1 /* crypto/bn/bntest.c */
2 /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
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.
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).
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.
23 * Redistribution and use in source and binary forms, with or without
24 * modification, are permitted provided that the following conditions
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)"
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
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.]
58 /* ====================================================================
59 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
61 * Portions of the attached software ("Contribution") are developed by
62 * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
64 * The Contribution is licensed pursuant to the Eric Young open source
65 * license provided above.
67 * The binary polynomial arithmetic software is originally written by
68 * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
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>
84 #include "../crypto/bn/bn_lcl.h"
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 */
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);
122 static int results = 0;
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";
128 static const char rnd_seed[] =
129 "string to make the random number generator think it has entropy";
131 static void message(BIO *out, char *m)
133 fprintf(stderr, "test %s\n", m);
134 BIO_puts(out, "print \"test ");
136 BIO_puts(out, "\\n\"\n");
139 int main(int argc, char *argv[])
143 char *outfile = NULL;
147 RAND_seed(rnd_seed, sizeof rnd_seed); /* or BN_generate_prime may fail */
152 if (strcmp(*argv, "-results") == 0)
154 else if (strcmp(*argv, "-out") == 0) {
167 out = BIO_new(BIO_s_file());
170 if (outfile == NULL) {
171 BIO_set_fp(out, stdout, BIO_NOCLOSE);
173 if (!BIO_write_filename(out, outfile)) {
180 BIO_puts(out, "obase=16\nibase=16\n");
182 message(out, "BN_add");
185 (void)BIO_flush(out);
187 message(out, "BN_sub");
190 (void)BIO_flush(out);
192 message(out, "BN_lshift1");
193 if (!test_lshift1(out))
195 (void)BIO_flush(out);
197 message(out, "BN_lshift (fixed)");
198 if (!test_lshift(out, ctx, BN_bin2bn(lst, sizeof(lst) - 1, NULL)))
200 (void)BIO_flush(out);
202 message(out, "BN_lshift");
203 if (!test_lshift(out, ctx, NULL))
205 (void)BIO_flush(out);
207 message(out, "BN_rshift1");
208 if (!test_rshift1(out))
210 (void)BIO_flush(out);
212 message(out, "BN_rshift");
213 if (!test_rshift(out, ctx))
215 (void)BIO_flush(out);
217 message(out, "BN_sqr");
218 if (!test_sqr(out, ctx))
220 (void)BIO_flush(out);
222 message(out, "BN_mul");
225 (void)BIO_flush(out);
227 message(out, "BN_div");
228 if (!test_div(out, ctx))
230 (void)BIO_flush(out);
232 message(out, "BN_div_word");
233 if (!test_div_word(out))
235 (void)BIO_flush(out);
237 message(out, "BN_div_recp");
238 if (!test_div_recp(out, ctx))
240 (void)BIO_flush(out);
242 message(out, "BN_mod");
243 if (!test_mod(out, ctx))
245 (void)BIO_flush(out);
247 message(out, "BN_mod_mul");
248 if (!test_mod_mul(out, ctx))
250 (void)BIO_flush(out);
252 message(out, "BN_mont");
253 if (!test_mont(out, ctx))
255 (void)BIO_flush(out);
257 message(out, "BN_mod_exp");
258 if (!test_mod_exp(out, ctx))
260 (void)BIO_flush(out);
262 message(out, "BN_mod_exp_mont_consttime");
263 if (!test_mod_exp_mont_consttime(out, ctx))
265 if (!test_mod_exp_mont5(out, ctx))
267 (void)BIO_flush(out);
269 message(out, "BN_exp");
270 if (!test_exp(out, ctx))
272 (void)BIO_flush(out);
274 message(out, "BN_kronecker");
275 if (!test_kron(out, ctx))
277 (void)BIO_flush(out);
279 message(out, "BN_mod_sqrt");
280 if (!test_sqrt(out, ctx))
282 (void)BIO_flush(out);
284 message(out, "Small prime generation");
285 if (!test_small_prime(out, ctx))
287 (void)BIO_flush(out);
289 #ifdef OPENSSL_SYS_WIN32
290 message(out, "Probable prime generation with coprimes disabled");
292 message(out, "Probable prime generation with coprimes");
293 if (!test_probable_prime_coprime(out, ctx))
296 (void)BIO_flush(out);
298 #ifndef OPENSSL_NO_EC2M
299 message(out, "BN_GF2m_add");
300 if (!test_gf2m_add(out))
302 (void)BIO_flush(out);
304 message(out, "BN_GF2m_mod");
305 if (!test_gf2m_mod(out))
307 (void)BIO_flush(out);
309 message(out, "BN_GF2m_mod_mul");
310 if (!test_gf2m_mod_mul(out, ctx))
312 (void)BIO_flush(out);
314 message(out, "BN_GF2m_mod_sqr");
315 if (!test_gf2m_mod_sqr(out, ctx))
317 (void)BIO_flush(out);
319 message(out, "BN_GF2m_mod_inv");
320 if (!test_gf2m_mod_inv(out, ctx))
322 (void)BIO_flush(out);
324 message(out, "BN_GF2m_mod_div");
325 if (!test_gf2m_mod_div(out, ctx))
327 (void)BIO_flush(out);
329 message(out, "BN_GF2m_mod_exp");
330 if (!test_gf2m_mod_exp(out, ctx))
332 (void)BIO_flush(out);
334 message(out, "BN_GF2m_mod_sqrt");
335 if (!test_gf2m_mod_sqrt(out, ctx))
337 (void)BIO_flush(out);
339 message(out, "BN_GF2m_mod_solve_quad");
340 if (!test_gf2m_mod_solve_quad(out, ctx))
342 (void)BIO_flush(out);
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);
358 int test_add(BIO *bp)
367 BN_bntest_rand(a, 512, 0, 0);
368 for (i = 0; i < num0; i++) {
369 BN_bntest_rand(b, 450 + i, 0, 0);
387 if (!BN_is_zero(c)) {
388 fprintf(stderr, "Add test failed!\n");
398 int test_sub(BIO *bp)
407 for (i = 0; i < num0 + num1; i++) {
409 BN_bntest_rand(a, 512, 0, 0);
411 if (BN_set_bit(a, i) == 0)
415 BN_bntest_rand(b, 400 + i - num1, 0, 0);
432 if (!BN_is_zero(c)) {
433 fprintf(stderr, "Subtract test failed!\n");
443 int test_div(BIO *bp, BN_CTX *ctx)
445 BIGNUM *a, *b, *c, *d, *e;
454 for (i = 0; i < num0 + num1; i++) {
456 BN_bntest_rand(a, 400, 0, 0);
461 BN_bntest_rand(b, 50 + 3 * (i - num1), 0, 0);
464 BN_div(d, c, a, b, ctx);
484 BN_mul(e, d, b, ctx);
487 if (!BN_is_zero(d)) {
488 fprintf(stderr, "Division test failed!\n");
500 static void print_word(BIO *bp, BN_ULONG w)
502 #ifdef SIXTY_FOUR_BIT
503 if (sizeof(w) > sizeof(unsigned long)) {
504 unsigned long h = (unsigned long)(w >> 32), l = (unsigned long)(w);
507 BIO_printf(bp, "%lX%08lX", h, l);
509 BIO_printf(bp, "%lX", l);
513 BIO_printf(bp, BN_HEX_FMT1, w);
516 int test_div_word(BIO *bp)
525 for (i = 0; i < num0; i++) {
527 BN_bntest_rand(a, 512, -1, 0);
528 BN_bntest_rand(b, BN_BITS2, -1, 0);
533 r = BN_div_word(b, s);
557 if (!BN_is_zero(b)) {
558 fprintf(stderr, "Division (word) test failed!\n");
567 int test_div_recp(BIO *bp, BN_CTX *ctx)
569 BIGNUM *a, *b, *c, *d, *e;
573 recp = BN_RECP_CTX_new();
580 for (i = 0; i < num0 + num1; i++) {
582 BN_bntest_rand(a, 400, 0, 0);
587 BN_bntest_rand(b, 50 + 3 * (i - num1), 0, 0);
590 BN_RECP_CTX_set(recp, b, ctx);
591 BN_div_recp(d, c, a, recp, ctx);
611 BN_mul(e, d, b, ctx);
614 if (!BN_is_zero(d)) {
615 fprintf(stderr, "Reciprocal division test failed!\n");
616 fprintf(stderr, "a=");
617 BN_print_fp(stderr, a);
618 fprintf(stderr, "\nb=");
619 BN_print_fp(stderr, b);
620 fprintf(stderr, "\n");
629 BN_RECP_CTX_free(recp);
633 int test_mul(BIO *bp)
635 BIGNUM *a, *b, *c, *d, *e;
649 for (i = 0; i < num0 + num1; i++) {
651 BN_bntest_rand(a, 100, 0, 0);
652 BN_bntest_rand(b, 100, 0, 0);
654 BN_bntest_rand(b, i - num1, 0, 0);
657 BN_mul(c, a, b, ctx);
668 BN_div(d, e, c, a, ctx);
670 if (!BN_is_zero(d) || !BN_is_zero(e)) {
671 fprintf(stderr, "Multiplication test failed!\n");
684 int test_sqr(BIO *bp, BN_CTX *ctx)
686 BIGNUM *a, *c, *d, *e;
693 if (a == NULL || c == NULL || d == NULL || e == NULL) {
697 for (i = 0; i < num0; i++) {
698 BN_bntest_rand(a, 40 + i * 10, 0, 0);
711 BN_div(d, e, c, a, ctx);
713 if (!BN_is_zero(d) || !BN_is_zero(e)) {
714 fprintf(stderr, "Square test failed!\n");
719 /* Regression test for a BN_sqr overflow bug. */
721 "80000000000000008000000000000001"
722 "FFFFFFFFFFFFFFFE0000000000000000");
734 BN_mul(d, a, a, ctx);
736 fprintf(stderr, "Square test failed: BN_sqr and BN_mul produce "
737 "different results!\n");
741 /* Regression test for a BN_sqr overflow bug. */
743 "80000000000000000000000080000001"
744 "FFFFFFFE000000000000000000000000");
756 BN_mul(d, a, a, ctx);
758 fprintf(stderr, "Square test failed: BN_sqr and BN_mul produce "
759 "different results!\n");
775 int test_mont(BIO *bp, BN_CTX *ctx)
777 BIGNUM *a, *b, *c, *d, *A, *B;
790 mont = BN_MONT_CTX_new();
794 BN_bntest_rand(a, 100, 0, 0);
795 BN_bntest_rand(b, 100, 0, 0);
796 for (i = 0; i < num2; i++) {
797 int bits = (200 * (i + 1)) / num2;
801 BN_bntest_rand(n, bits, 0, 1);
802 BN_MONT_CTX_set(mont, n, ctx);
804 BN_nnmod(a, a, n, ctx);
805 BN_nnmod(b, b, n, ctx);
807 BN_to_montgomery(A, a, mont, ctx);
808 BN_to_montgomery(B, b, mont, ctx);
810 BN_mod_mul_montgomery(c, A, B, mont, ctx);
811 BN_from_montgomery(A, c, mont, ctx);
818 BN_print(bp, &mont->N);
824 BN_mod_mul(d, a, b, n, ctx);
826 if (!BN_is_zero(d)) {
827 fprintf(stderr, "Montgomery multiplication test failed!\n");
831 BN_MONT_CTX_free(mont);
842 int test_mod(BIO *bp, BN_CTX *ctx)
844 BIGNUM *a, *b, *c, *d, *e;
853 BN_bntest_rand(a, 1024, 0, 0);
854 for (i = 0; i < num0; i++) {
855 BN_bntest_rand(b, 450 + i * 10, 0, 0);
858 BN_mod(c, a, b, ctx);
869 BN_div(d, e, a, b, ctx);
871 if (!BN_is_zero(e)) {
872 fprintf(stderr, "Modulo test failed!\n");
884 int test_mod_mul(BIO *bp, BN_CTX *ctx)
886 BIGNUM *a, *b, *c, *d, *e;
895 for (j = 0; j < 3; j++) {
896 BN_bntest_rand(c, 1024, 0, 0);
897 for (i = 0; i < num0; i++) {
898 BN_bntest_rand(a, 475 + i * 10, 0, 0);
899 BN_bntest_rand(b, 425 + i * 11, 0, 0);
902 if (!BN_mod_mul(e, a, b, c, ctx)) {
905 while ((l = ERR_get_error()))
906 fprintf(stderr, "ERROR:%s\n", ERR_error_string(l, NULL));
916 if ((a->neg ^ b->neg) && !BN_is_zero(e)) {
918 * If (a*b) % c is negative, c must be added in order
919 * to obtain the normalized remainder (new with
920 * OpenSSL 0.9.7, previous versions of BN_mod_mul
921 * could generate negative results)
931 BN_mul(d, a, b, ctx);
933 BN_div(a, b, d, c, ctx);
934 if (!BN_is_zero(b)) {
935 fprintf(stderr, "Modulo multiply test failed!\n");
936 ERR_print_errors_fp(stderr);
949 int test_mod_exp(BIO *bp, BN_CTX *ctx)
951 BIGNUM *a, *b, *c, *d, *e;
960 BN_bntest_rand(c, 30, 0, 1); /* must be odd for montgomery */
961 for (i = 0; i < num2; i++) {
962 BN_bntest_rand(a, 20 + i * 5, 0, 0);
963 BN_bntest_rand(b, 2 + i, 0, 0);
965 if (!BN_mod_exp(d, a, b, c, ctx))
980 BN_exp(e, a, b, ctx);
982 BN_div(a, b, e, c, ctx);
983 if (!BN_is_zero(b)) {
984 fprintf(stderr, "Modulo exponentiation test failed!\n");
996 int test_mod_exp_mont_consttime(BIO *bp, BN_CTX *ctx)
998 BIGNUM *a, *b, *c, *d, *e;
1007 BN_bntest_rand(c, 30, 0, 1); /* must be odd for montgomery */
1008 for (i = 0; i < num2; i++) {
1009 BN_bntest_rand(a, 20 + i * 5, 0, 0);
1010 BN_bntest_rand(b, 2 + i, 0, 0);
1012 if (!BN_mod_exp_mont_consttime(d, a, b, c, ctx, NULL))
1018 BIO_puts(bp, " ^ ");
1020 BIO_puts(bp, " % ");
1022 BIO_puts(bp, " - ");
1027 BN_exp(e, a, b, ctx);
1029 BN_div(a, b, e, c, ctx);
1030 if (!BN_is_zero(b)) {
1031 fprintf(stderr, "Modulo exponentiation test failed!\n");
1044 * Test constant-time modular exponentiation with 1024-bit inputs, which on
1045 * x86_64 cause a different code branch to be taken.
1047 int test_mod_exp_mont5(BIO *bp, BN_CTX *ctx)
1049 BIGNUM *a, *p, *m, *d, *e;
1059 mont = BN_MONT_CTX_new();
1061 BN_bntest_rand(m, 1024, 0, 1); /* must be odd for montgomery */
1063 BN_bntest_rand(a, 1024, 0, 0);
1065 if (!BN_mod_exp_mont_consttime(d, a, p, m, ctx, NULL))
1067 if (!BN_is_one(d)) {
1068 fprintf(stderr, "Modular exponentiation test failed!\n");
1072 BN_bntest_rand(p, 1024, 0, 0);
1074 if (!BN_mod_exp_mont_consttime(d, a, p, m, ctx, NULL))
1076 if (!BN_is_zero(d)) {
1077 fprintf(stderr, "Modular exponentiation test failed!\n");
1081 * Craft an input whose Montgomery representation is 1, i.e., shorter
1082 * than the modulus m, in order to test the const time precomputation
1083 * scattering/gathering.
1086 BN_MONT_CTX_set(mont, m, ctx);
1087 if (!BN_from_montgomery(e, a, mont, ctx))
1089 if (!BN_mod_exp_mont_consttime(d, e, p, m, ctx, NULL))
1091 if (!BN_mod_exp_simple(a, e, p, m, ctx))
1093 if (BN_cmp(a, d) != 0) {
1094 fprintf(stderr, "Modular exponentiation test failed!\n");
1097 /* Finally, some regular test vectors. */
1098 BN_bntest_rand(e, 1024, 0, 0);
1099 if (!BN_mod_exp_mont_consttime(d, e, p, m, ctx, NULL))
1101 if (!BN_mod_exp_simple(a, e, p, m, ctx))
1103 if (BN_cmp(a, d) != 0) {
1104 fprintf(stderr, "Modular exponentiation test failed!\n");
1115 int test_exp(BIO *bp, BN_CTX *ctx)
1117 BIGNUM *a, *b, *d, *e, *one;
1127 for (i = 0; i < num2; i++) {
1128 BN_bntest_rand(a, 20 + i * 5, 0, 0);
1129 BN_bntest_rand(b, 2 + i, 0, 0);
1131 if (BN_exp(d, a, b, ctx) <= 0)
1137 BIO_puts(bp, " ^ ");
1139 BIO_puts(bp, " - ");
1145 for (; !BN_is_zero(b); BN_sub(b, b, one))
1146 BN_mul(e, e, a, ctx);
1148 if (!BN_is_zero(e)) {
1149 fprintf(stderr, "Exponentiation test failed!\n");
1161 #ifndef OPENSSL_NO_EC2M
1162 int test_gf2m_add(BIO *bp)
1171 for (i = 0; i < num0; i++) {
1172 BN_rand(a, 512, 0, 0);
1173 BN_copy(b, BN_value_one());
1174 a->neg = rand_neg();
1175 b->neg = rand_neg();
1176 BN_GF2m_add(c, a, b);
1177 /* Test that two added values have the correct parity. */
1178 if ((BN_is_odd(a) && BN_is_odd(c))
1179 || (!BN_is_odd(a) && !BN_is_odd(c))) {
1180 fprintf(stderr, "GF(2^m) addition test (a) failed!\n");
1183 BN_GF2m_add(c, c, c);
1184 /* Test that c + c = 0. */
1185 if (!BN_is_zero(c)) {
1186 fprintf(stderr, "GF(2^m) addition test (b) failed!\n");
1198 int test_gf2m_mod(BIO *bp)
1200 BIGNUM *a, *b[2], *c, *d, *e;
1202 int p0[] = { 163, 7, 6, 3, 0, -1 };
1203 int p1[] = { 193, 15, 0, -1 };
1212 BN_GF2m_arr2poly(p0, b[0]);
1213 BN_GF2m_arr2poly(p1, b[1]);
1215 for (i = 0; i < num0; i++) {
1216 BN_bntest_rand(a, 1024, 0, 0);
1217 for (j = 0; j < 2; j++) {
1218 BN_GF2m_mod(c, a, b[j]);
1219 BN_GF2m_add(d, a, c);
1220 BN_GF2m_mod(e, d, b[j]);
1221 /* Test that a + (a mod p) mod p == 0. */
1222 if (!BN_is_zero(e)) {
1223 fprintf(stderr, "GF(2^m) modulo test failed!\n");
1239 int test_gf2m_mod_mul(BIO *bp, BN_CTX *ctx)
1241 BIGNUM *a, *b[2], *c, *d, *e, *f, *g, *h;
1243 int p0[] = { 163, 7, 6, 3, 0, -1 };
1244 int p1[] = { 193, 15, 0, -1 };
1256 BN_GF2m_arr2poly(p0, b[0]);
1257 BN_GF2m_arr2poly(p1, b[1]);
1259 for (i = 0; i < num0; i++) {
1260 BN_bntest_rand(a, 1024, 0, 0);
1261 BN_bntest_rand(c, 1024, 0, 0);
1262 BN_bntest_rand(d, 1024, 0, 0);
1263 for (j = 0; j < 2; j++) {
1264 BN_GF2m_mod_mul(e, a, c, b[j], ctx);
1265 BN_GF2m_add(f, a, d);
1266 BN_GF2m_mod_mul(g, f, c, b[j], ctx);
1267 BN_GF2m_mod_mul(h, d, c, b[j], ctx);
1268 BN_GF2m_add(f, e, g);
1269 BN_GF2m_add(f, f, h);
1270 /* Test that (a+d)*c = a*c + d*c. */
1271 if (!BN_is_zero(f)) {
1273 "GF(2^m) modular multiplication test failed!\n");
1292 int test_gf2m_mod_sqr(BIO *bp, BN_CTX *ctx)
1294 BIGNUM *a, *b[2], *c, *d;
1296 int p0[] = { 163, 7, 6, 3, 0, -1 };
1297 int p1[] = { 193, 15, 0, -1 };
1305 BN_GF2m_arr2poly(p0, b[0]);
1306 BN_GF2m_arr2poly(p1, b[1]);
1308 for (i = 0; i < num0; i++) {
1309 BN_bntest_rand(a, 1024, 0, 0);
1310 for (j = 0; j < 2; j++) {
1311 BN_GF2m_mod_sqr(c, a, b[j], ctx);
1313 BN_GF2m_mod_mul(d, a, d, b[j], ctx);
1314 BN_GF2m_add(d, c, d);
1315 /* Test that a*a = a^2. */
1316 if (!BN_is_zero(d)) {
1317 fprintf(stderr, "GF(2^m) modular squaring test failed!\n");
1332 int test_gf2m_mod_inv(BIO *bp, BN_CTX *ctx)
1334 BIGNUM *a, *b[2], *c, *d;
1336 int p0[] = { 163, 7, 6, 3, 0, -1 };
1337 int p1[] = { 193, 15, 0, -1 };
1345 BN_GF2m_arr2poly(p0, b[0]);
1346 BN_GF2m_arr2poly(p1, b[1]);
1348 for (i = 0; i < num0; i++) {
1349 BN_bntest_rand(a, 512, 0, 0);
1350 for (j = 0; j < 2; j++) {
1351 BN_GF2m_mod_inv(c, a, b[j], ctx);
1352 BN_GF2m_mod_mul(d, a, c, b[j], ctx);
1353 /* Test that ((1/a)*a) = 1. */
1354 if (!BN_is_one(d)) {
1355 fprintf(stderr, "GF(2^m) modular inversion test failed!\n");
1370 int test_gf2m_mod_div(BIO *bp, BN_CTX *ctx)
1372 BIGNUM *a, *b[2], *c, *d, *e, *f;
1374 int p0[] = { 163, 7, 6, 3, 0, -1 };
1375 int p1[] = { 193, 15, 0, -1 };
1385 BN_GF2m_arr2poly(p0, b[0]);
1386 BN_GF2m_arr2poly(p1, b[1]);
1388 for (i = 0; i < num0; i++) {
1389 BN_bntest_rand(a, 512, 0, 0);
1390 BN_bntest_rand(c, 512, 0, 0);
1391 for (j = 0; j < 2; j++) {
1392 BN_GF2m_mod_div(d, a, c, b[j], ctx);
1393 BN_GF2m_mod_mul(e, d, c, b[j], ctx);
1394 BN_GF2m_mod_div(f, a, e, b[j], ctx);
1395 /* Test that ((a/c)*c)/a = 1. */
1396 if (!BN_is_one(f)) {
1397 fprintf(stderr, "GF(2^m) modular division test failed!\n");
1414 int test_gf2m_mod_exp(BIO *bp, BN_CTX *ctx)
1416 BIGNUM *a, *b[2], *c, *d, *e, *f;
1418 int p0[] = { 163, 7, 6, 3, 0, -1 };
1419 int p1[] = { 193, 15, 0, -1 };
1429 BN_GF2m_arr2poly(p0, b[0]);
1430 BN_GF2m_arr2poly(p1, b[1]);
1432 for (i = 0; i < num0; i++) {
1433 BN_bntest_rand(a, 512, 0, 0);
1434 BN_bntest_rand(c, 512, 0, 0);
1435 BN_bntest_rand(d, 512, 0, 0);
1436 for (j = 0; j < 2; j++) {
1437 BN_GF2m_mod_exp(e, a, c, b[j], ctx);
1438 BN_GF2m_mod_exp(f, a, d, b[j], ctx);
1439 BN_GF2m_mod_mul(e, e, f, b[j], ctx);
1441 BN_GF2m_mod_exp(f, a, f, b[j], ctx);
1442 BN_GF2m_add(f, e, f);
1443 /* Test that a^(c+d)=a^c*a^d. */
1444 if (!BN_is_zero(f)) {
1446 "GF(2^m) modular exponentiation test failed!\n");
1463 int test_gf2m_mod_sqrt(BIO *bp, BN_CTX *ctx)
1465 BIGNUM *a, *b[2], *c, *d, *e, *f;
1467 int p0[] = { 163, 7, 6, 3, 0, -1 };
1468 int p1[] = { 193, 15, 0, -1 };
1478 BN_GF2m_arr2poly(p0, b[0]);
1479 BN_GF2m_arr2poly(p1, b[1]);
1481 for (i = 0; i < num0; i++) {
1482 BN_bntest_rand(a, 512, 0, 0);
1483 for (j = 0; j < 2; j++) {
1484 BN_GF2m_mod(c, a, b[j]);
1485 BN_GF2m_mod_sqrt(d, a, b[j], ctx);
1486 BN_GF2m_mod_sqr(e, d, b[j], ctx);
1487 BN_GF2m_add(f, c, e);
1488 /* Test that d^2 = a, where d = sqrt(a). */
1489 if (!BN_is_zero(f)) {
1490 fprintf(stderr, "GF(2^m) modular square root test failed!\n");
1507 int test_gf2m_mod_solve_quad(BIO *bp, BN_CTX *ctx)
1509 BIGNUM *a, *b[2], *c, *d, *e;
1510 int i, j, s = 0, t, ret = 0;
1511 int p0[] = { 163, 7, 6, 3, 0, -1 };
1512 int p1[] = { 193, 15, 0, -1 };
1521 BN_GF2m_arr2poly(p0, b[0]);
1522 BN_GF2m_arr2poly(p1, b[1]);
1524 for (i = 0; i < num0; i++) {
1525 BN_bntest_rand(a, 512, 0, 0);
1526 for (j = 0; j < 2; j++) {
1527 t = BN_GF2m_mod_solve_quad(c, a, b[j], ctx);
1530 BN_GF2m_mod_sqr(d, c, b[j], ctx);
1531 BN_GF2m_add(d, c, d);
1532 BN_GF2m_mod(e, a, b[j]);
1533 BN_GF2m_add(e, e, d);
1535 * Test that solution of quadratic c satisfies c^2 + c = a.
1537 if (!BN_is_zero(e)) {
1539 "GF(2^m) modular solve quadratic test failed!\n");
1548 "All %i tests of GF(2^m) modular solve quadratic resulted in no roots;\n",
1551 "this is very unlikely and probably indicates an error.\n");
1565 static int genprime_cb(int p, int n, BN_GENCB *arg)
1582 int test_kron(BIO *bp, BN_CTX *ctx)
1585 BIGNUM *a, *b, *r, *t;
1587 int legendre, kronecker;
1594 if (a == NULL || b == NULL || r == NULL || t == NULL)
1597 BN_GENCB_set(&cb, genprime_cb, NULL);
1600 * We test BN_kronecker(a, b, ctx) just for b odd (Jacobi symbol). In
1601 * this case we know that if b is prime, then BN_kronecker(a, b, ctx) is
1602 * congruent to $a^{(b-1)/2}$, modulo $b$ (Legendre symbol). So we
1603 * generate a random prime b and compare these values for a number of
1604 * random a's. (That is, we run the Solovay-Strassen primality test to
1605 * confirm that b is prime, except that we don't want to test whether b
1606 * is prime but whether BN_kronecker works.)
1609 if (!BN_generate_prime_ex(b, 512, 0, NULL, NULL, &cb))
1611 b->neg = rand_neg();
1614 for (i = 0; i < num0; i++) {
1615 if (!BN_bntest_rand(a, 512, 0, 0))
1617 a->neg = rand_neg();
1619 /* t := (|b|-1)/2 (note that b is odd) */
1623 if (!BN_sub_word(t, 1))
1625 if (!BN_rshift1(t, t))
1627 /* r := a^t mod b */
1630 if (!BN_mod_exp_recp(r, a, t, b, ctx))
1634 if (BN_is_word(r, 1))
1636 else if (BN_is_zero(r))
1639 if (!BN_add_word(r, 1))
1641 if (0 != BN_ucmp(r, b)) {
1642 fprintf(stderr, "Legendre symbol computation failed\n");
1648 kronecker = BN_kronecker(a, b, ctx);
1651 /* we actually need BN_kronecker(a, |b|) */
1652 if (a->neg && b->neg)
1653 kronecker = -kronecker;
1655 if (legendre != kronecker) {
1656 fprintf(stderr, "legendre != kronecker; a = ");
1657 BN_print_fp(stderr, a);
1658 fprintf(stderr, ", b = ");
1659 BN_print_fp(stderr, b);
1660 fprintf(stderr, "\n");
1683 int test_sqrt(BIO *bp, BN_CTX *ctx)
1693 if (a == NULL || p == NULL || r == NULL)
1696 BN_GENCB_set(&cb, genprime_cb, NULL);
1698 for (i = 0; i < 16; i++) {
1700 unsigned primes[8] = { 2, 3, 5, 7, 11, 13, 17, 19 };
1702 if (!BN_set_word(p, primes[i]))
1705 if (!BN_set_word(a, 32))
1707 if (!BN_set_word(r, 2 * i + 1))
1710 if (!BN_generate_prime_ex(p, 256, 0, a, r, &cb))
1714 p->neg = rand_neg();
1716 for (j = 0; j < num2; j++) {
1718 * construct 'a' such that it is a square modulo p, but in
1719 * general not a proper square and not reduced modulo p
1721 if (!BN_bntest_rand(r, 256, 0, 3))
1723 if (!BN_nnmod(r, r, p, ctx))
1725 if (!BN_mod_sqr(r, r, p, ctx))
1727 if (!BN_bntest_rand(a, 256, 0, 3))
1729 if (!BN_nnmod(a, a, p, ctx))
1731 if (!BN_mod_sqr(a, a, p, ctx))
1733 if (!BN_mul(a, a, r, ctx))
1736 if (!BN_sub(a, a, p))
1739 if (!BN_mod_sqrt(r, a, p, ctx))
1741 if (!BN_mod_sqr(r, r, p, ctx))
1744 if (!BN_nnmod(a, a, p, ctx))
1747 if (BN_cmp(a, r) != 0) {
1748 fprintf(stderr, "BN_mod_sqrt failed: a = ");
1749 BN_print_fp(stderr, a);
1750 fprintf(stderr, ", r = ");
1751 BN_print_fp(stderr, r);
1752 fprintf(stderr, ", p = ");
1753 BN_print_fp(stderr, p);
1754 fprintf(stderr, "\n");
1776 int test_small_prime(BIO *bp, BN_CTX *ctx)
1778 static const int bits = 10;
1783 if (!BN_generate_prime_ex(r, bits, 0, NULL, NULL, NULL))
1785 if (BN_num_bits(r) != bits) {
1786 BIO_printf(bp, "Expected %d bit prime, got %d bit number\n", bits,
1798 #ifndef OPENSSL_SYS_WIN32
1799 int test_probable_prime_coprime(BIO *bp, BN_CTX *ctx)
1803 BN_ULONG primes[5] = { 2, 3, 5, 7, 11 };
1807 for (i = 0; i < 1000; i++) {
1808 if (!bn_probable_prime_dh_coprime(r, 1024, ctx))
1811 for (j = 0; j < 5; j++) {
1812 if (BN_mod_word(r, primes[j]) == 0) {
1813 BIO_printf(bp, "Number generated is not coprime to %ld:\n",
1815 BN_print_fp(stdout, r);
1816 BIO_printf(bp, "\n");
1829 int test_lshift(BIO *bp, BN_CTX *ctx, BIGNUM *a_)
1831 BIGNUM *a, *b, *c, *d;
1843 BN_bntest_rand(a, 200, 0, 0);
1844 a->neg = rand_neg();
1846 for (i = 0; i < num0; i++) {
1847 BN_lshift(b, a, i + 1);
1852 BIO_puts(bp, " * ");
1854 BIO_puts(bp, " - ");
1859 BN_mul(d, a, c, ctx);
1861 if (!BN_is_zero(d)) {
1862 fprintf(stderr, "Left shift test failed!\n");
1863 fprintf(stderr, "a=");
1864 BN_print_fp(stderr, a);
1865 fprintf(stderr, "\nb=");
1866 BN_print_fp(stderr, b);
1867 fprintf(stderr, "\nc=");
1868 BN_print_fp(stderr, c);
1869 fprintf(stderr, "\nd=");
1870 BN_print_fp(stderr, d);
1871 fprintf(stderr, "\n");
1882 int test_lshift1(BIO *bp)
1891 BN_bntest_rand(a, 200, 0, 0);
1892 a->neg = rand_neg();
1893 for (i = 0; i < num0; i++) {
1898 BIO_puts(bp, " * 2");
1899 BIO_puts(bp, " - ");
1906 if (!BN_is_zero(a)) {
1907 fprintf(stderr, "Left shift one test failed!\n");
1919 int test_rshift(BIO *bp, BN_CTX *ctx)
1921 BIGNUM *a, *b, *c, *d, *e;
1931 BN_bntest_rand(a, 200, 0, 0);
1932 a->neg = rand_neg();
1933 for (i = 0; i < num0; i++) {
1934 BN_rshift(b, a, i + 1);
1939 BIO_puts(bp, " / ");
1941 BIO_puts(bp, " - ");
1946 BN_div(d, e, a, c, ctx);
1948 if (!BN_is_zero(d)) {
1949 fprintf(stderr, "Right shift test failed!\n");
1961 int test_rshift1(BIO *bp)
1970 BN_bntest_rand(a, 200, 0, 0);
1971 a->neg = rand_neg();
1972 for (i = 0; i < num0; i++) {
1977 BIO_puts(bp, " / 2");
1978 BIO_puts(bp, " - ");
1985 if (!BN_is_zero(c) && !BN_abs_is_word(c, 1)) {
1986 fprintf(stderr, "Right shift one test failed!\n");
1999 static unsigned int neg = 0;
2000 static int sign[8] = { 0, 0, 0, 1, 1, 0, 1, 1 };
2002 return (sign[(neg++) % 8]);