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.
73 * Until the key-gen callbacks are modified to use newer prototypes, we allow
74 * deprecated functions for openssl-internal code
76 #ifdef OPENSSL_NO_DEPRECATED
77 # undef OPENSSL_NO_DEPRECATED
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>
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 */
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);
126 static int results = 0;
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";
132 static const char rnd_seed[] =
133 "string to make the random number generator think it has entropy";
135 static void message(BIO *out, char *m)
137 fprintf(stderr, "test %s\n", m);
138 BIO_puts(out, "print \"test ");
140 BIO_puts(out, "\\n\"\n");
143 int main(int argc, char *argv[])
147 char *outfile = NULL;
151 RAND_seed(rnd_seed, sizeof rnd_seed); /* or BN_generate_prime may fail */
156 if (strcmp(*argv, "-results") == 0)
158 else if (strcmp(*argv, "-out") == 0) {
171 out = BIO_new(BIO_s_file());
174 if (outfile == NULL) {
175 BIO_set_fp(out, stdout, BIO_NOCLOSE);
177 if (!BIO_write_filename(out, outfile)) {
184 BIO_puts(out, "obase=16\nibase=16\n");
186 message(out, "BN_add");
189 (void)BIO_flush(out);
191 message(out, "BN_sub");
194 (void)BIO_flush(out);
196 message(out, "BN_lshift1");
197 if (!test_lshift1(out))
199 (void)BIO_flush(out);
201 message(out, "BN_lshift (fixed)");
202 if (!test_lshift(out, ctx, BN_bin2bn(lst, sizeof(lst) - 1, NULL)))
204 (void)BIO_flush(out);
206 message(out, "BN_lshift");
207 if (!test_lshift(out, ctx, NULL))
209 (void)BIO_flush(out);
211 message(out, "BN_rshift1");
212 if (!test_rshift1(out))
214 (void)BIO_flush(out);
216 message(out, "BN_rshift");
217 if (!test_rshift(out, ctx))
219 (void)BIO_flush(out);
221 message(out, "BN_sqr");
222 if (!test_sqr(out, ctx))
224 (void)BIO_flush(out);
226 message(out, "BN_mul");
229 (void)BIO_flush(out);
231 message(out, "BN_div");
232 if (!test_div(out, ctx))
234 (void)BIO_flush(out);
236 message(out, "BN_div_word");
237 if (!test_div_word(out))
239 (void)BIO_flush(out);
241 message(out, "BN_div_recp");
242 if (!test_div_recp(out, ctx))
244 (void)BIO_flush(out);
246 message(out, "BN_mod");
247 if (!test_mod(out, ctx))
249 (void)BIO_flush(out);
251 message(out, "BN_mod_mul");
252 if (!test_mod_mul(out, ctx))
254 (void)BIO_flush(out);
256 message(out, "BN_mont");
257 if (!test_mont(out, ctx))
259 (void)BIO_flush(out);
261 message(out, "BN_mod_exp");
262 if (!test_mod_exp(out, ctx))
264 (void)BIO_flush(out);
266 message(out, "BN_mod_exp_mont_consttime");
267 if (!test_mod_exp_mont_consttime(out, ctx))
269 if (!test_mod_exp_mont5(out, ctx))
271 (void)BIO_flush(out);
273 message(out, "BN_exp");
274 if (!test_exp(out, ctx))
276 (void)BIO_flush(out);
278 message(out, "BN_kronecker");
279 if (!test_kron(out, ctx))
281 (void)BIO_flush(out);
283 message(out, "BN_mod_sqrt");
284 if (!test_sqrt(out, ctx))
286 (void)BIO_flush(out);
287 #ifndef OPENSSL_NO_EC2M
288 message(out, "BN_GF2m_add");
289 if (!test_gf2m_add(out))
291 (void)BIO_flush(out);
293 message(out, "BN_GF2m_mod");
294 if (!test_gf2m_mod(out))
296 (void)BIO_flush(out);
298 message(out, "BN_GF2m_mod_mul");
299 if (!test_gf2m_mod_mul(out, ctx))
301 (void)BIO_flush(out);
303 message(out, "BN_GF2m_mod_sqr");
304 if (!test_gf2m_mod_sqr(out, ctx))
306 (void)BIO_flush(out);
308 message(out, "BN_GF2m_mod_inv");
309 if (!test_gf2m_mod_inv(out, ctx))
311 (void)BIO_flush(out);
313 message(out, "BN_GF2m_mod_div");
314 if (!test_gf2m_mod_div(out, ctx))
316 (void)BIO_flush(out);
318 message(out, "BN_GF2m_mod_exp");
319 if (!test_gf2m_mod_exp(out, ctx))
321 (void)BIO_flush(out);
323 message(out, "BN_GF2m_mod_sqrt");
324 if (!test_gf2m_mod_sqrt(out, ctx))
326 (void)BIO_flush(out);
328 message(out, "BN_GF2m_mod_solve_quad");
329 if (!test_gf2m_mod_solve_quad(out, ctx))
331 (void)BIO_flush(out);
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);
348 int test_add(BIO *bp)
357 BN_bntest_rand(&a, 512, 0, 0);
358 for (i = 0; i < num0; i++) {
359 BN_bntest_rand(&b, 450 + i, 0, 0);
377 if (!BN_is_zero(&c)) {
378 fprintf(stderr, "Add test failed!\n");
388 int test_sub(BIO *bp)
397 for (i = 0; i < num0 + num1; i++) {
399 BN_bntest_rand(&a, 512, 0, 0);
401 if (BN_set_bit(&a, i) == 0)
405 BN_bntest_rand(&b, 400 + i - num1, 0, 0);
422 if (!BN_is_zero(&c)) {
423 fprintf(stderr, "Subtract test failed!\n");
433 int test_div(BIO *bp, BN_CTX *ctx)
435 BIGNUM a, b, c, d, e;
447 if (BN_div(&d, &c, &a, &b, ctx)) {
448 fprintf(stderr, "Division by zero succeeded!\n");
452 for (i = 0; i < num0 + num1; i++) {
454 BN_bntest_rand(&a, 400, 0, 0);
456 BN_lshift(&a, &a, i);
459 BN_bntest_rand(&b, 50 + 3 * (i - num1), 0, 0);
462 BN_div(&d, &c, &a, &b, ctx);
482 BN_mul(&e, &d, &b, ctx);
485 if (!BN_is_zero(&d)) {
486 fprintf(stderr, "Division test failed!\n");
498 static void print_word(BIO *bp, BN_ULONG w)
500 #ifdef SIXTY_FOUR_BIT
501 if (sizeof(w) > sizeof(unsigned long)) {
502 unsigned long h = (unsigned long)(w >> 32), l = (unsigned long)(w);
505 BIO_printf(bp, "%lX%08lX", h, l);
507 BIO_printf(bp, "%lX", l);
511 BIO_printf(bp, BN_HEX_FMT1, w);
514 int test_div_word(BIO *bp)
523 for (i = 0; i < num0; i++) {
525 BN_bntest_rand(&a, 512, -1, 0);
526 BN_bntest_rand(&b, BN_BITS2, -1, 0);
527 } while (BN_is_zero(&b));
531 r = BN_div_word(&b, s);
555 if (!BN_is_zero(&b)) {
556 fprintf(stderr, "Division (word) test failed!\n");
565 int test_div_recp(BIO *bp, BN_CTX *ctx)
567 BIGNUM a, b, c, d, e;
571 BN_RECP_CTX_init(&recp);
578 for (i = 0; i < num0 + num1; i++) {
580 BN_bntest_rand(&a, 400, 0, 0);
582 BN_lshift(&a, &a, i);
585 BN_bntest_rand(&b, 50 + 3 * (i - num1), 0, 0);
588 BN_RECP_CTX_set(&recp, &b, ctx);
589 BN_div_recp(&d, &c, &a, &recp, ctx);
609 BN_mul(&e, &d, &b, ctx);
612 if (!BN_is_zero(&d)) {
613 fprintf(stderr, "Reciprocal division test failed!\n");
614 fprintf(stderr, "a=");
615 BN_print_fp(stderr, &a);
616 fprintf(stderr, "\nb=");
617 BN_print_fp(stderr, &b);
618 fprintf(stderr, "\n");
627 BN_RECP_CTX_free(&recp);
631 int test_mul(BIO *bp)
633 BIGNUM a, b, c, d, e;
647 for (i = 0; i < num0 + num1; i++) {
649 BN_bntest_rand(&a, 100, 0, 0);
650 BN_bntest_rand(&b, 100, 0, 0);
652 BN_bntest_rand(&b, i - num1, 0, 0);
655 BN_mul(&c, &a, &b, ctx);
666 BN_div(&d, &e, &c, &a, ctx);
668 if (!BN_is_zero(&d) || !BN_is_zero(&e)) {
669 fprintf(stderr, "Multiplication test failed!\n");
682 int test_sqr(BIO *bp, BN_CTX *ctx)
684 BIGNUM *a, *c, *d, *e;
691 if (a == NULL || c == NULL || d == NULL || e == NULL) {
695 for (i = 0; i < num0; i++) {
696 BN_bntest_rand(a, 40 + i * 10, 0, 0);
709 BN_div(d, e, c, a, ctx);
711 if (!BN_is_zero(d) || !BN_is_zero(e)) {
712 fprintf(stderr, "Square test failed!\n");
717 /* Regression test for a BN_sqr overflow bug. */
719 "80000000000000008000000000000001"
720 "FFFFFFFFFFFFFFFE0000000000000000");
732 BN_mul(d, a, a, ctx);
734 fprintf(stderr, "Square test failed: BN_sqr and BN_mul produce "
735 "different results!\n");
739 /* Regression test for a BN_sqr overflow bug. */
741 "80000000000000000000000080000001"
742 "FFFFFFFE000000000000000000000000");
754 BN_mul(d, a, a, ctx);
756 fprintf(stderr, "Square test failed: BN_sqr and BN_mul produce "
757 "different results!\n");
773 int test_mont(BIO *bp, BN_CTX *ctx)
775 BIGNUM a, b, c, d, A, B;
788 mont = BN_MONT_CTX_new();
793 if (BN_MONT_CTX_set(mont, &n, ctx)) {
794 fprintf(stderr, "BN_MONT_CTX_set succeeded for zero modulus!\n");
799 if (BN_MONT_CTX_set(mont, &n, ctx)) {
800 fprintf(stderr, "BN_MONT_CTX_set succeeded for even modulus!\n");
804 BN_bntest_rand(&a, 100, 0, 0);
805 BN_bntest_rand(&b, 100, 0, 0);
806 for (i = 0; i < num2; i++) {
807 int bits = (200 * (i + 1)) / num2;
811 BN_bntest_rand(&n, bits, 0, 1);
812 BN_MONT_CTX_set(mont, &n, ctx);
814 BN_nnmod(&a, &a, &n, ctx);
815 BN_nnmod(&b, &b, &n, ctx);
817 BN_to_montgomery(&A, &a, mont, ctx);
818 BN_to_montgomery(&B, &b, mont, ctx);
820 BN_mod_mul_montgomery(&c, &A, &B, mont, ctx);
821 BN_from_montgomery(&A, &c, mont, ctx);
825 fprintf(stderr, "%d * %d %% %d\n",
827 BN_num_bits(&b), BN_num_bits(mont->N));
833 BN_print(bp, &(mont->N));
839 BN_mod_mul(&d, &a, &b, &n, ctx);
841 if (!BN_is_zero(&d)) {
842 fprintf(stderr, "Montgomery multiplication test failed!\n");
846 BN_MONT_CTX_free(mont);
857 int test_mod(BIO *bp, BN_CTX *ctx)
859 BIGNUM *a, *b, *c, *d, *e;
868 BN_bntest_rand(a, 1024, 0, 0);
869 for (i = 0; i < num0; i++) {
870 BN_bntest_rand(b, 450 + i * 10, 0, 0);
873 BN_mod(c, a, b, ctx);
884 BN_div(d, e, a, b, ctx);
886 if (!BN_is_zero(e)) {
887 fprintf(stderr, "Modulo test failed!\n");
899 int test_mod_mul(BIO *bp, BN_CTX *ctx)
901 BIGNUM *a, *b, *c, *d, *e;
913 if (BN_mod_mul(e, a, b, c, ctx)) {
914 fprintf(stderr, "BN_mod_mul with zero modulus succeeded!\n");
918 for (j = 0; j < 3; j++) {
919 BN_bntest_rand(c, 1024, 0, 0);
920 for (i = 0; i < num0; i++) {
921 BN_bntest_rand(a, 475 + i * 10, 0, 0);
922 BN_bntest_rand(b, 425 + i * 11, 0, 0);
925 if (!BN_mod_mul(e, a, b, c, ctx)) {
928 while ((l = ERR_get_error()))
929 fprintf(stderr, "ERROR:%s\n", ERR_error_string(l, NULL));
939 if ((a->neg ^ b->neg) && !BN_is_zero(e)) {
941 * If (a*b) % c is negative, c must be added in order
942 * to obtain the normalized remainder (new with
943 * OpenSSL 0.9.7, previous versions of BN_mod_mul
944 * could generate negative results)
954 BN_mul(d, a, b, ctx);
956 BN_div(a, b, d, c, ctx);
957 if (!BN_is_zero(b)) {
958 fprintf(stderr, "Modulo multiply test failed!\n");
959 ERR_print_errors_fp(stderr);
972 int test_mod_exp(BIO *bp, BN_CTX *ctx)
974 BIGNUM *a, *b, *c, *d, *e;
986 if (BN_mod_exp(d, a, b, c, ctx)) {
987 fprintf(stderr, "BN_mod_exp with zero modulus succeeded!\n");
991 BN_bntest_rand(c, 30, 0, 1); /* must be odd for montgomery */
992 for (i = 0; i < num2; i++) {
993 BN_bntest_rand(a, 20 + i * 5, 0, 0);
994 BN_bntest_rand(b, 2 + i, 0, 0);
996 if (!BN_mod_exp(d, a, b, c, ctx))
1002 BIO_puts(bp, " ^ ");
1004 BIO_puts(bp, " % ");
1006 BIO_puts(bp, " - ");
1011 BN_exp(e, a, b, ctx);
1013 BN_div(a, b, e, c, ctx);
1014 if (!BN_is_zero(b)) {
1015 fprintf(stderr, "Modulo exponentiation test failed!\n");
1027 int test_mod_exp_mont_consttime(BIO *bp, BN_CTX *ctx)
1029 BIGNUM *a, *b, *c, *d, *e;
1041 if (BN_mod_exp_mont_consttime(d, a, b, c, ctx, NULL)) {
1042 fprintf(stderr, "BN_mod_exp_mont_consttime with zero modulus "
1048 if (BN_mod_exp_mont_consttime(d, a, b, c, ctx, NULL)) {
1049 fprintf(stderr, "BN_mod_exp_mont_consttime with even modulus "
1054 BN_bntest_rand(c, 30, 0, 1); /* must be odd for montgomery */
1055 for (i = 0; i < num2; i++) {
1056 BN_bntest_rand(a, 20 + i * 5, 0, 0);
1057 BN_bntest_rand(b, 2 + i, 0, 0);
1059 if (!BN_mod_exp_mont_consttime(d, a, b, c, ctx, NULL))
1065 BIO_puts(bp, " ^ ");
1067 BIO_puts(bp, " % ");
1069 BIO_puts(bp, " - ");
1074 BN_exp(e, a, b, ctx);
1076 BN_div(a, b, e, c, ctx);
1077 if (!BN_is_zero(b)) {
1078 fprintf(stderr, "Modulo exponentiation test failed!\n");
1091 * Test constant-time modular exponentiation with 1024-bit inputs, which on
1092 * x86_64 cause a different code branch to be taken.
1094 int test_mod_exp_mont5(BIO *bp, BN_CTX *ctx)
1096 BIGNUM *a, *p, *m, *d, *e;
1104 mont = BN_MONT_CTX_new();
1106 BN_bntest_rand(m, 1024, 0, 1); /* must be odd for montgomery */
1108 BN_bntest_rand(a, 1024, 0, 0);
1110 if (!BN_mod_exp_mont_consttime(d, a, p, m, ctx, NULL))
1112 if (!BN_is_one(d)) {
1113 fprintf(stderr, "Modular exponentiation test failed!\n");
1117 BN_bntest_rand(p, 1024, 0, 0);
1119 if (!BN_mod_exp_mont_consttime(d, a, p, m, ctx, NULL))
1121 if (!BN_is_zero(d)) {
1122 fprintf(stderr, "Modular exponentiation test failed!\n");
1126 * Craft an input whose Montgomery representation is 1, i.e., shorter
1127 * than the modulus m, in order to test the const time precomputation
1128 * scattering/gathering.
1131 BN_MONT_CTX_set(mont, m, ctx);
1132 if (!BN_from_montgomery(e, a, mont, ctx))
1134 if (!BN_mod_exp_mont_consttime(d, e, p, m, ctx, NULL))
1136 if (!BN_mod_exp_simple(a, e, p, m, ctx))
1138 if (BN_cmp(a, d) != 0) {
1139 fprintf(stderr, "Modular exponentiation test failed!\n");
1142 /* Finally, some regular test vectors. */
1143 BN_bntest_rand(e, 1024, 0, 0);
1144 if (!BN_mod_exp_mont_consttime(d, e, p, m, ctx, NULL))
1146 if (!BN_mod_exp_simple(a, e, p, m, ctx))
1148 if (BN_cmp(a, d) != 0) {
1149 fprintf(stderr, "Modular exponentiation test failed!\n");
1152 BN_MONT_CTX_free(mont);
1161 int test_exp(BIO *bp, BN_CTX *ctx)
1163 BIGNUM *a, *b, *d, *e, *one;
1173 for (i = 0; i < num2; i++) {
1174 BN_bntest_rand(a, 20 + i * 5, 0, 0);
1175 BN_bntest_rand(b, 2 + i, 0, 0);
1177 if (BN_exp(d, a, b, ctx) <= 0)
1183 BIO_puts(bp, " ^ ");
1185 BIO_puts(bp, " - ");
1191 for (; !BN_is_zero(b); BN_sub(b, b, one))
1192 BN_mul(e, e, a, ctx);
1194 if (!BN_is_zero(e)) {
1195 fprintf(stderr, "Exponentiation test failed!\n");
1207 #ifndef OPENSSL_NO_EC2M
1208 int test_gf2m_add(BIO *bp)
1217 for (i = 0; i < num0; i++) {
1218 BN_rand(&a, 512, 0, 0);
1219 BN_copy(&b, BN_value_one());
1222 BN_GF2m_add(&c, &a, &b);
1223 # if 0 /* make test uses ouput in bc but bc can't
1224 * handle GF(2^m) arithmetic */
1228 BIO_puts(bp, " ^ ");
1230 BIO_puts(bp, " = ");
1236 /* Test that two added values have the correct parity. */
1237 if ((BN_is_odd(&a) && BN_is_odd(&c))
1238 || (!BN_is_odd(&a) && !BN_is_odd(&c))) {
1239 fprintf(stderr, "GF(2^m) addition test (a) failed!\n");
1242 BN_GF2m_add(&c, &c, &c);
1243 /* Test that c + c = 0. */
1244 if (!BN_is_zero(&c)) {
1245 fprintf(stderr, "GF(2^m) addition test (b) failed!\n");
1257 int test_gf2m_mod(BIO *bp)
1259 BIGNUM *a, *b[2], *c, *d, *e;
1261 int p0[] = { 163, 7, 6, 3, 0, -1 };
1262 int p1[] = { 193, 15, 0, -1 };
1271 BN_GF2m_arr2poly(p0, b[0]);
1272 BN_GF2m_arr2poly(p1, b[1]);
1274 for (i = 0; i < num0; i++) {
1275 BN_bntest_rand(a, 1024, 0, 0);
1276 for (j = 0; j < 2; j++) {
1277 BN_GF2m_mod(c, a, b[j]);
1278 # if 0 /* make test uses ouput in bc but bc can't
1279 * handle GF(2^m) arithmetic */
1283 BIO_puts(bp, " % ");
1285 BIO_puts(bp, " - ");
1291 BN_GF2m_add(d, a, c);
1292 BN_GF2m_mod(e, d, b[j]);
1293 /* Test that a + (a mod p) mod p == 0. */
1294 if (!BN_is_zero(e)) {
1295 fprintf(stderr, "GF(2^m) modulo test failed!\n");
1311 int test_gf2m_mod_mul(BIO *bp, BN_CTX *ctx)
1313 BIGNUM *a, *b[2], *c, *d, *e, *f, *g, *h;
1315 int p0[] = { 163, 7, 6, 3, 0, -1 };
1316 int p1[] = { 193, 15, 0, -1 };
1328 BN_GF2m_arr2poly(p0, b[0]);
1329 BN_GF2m_arr2poly(p1, b[1]);
1331 for (i = 0; i < num0; i++) {
1332 BN_bntest_rand(a, 1024, 0, 0);
1333 BN_bntest_rand(c, 1024, 0, 0);
1334 BN_bntest_rand(d, 1024, 0, 0);
1335 for (j = 0; j < 2; j++) {
1336 BN_GF2m_mod_mul(e, a, c, b[j], ctx);
1337 # if 0 /* make test uses ouput in bc but bc can't
1338 * handle GF(2^m) arithmetic */
1342 BIO_puts(bp, " * ");
1344 BIO_puts(bp, " % ");
1346 BIO_puts(bp, " - ");
1352 BN_GF2m_add(f, a, d);
1353 BN_GF2m_mod_mul(g, f, c, b[j], ctx);
1354 BN_GF2m_mod_mul(h, d, c, b[j], ctx);
1355 BN_GF2m_add(f, e, g);
1356 BN_GF2m_add(f, f, h);
1357 /* Test that (a+d)*c = a*c + d*c. */
1358 if (!BN_is_zero(f)) {
1360 "GF(2^m) modular multiplication test failed!\n");
1379 int test_gf2m_mod_sqr(BIO *bp, BN_CTX *ctx)
1381 BIGNUM *a, *b[2], *c, *d;
1383 int p0[] = { 163, 7, 6, 3, 0, -1 };
1384 int p1[] = { 193, 15, 0, -1 };
1392 BN_GF2m_arr2poly(p0, b[0]);
1393 BN_GF2m_arr2poly(p1, b[1]);
1395 for (i = 0; i < num0; i++) {
1396 BN_bntest_rand(a, 1024, 0, 0);
1397 for (j = 0; j < 2; j++) {
1398 BN_GF2m_mod_sqr(c, a, b[j], ctx);
1400 BN_GF2m_mod_mul(d, a, d, b[j], ctx);
1401 # if 0 /* make test uses ouput in bc but bc can't
1402 * handle GF(2^m) arithmetic */
1406 BIO_puts(bp, " ^ 2 % ");
1408 BIO_puts(bp, " = ");
1410 BIO_puts(bp, "; a * a = ");
1416 BN_GF2m_add(d, c, d);
1417 /* Test that a*a = a^2. */
1418 if (!BN_is_zero(d)) {
1419 fprintf(stderr, "GF(2^m) modular squaring test failed!\n");
1434 int test_gf2m_mod_inv(BIO *bp, BN_CTX *ctx)
1436 BIGNUM *a, *b[2], *c, *d;
1438 int p0[] = { 163, 7, 6, 3, 0, -1 };
1439 int p1[] = { 193, 15, 0, -1 };
1447 BN_GF2m_arr2poly(p0, b[0]);
1448 BN_GF2m_arr2poly(p1, b[1]);
1450 for (i = 0; i < num0; i++) {
1451 BN_bntest_rand(a, 512, 0, 0);
1452 for (j = 0; j < 2; j++) {
1453 BN_GF2m_mod_inv(c, a, b[j], ctx);
1454 BN_GF2m_mod_mul(d, a, c, b[j], ctx);
1455 # if 0 /* make test uses ouput in bc but bc can't
1456 * handle GF(2^m) arithmetic */
1460 BIO_puts(bp, " * ");
1462 BIO_puts(bp, " - 1 % ");
1468 /* Test that ((1/a)*a) = 1. */
1469 if (!BN_is_one(d)) {
1470 fprintf(stderr, "GF(2^m) modular inversion test failed!\n");
1485 int test_gf2m_mod_div(BIO *bp, BN_CTX *ctx)
1487 BIGNUM *a, *b[2], *c, *d, *e, *f;
1489 int p0[] = { 163, 7, 6, 3, 0, -1 };
1490 int p1[] = { 193, 15, 0, -1 };
1500 BN_GF2m_arr2poly(p0, b[0]);
1501 BN_GF2m_arr2poly(p1, b[1]);
1503 for (i = 0; i < num0; i++) {
1504 BN_bntest_rand(a, 512, 0, 0);
1505 BN_bntest_rand(c, 512, 0, 0);
1506 for (j = 0; j < 2; j++) {
1507 BN_GF2m_mod_div(d, a, c, b[j], ctx);
1508 BN_GF2m_mod_mul(e, d, c, b[j], ctx);
1509 BN_GF2m_mod_div(f, a, e, b[j], ctx);
1510 # if 0 /* make test uses ouput in bc but bc can't
1511 * handle GF(2^m) arithmetic */
1515 BIO_puts(bp, " = ");
1517 BIO_puts(bp, " * ");
1519 BIO_puts(bp, " % ");
1525 /* Test that ((a/c)*c)/a = 1. */
1526 if (!BN_is_one(f)) {
1527 fprintf(stderr, "GF(2^m) modular division test failed!\n");
1544 int test_gf2m_mod_exp(BIO *bp, BN_CTX *ctx)
1546 BIGNUM *a, *b[2], *c, *d, *e, *f;
1548 int p0[] = { 163, 7, 6, 3, 0, -1 };
1549 int p1[] = { 193, 15, 0, -1 };
1559 BN_GF2m_arr2poly(p0, b[0]);
1560 BN_GF2m_arr2poly(p1, b[1]);
1562 for (i = 0; i < num0; i++) {
1563 BN_bntest_rand(a, 512, 0, 0);
1564 BN_bntest_rand(c, 512, 0, 0);
1565 BN_bntest_rand(d, 512, 0, 0);
1566 for (j = 0; j < 2; j++) {
1567 BN_GF2m_mod_exp(e, a, c, b[j], ctx);
1568 BN_GF2m_mod_exp(f, a, d, b[j], ctx);
1569 BN_GF2m_mod_mul(e, e, f, b[j], ctx);
1571 BN_GF2m_mod_exp(f, a, f, b[j], ctx);
1572 # if 0 /* make test uses ouput in bc but bc can't
1573 * handle GF(2^m) arithmetic */
1577 BIO_puts(bp, " ^ (");
1579 BIO_puts(bp, " + ");
1581 BIO_puts(bp, ") = ");
1583 BIO_puts(bp, "; - ");
1585 BIO_puts(bp, " % ");
1591 BN_GF2m_add(f, e, f);
1592 /* Test that a^(c+d)=a^c*a^d. */
1593 if (!BN_is_zero(f)) {
1595 "GF(2^m) modular exponentiation test failed!\n");
1612 int test_gf2m_mod_sqrt(BIO *bp, BN_CTX *ctx)
1614 BIGNUM *a, *b[2], *c, *d, *e, *f;
1616 int p0[] = { 163, 7, 6, 3, 0, -1 };
1617 int p1[] = { 193, 15, 0, -1 };
1627 BN_GF2m_arr2poly(p0, b[0]);
1628 BN_GF2m_arr2poly(p1, b[1]);
1630 for (i = 0; i < num0; i++) {
1631 BN_bntest_rand(a, 512, 0, 0);
1632 for (j = 0; j < 2; j++) {
1633 BN_GF2m_mod(c, a, b[j]);
1634 BN_GF2m_mod_sqrt(d, a, b[j], ctx);
1635 BN_GF2m_mod_sqr(e, d, b[j], ctx);
1636 # if 0 /* make test uses ouput in bc but bc can't
1637 * handle GF(2^m) arithmetic */
1641 BIO_puts(bp, " ^ 2 - ");
1647 BN_GF2m_add(f, c, e);
1648 /* Test that d^2 = a, where d = sqrt(a). */
1649 if (!BN_is_zero(f)) {
1650 fprintf(stderr, "GF(2^m) modular square root test failed!\n");
1667 int test_gf2m_mod_solve_quad(BIO *bp, BN_CTX *ctx)
1669 BIGNUM *a, *b[2], *c, *d, *e;
1670 int i, j, s = 0, t, ret = 0;
1671 int p0[] = { 163, 7, 6, 3, 0, -1 };
1672 int p1[] = { 193, 15, 0, -1 };
1681 BN_GF2m_arr2poly(p0, b[0]);
1682 BN_GF2m_arr2poly(p1, b[1]);
1684 for (i = 0; i < num0; i++) {
1685 BN_bntest_rand(a, 512, 0, 0);
1686 for (j = 0; j < 2; j++) {
1687 t = BN_GF2m_mod_solve_quad(c, a, b[j], ctx);
1690 BN_GF2m_mod_sqr(d, c, b[j], ctx);
1691 BN_GF2m_add(d, c, d);
1692 BN_GF2m_mod(e, a, b[j]);
1693 # if 0 /* make test uses ouput in bc but bc can't
1694 * handle GF(2^m) arithmetic */
1698 BIO_puts(bp, " is root of z^2 + z = ");
1700 BIO_puts(bp, " % ");
1706 BN_GF2m_add(e, e, d);
1708 * Test that solution of quadratic c satisfies c^2 + c = a.
1710 if (!BN_is_zero(e)) {
1712 "GF(2^m) modular solve quadratic test failed!\n");
1717 # if 0 /* make test uses ouput in bc but bc can't
1718 * handle GF(2^m) arithmetic */
1721 BIO_puts(bp, "There are no roots of z^2 + z = ");
1723 BIO_puts(bp, " % ");
1734 "All %i tests of GF(2^m) modular solve quadratic resulted in no roots;\n",
1737 "this is very unlikely and probably indicates an error.\n");
1751 static int genprime_cb(int p, int n, BN_GENCB *arg)
1768 int test_kron(BIO *bp, BN_CTX *ctx)
1771 BIGNUM *a, *b, *r, *t;
1773 int legendre, kronecker;
1780 if (a == NULL || b == NULL || r == NULL || t == NULL)
1783 BN_GENCB_set(&cb, genprime_cb, NULL);
1786 * We test BN_kronecker(a, b, ctx) just for b odd (Jacobi symbol). In
1787 * this case we know that if b is prime, then BN_kronecker(a, b, ctx) is
1788 * congruent to $a^{(b-1)/2}$, modulo $b$ (Legendre symbol). So we
1789 * generate a random prime b and compare these values for a number of
1790 * random a's. (That is, we run the Solovay-Strassen primality test to
1791 * confirm that b is prime, except that we don't want to test whether b
1792 * is prime but whether BN_kronecker works.)
1795 if (!BN_generate_prime_ex(b, 512, 0, NULL, NULL, &cb))
1797 b->neg = rand_neg();
1800 for (i = 0; i < num0; i++) {
1801 if (!BN_bntest_rand(a, 512, 0, 0))
1803 a->neg = rand_neg();
1805 /* t := (|b|-1)/2 (note that b is odd) */
1809 if (!BN_sub_word(t, 1))
1811 if (!BN_rshift1(t, t))
1813 /* r := a^t mod b */
1816 if (!BN_mod_exp_recp(r, a, t, b, ctx))
1820 if (BN_is_word(r, 1))
1822 else if (BN_is_zero(r))
1825 if (!BN_add_word(r, 1))
1827 if (0 != BN_ucmp(r, b)) {
1828 fprintf(stderr, "Legendre symbol computation failed\n");
1834 kronecker = BN_kronecker(a, b, ctx);
1837 /* we actually need BN_kronecker(a, |b|) */
1838 if (a->neg && b->neg)
1839 kronecker = -kronecker;
1841 if (legendre != kronecker) {
1842 fprintf(stderr, "legendre != kronecker; a = ");
1843 BN_print_fp(stderr, a);
1844 fprintf(stderr, ", b = ");
1845 BN_print_fp(stderr, b);
1846 fprintf(stderr, "\n");
1869 int test_sqrt(BIO *bp, BN_CTX *ctx)
1879 if (a == NULL || p == NULL || r == NULL)
1882 BN_GENCB_set(&cb, genprime_cb, NULL);
1884 for (i = 0; i < 16; i++) {
1886 unsigned primes[8] = { 2, 3, 5, 7, 11, 13, 17, 19 };
1888 if (!BN_set_word(p, primes[i]))
1891 if (!BN_set_word(a, 32))
1893 if (!BN_set_word(r, 2 * i + 1))
1896 if (!BN_generate_prime_ex(p, 256, 0, a, r, &cb))
1900 p->neg = rand_neg();
1902 for (j = 0; j < num2; j++) {
1904 * construct 'a' such that it is a square modulo p, but in
1905 * general not a proper square and not reduced modulo p
1907 if (!BN_bntest_rand(r, 256, 0, 3))
1909 if (!BN_nnmod(r, r, p, ctx))
1911 if (!BN_mod_sqr(r, r, p, ctx))
1913 if (!BN_bntest_rand(a, 256, 0, 3))
1915 if (!BN_nnmod(a, a, p, ctx))
1917 if (!BN_mod_sqr(a, a, p, ctx))
1919 if (!BN_mul(a, a, r, ctx))
1922 if (!BN_sub(a, a, p))
1925 if (!BN_mod_sqrt(r, a, p, ctx))
1927 if (!BN_mod_sqr(r, r, p, ctx))
1930 if (!BN_nnmod(a, a, p, ctx))
1933 if (BN_cmp(a, r) != 0) {
1934 fprintf(stderr, "BN_mod_sqrt failed: a = ");
1935 BN_print_fp(stderr, a);
1936 fprintf(stderr, ", r = ");
1937 BN_print_fp(stderr, r);
1938 fprintf(stderr, ", p = ");
1939 BN_print_fp(stderr, p);
1940 fprintf(stderr, "\n");
1962 int test_lshift(BIO *bp, BN_CTX *ctx, BIGNUM *a_)
1964 BIGNUM *a, *b, *c, *d;
1976 BN_bntest_rand(a, 200, 0, 0);
1977 a->neg = rand_neg();
1979 for (i = 0; i < num0; i++) {
1980 BN_lshift(b, a, i + 1);
1985 BIO_puts(bp, " * ");
1987 BIO_puts(bp, " - ");
1992 BN_mul(d, a, c, ctx);
1994 if (!BN_is_zero(d)) {
1995 fprintf(stderr, "Left shift test failed!\n");
1996 fprintf(stderr, "a=");
1997 BN_print_fp(stderr, a);
1998 fprintf(stderr, "\nb=");
1999 BN_print_fp(stderr, b);
2000 fprintf(stderr, "\nc=");
2001 BN_print_fp(stderr, c);
2002 fprintf(stderr, "\nd=");
2003 BN_print_fp(stderr, d);
2004 fprintf(stderr, "\n");
2015 int test_lshift1(BIO *bp)
2024 BN_bntest_rand(a, 200, 0, 0);
2025 a->neg = rand_neg();
2026 for (i = 0; i < num0; i++) {
2031 BIO_puts(bp, " * 2");
2032 BIO_puts(bp, " - ");
2039 if (!BN_is_zero(a)) {
2040 fprintf(stderr, "Left shift one test failed!\n");
2052 int test_rshift(BIO *bp, BN_CTX *ctx)
2054 BIGNUM *a, *b, *c, *d, *e;
2064 BN_bntest_rand(a, 200, 0, 0);
2065 a->neg = rand_neg();
2066 for (i = 0; i < num0; i++) {
2067 BN_rshift(b, a, i + 1);
2072 BIO_puts(bp, " / ");
2074 BIO_puts(bp, " - ");
2079 BN_div(d, e, a, c, ctx);
2081 if (!BN_is_zero(d)) {
2082 fprintf(stderr, "Right shift test failed!\n");
2094 int test_rshift1(BIO *bp)
2103 BN_bntest_rand(a, 200, 0, 0);
2104 a->neg = rand_neg();
2105 for (i = 0; i < num0; i++) {
2110 BIO_puts(bp, " / 2");
2111 BIO_puts(bp, " - ");
2118 if (!BN_is_zero(c) && !BN_abs_is_word(c, 1)) {
2119 fprintf(stderr, "Right shift one test failed!\n");
2132 static unsigned int neg = 0;
2133 static int sign[8] = { 0, 0, 0, 1, 1, 0, 1, 1 };
2135 return (sign[(neg++) % 8]);