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;
444 for (i = 0; i < num0 + num1; i++) {
446 BN_bntest_rand(&a, 400, 0, 0);
448 BN_lshift(&a, &a, i);
451 BN_bntest_rand(&b, 50 + 3 * (i - num1), 0, 0);
454 BN_div(&d, &c, &a, &b, ctx);
474 BN_mul(&e, &d, &b, ctx);
477 if (!BN_is_zero(&d)) {
478 fprintf(stderr, "Division test failed!\n");
490 static void print_word(BIO *bp, BN_ULONG w)
492 #ifdef SIXTY_FOUR_BIT
493 if (sizeof(w) > sizeof(unsigned long)) {
494 unsigned long h = (unsigned long)(w >> 32), l = (unsigned long)(w);
497 BIO_printf(bp, "%lX%08lX", h, l);
499 BIO_printf(bp, "%lX", l);
503 BIO_printf(bp, BN_HEX_FMT1, w);
506 int test_div_word(BIO *bp)
515 for (i = 0; i < num0; i++) {
517 BN_bntest_rand(&a, 512, -1, 0);
518 BN_bntest_rand(&b, BN_BITS2, -1, 0);
523 r = BN_div_word(&b, s);
547 if (!BN_is_zero(&b)) {
548 fprintf(stderr, "Division (word) test failed!\n");
557 int test_div_recp(BIO *bp, BN_CTX *ctx)
559 BIGNUM a, b, c, d, e;
563 BN_RECP_CTX_init(&recp);
570 for (i = 0; i < num0 + num1; i++) {
572 BN_bntest_rand(&a, 400, 0, 0);
574 BN_lshift(&a, &a, i);
577 BN_bntest_rand(&b, 50 + 3 * (i - num1), 0, 0);
580 BN_RECP_CTX_set(&recp, &b, ctx);
581 BN_div_recp(&d, &c, &a, &recp, ctx);
601 BN_mul(&e, &d, &b, ctx);
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");
619 BN_RECP_CTX_free(&recp);
623 int test_mul(BIO *bp)
625 BIGNUM a, b, c, d, e;
639 for (i = 0; i < num0 + num1; i++) {
641 BN_bntest_rand(&a, 100, 0, 0);
642 BN_bntest_rand(&b, 100, 0, 0);
644 BN_bntest_rand(&b, i - num1, 0, 0);
647 BN_mul(&c, &a, &b, ctx);
658 BN_div(&d, &e, &c, &a, ctx);
660 if (!BN_is_zero(&d) || !BN_is_zero(&e)) {
661 fprintf(stderr, "Multiplication test failed!\n");
674 int test_sqr(BIO *bp, BN_CTX *ctx)
676 BIGNUM *a, *c, *d, *e;
683 if (a == NULL || c == NULL || d == NULL || e == NULL) {
687 for (i = 0; i < num0; i++) {
688 BN_bntest_rand(a, 40 + i * 10, 0, 0);
701 BN_div(d, e, c, a, ctx);
703 if (!BN_is_zero(d) || !BN_is_zero(e)) {
704 fprintf(stderr, "Square test failed!\n");
709 /* Regression test for a BN_sqr overflow bug. */
711 "80000000000000008000000000000001"
712 "FFFFFFFFFFFFFFFE0000000000000000");
724 BN_mul(d, a, a, ctx);
726 fprintf(stderr, "Square test failed: BN_sqr and BN_mul produce "
727 "different results!\n");
731 /* Regression test for a BN_sqr overflow bug. */
733 "80000000000000000000000080000001"
734 "FFFFFFFE000000000000000000000000");
746 BN_mul(d, a, a, ctx);
748 fprintf(stderr, "Square test failed: BN_sqr and BN_mul produce "
749 "different results!\n");
765 int test_mont(BIO *bp, BN_CTX *ctx)
767 BIGNUM a, b, c, d, A, B;
780 mont = BN_MONT_CTX_new();
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;
791 BN_bntest_rand(&n, bits, 0, 1);
792 BN_MONT_CTX_set(mont, &n, ctx);
794 BN_nnmod(&a, &a, &n, ctx);
795 BN_nnmod(&b, &b, &n, ctx);
797 BN_to_montgomery(&A, &a, mont, ctx);
798 BN_to_montgomery(&B, &b, mont, ctx);
800 BN_mod_mul_montgomery(&c, &A, &B, mont, ctx);
801 BN_from_montgomery(&A, &c, mont, ctx);
805 fprintf(stderr, "%d * %d %% %d\n",
807 BN_num_bits(&b), BN_num_bits(mont->N));
813 BN_print(bp, &(mont->N));
819 BN_mod_mul(&d, &a, &b, &n, ctx);
821 if (!BN_is_zero(&d)) {
822 fprintf(stderr, "Montgomery multiplication test failed!\n");
826 BN_MONT_CTX_free(mont);
837 int test_mod(BIO *bp, BN_CTX *ctx)
839 BIGNUM *a, *b, *c, *d, *e;
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);
853 BN_mod(c, a, b, ctx);
864 BN_div(d, e, a, b, ctx);
866 if (!BN_is_zero(e)) {
867 fprintf(stderr, "Modulo test failed!\n");
879 int test_mod_mul(BIO *bp, BN_CTX *ctx)
881 BIGNUM *a, *b, *c, *d, *e;
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);
897 if (!BN_mod_mul(e, a, b, c, ctx)) {
900 while ((l = ERR_get_error()))
901 fprintf(stderr, "ERROR:%s\n", ERR_error_string(l, NULL));
911 if ((a->neg ^ b->neg) && !BN_is_zero(e)) {
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)
926 BN_mul(d, a, b, ctx);
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);
944 int test_mod_exp(BIO *bp, BN_CTX *ctx)
946 BIGNUM *a, *b, *c, *d, *e;
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);
960 if (!BN_mod_exp(d, a, b, c, ctx))
975 BN_exp(e, a, b, ctx);
977 BN_div(a, b, e, c, ctx);
978 if (!BN_is_zero(b)) {
979 fprintf(stderr, "Modulo exponentiation test failed!\n");
991 int test_mod_exp_mont_consttime(BIO *bp, BN_CTX *ctx)
993 BIGNUM *a, *b, *c, *d, *e;
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);
1007 if (!BN_mod_exp_mont_consttime(d, a, b, c, ctx, NULL))
1013 BIO_puts(bp, " ^ ");
1015 BIO_puts(bp, " % ");
1017 BIO_puts(bp, " - ");
1022 BN_exp(e, a, b, ctx);
1024 BN_div(a, b, e, c, ctx);
1025 if (!BN_is_zero(b)) {
1026 fprintf(stderr, "Modulo exponentiation test failed!\n");
1039 * Test constant-time modular exponentiation with 1024-bit inputs, which on
1040 * x86_64 cause a different code branch to be taken.
1042 int test_mod_exp_mont5(BIO *bp, BN_CTX *ctx)
1044 BIGNUM *a, *p, *m, *d, *e;
1054 mont = BN_MONT_CTX_new();
1056 BN_bntest_rand(m, 1024, 0, 1); /* must be odd for montgomery */
1058 BN_bntest_rand(a, 1024, 0, 0);
1060 if (!BN_mod_exp_mont_consttime(d, a, p, m, ctx, NULL))
1062 if (!BN_is_one(d)) {
1063 fprintf(stderr, "Modular exponentiation test failed!\n");
1067 BN_bntest_rand(p, 1024, 0, 0);
1069 if (!BN_mod_exp_mont_consttime(d, a, p, m, ctx, NULL))
1071 if (!BN_is_zero(d)) {
1072 fprintf(stderr, "Modular exponentiation test failed!\n");
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.
1081 BN_MONT_CTX_set(mont, m, ctx);
1082 if (!BN_from_montgomery(e, a, mont, ctx))
1084 if (!BN_mod_exp_mont_consttime(d, e, p, m, ctx, NULL))
1086 if (!BN_mod_exp_simple(a, e, p, m, ctx))
1088 if (BN_cmp(a, d) != 0) {
1089 fprintf(stderr, "Modular exponentiation test failed!\n");
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))
1096 if (!BN_mod_exp_simple(a, e, p, m, ctx))
1098 if (BN_cmp(a, d) != 0) {
1099 fprintf(stderr, "Modular exponentiation test failed!\n");
1110 int test_exp(BIO *bp, BN_CTX *ctx)
1112 BIGNUM *a, *b, *d, *e, *one;
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);
1126 if (BN_exp(d, a, b, ctx) <= 0)
1132 BIO_puts(bp, " ^ ");
1134 BIO_puts(bp, " - ");
1140 for (; !BN_is_zero(b); BN_sub(b, b, one))
1141 BN_mul(e, e, a, ctx);
1143 if (!BN_is_zero(e)) {
1144 fprintf(stderr, "Exponentiation test failed!\n");
1156 #ifndef OPENSSL_NO_EC2M
1157 int test_gf2m_add(BIO *bp)
1166 for (i = 0; i < num0; i++) {
1167 BN_rand(&a, 512, 0, 0);
1168 BN_copy(&b, BN_value_one());
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 */
1177 BIO_puts(bp, " ^ ");
1179 BIO_puts(bp, " = ");
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");
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");
1206 int test_gf2m_mod(BIO *bp)
1208 BIGNUM *a, *b[2], *c, *d, *e;
1210 int p0[] = { 163, 7, 6, 3, 0, -1 };
1211 int p1[] = { 193, 15, 0, -1 };
1220 BN_GF2m_arr2poly(p0, b[0]);
1221 BN_GF2m_arr2poly(p1, b[1]);
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 */
1232 BIO_puts(bp, " % ");
1234 BIO_puts(bp, " - ");
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");
1260 int test_gf2m_mod_mul(BIO *bp, BN_CTX *ctx)
1262 BIGNUM *a, *b[2], *c, *d, *e, *f, *g, *h;
1264 int p0[] = { 163, 7, 6, 3, 0, -1 };
1265 int p1[] = { 193, 15, 0, -1 };
1277 BN_GF2m_arr2poly(p0, b[0]);
1278 BN_GF2m_arr2poly(p1, b[1]);
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 */
1291 BIO_puts(bp, " * ");
1293 BIO_puts(bp, " % ");
1295 BIO_puts(bp, " - ");
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)) {
1309 "GF(2^m) modular multiplication test failed!\n");
1328 int test_gf2m_mod_sqr(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, 1024, 0, 0);
1346 for (j = 0; j < 2; j++) {
1347 BN_GF2m_mod_sqr(c, a, b[j], ctx);
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 */
1355 BIO_puts(bp, " ^ 2 % ");
1357 BIO_puts(bp, " = ");
1359 BIO_puts(bp, "; a * a = ");
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");
1383 int test_gf2m_mod_inv(BIO *bp, BN_CTX *ctx)
1385 BIGNUM *a, *b[2], *c, *d;
1387 int p0[] = { 163, 7, 6, 3, 0, -1 };
1388 int p1[] = { 193, 15, 0, -1 };
1396 BN_GF2m_arr2poly(p0, b[0]);
1397 BN_GF2m_arr2poly(p1, b[1]);
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 */
1409 BIO_puts(bp, " * ");
1411 BIO_puts(bp, " - 1 % ");
1417 /* Test that ((1/a)*a) = 1. */
1418 if (!BN_is_one(d)) {
1419 fprintf(stderr, "GF(2^m) modular inversion test failed!\n");
1434 int test_gf2m_mod_div(BIO *bp, BN_CTX *ctx)
1436 BIGNUM *a, *b[2], *c, *d, *e, *f;
1438 int p0[] = { 163, 7, 6, 3, 0, -1 };
1439 int p1[] = { 193, 15, 0, -1 };
1449 BN_GF2m_arr2poly(p0, b[0]);
1450 BN_GF2m_arr2poly(p1, b[1]);
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 */
1464 BIO_puts(bp, " = ");
1466 BIO_puts(bp, " * ");
1468 BIO_puts(bp, " % ");
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");
1493 int test_gf2m_mod_exp(BIO *bp, BN_CTX *ctx)
1495 BIGNUM *a, *b[2], *c, *d, *e, *f;
1497 int p0[] = { 163, 7, 6, 3, 0, -1 };
1498 int p1[] = { 193, 15, 0, -1 };
1508 BN_GF2m_arr2poly(p0, b[0]);
1509 BN_GF2m_arr2poly(p1, b[1]);
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);
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 */
1526 BIO_puts(bp, " ^ (");
1528 BIO_puts(bp, " + ");
1530 BIO_puts(bp, ") = ");
1532 BIO_puts(bp, "; - ");
1534 BIO_puts(bp, " % ");
1540 BN_GF2m_add(f, e, f);
1541 /* Test that a^(c+d)=a^c*a^d. */
1542 if (!BN_is_zero(f)) {
1544 "GF(2^m) modular exponentiation test failed!\n");
1561 int test_gf2m_mod_sqrt(BIO *bp, BN_CTX *ctx)
1563 BIGNUM *a, *b[2], *c, *d, *e, *f;
1565 int p0[] = { 163, 7, 6, 3, 0, -1 };
1566 int p1[] = { 193, 15, 0, -1 };
1576 BN_GF2m_arr2poly(p0, b[0]);
1577 BN_GF2m_arr2poly(p1, b[1]);
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 */
1590 BIO_puts(bp, " ^ 2 - ");
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");
1616 int test_gf2m_mod_solve_quad(BIO *bp, BN_CTX *ctx)
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 };
1630 BN_GF2m_arr2poly(p0, b[0]);
1631 BN_GF2m_arr2poly(p1, b[1]);
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);
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 */
1647 BIO_puts(bp, " is root of z^2 + z = ");
1649 BIO_puts(bp, " % ");
1655 BN_GF2m_add(e, e, d);
1657 * Test that solution of quadratic c satisfies c^2 + c = a.
1659 if (!BN_is_zero(e)) {
1661 "GF(2^m) modular solve quadratic test failed!\n");
1666 # if 0 /* make test uses ouput in bc but bc can't
1667 * handle GF(2^m) arithmetic */
1670 BIO_puts(bp, "There are no roots of z^2 + z = ");
1672 BIO_puts(bp, " % ");
1683 "All %i tests of GF(2^m) modular solve quadratic resulted in no roots;\n",
1686 "this is very unlikely and probably indicates an error.\n");
1700 static int genprime_cb(int p, int n, BN_GENCB *arg)
1717 int test_kron(BIO *bp, BN_CTX *ctx)
1720 BIGNUM *a, *b, *r, *t;
1722 int legendre, kronecker;
1729 if (a == NULL || b == NULL || r == NULL || t == NULL)
1732 BN_GENCB_set(&cb, genprime_cb, NULL);
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.)
1744 if (!BN_generate_prime_ex(b, 512, 0, NULL, NULL, &cb))
1746 b->neg = rand_neg();
1749 for (i = 0; i < num0; i++) {
1750 if (!BN_bntest_rand(a, 512, 0, 0))
1752 a->neg = rand_neg();
1754 /* t := (|b|-1)/2 (note that b is odd) */
1758 if (!BN_sub_word(t, 1))
1760 if (!BN_rshift1(t, t))
1762 /* r := a^t mod b */
1765 if (!BN_mod_exp_recp(r, a, t, b, ctx))
1769 if (BN_is_word(r, 1))
1771 else if (BN_is_zero(r))
1774 if (!BN_add_word(r, 1))
1776 if (0 != BN_ucmp(r, b)) {
1777 fprintf(stderr, "Legendre symbol computation failed\n");
1783 kronecker = BN_kronecker(a, b, ctx);
1786 /* we actually need BN_kronecker(a, |b|) */
1787 if (a->neg && b->neg)
1788 kronecker = -kronecker;
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");
1818 int test_sqrt(BIO *bp, BN_CTX *ctx)
1828 if (a == NULL || p == NULL || r == NULL)
1831 BN_GENCB_set(&cb, genprime_cb, NULL);
1833 for (i = 0; i < 16; i++) {
1835 unsigned primes[8] = { 2, 3, 5, 7, 11, 13, 17, 19 };
1837 if (!BN_set_word(p, primes[i]))
1840 if (!BN_set_word(a, 32))
1842 if (!BN_set_word(r, 2 * i + 1))
1845 if (!BN_generate_prime_ex(p, 256, 0, a, r, &cb))
1849 p->neg = rand_neg();
1851 for (j = 0; j < num2; j++) {
1853 * construct 'a' such that it is a square modulo p, but in
1854 * general not a proper square and not reduced modulo p
1856 if (!BN_bntest_rand(r, 256, 0, 3))
1858 if (!BN_nnmod(r, r, p, ctx))
1860 if (!BN_mod_sqr(r, r, p, ctx))
1862 if (!BN_bntest_rand(a, 256, 0, 3))
1864 if (!BN_nnmod(a, a, p, ctx))
1866 if (!BN_mod_sqr(a, a, p, ctx))
1868 if (!BN_mul(a, a, r, ctx))
1871 if (!BN_sub(a, a, p))
1874 if (!BN_mod_sqrt(r, a, p, ctx))
1876 if (!BN_mod_sqr(r, r, p, ctx))
1879 if (!BN_nnmod(a, a, p, ctx))
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");
1911 int test_lshift(BIO *bp, BN_CTX *ctx, BIGNUM *a_)
1913 BIGNUM *a, *b, *c, *d;
1925 BN_bntest_rand(a, 200, 0, 0);
1926 a->neg = rand_neg();
1928 for (i = 0; i < num0; i++) {
1929 BN_lshift(b, a, i + 1);
1934 BIO_puts(bp, " * ");
1936 BIO_puts(bp, " - ");
1941 BN_mul(d, a, c, ctx);
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");
1964 int test_lshift1(BIO *bp)
1973 BN_bntest_rand(a, 200, 0, 0);
1974 a->neg = rand_neg();
1975 for (i = 0; i < num0; i++) {
1980 BIO_puts(bp, " * 2");
1981 BIO_puts(bp, " - ");
1988 if (!BN_is_zero(a)) {
1989 fprintf(stderr, "Left shift one test failed!\n");
2001 int test_rshift(BIO *bp, BN_CTX *ctx)
2003 BIGNUM *a, *b, *c, *d, *e;
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);
2021 BIO_puts(bp, " / ");
2023 BIO_puts(bp, " - ");
2028 BN_div(d, e, a, c, ctx);
2030 if (!BN_is_zero(d)) {
2031 fprintf(stderr, "Right shift test failed!\n");
2043 int test_rshift1(BIO *bp)
2052 BN_bntest_rand(a, 200, 0, 0);
2053 a->neg = rand_neg();
2054 for (i = 0; i < num0; i++) {
2059 BIO_puts(bp, " / 2");
2060 BIO_puts(bp, " - ");
2067 if (!BN_is_zero(c) && !BN_abs_is_word(c, 1)) {
2068 fprintf(stderr, "Right shift one test failed!\n");
2081 static unsigned int neg = 0;
2082 static int sign[8] = { 0, 0, 0, 1, 1, 0, 1, 1 };
2084 return (sign[(neg++) % 8]);