BN_free(a);
1103 BN_free(p);
1104 BN_free(m);
1105 BN_free(d);
1106 BN_free(e);
1107 return (1);
1108 }
1109
1110 int test_exp(BIO *bp, BN_CTX *ctx)
1111 {
1112 BIGNUM *a, *b, *d, *e, *one;
1113 int i;
1114
1115 a = BN_new();
1116 b = BN_new();
1117 d = BN_new();
1118 e = BN_new();
1119 one = BN_new();
1120 BN_one(one);
1121
1122 for (i = 0; i < num2; i++) {
1123 BN_bntest_rand(a, 20 + i * 5, 0, 0);
1124 BN_bntest_rand(b, 2 + i, 0, 0);
1125
1126 if (BN_exp(d, a, b, ctx) <= 0)
1127 return (0);
1128
1129 if (bp != NULL) {
1130 if (!results) {
1131 BN_print(bp, a);
1132 BIO_puts(bp, " ^ ");
1133 BN_print(bp, b);
1134 BIO_puts(bp, " - ");
1135 }
1136 BN_print(bp, d);
1137 BIO_puts(bp, "\n");
1138 }
1139 BN_one(e);
1140 for (; !BN_is_zero(b); BN_sub(b, b, one))
1141 BN_mul(e, e, a, ctx);
1142 BN_sub(e, e, d);
1143 if (!BN_is_zero(e)) {
1144 fprintf(stderr, "Exponentiation test failed!\n");
1145 return 0;
1146 }
1147 }
1148 BN_free(a);
1149 BN_free(b);
1150 BN_free(d);
1151 BN_free(e);
1152 BN_free(one);
1153 return (1);
1154 }
1155
1156 #ifndef OPENSSL_NO_EC2M
1157 int test_gf2m_add(BIO *bp)
1158 {
1159 BIGNUM a, b, c;
1160 int i, ret = 0;
1161
1162 BN_init(&a);
1163 BN_init(&b);
1164 BN_init(&c);
1165
1166 for (i = 0; i < num0; i++) {
1167 BN_rand(&a, 512, 0, 0);
1168 BN_copy(&b, BN_value_one());
1169 a.neg = rand_neg();
1170 b.neg = rand_neg();
1171 BN_GF2m_add(&c, &a, &b);
1172 # if 0 /* make test uses ouput in bc but bc can't
1173 * handle GF(2^m) arithmetic */
1174 if (bp != NULL) {
1175 if (!results) {
1176 BN_print(bp, &a);
1177 BIO_puts(bp, " ^ ");
1178 BN_print(bp, &b);
1179 BIO_puts(bp, " = ");
1180 }
1181 BN_print(bp, &c);
1182 BIO_puts(bp, "\n");
1183 }
1184 # endif
1185 /* Test that two added values have the correct parity. */
1186 if ((BN_is_odd(&a) && BN_is_odd(&c))
1187 || (!BN_is_odd(&a) && !BN_is_odd(&c))) {
1188 fprintf(stderr, "GF(2^m) addition test (a) failed!\n");
1189 goto err;
1190 }
1191 BN_GF2m_add(&c, &c, &c);
1192 /* Test that c + c = 0. */
1193 if (!BN_is_zero(&c)) {
1194 fprintf(stderr, "GF(2^m) addition test (b) failed!\n");
1195 goto err;
1196 }
1197 }
1198 ret = 1;
1199 err:
1200 BN_free(&a);
1201 BN_free(&b);
1202 BN_free(&c);
1203 return ret;
1204 }
1205
1206 int test_gf2m_mod(BIO *bp)
1207 {
1208 BIGNUM *a, *b[2], *c, *d, *e;
1209 int i, j, ret = 0;
1210 int p0[] = { 163, 7, 6, 3, 0, -1 };
1211 int p1[] = { 193, 15, 0, -1 };
1212
1213 a = BN_new();
1214 b[0] = BN_new();
1215 b[1] = BN_new();
1216 c = BN_new();
1217 d = BN_new();
1218 e = BN_new();
1219
1220 BN_GF2m_arr2poly(p0, b[0]);
1221 BN_GF2m_arr2poly(p1, b[1]);
1222
1223 for (i = 0; i < num0; i++) {
1224 BN_bntest_rand(a, 1024, 0, 0);
1225 for (j = 0; j < 2; j++) {
1226 BN_GF2m_mod(c, a, b[j]);
1227 # if 0 /* make test uses ouput in bc but bc can't
1228 * handle GF(2^m) arithmetic */
1229 if (bp != NULL) {
1230 if (!results) {
1231 BN_print(bp, a);
1232 BIO_puts(bp, " % ");
1233 BN_print(bp, b[j]);
1234 BIO_puts(bp, " - ");
1235 BN_print(bp, c);
1236 BIO_puts(bp, "\n");
1237 }
1238 }
1239 # endif
1240 BN_GF2m_add(d, a, c);
1241 BN_GF2m_mod(e, d, b[j]);
1242 /* Test that a + (a mod p) mod p == 0. */
1243 if (!BN_is_zero(e)) {
1244 fprintf(stderr, "GF(2^m) modulo test failed!\n");
1245 goto err;
1246 }
1247 }
1248 }
1249 ret = 1;
1250 err:
1251 BN_free(a);
1252 BN_free(b[0]);
1253 BN_free(b[1]);
1254 BN_free(c);
1255 BN_free(d);
1256 BN_free(e);
1257 return ret;
1258 }
1259
1260 int test_gf2m_mod_mul(BIO *bp, BN_CTX *ctx)
1261 {
1262 BIGNUM *a, *b[2], *c, *d, *e, *f, *g, *h;
1263 int i, j, ret = 0;
1264 int p0[] = { 163, 7, 6, 3, 0, -1 };
1265 int p1[] = { 193, 15, 0, -1 };
1266
1267 a = BN_new();
1268 b[0] = BN_new();
1269 b[1] = BN_new();
1270 c = BN_new();
1271 d = BN_new();
1272 e = BN_new();
1273 f = BN_new();
1274 g = BN_new();
1275 h = BN_new();
1276
1277 BN_GF2m_arr2poly(p0, b[0]);
1278 BN_GF2m_arr2poly(p1, b[1]);
1279
1280 for (i = 0; i < num0; i++) {
1281 BN_bntest_rand(a, 1024, 0, 0);
1282 BN_bntest_rand(c, 1024, 0, 0);
1283 BN_bntest_rand(d, 1024, 0, 0);
1284 for (j = 0; j < 2; j++) {
1285 BN_GF2m_mod_mul(e, a, c, b[j], ctx);
1286 # if 0 /* make test uses ouput in bc but bc can't
1287 * handle GF(2^m) arithmetic */
1288 if (bp != NULL) {
1289 if (!results) {
1290 BN_print(bp, a);
1291 BIO_puts(bp, " * ");
1292 BN_print(bp, c);
1293 BIO_puts(bp, " % ");
1294 BN_print(bp, b[j]);
1295 BIO_puts(bp, " - ");
1296 BN_print(bp, e);
1297 BIO_puts(bp, "\n");
1298 }
1299 }
1300 # endif
1301 BN_GF2m_add(f, a, d);
1302 BN_GF2m_mod_mul(g, f, c, b[j], ctx);
1303 BN_GF2m_mod_mul(h, d, c, b[j], ctx);
1304 BN_GF2m_add(f, e, g);
1305 BN_GF2m_add(f, f, h);
1306 /* Test that (a+d)*c = a*c + d*c. */
1307 if (!BN_is_zero(f)) {
1308 fprintf(stderr,
1309 "GF(2^m) modular multiplication test failed!\n");
1310 goto err;
1311 }
1312 }
1313 }
1314 ret = 1;
1315 err:
1316 BN_free(a);
1317 BN_free(b[0]);
1318 BN_free(b[1]);
1319 BN_free(c);
1320 BN_free(d);
1321 BN_free(e);
1322 BN_free(f);
1323 BN_free(g);
1324 BN_free(h);
1325 return ret;
1326 }
1327
1328 int test_gf2m_mod_sqr(BIO *bp, BN_CTX *ctx)
1329 {
1330 BIGNUM *a, *b[2], *c, *d;
1331 int i, j, ret = 0;
1332 int p0[] = { 163, 7, 6, 3, 0, -1 };
1333 int p1[] = { 193, 15, 0, -1 };
1334
1335 a = BN_new();
1336 b[0] = BN_new();
1337 b[1] = BN_new();
1338 c = BN_new();
1339 d = BN_new();
1340
1341 BN_GF2m_arr2poly(p0, b[0]);
1342 BN_GF2m_arr2poly(p1, b[1]);
1343
1344 for (i = 0; i < num0; i++) {
1345 BN_bntest_rand(a, 1024, 0, 0);
1346 for (j = 0; j < 2; j++) {
1347 BN_GF2m_mod_sqr(c, a, b[j], ctx);
1348 BN_copy(d, a);
1349 BN_GF2m_mod_mul(d, a, d, b[j], ctx);
1350 # if 0 /* make test uses ouput in bc but bc can't
1351 * handle GF(2^m) arithmetic */
1352 if (bp != NULL) {
1353 if (!results) {
1354 BN_print(bp, a);
1355 BIO_puts(bp, " ^ 2 % ");
1356 BN_print(bp, b[j]);
1357 BIO_puts(bp, " = ");
1358 BN_print(bp, c);
1359 BIO_puts(bp, "; a * a = ");
1360 BN_print(bp, d);
1361 BIO_puts(bp, "\n");
1362 }
1363 }
1364 # endif
1365 BN_GF2m_add(d, c, d);
1366 /* Test that a*a = a^2. */
1367 if (!BN_is_zero(d)) {
1368 fprintf(stderr, "GF(2^m) modular squaring test failed!\n");
1369 goto err;
1370 }
1371 }
1372 }
1373 ret = 1;
1374 err:
1375 BN_free(a);
1376 BN_free(b[0]);
1377 BN_free(b[1]);
1378 BN_free(c);
1379 BN_free(d);
1380 return ret;
1381 }
1382
1383 int test_gf2m_mod_inv(BIO *bp, BN_CTX *ctx)
1384 {
1385 BIGNUM *a, *b[2], *c, *d;
1386 int i, j, ret = 0;
1387 int p0[] = { 163, 7, 6, 3, 0, -1 };
1388 int p1[] = { 193, 15, 0, -1 };
1389
1390 a = BN_new();
1391 b[0] = BN_new();
1392 b[1] = BN_new();
1393 c = BN_new();
1394 d = BN_new();
1395
1396 BN_GF2m_arr2poly(p0, b[0]);
1397 BN_GF2m_arr2poly(p1, b[1]);
1398
1399 for (i = 0; i < num0; i++) {
1400 BN_bntest_rand(a, 512, 0, 0);
1401 for (j = 0; j < 2; j++) {
1402 BN_GF2m_mod_inv(c, a, b[j], ctx);
1403 BN_GF2m_mod_mul(d, a, c, b[j], ctx);
1404 # if 0 /* make test uses ouput in bc but bc can't
1405 * handle GF(2^m) arithmetic */
1406 if (bp != NULL) {
1407 if (!results) {
1408 BN_print(bp, a);
1409 BIO_puts(bp, " * ");
1410 BN_print(bp, c);
1411 BIO_puts(bp, " - 1 % ");
1412 BN_print(bp, b[j]);
1413 BIO_puts(bp, "\n");
1414 }
1415 }
1416 # endif
1417 /* Test that ((1/a)*a) = 1. */
1418 if (!BN_is_one(d)) {
1419 fprintf(stderr, "GF(2^m) modular inversion test failed!\n");
1420 goto err;
1421 }
1422 }
1423 }
1424 ret = 1;
1425 err:
1426 BN_free(a);
1427 BN_free(b[0]);
1428 BN_free(b[1]);
1429 BN_free(c);
1430 BN_free(d);
1431 return ret;
1432 }
1433
1434 int test_gf2m_mod_div(BIO *bp, BN_CTX *ctx)
1435 {
1436 BIGNUM *a, *b[2], *c, *d, *e, *f;
1437 int i, j, ret = 0;
1438 int p0[] = { 163, 7, 6, 3, 0, -1 };
1439 int p1[] = { 193, 15, 0, -1 };
1440
1441 a = BN_new();
1442 b[0] = BN_new();
1443 b[1] = BN_new();
1444 c = BN_new();
1445 d = BN_new();
1446 e = BN_new();
1447 f = BN_new();
1448
1449 BN_GF2m_arr2poly(p0, b[0]);
1450 BN_GF2m_arr2poly(p1, b[1]);
1451
1452 for (i = 0; i < num0; i++) {
1453 BN_bntest_rand(a, 512, 0, 0);
1454 BN_bntest_rand(c, 512, 0, 0);
1455 for (j = 0; j < 2; j++) {
1456 BN_GF2m_mod_div(d, a, c, b[j], ctx);
1457 BN_GF2m_mod_mul(e, d, c, b[j], ctx);
1458 BN_GF2m_mod_div(f, a, e, b[j], ctx);
1459 # if 0 /* make test uses ouput in bc but bc can't
1460 * handle GF(2^m) arithmetic */
1461 if (bp != NULL) {
1462 if (!results) {
1463 BN_print(bp, a);
1464 BIO_puts(bp, " = ");
1465 BN_print(bp, c);
1466 BIO_puts(bp, " * ");
1467 BN_print(bp, d);
1468 BIO_puts(bp, " % ");
1469 BN_print(bp, b[j]);
1470 BIO_puts(bp, "\n");
1471 }
1472 }
1473 # endif
1474 /* Test that ((a/c)*c)/a = 1. */
1475 if (!BN_is_one(f)) {
1476 fprintf(stderr, "GF(2^m) modular division test failed!\n");
1477 goto err;
1478 }
1479 }
1480 }
1481 ret = 1;
1482 err:
1483 BN_free(a);
1484 BN_free(b[0]);
1485 BN_free(b[1]);
1486 BN_free(c);
1487 BN_free(d);
1488 BN_free(e);
1489 BN_free(f);
1490 return ret;
1491 }
1492
1493 int test_gf2m_mod_exp(BIO *bp, BN_CTX *ctx)
1494 {
1495 BIGNUM *a, *b[2], *c, *d, *e, *f;
1496 int i, j, ret = 0;
1497 int p0[] = { 163, 7, 6, 3, 0, -1 };
1498 int p1[] = { 193, 15, 0, -1 };
1499
1500 a = BN_new();
1501 b[0] = BN_new();
1502 b[1] = BN_new();
1503 c = BN_new();
1504 d = BN_new();
1505 e = BN_new();
1506 f = BN_new();
1507
1508 BN_GF2m_arr2poly(p0, b[0]);
1509 BN_GF2m_arr2poly(p1, b[1]);
1510
1511 for (i = 0; i < num0; i++) {
1512 BN_bntest_rand(a, 512, 0, 0);
1513 BN_bntest_rand(c, 512, 0, 0);
1514 BN_bntest_rand(d, 512, 0, 0);
1515 for (j = 0; j < 2; j++) {
1516 BN_GF2m_mod_exp(e, a, c, b[j], ctx);
1517 BN_GF2m_mod_exp(f, a, d, b[j], ctx);
1518 BN_GF2m_mod_mul(e, e, f, b[j], ctx);
1519 BN_add(f, c, d);
1520 BN_GF2m_mod_exp(f, a, f, b[j], ctx);
1521 # if 0 /* make test uses ouput in bc but bc can't
1522 * handle GF(2^m) arithmetic */
1523 if (bp != NULL) {
1524 if (!results) {
1525 BN_print(bp, a);
1526 BIO_puts(bp, " ^ (");
1527 BN_print(bp, c);
1528 BIO_puts(bp, " + ");
1529 BN_print(bp, d);
1530 BIO_puts(bp, ") = ");
1531 BN_print(bp, e);
1532 BIO_puts(bp, "; - ");
1533 BN_print(bp, f);
1534 BIO_puts(bp, " % ");
1535 BN_print(bp, b[j]);
1536 BIO_puts(bp, "\n");
1537 }
1538 }
1539 # endif
1540 BN_GF2m_add(f, e, f);
1541 /* Test that a^(c+d)=a^c*a^d. */
1542 if (!BN_is_zero(f)) {
1543 fprintf(stderr,
1544 "GF(2^m) modular exponentiation test failed!\n");
1545 goto err;
1546 }
1547 }
1548 }
1549 ret = 1;
1550 err:
1551 BN_free(a);
1552 BN_free(b[0]);
1553 BN_free(b[1]);
1554 BN_free(c);
1555 BN_free(d);
1556 BN_free(e);
1557 BN_free(f);
1558 return ret;
1559 }
1560
1561 int test_gf2m_mod_sqrt(BIO *bp, BN_CTX *ctx)
1562 {
1563 BIGNUM *a, *b[2], *c, *d, *e, *f;
1564 int i, j, ret = 0;
1565 int p0[] = { 163, 7, 6, 3, 0, -1 };
1566 int p1[] = { 193, 15, 0, -1 };
1567
1568 a = BN_new();
1569 b[0] = BN_new();
1570 b[1] = BN_new();
1571 c = BN_new();
1572 d = BN_new();
1573 e = BN_new();
1574 f = BN_new();
1575
1576 BN_GF2m_arr2poly(p0, b[0]);
1577 BN_GF2m_arr2poly(p1, b[1]);
1578
1579 for (i = 0; i < num0; i++) {
1580 BN_bntest_rand(a, 512, 0, 0);
1581 for (j = 0; j < 2; j++) {
1582 BN_GF2m_mod(c, a, b[j]);
1583 BN_GF2m_mod_sqrt(d, a, b[j], ctx);
1584 BN_GF2m_mod_sqr(e, d, b[j], ctx);
1585 # if 0 /* make test uses ouput in bc but bc can't
1586 * handle GF(2^m) arithmetic */
1587 if (bp != NULL) {
1588 if (!results) {
1589 BN_print(bp, d);
1590 BIO_puts(bp, " ^ 2 - ");
1591 BN_print(bp, a);
1592 BIO_puts(bp, "\n");
1593 }
1594 }
1595 # endif
1596 BN_GF2m_add(f, c, e);
1597 /* Test that d^2 = a, where d = sqrt(a). */
1598 if (!BN_is_zero(f)) {
1599 fprintf(stderr, "GF(2^m) modular square root test failed!\n");
1600 goto err;
1601 }
1602 }
1603 }
1604 ret = 1;
1605 err:
1606 BN_free(a);
1607 BN_free(b[0]);
1608 BN_free(b[1]);
1609 BN_free(c);
1610 BN_free(d);
1611 BN_free(e);
1612 BN_free(f);
1613 return ret;
1614 }
1615
1616 int test_gf2m_mod_solve_quad(BIO *bp, BN_CTX *ctx)
1617 {
1618 BIGNUM *a, *b[2], *c, *d, *e;
1619 int i, j, s = 0, t, ret = 0;
1620 int p0[] = { 163, 7, 6, 3, 0, -1 };
1621 int p1[] = { 193, 15, 0, -1 };
1622
1623 a = BN_new();
1624 b[0] = BN_new();
1625 b[1] = BN_new();
1626 c = BN_new();
1627 d = BN_new();
1628 e = BN_new();
1629
1630 BN_GF2m_arr2poly(p0, b[0]);
1631 BN_GF2m_arr2poly(p1, b[1]);
1632
1633 for (i = 0; i < num0; i++) {
1634 BN_bntest_rand(a, 512, 0, 0);
1635 for (j = 0; j < 2; j++) {
1636 t = BN_GF2m_mod_solve_quad(c, a, b[j], ctx);
1637 if (t) {
1638 s++;
1639 BN_GF2m_mod_sqr(d, c, b[j], ctx);
1640 BN_GF2m_add(d, c, d);
1641 BN_GF2m_mod(e, a, b[j]);
1642 # if 0 /* make test uses ouput in bc but bc can't
1643 * handle GF(2^m) arithmetic */
1644 if (bp != NULL) {
1645 if (!results) {
1646 BN_print(bp, c);
1647 BIO_puts(bp, " is root of z^2 + z = ");
1648 BN_print(bp, a);
1649 BIO_puts(bp, " % ");
1650 BN_print(bp, b[j]);
1651 BIO_puts(bp, "\n");
1652 }
1653 }
1654 # endif
1655 BN_GF2m_add(e, e, d);
1656 /*
1657 * Test that solution of quadratic c satisfies c^2 + c = a.
1658 */
1659 if (!BN_is_zero(e)) {
1660 fprintf(stderr,
1661 "GF(2^m) modular solve quadratic test failed!\n");
1662 goto err;
1663 }
1664
1665 } else {
1666 # if 0 /* make test uses ouput in bc but bc can't
1667 * handle GF(2^m) arithmetic */
1668 if (bp != NULL) {
1669 if (!results) {
1670 BIO_puts(bp, "There are no roots of z^2 + z = ");
1671 BN_print(bp, a);
1672 BIO_puts(bp, " % ");
1673 BN_print(bp, b[j]);
1674 BIO_puts(bp, "\n");
1675 }
1676 }
1677 # endif
1678 }
1679 }
1680 }
1681 if (s == 0) {
1682 fprintf(stderr,
1683 "All %i tests of GF(2^m) modular solve quadratic resulted in no roots;\n",
1684 num0);
1685 fprintf(stderr,
1686 "this is very unlikely and probably indicates an error.\n");
1687 goto err;
1688 }
1689 ret = 1;
1690 err:
1691 BN_free(a);
1692 BN_free(b[0]);
1693 BN_free(b[1]);
1694 BN_free(c);
1695 BN_free(d);
1696 BN_free(e);
1697 return ret;
1698 }
1699 #endif
1700 static int genprime_cb(int p, int n, BN_GENCB *arg)
1701 {
1702 char c = '*';
1703
1704 if (p == 0)
1705 c = '.';
1706 if (p == 1)
1707 c = '+';
1708 if (p == 2)
1709 c = '*';
1710 if (p == 3)
1711 c = '\n';
1712 putc(c, stderr);
1713 fflush(stderr);
1714 return 1;
1715 }
1716
1717 int test_kron(BIO *bp, BN_CTX *ctx)
1718 {
1719 BN_GENCB cb;
1720 BIGNUM *a, *b, *r, *t;
1721 int i;
1722 int legendre, kronecker;
1723 int ret = 0;
1724
1725 a = BN_new();
1726 b = BN_new();
1727 r = BN_new();
1728 t = BN_new();
1729 if (a == NULL || b == NULL || r == NULL || t == NULL)
1730 goto err;
1731
1732 BN_GENCB_set(&cb, genprime_cb, NULL);
1733
1734 /*
1735 * We test BN_kronecker(a, b, ctx) just for b odd (Jacobi symbol). In
1736 * this case we know that if b is prime, then BN_kronecker(a, b, ctx) is
1737 * congruent to $a^{(b-1)/2}$, modulo $b$ (Legendre symbol). So we
1738 * generate a random prime b and compare these values for a number of
1739 * random a's. (That is, we run the Solovay-Strassen primality test to
1740 * confirm that b is prime, except that we don't want to test whether b
1741 * is prime but whether BN_kronecker works.)
1742 */
1743
1744 if (!BN_generate_prime_ex(b, 512, 0, NULL, NULL, &cb))
1745 goto err;
1746 b->neg = rand_neg();
1747 putc('\n', stderr);
1748
1749 for (i = 0; i < num0; i++) {
1750 if (!BN_bntest_rand(a, 512, 0, 0))
1751 goto err;
1752 a->neg = rand_neg();
1753
1754 /* t := (|b|-1)/2 (note that b is odd) */
1755 if (!BN_copy(t, b))
1756 goto err;
1757 t->neg = 0;
1758 if (!BN_sub_word(t, 1))
1759 goto err;
1760 if (!BN_rshift1(t, t))
1761 goto err;
1762 /* r := a^t mod b */
1763 b->neg = 0;
1764
1765 if (!BN_mod_exp_recp(r, a, t, b, ctx))
1766 goto err;
1767 b->neg = 1;
1768
1769 if (BN_is_word(r, 1))
1770 legendre = 1;
1771 else if (BN_is_zero(r))
1772 legendre = 0;
1773 else {
1774 if (!BN_add_word(r, 1))
1775 goto err;
1776 if (0 != BN_ucmp(r, b)) {
1777 fprintf(stderr, "Legendre symbol computation failed\n");
1778 goto err;
1779 }
1780 legendre = -1;
1781 }
1782
1783 kronecker = BN_kronecker(a, b, ctx);
1784 if (kronecker < -1)
1785 goto err;
1786 /* we actually need BN_kronecker(a, |b|) */
1787 if (a->neg && b->neg)
1788 kronecker = -kronecker;
1789
1790 if (legendre != kronecker) {
1791 fprintf(stderr, "legendre != kronecker; a = ");
1792 BN_print_fp(stderr, a);
1793 fprintf(stderr, ", b = ");
1794 BN_print_fp(stderr, b);
1795 fprintf(stderr, "\n");
1796 goto err;
1797 }
1798
1799 putc('.', stderr);
1800 fflush(stderr);
1801 }
1802
1803 putc('\n', stderr);
1804 fflush(stderr);
1805 ret = 1;
1806 err:
1807 if (a != NULL)
1808 BN_free(a);
1809 if (b != NULL)
1810 BN_free(b);
1811 if (r != NULL)
1812 BN_free(r);
1813 if (t != NULL)
1814 BN_free(t);
1815 return ret;
1816 }
1817
1818 int test_sqrt(BIO *bp, BN_CTX *ctx)
1819 {
1820 BN_GENCB cb;
1821 BIGNUM *a, *p, *r;
1822 int i, j;
1823 int ret = 0;
1824
1825 a = BN_new();
1826 p = BN_new();
1827 r = BN_new();
1828 if (a == NULL || p == NULL || r == NULL)
1829 goto err;
1830
1831 BN_GENCB_set(&cb, genprime_cb, NULL);
1832
1833 for (i = 0; i < 16; i++) {
1834 if (i < 8) {
1835 unsigned primes[8] = { 2, 3, 5, 7, 11, 13, 17, 19 };
1836
1837 if (!BN_set_word(p, primes[i]))
1838 goto err;
1839 } else {
1840 if (!BN_set_word(a, 32))
1841 goto err;
1842 if (!BN_set_word(r, 2 * i + 1))
1843 goto err;
1844
1845 if (!BN_generate_prime_ex(p, 256, 0, a, r, &cb))
1846 goto err;
1847 putc('\n', stderr);
1848 }
1849 p->neg = rand_neg();
1850
1851 for (j = 0; j < num2; j++) {
1852 /*
1853 * construct 'a' such that it is a square modulo p, but in
1854 * general not a proper square and not reduced modulo p
1855 */
1856 if (!BN_bntest_rand(r, 256, 0, 3))
1857 goto err;
1858 if (!BN_nnmod(r, r, p, ctx))
1859 goto err;
1860 if (!BN_mod_sqr(r, r, p, ctx))
1861 goto err;
1862 if (!BN_bntest_rand(a, 256, 0, 3))
1863 goto err;
1864 if (!BN_nnmod(a, a, p, ctx))
1865 goto err;
1866 if (!BN_mod_sqr(a, a, p, ctx))
1867 goto err;
1868 if (!BN_mul(a, a, r, ctx))
1869 goto err;
1870 if (rand_neg())
1871 if (!BN_sub(a, a, p))
1872 goto err;
1873
1874 if (!BN_mod_sqrt(r, a, p, ctx))
1875 goto err;
1876 if (!BN_mod_sqr(r, r, p, ctx))
1877 goto err;
1878
1879 if (!BN_nnmod(a, a, p, ctx))
1880 goto err;
1881
1882 if (BN_cmp(a, r) != 0) {
1883 fprintf(stderr, "BN_mod_sqrt failed: a = ");
1884 BN_print_fp(stderr, a);
1885 fprintf(stderr, ", r = ");
1886 BN_print_fp(stderr, r);
1887 fprintf(stderr, ", p = ");
1888 BN_print_fp(stderr, p);
1889 fprintf(stderr, "\n");
1890 goto err;
1891 }
1892
1893 putc('.', stderr);
1894 fflush(stderr);
1895 }
1896
1897 putc('\n', stderr);
1898 fflush(stderr);
1899 }
1900 ret = 1;
1901 err:
1902 if (a != NULL)
1903 BN_free(a);
1904 if (p != NULL)
1905 BN_free(p);
1906 if (r != NULL)
1907 BN_free(r);
1908 return ret;
1909 }
1910
1911 int test_lshift(BIO *bp, BN_CTX *ctx, BIGNUM *a_)
1912 {
1913 BIGNUM *a, *b, *c, *d;
1914 int i;
1915
1916 b = BN_new();
1917 c = BN_new();
1918 d = BN_new();
1919 BN_one(c);
1920
1921 if (a_)
1922 a = a_;
1923 else {
1924 a = BN_new();
1925 BN_bntest_rand(a, 200, 0, 0);
1926 a->neg = rand_neg();
1927 }
1928 for (i = 0; i < num0; i++) {
1929 BN_lshift(b, a, i + 1);
1930 BN_add(c, c, c);
1931 if (bp != NULL) {
1932 if (!results) {
1933 BN_print(bp, a);
1934 BIO_puts(bp, " * ");
1935 BN_print(bp, c);
1936 BIO_puts(bp, " - ");
1937 }
1938 BN_print(bp, b);
1939 BIO_puts(bp, "\n");
1940 }
1941 BN_mul(d, a, c, ctx);
1942 BN_sub(d, d, b);
1943 if (!BN_is_zero(d)) {
1944 fprintf(stderr, "Left shift test failed!\n");
1945 fprintf(stderr, "a=");
1946 BN_print_fp(stderr, a);
1947 fprintf(stderr, "\nb=");
1948 BN_print_fp(stderr, b);
1949 fprintf(stderr, "\nc=");
1950 BN_print_fp(stderr, c);
1951 fprintf(stderr, "\nd=");
1952 BN_print_fp(stderr, d);
1953 fprintf(stderr, "\n");
1954 return 0;
1955 }
1956 }
1957 BN_free(a);
1958 BN_free(b);
1959 BN_free(c);
1960 BN_free(d);
1961 return (1);
1962 }
1963
1964 int test_lshift1(BIO *bp)
1965 {
1966 BIGNUM *a, *b, *c;
1967 int i;
1968
1969 a = BN_new();
1970 b = BN_new();
1971 c = BN_new();
1972
1973 BN_bntest_rand(a, 200, 0, 0);
1974 a->neg = rand_neg();
1975 for (i = 0; i < num0; i++) {
1976 BN_lshift1(b, a);
1977 if (bp != NULL) {
1978 if (!results) {
1979 BN_print(bp, a);
1980 BIO_puts(bp, " * 2");
1981 BIO_puts(bp, " - ");
1982 }
1983 BN_print(bp, b);
1984 BIO_puts(bp, "\n");
1985 }
1986 BN_add(c, a, a);
1987 BN_sub(a, b, c);
1988 if (!BN_is_zero(a)) {
1989 fprintf(stderr, "Left shift one test failed!\n");
1990 return 0;
1991 }
1992
1993 BN_copy(a, b);
1994 }
1995 BN_free(a);
1996 BN_free(b);
1997 BN_free(c);
1998 return (1);
1999 }
2000
2001 int test_rshift(BIO *bp, BN_CTX *ctx)
2002 {
2003 BIGNUM *a, *b, *c, *d, *e;
2004 int i;
2005
2006 a = BN_new();
2007 b = BN_new();
2008 c = BN_new();
2009 d = BN_new();
2010 e = BN_new();
2011 BN_one(c);
2012
2013 BN_bntest_rand(a, 200, 0, 0);
2014 a->neg = rand_neg();
2015 for (i = 0; i < num0; i++) {
2016 BN_rshift(b, a, i + 1);
2017 BN_add(c, c, c);
2018 if (bp != NULL) {
2019 if (!results) {
2020 BN_print(bp, a);
2021 BIO_puts(bp, " / ");
2022 BN_print(bp, c);
2023 BIO_puts(bp, " - ");
2024 }
2025 BN_print(bp, b);
2026 BIO_puts(bp, "\n");
2027 }
2028 BN_div(d, e, a, c, ctx);
2029 BN_sub(d, d, b);
2030 if (!BN_is_zero(d)) {
2031 fprintf(stderr, "Right shift test failed!\n");
2032 return 0;
2033 }
2034 }
2035 BN_free(a);
2036 BN_free(b);
2037 BN_free(c);
2038 BN_free(d);
2039 BN_free(e);
2040 return (1);
2041 }
2042
2043 int test_rshift1(BIO *bp)
2044 {
2045 BIGNUM *a, *b, *c;
2046 int i;
2047
2048 a = BN_new();
2049 b = BN_new();
2050 c = BN_new();
2051
2052 BN_bntest_rand(a, 200, 0, 0);
2053 a->neg = rand_neg();
2054 for (i = 0; i < num0; i++) {
2055 BN_rshift1(b, a);
2056 if (bp != NULL) {
2057 if (!results) {
2058 BN_print(bp, a);
2059 BIO_puts(bp, " / 2");
2060 BIO_puts(bp, " - ");
2061 }
2062 BN_print(bp, b);
2063 BIO_puts(bp, "\n");
2064 }
2065 BN_sub(c, a, b);
2066 BN_sub(c, c, b);
2067 if (!BN_is_zero(c) && !BN_abs_is_word(c, 1)) {
2068 fprintf(stderr, "Right shift one test failed!\n");
2069 return 0;
2070 }
2071 BN_copy(a, b);
2072 }
2073 BN_free(a);
2074 BN_free(b);
2075 BN_free(c);
2076 return (1);
2077 }
2078
2079 int rand_neg(void)
2080 {
2081 static unsigned int neg = 0;
2082 static int sign[8] = { 0, 0, 0, 1, 1, 0, 1, 1 };
2083
2084 return (sign[(neg++) % 8]);
2085 }
Tomato firmware and modifications.