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");
771 int test_mont(BIO *bp, BN_CTX *ctx)
773 BIGNUM *a, *b, *c, *d, *A, *B;
786 mont = BN_MONT_CTX_new();
790 BN_bntest_rand(a, 100, 0, 0);
791 BN_bntest_rand(b, 100, 0, 0);
792 for (i = 0; i < num2; i++) {
793 int bits = (200 * (i + 1)) / num2;
797 BN_bntest_rand(n, bits, 0, 1);
798 BN_MONT_CTX_set(mont, n, ctx);
800 BN_nnmod(a, a, n, ctx);
801 BN_nnmod(b, b, n, ctx);
803 BN_to_montgomery(A, a, mont, ctx);
804 BN_to_montgomery(B, b, mont, ctx);
806 BN_mod_mul_montgomery(c, A, B, mont, ctx);
807 BN_from_montgomery(A, c, mont, ctx);
814 BN_print(bp, &mont->N);
820 BN_mod_mul(d, a, b, n, ctx);
822 if (!BN_is_zero(d)) {
823 fprintf(stderr, "Montgomery multiplication test failed!\n");
827 BN_MONT_CTX_free(mont);
838 int test_mod(BIO *bp, BN_CTX *ctx)
840 BIGNUM *a, *b, *c, *d, *e;
849 BN_bntest_rand(a, 1024, 0, 0);
850 for (i = 0; i < num0; i++) {
851 BN_bntest_rand(b, 450 + i * 10, 0, 0);
854 BN_mod(c, a, b, ctx);
865 BN_div(d, e, a, b, ctx);
867 if (!BN_is_zero(e)) {
868 fprintf(stderr, "Modulo test failed!\n");
880 int test_mod_mul(BIO *bp, BN_CTX *ctx)
882 BIGNUM *a, *b, *c, *d, *e;
891 for (j = 0; j < 3; j++) {
892 BN_bntest_rand(c, 1024, 0, 0);
893 for (i = 0; i < num0; i++) {
894 BN_bntest_rand(a, 475 + i * 10, 0, 0);
895 BN_bntest_rand(b, 425 + i * 11, 0, 0);
898 if (!BN_mod_mul(e, a, b, c, ctx)) {
901 while ((l = ERR_get_error()))
902 fprintf(stderr, "ERROR:%s\n", ERR_error_string(l, NULL));
912 if ((a->neg ^ b->neg) && !BN_is_zero(e)) {
914 * If (a*b) % c is negative, c must be added in order
915 * to obtain the normalized remainder (new with
916 * OpenSSL 0.9.7, previous versions of BN_mod_mul
917 * could generate negative results)
927 BN_mul(d, a, b, ctx);
929 BN_div(a, b, d, c, ctx);
930 if (!BN_is_zero(b)) {
931 fprintf(stderr, "Modulo multiply test failed!\n");
932 ERR_print_errors_fp(stderr);
945 int test_mod_exp(BIO *bp, BN_CTX *ctx)
947 BIGNUM *a, *b, *c, *d, *e;
956 BN_bntest_rand(c, 30, 0, 1); /* must be odd for montgomery */
957 for (i = 0; i < num2; i++) {
958 BN_bntest_rand(a, 20 + i * 5, 0, 0);
959 BN_bntest_rand(b, 2 + i, 0, 0);
961 if (!BN_mod_exp(d, a, b, c, ctx))
976 BN_exp(e, a, b, ctx);
978 BN_div(a, b, e, c, ctx);
979 if (!BN_is_zero(b)) {
980 fprintf(stderr, "Modulo exponentiation test failed!\n");
992 int test_mod_exp_mont_consttime(BIO *bp, BN_CTX *ctx)
994 BIGNUM *a, *b, *c, *d, *e;
1003 BN_bntest_rand(c, 30, 0, 1); /* must be odd for montgomery */
1004 for (i = 0; i < num2; i++) {
1005 BN_bntest_rand(a, 20 + i * 5, 0, 0);
1006 BN_bntest_rand(b, 2 + i, 0, 0);
1008 if (!BN_mod_exp_mont_consttime(d, a, b, c, ctx, NULL))
1014 BIO_puts(bp, " ^ ");
1016 BIO_puts(bp, " % ");
1018 BIO_puts(bp, " - ");
1023 BN_exp(e, a, b, ctx);
1025 BN_div(a, b, e, c, ctx);
1026 if (!BN_is_zero(b)) {
1027 fprintf(stderr, "Modulo exponentiation test failed!\n");
1040 * Test constant-time modular exponentiation with 1024-bit inputs, which on
1041 * x86_64 cause a different code branch to be taken.
1043 int test_mod_exp_mont5(BIO *bp, BN_CTX *ctx)
1045 BIGNUM *a, *p, *m, *d, *e;
1055 mont = BN_MONT_CTX_new();
1057 BN_bntest_rand(m, 1024, 0, 1); /* must be odd for montgomery */
1059 BN_bntest_rand(a, 1024, 0, 0);
1061 if (!BN_mod_exp_mont_consttime(d, a, p, m, ctx, NULL))
1063 if (!BN_is_one(d)) {
1064 fprintf(stderr, "Modular exponentiation test failed!\n");
1068 BN_bntest_rand(p, 1024, 0, 0);
1070 if (!BN_mod_exp_mont_consttime(d, a, p, m, ctx, NULL))
1072 if (!BN_is_zero(d)) {
1073 fprintf(stderr, "Modular exponentiation test failed!\n");
1077 * Craft an input whose Montgomery representation is 1, i.e., shorter
1078 * than the modulus m, in order to test the const time precomputation
1079 * scattering/gathering.
1082 BN_MONT_CTX_set(mont, m, ctx);
1083 if (!BN_from_montgomery(e, a, mont, ctx))
1085 if (!BN_mod_exp_mont_consttime(d, e, p, m, ctx, NULL))
1087 if (!BN_mod_exp_simple(a, e, p, m, ctx))
1089 if (BN_cmp(a, d) != 0) {
1090 fprintf(stderr, "Modular exponentiation test failed!\n");
1093 /* Finally, some regular test vectors. */
1094 BN_bntest_rand(e, 1024, 0, 0);
1095 if (!BN_mod_exp_mont_consttime(d, e, p, m, ctx, NULL))
1097 if (!BN_mod_exp_simple(a, e, p, m, ctx))
1099 if (BN_cmp(a, d) != 0) {
1100 fprintf(stderr, "Modular exponentiation test failed!\n");
1111 int test_exp(BIO *bp, BN_CTX *ctx)
1113 BIGNUM *a, *b, *d, *e, *one;
1123 for (i = 0; i < num2; i++) {
1124 BN_bntest_rand(a, 20 + i * 5, 0, 0);
1125 BN_bntest_rand(b, 2 + i, 0, 0);
1127 if (BN_exp(d, a, b, ctx) <= 0)
1133 BIO_puts(bp, " ^ ");
1135 BIO_puts(bp, " - ");
1141 for (; !BN_is_zero(b); BN_sub(b, b, one))
1142 BN_mul(e, e, a, ctx);
1144 if (!BN_is_zero(e)) {
1145 fprintf(stderr, "Exponentiation test failed!\n");
1157 #ifndef OPENSSL_NO_EC2M
1158 int test_gf2m_add(BIO *bp)
1167 for (i = 0; i < num0; i++) {
1168 BN_rand(a, 512, 0, 0);
1169 BN_copy(b, BN_value_one());
1170 a->neg = rand_neg();
1171 b->neg = rand_neg();
1172 BN_GF2m_add(c, a, b);
1173 /* Test that two added values have the correct parity. */
1174 if ((BN_is_odd(a) && BN_is_odd(c))
1175 || (!BN_is_odd(a) && !BN_is_odd(c))) {
1176 fprintf(stderr, "GF(2^m) addition test (a) failed!\n");
1179 BN_GF2m_add(c, c, c);
1180 /* Test that c + c = 0. */
1181 if (!BN_is_zero(c)) {
1182 fprintf(stderr, "GF(2^m) addition test (b) failed!\n");
1194 int test_gf2m_mod(BIO *bp)
1196 BIGNUM *a, *b[2], *c, *d, *e;
1198 int p0[] = { 163, 7, 6, 3, 0, -1 };
1199 int p1[] = { 193, 15, 0, -1 };
1208 BN_GF2m_arr2poly(p0, b[0]);
1209 BN_GF2m_arr2poly(p1, b[1]);
1211 for (i = 0; i < num0; i++) {
1212 BN_bntest_rand(a, 1024, 0, 0);
1213 for (j = 0; j < 2; j++) {
1214 BN_GF2m_mod(c, a, b[j]);
1215 BN_GF2m_add(d, a, c);
1216 BN_GF2m_mod(e, d, b[j]);
1217 /* Test that a + (a mod p) mod p == 0. */
1218 if (!BN_is_zero(e)) {
1219 fprintf(stderr, "GF(2^m) modulo test failed!\n");
1235 int test_gf2m_mod_mul(BIO *bp, BN_CTX *ctx)
1237 BIGNUM *a, *b[2], *c, *d, *e, *f, *g, *h;
1239 int p0[] = { 163, 7, 6, 3, 0, -1 };
1240 int p1[] = { 193, 15, 0, -1 };
1252 BN_GF2m_arr2poly(p0, b[0]);
1253 BN_GF2m_arr2poly(p1, b[1]);
1255 for (i = 0; i < num0; i++) {
1256 BN_bntest_rand(a, 1024, 0, 0);
1257 BN_bntest_rand(c, 1024, 0, 0);
1258 BN_bntest_rand(d, 1024, 0, 0);
1259 for (j = 0; j < 2; j++) {
1260 BN_GF2m_mod_mul(e, a, c, b[j], ctx);
1261 BN_GF2m_add(f, a, d);
1262 BN_GF2m_mod_mul(g, f, c, b[j], ctx);
1263 BN_GF2m_mod_mul(h, d, c, b[j], ctx);
1264 BN_GF2m_add(f, e, g);
1265 BN_GF2m_add(f, f, h);
1266 /* Test that (a+d)*c = a*c + d*c. */
1267 if (!BN_is_zero(f)) {
1269 "GF(2^m) modular multiplication test failed!\n");
1288 int test_gf2m_mod_sqr(BIO *bp, BN_CTX *ctx)
1290 BIGNUM *a, *b[2], *c, *d;
1292 int p0[] = { 163, 7, 6, 3, 0, -1 };
1293 int p1[] = { 193, 15, 0, -1 };
1301 BN_GF2m_arr2poly(p0, b[0]);
1302 BN_GF2m_arr2poly(p1, b[1]);
1304 for (i = 0; i < num0; i++) {
1305 BN_bntest_rand(a, 1024, 0, 0);
1306 for (j = 0; j < 2; j++) {
1307 BN_GF2m_mod_sqr(c, a, b[j], ctx);
1309 BN_GF2m_mod_mul(d, a, d, b[j], ctx);
1310 BN_GF2m_add(d, c, d);
1311 /* Test that a*a = a^2. */
1312 if (!BN_is_zero(d)) {
1313 fprintf(stderr, "GF(2^m) modular squaring test failed!\n");
1328 int test_gf2m_mod_inv(BIO *bp, BN_CTX *ctx)
1330 BIGNUM *a, *b[2], *c, *d;
1332 int p0[] = { 163, 7, 6, 3, 0, -1 };
1333 int p1[] = { 193, 15, 0, -1 };
1341 BN_GF2m_arr2poly(p0, b[0]);
1342 BN_GF2m_arr2poly(p1, b[1]);
1344 for (i = 0; i < num0; i++) {
1345 BN_bntest_rand(a, 512, 0, 0);
1346 for (j = 0; j < 2; j++) {
1347 BN_GF2m_mod_inv(c, a, b[j], ctx);
1348 BN_GF2m_mod_mul(d, a, c, b[j], ctx);
1349 /* Test that ((1/a)*a) = 1. */
1350 if (!BN_is_one(d)) {
1351 fprintf(stderr, "GF(2^m) modular inversion test failed!\n");
1366 int test_gf2m_mod_div(BIO *bp, BN_CTX *ctx)
1368 BIGNUM *a, *b[2], *c, *d, *e, *f;
1370 int p0[] = { 163, 7, 6, 3, 0, -1 };
1371 int p1[] = { 193, 15, 0, -1 };
1381 BN_GF2m_arr2poly(p0, b[0]);
1382 BN_GF2m_arr2poly(p1, b[1]);
1384 for (i = 0; i < num0; i++) {
1385 BN_bntest_rand(a, 512, 0, 0);
1386 BN_bntest_rand(c, 512, 0, 0);
1387 for (j = 0; j < 2; j++) {
1388 BN_GF2m_mod_div(d, a, c, b[j], ctx);
1389 BN_GF2m_mod_mul(e, d, c, b[j], ctx);
1390 BN_GF2m_mod_div(f, a, e, b[j], ctx);
1391 /* Test that ((a/c)*c)/a = 1. */
1392 if (!BN_is_one(f)) {
1393 fprintf(stderr, "GF(2^m) modular division test failed!\n");
1410 int test_gf2m_mod_exp(BIO *bp, BN_CTX *ctx)
1412 BIGNUM *a, *b[2], *c, *d, *e, *f;
1414 int p0[] = { 163, 7, 6, 3, 0, -1 };
1415 int p1[] = { 193, 15, 0, -1 };
1425 BN_GF2m_arr2poly(p0, b[0]);
1426 BN_GF2m_arr2poly(p1, b[1]);
1428 for (i = 0; i < num0; i++) {
1429 BN_bntest_rand(a, 512, 0, 0);
1430 BN_bntest_rand(c, 512, 0, 0);
1431 BN_bntest_rand(d, 512, 0, 0);
1432 for (j = 0; j < 2; j++) {
1433 BN_GF2m_mod_exp(e, a, c, b[j], ctx);
1434 BN_GF2m_mod_exp(f, a, d, b[j], ctx);
1435 BN_GF2m_mod_mul(e, e, f, b[j], ctx);
1437 BN_GF2m_mod_exp(f, a, f, b[j], ctx);
1438 BN_GF2m_add(f, e, f);
1439 /* Test that a^(c+d)=a^c*a^d. */
1440 if (!BN_is_zero(f)) {
1442 "GF(2^m) modular exponentiation test failed!\n");
1459 int test_gf2m_mod_sqrt(BIO *bp, BN_CTX *ctx)
1461 BIGNUM *a, *b[2], *c, *d, *e, *f;
1463 int p0[] = { 163, 7, 6, 3, 0, -1 };
1464 int p1[] = { 193, 15, 0, -1 };
1474 BN_GF2m_arr2poly(p0, b[0]);
1475 BN_GF2m_arr2poly(p1, b[1]);
1477 for (i = 0; i < num0; i++) {
1478 BN_bntest_rand(a, 512, 0, 0);
1479 for (j = 0; j < 2; j++) {
1480 BN_GF2m_mod(c, a, b[j]);
1481 BN_GF2m_mod_sqrt(d, a, b[j], ctx);
1482 BN_GF2m_mod_sqr(e, d, b[j], ctx);
1483 BN_GF2m_add(f, c, e);
1484 /* Test that d^2 = a, where d = sqrt(a). */
1485 if (!BN_is_zero(f)) {
1486 fprintf(stderr, "GF(2^m) modular square root test failed!\n");
1503 int test_gf2m_mod_solve_quad(BIO *bp, BN_CTX *ctx)
1505 BIGNUM *a, *b[2], *c, *d, *e;
1506 int i, j, s = 0, t, ret = 0;
1507 int p0[] = { 163, 7, 6, 3, 0, -1 };
1508 int p1[] = { 193, 15, 0, -1 };
1517 BN_GF2m_arr2poly(p0, b[0]);
1518 BN_GF2m_arr2poly(p1, b[1]);
1520 for (i = 0; i < num0; i++) {
1521 BN_bntest_rand(a, 512, 0, 0);
1522 for (j = 0; j < 2; j++) {
1523 t = BN_GF2m_mod_solve_quad(c, a, b[j], ctx);
1526 BN_GF2m_mod_sqr(d, c, b[j], ctx);
1527 BN_GF2m_add(d, c, d);
1528 BN_GF2m_mod(e, a, b[j]);
1529 BN_GF2m_add(e, e, d);
1531 * Test that solution of quadratic c satisfies c^2 + c = a.
1533 if (!BN_is_zero(e)) {
1535 "GF(2^m) modular solve quadratic test failed!\n");
1544 "All %i tests of GF(2^m) modular solve quadratic resulted in no roots;\n",
1547 "this is very unlikely and probably indicates an error.\n");
1561 static int genprime_cb(int p, int n, BN_GENCB *arg)
1578 int test_kron(BIO *bp, BN_CTX *ctx)
1581 BIGNUM *a, *b, *r, *t;
1583 int legendre, kronecker;
1590 if (a == NULL || b == NULL || r == NULL || t == NULL)
1593 BN_GENCB_set(&cb, genprime_cb, NULL);
1596 * We test BN_kronecker(a, b, ctx) just for b odd (Jacobi symbol). In
1597 * this case we know that if b is prime, then BN_kronecker(a, b, ctx) is
1598 * congruent to $a^{(b-1)/2}$, modulo $b$ (Legendre symbol). So we
1599 * generate a random prime b and compare these values for a number of
1600 * random a's. (That is, we run the Solovay-Strassen primality test to
1601 * confirm that b is prime, except that we don't want to test whether b
1602 * is prime but whether BN_kronecker works.)
1605 if (!BN_generate_prime_ex(b, 512, 0, NULL, NULL, &cb))
1607 b->neg = rand_neg();
1610 for (i = 0; i < num0; i++) {
1611 if (!BN_bntest_rand(a, 512, 0, 0))
1613 a->neg = rand_neg();
1615 /* t := (|b|-1)/2 (note that b is odd) */
1619 if (!BN_sub_word(t, 1))
1621 if (!BN_rshift1(t, t))
1623 /* r := a^t mod b */
1626 if (!BN_mod_exp_recp(r, a, t, b, ctx))
1630 if (BN_is_word(r, 1))
1632 else if (BN_is_zero(r))
1635 if (!BN_add_word(r, 1))
1637 if (0 != BN_ucmp(r, b)) {
1638 fprintf(stderr, "Legendre symbol computation failed\n");
1644 kronecker = BN_kronecker(a, b, ctx);
1647 /* we actually need BN_kronecker(a, |b|) */
1648 if (a->neg && b->neg)
1649 kronecker = -kronecker;
1651 if (legendre != kronecker) {
1652 fprintf(stderr, "legendre != kronecker; a = ");
1653 BN_print_fp(stderr, a);
1654 fprintf(stderr, ", b = ");
1655 BN_print_fp(stderr, b);
1656 fprintf(stderr, "\n");
1675 int test_sqrt(BIO *bp, BN_CTX *ctx)
1685 if (a == NULL || p == NULL || r == NULL)
1688 BN_GENCB_set(&cb, genprime_cb, NULL);
1690 for (i = 0; i < 16; i++) {
1692 unsigned primes[8] = { 2, 3, 5, 7, 11, 13, 17, 19 };
1694 if (!BN_set_word(p, primes[i]))
1697 if (!BN_set_word(a, 32))
1699 if (!BN_set_word(r, 2 * i + 1))
1702 if (!BN_generate_prime_ex(p, 256, 0, a, r, &cb))
1706 p->neg = rand_neg();
1708 for (j = 0; j < num2; j++) {
1710 * construct 'a' such that it is a square modulo p, but in
1711 * general not a proper square and not reduced modulo p
1713 if (!BN_bntest_rand(r, 256, 0, 3))
1715 if (!BN_nnmod(r, r, p, ctx))
1717 if (!BN_mod_sqr(r, r, p, ctx))
1719 if (!BN_bntest_rand(a, 256, 0, 3))
1721 if (!BN_nnmod(a, a, p, ctx))
1723 if (!BN_mod_sqr(a, a, p, ctx))
1725 if (!BN_mul(a, a, r, ctx))
1728 if (!BN_sub(a, a, p))
1731 if (!BN_mod_sqrt(r, a, p, ctx))
1733 if (!BN_mod_sqr(r, r, p, ctx))
1736 if (!BN_nnmod(a, a, p, ctx))
1739 if (BN_cmp(a, r) != 0) {
1740 fprintf(stderr, "BN_mod_sqrt failed: a = ");
1741 BN_print_fp(stderr, a);
1742 fprintf(stderr, ", r = ");
1743 BN_print_fp(stderr, r);
1744 fprintf(stderr, ", p = ");
1745 BN_print_fp(stderr, p);
1746 fprintf(stderr, "\n");
1765 int test_small_prime(BIO *bp, BN_CTX *ctx)
1767 static const int bits = 10;
1772 if (!BN_generate_prime_ex(r, bits, 0, NULL, NULL, NULL))
1774 if (BN_num_bits(r) != bits) {
1775 BIO_printf(bp, "Expected %d bit prime, got %d bit number\n", bits,
1787 #ifndef OPENSSL_SYS_WIN32
1788 int test_probable_prime_coprime(BIO *bp, BN_CTX *ctx)
1792 BN_ULONG primes[5] = { 2, 3, 5, 7, 11 };
1796 for (i = 0; i < 1000; i++) {
1797 if (!bn_probable_prime_dh_coprime(r, 1024, ctx))
1800 for (j = 0; j < 5; j++) {
1801 if (BN_mod_word(r, primes[j]) == 0) {
1802 BIO_printf(bp, "Number generated is not coprime to "
1803 BN_DEC_FMT1 ":\n", primes[j]);
1804 BN_print_fp(stdout, r);
1805 BIO_printf(bp, "\n");
1818 int test_lshift(BIO *bp, BN_CTX *ctx, BIGNUM *a_)
1820 BIGNUM *a, *b, *c, *d;
1832 BN_bntest_rand(a, 200, 0, 0);
1833 a->neg = rand_neg();
1835 for (i = 0; i < num0; i++) {
1836 BN_lshift(b, a, i + 1);
1841 BIO_puts(bp, " * ");
1843 BIO_puts(bp, " - ");
1848 BN_mul(d, a, c, ctx);
1850 if (!BN_is_zero(d)) {
1851 fprintf(stderr, "Left shift test failed!\n");
1852 fprintf(stderr, "a=");
1853 BN_print_fp(stderr, a);
1854 fprintf(stderr, "\nb=");
1855 BN_print_fp(stderr, b);
1856 fprintf(stderr, "\nc=");
1857 BN_print_fp(stderr, c);
1858 fprintf(stderr, "\nd=");
1859 BN_print_fp(stderr, d);
1860 fprintf(stderr, "\n");
1871 int test_lshift1(BIO *bp)
1880 BN_bntest_rand(a, 200, 0, 0);
1881 a->neg = rand_neg();
1882 for (i = 0; i < num0; i++) {
1887 BIO_puts(bp, " * 2");
1888 BIO_puts(bp, " - ");
1895 if (!BN_is_zero(a)) {
1896 fprintf(stderr, "Left shift one test failed!\n");
1908 int test_rshift(BIO *bp, BN_CTX *ctx)
1910 BIGNUM *a, *b, *c, *d, *e;
1920 BN_bntest_rand(a, 200, 0, 0);
1921 a->neg = rand_neg();
1922 for (i = 0; i < num0; i++) {
1923 BN_rshift(b, a, i + 1);
1928 BIO_puts(bp, " / ");
1930 BIO_puts(bp, " - ");
1935 BN_div(d, e, a, c, ctx);
1937 if (!BN_is_zero(d)) {
1938 fprintf(stderr, "Right shift test failed!\n");
1950 int test_rshift1(BIO *bp)
1959 BN_bntest_rand(a, 200, 0, 0);
1960 a->neg = rand_neg();
1961 for (i = 0; i < num0; i++) {
1966 BIO_puts(bp, " / 2");
1967 BIO_puts(bp, " - ");
1974 if (!BN_is_zero(c) && !BN_abs_is_word(c, 1)) {
1975 fprintf(stderr, "Right shift one test failed!\n");
1988 static unsigned int neg = 0;
1989 static int sign[8] = { 0, 0, 0, 1, 1, 0, 1, 1 };
1991 return (sign[(neg++) % 8]);