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git.ipfire.org Git - thirdparty/openssl.git/blob - crypto/bn/bntest.c
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_exp(BIO
*bp
, BN_CTX
*ctx
);
113 int test_gf2m_add(BIO
*bp
);
114 int test_gf2m_mod(BIO
*bp
);
115 int test_gf2m_mod_mul(BIO
*bp
, BN_CTX
*ctx
);
116 int test_gf2m_mod_sqr(BIO
*bp
, BN_CTX
*ctx
);
117 int test_gf2m_mod_inv(BIO
*bp
, BN_CTX
*ctx
);
118 int test_gf2m_mod_div(BIO
*bp
, BN_CTX
*ctx
);
119 int test_gf2m_mod_exp(BIO
*bp
, BN_CTX
*ctx
);
120 int test_gf2m_mod_sqrt(BIO
*bp
, BN_CTX
*ctx
);
121 int test_gf2m_mod_solve_quad(BIO
*bp
, BN_CTX
*ctx
);
122 int test_kron(BIO
*bp
, BN_CTX
*ctx
);
123 int test_sqrt(BIO
*bp
, BN_CTX
*ctx
);
125 static int results
= 0;
127 static unsigned char lst
[] =
128 "\xC6\x4F\x43\x04\x2A\xEA\xCA\x6E\x58\x36\x80\x5B\xE8\xC9"
129 "\x9B\x04\x5D\x48\x36\xC2\xFD\x16\xC9\x64\xF0";
131 static const char rnd_seed
[] =
132 "string to make the random number generator think it has entropy";
134 static void message(BIO
*out
, char *m
)
136 fprintf(stderr
, "test %s\n", m
);
137 BIO_puts(out
, "print \"test ");
139 BIO_puts(out
, "\\n\"\n");
142 int main(int argc
, char *argv
[])
146 char *outfile
= NULL
;
150 RAND_seed(rnd_seed
, sizeof rnd_seed
); /* or BN_generate_prime may fail */
155 if (strcmp(*argv
, "-results") == 0)
157 else if (strcmp(*argv
, "-out") == 0) {
170 out
= BIO_new(BIO_s_file());
173 if (outfile
== NULL
) {
174 BIO_set_fp(out
, stdout
, BIO_NOCLOSE
);
176 if (!BIO_write_filename(out
, outfile
)) {
183 BIO_puts(out
, "obase=16\nibase=16\n");
185 message(out
, "BN_add");
188 (void)BIO_flush(out
);
190 message(out
, "BN_sub");
193 (void)BIO_flush(out
);
195 message(out
, "BN_lshift1");
196 if (!test_lshift1(out
))
198 (void)BIO_flush(out
);
200 message(out
, "BN_lshift (fixed)");
201 if (!test_lshift(out
, ctx
, BN_bin2bn(lst
, sizeof(lst
) - 1, NULL
)))
203 (void)BIO_flush(out
);
205 message(out
, "BN_lshift");
206 if (!test_lshift(out
, ctx
, NULL
))
208 (void)BIO_flush(out
);
210 message(out
, "BN_rshift1");
211 if (!test_rshift1(out
))
213 (void)BIO_flush(out
);
215 message(out
, "BN_rshift");
216 if (!test_rshift(out
, ctx
))
218 (void)BIO_flush(out
);
220 message(out
, "BN_sqr");
221 if (!test_sqr(out
, ctx
))
223 (void)BIO_flush(out
);
225 message(out
, "BN_mul");
228 (void)BIO_flush(out
);
230 message(out
, "BN_div");
231 if (!test_div(out
, ctx
))
233 (void)BIO_flush(out
);
235 message(out
, "BN_div_word");
236 if (!test_div_word(out
))
238 (void)BIO_flush(out
);
240 message(out
, "BN_div_recp");
241 if (!test_div_recp(out
, ctx
))
243 (void)BIO_flush(out
);
245 message(out
, "BN_mod");
246 if (!test_mod(out
, ctx
))
248 (void)BIO_flush(out
);
250 message(out
, "BN_mod_mul");
251 if (!test_mod_mul(out
, ctx
))
253 (void)BIO_flush(out
);
255 message(out
, "BN_mont");
256 if (!test_mont(out
, ctx
))
258 (void)BIO_flush(out
);
260 message(out
, "BN_mod_exp");
261 if (!test_mod_exp(out
, ctx
))
263 (void)BIO_flush(out
);
265 message(out
, "BN_mod_exp_mont_consttime");
266 if (!test_mod_exp_mont_consttime(out
, ctx
))
268 (void)BIO_flush(out
);
270 message(out
, "BN_exp");
271 if (!test_exp(out
, ctx
))
273 (void)BIO_flush(out
);
275 message(out
, "BN_kronecker");
276 if (!test_kron(out
, ctx
))
278 (void)BIO_flush(out
);
280 message(out
, "BN_mod_sqrt");
281 if (!test_sqrt(out
, ctx
))
283 (void)BIO_flush(out
);
285 message(out
, "BN_GF2m_add");
286 if (!test_gf2m_add(out
))
288 (void)BIO_flush(out
);
290 message(out
, "BN_GF2m_mod");
291 if (!test_gf2m_mod(out
))
293 (void)BIO_flush(out
);
295 message(out
, "BN_GF2m_mod_mul");
296 if (!test_gf2m_mod_mul(out
, ctx
))
298 (void)BIO_flush(out
);
300 message(out
, "BN_GF2m_mod_sqr");
301 if (!test_gf2m_mod_sqr(out
, ctx
))
303 (void)BIO_flush(out
);
305 message(out
, "BN_GF2m_mod_inv");
306 if (!test_gf2m_mod_inv(out
, ctx
))
308 (void)BIO_flush(out
);
310 message(out
, "BN_GF2m_mod_div");
311 if (!test_gf2m_mod_div(out
, ctx
))
313 (void)BIO_flush(out
);
315 message(out
, "BN_GF2m_mod_exp");
316 if (!test_gf2m_mod_exp(out
, ctx
))
318 (void)BIO_flush(out
);
320 message(out
, "BN_GF2m_mod_sqrt");
321 if (!test_gf2m_mod_sqrt(out
, ctx
))
323 (void)BIO_flush(out
);
325 message(out
, "BN_GF2m_mod_solve_quad");
326 if (!test_gf2m_mod_solve_quad(out
, ctx
))
328 (void)BIO_flush(out
);
335 BIO_puts(out
, "1\n"); /* make sure the Perl script fed by bc
336 * notices the failure, see test_bn in
337 * test/Makefile.ssl */
338 (void)BIO_flush(out
);
339 ERR_load_crypto_strings();
340 ERR_print_errors_fp(stderr
);
345 int test_add(BIO
*bp
)
354 BN_bntest_rand(&a
, 512, 0, 0);
355 for (i
= 0; i
< num0
; i
++) {
356 BN_bntest_rand(&b
, 450 + i
, 0, 0);
374 if (!BN_is_zero(&c
)) {
375 fprintf(stderr
, "Add test failed!\n");
385 int test_sub(BIO
*bp
)
394 for (i
= 0; i
< num0
+ num1
; i
++) {
396 BN_bntest_rand(&a
, 512, 0, 0);
398 if (BN_set_bit(&a
, i
) == 0)
402 BN_bntest_rand(&b
, 400 + i
- num1
, 0, 0);
419 if (!BN_is_zero(&c
)) {
420 fprintf(stderr
, "Subtract test failed!\n");
430 int test_div(BIO
*bp
, BN_CTX
*ctx
)
432 BIGNUM a
, b
, c
, d
, e
;
441 for (i
= 0; i
< num0
+ num1
; i
++) {
443 BN_bntest_rand(&a
, 400, 0, 0);
445 BN_lshift(&a
, &a
, i
);
448 BN_bntest_rand(&b
, 50 + 3 * (i
- num1
), 0, 0);
451 BN_div(&d
, &c
, &a
, &b
, ctx
);
471 BN_mul(&e
, &d
, &b
, ctx
);
474 if (!BN_is_zero(&d
)) {
475 fprintf(stderr
, "Division test failed!\n");
487 static void print_word(BIO
*bp
, BN_ULONG w
)
489 #ifdef SIXTY_FOUR_BIT
490 if (sizeof(w
) > sizeof(unsigned long)) {
491 unsigned long h
= (unsigned long)(w
>> 32), l
= (unsigned long)(w
);
494 BIO_printf(bp
, "%lX%08lX", h
, l
);
496 BIO_printf(bp
, "%lX", l
);
500 BIO_printf(bp
, "%lX", w
);
503 int test_div_word(BIO
*bp
)
512 for (i
= 0; i
< num0
; i
++) {
514 BN_bntest_rand(&a
, 512, -1, 0);
515 BN_bntest_rand(&b
, BN_BITS2
, -1, 0);
520 r
= BN_div_word(&b
, s
);
544 if (!BN_is_zero(&b
)) {
545 fprintf(stderr
, "Division (word) test failed!\n");
554 int test_div_recp(BIO
*bp
, BN_CTX
*ctx
)
556 BIGNUM a
, b
, c
, d
, e
;
560 BN_RECP_CTX_init(&recp
);
567 for (i
= 0; i
< num0
+ num1
; i
++) {
569 BN_bntest_rand(&a
, 400, 0, 0);
571 BN_lshift(&a
, &a
, i
);
574 BN_bntest_rand(&b
, 50 + 3 * (i
- num1
), 0, 0);
577 BN_RECP_CTX_set(&recp
, &b
, ctx
);
578 BN_div_recp(&d
, &c
, &a
, &recp
, ctx
);
598 BN_mul(&e
, &d
, &b
, ctx
);
601 if (!BN_is_zero(&d
)) {
602 fprintf(stderr
, "Reciprocal division test failed!\n");
603 fprintf(stderr
, "a=");
604 BN_print_fp(stderr
, &a
);
605 fprintf(stderr
, "\nb=");
606 BN_print_fp(stderr
, &b
);
607 fprintf(stderr
, "\n");
616 BN_RECP_CTX_free(&recp
);
620 int test_mul(BIO
*bp
)
622 BIGNUM a
, b
, c
, d
, e
;
636 for (i
= 0; i
< num0
+ num1
; i
++) {
638 BN_bntest_rand(&a
, 100, 0, 0);
639 BN_bntest_rand(&b
, 100, 0, 0);
641 BN_bntest_rand(&b
, i
- num1
, 0, 0);
644 BN_mul(&c
, &a
, &b
, ctx
);
655 BN_div(&d
, &e
, &c
, &a
, ctx
);
657 if (!BN_is_zero(&d
) || !BN_is_zero(&e
)) {
658 fprintf(stderr
, "Multiplication test failed!\n");
671 int test_sqr(BIO
*bp
, BN_CTX
*ctx
)
673 BIGNUM
*a
, *c
, *d
, *e
;
680 if (a
== NULL
|| c
== NULL
|| d
== NULL
|| e
== NULL
) {
684 for (i
= 0; i
< num0
; i
++) {
685 BN_bntest_rand(a
, 40 + i
* 10, 0, 0);
698 BN_div(d
, e
, c
, a
, ctx
);
700 if (!BN_is_zero(d
) || !BN_is_zero(e
)) {
701 fprintf(stderr
, "Square test failed!\n");
706 /* Regression test for a BN_sqr overflow bug. */
708 "80000000000000008000000000000001"
709 "FFFFFFFFFFFFFFFE0000000000000000");
721 BN_mul(d
, a
, a
, ctx
);
723 fprintf(stderr
, "Square test failed: BN_sqr and BN_mul produce "
724 "different results!\n");
728 /* Regression test for a BN_sqr overflow bug. */
730 "80000000000000000000000080000001"
731 "FFFFFFFE000000000000000000000000");
743 BN_mul(d
, a
, a
, ctx
);
745 fprintf(stderr
, "Square test failed: BN_sqr and BN_mul produce "
746 "different results!\n");
762 int test_mont(BIO
*bp
, BN_CTX
*ctx
)
764 BIGNUM a
, b
, c
, d
, A
, B
;
777 mont
= BN_MONT_CTX_new();
779 BN_bntest_rand(&a
, 100, 0, 0);
780 BN_bntest_rand(&b
, 100, 0, 0);
781 for (i
= 0; i
< num2
; i
++) {
782 int bits
= (200 * (i
+ 1)) / num2
;
786 BN_bntest_rand(&n
, bits
, 0, 1);
787 BN_MONT_CTX_set(mont
, &n
, ctx
);
789 BN_nnmod(&a
, &a
, &n
, ctx
);
790 BN_nnmod(&b
, &b
, &n
, ctx
);
792 BN_to_montgomery(&A
, &a
, mont
, ctx
);
793 BN_to_montgomery(&B
, &b
, mont
, ctx
);
795 BN_mod_mul_montgomery(&c
, &A
, &B
, mont
, ctx
);
796 BN_from_montgomery(&A
, &c
, mont
, ctx
);
800 fprintf(stderr
, "%d * %d %% %d\n",
802 BN_num_bits(&b
), BN_num_bits(mont
->N
));
808 BN_print(bp
, &(mont
->N
));
814 BN_mod_mul(&d
, &a
, &b
, &n
, ctx
);
816 if (!BN_is_zero(&d
)) {
817 fprintf(stderr
, "Montgomery multiplication test failed!\n");
821 BN_MONT_CTX_free(mont
);
832 int test_mod(BIO
*bp
, BN_CTX
*ctx
)
834 BIGNUM
*a
, *b
, *c
, *d
, *e
;
843 BN_bntest_rand(a
, 1024, 0, 0);
844 for (i
= 0; i
< num0
; i
++) {
845 BN_bntest_rand(b
, 450 + i
* 10, 0, 0);
848 BN_mod(c
, a
, b
, ctx
);
859 BN_div(d
, e
, a
, b
, ctx
);
861 if (!BN_is_zero(e
)) {
862 fprintf(stderr
, "Modulo test failed!\n");
874 int test_mod_mul(BIO
*bp
, BN_CTX
*ctx
)
876 BIGNUM
*a
, *b
, *c
, *d
, *e
;
885 for (j
= 0; j
< 3; j
++) {
886 BN_bntest_rand(c
, 1024, 0, 0);
887 for (i
= 0; i
< num0
; i
++) {
888 BN_bntest_rand(a
, 475 + i
* 10, 0, 0);
889 BN_bntest_rand(b
, 425 + i
* 11, 0, 0);
892 if (!BN_mod_mul(e
, a
, b
, c
, ctx
)) {
895 while ((l
= ERR_get_error()))
896 fprintf(stderr
, "ERROR:%s\n", ERR_error_string(l
, NULL
));
906 if ((a
->neg
^ b
->neg
) && !BN_is_zero(e
)) {
908 * If (a*b) % c is negative, c must be added in order
909 * to obtain the normalized remainder (new with
910 * OpenSSL 0.9.7, previous versions of BN_mod_mul
911 * could generate negative results)
921 BN_mul(d
, a
, b
, ctx
);
923 BN_div(a
, b
, d
, c
, ctx
);
924 if (!BN_is_zero(b
)) {
925 fprintf(stderr
, "Modulo multiply test failed!\n");
926 ERR_print_errors_fp(stderr
);
939 int test_mod_exp(BIO
*bp
, BN_CTX
*ctx
)
941 BIGNUM
*a
, *b
, *c
, *d
, *e
;
950 BN_bntest_rand(c
, 30, 0, 1); /* must be odd for montgomery */
951 for (i
= 0; i
< num2
; i
++) {
952 BN_bntest_rand(a
, 20 + i
* 5, 0, 0);
953 BN_bntest_rand(b
, 2 + i
, 0, 0);
955 if (!BN_mod_exp(d
, a
, b
, c
, ctx
))
970 BN_exp(e
, a
, b
, ctx
);
972 BN_div(a
, b
, e
, c
, ctx
);
973 if (!BN_is_zero(b
)) {
974 fprintf(stderr
, "Modulo exponentiation test failed!\n");
986 int test_mod_exp_mont_consttime(BIO
*bp
, BN_CTX
*ctx
)
988 BIGNUM
*a
, *b
, *c
, *d
, *e
;
997 BN_bntest_rand(c
, 30, 0, 1); /* must be odd for montgomery */
998 for (i
= 0; i
< num2
; i
++) {
999 BN_bntest_rand(a
, 20 + i
* 5, 0, 0);
1000 BN_bntest_rand(b
, 2 + i
, 0, 0);
1002 if (!BN_mod_exp_mont_consttime(d
, a
, b
, c
, ctx
, NULL
))
1008 BIO_puts(bp
, " ^ ");
1010 BIO_puts(bp
, " % ");
1012 BIO_puts(bp
, " - ");
1017 BN_exp(e
, a
, b
, ctx
);
1019 BN_div(a
, b
, e
, c
, ctx
);
1020 if (!BN_is_zero(b
)) {
1021 fprintf(stderr
, "Modulo exponentiation test failed!\n");
1033 int test_exp(BIO
*bp
, BN_CTX
*ctx
)
1035 BIGNUM
*a
, *b
, *d
, *e
, *one
;
1045 for (i
= 0; i
< num2
; i
++) {
1046 BN_bntest_rand(a
, 20 + i
* 5, 0, 0);
1047 BN_bntest_rand(b
, 2 + i
, 0, 0);
1049 if (BN_exp(d
, a
, b
, ctx
) <= 0)
1055 BIO_puts(bp
, " ^ ");
1057 BIO_puts(bp
, " - ");
1063 for (; !BN_is_zero(b
); BN_sub(b
, b
, one
))
1064 BN_mul(e
, e
, a
, ctx
);
1066 if (!BN_is_zero(e
)) {
1067 fprintf(stderr
, "Exponentiation test failed!\n");
1079 int test_gf2m_add(BIO
*bp
)
1088 for (i
= 0; i
< num0
; i
++) {
1089 BN_rand(&a
, 512, 0, 0);
1090 BN_copy(&b
, BN_value_one());
1093 BN_GF2m_add(&c
, &a
, &b
);
1094 #if 0 /* make test uses ouput in bc but bc can't
1095 * handle GF(2^m) arithmetic */
1099 BIO_puts(bp
, " ^ ");
1101 BIO_puts(bp
, " = ");
1107 /* Test that two added values have the correct parity. */
1108 if ((BN_is_odd(&a
) && BN_is_odd(&c
))
1109 || (!BN_is_odd(&a
) && !BN_is_odd(&c
))) {
1110 fprintf(stderr
, "GF(2^m) addition test (a) failed!\n");
1113 BN_GF2m_add(&c
, &c
, &c
);
1114 /* Test that c + c = 0. */
1115 if (!BN_is_zero(&c
)) {
1116 fprintf(stderr
, "GF(2^m) addition test (b) failed!\n");
1128 int test_gf2m_mod(BIO
*bp
)
1130 BIGNUM
*a
, *b
[2], *c
, *d
, *e
;
1132 unsigned int p0
[] = { 163, 7, 6, 3, 0 };
1133 unsigned int p1
[] = { 193, 15, 0 };
1142 BN_GF2m_arr2poly(p0
, b
[0]);
1143 BN_GF2m_arr2poly(p1
, b
[1]);
1145 for (i
= 0; i
< num0
; i
++) {
1146 BN_bntest_rand(a
, 1024, 0, 0);
1147 for (j
= 0; j
< 2; j
++) {
1148 BN_GF2m_mod(c
, a
, b
[j
]);
1149 #if 0 /* make test uses ouput in bc but bc can't
1150 * handle GF(2^m) arithmetic */
1154 BIO_puts(bp
, " % ");
1156 BIO_puts(bp
, " - ");
1162 BN_GF2m_add(d
, a
, c
);
1163 BN_GF2m_mod(e
, d
, b
[j
]);
1164 /* Test that a + (a mod p) mod p == 0. */
1165 if (!BN_is_zero(e
)) {
1166 fprintf(stderr
, "GF(2^m) modulo test failed!\n");
1182 int test_gf2m_mod_mul(BIO
*bp
, BN_CTX
*ctx
)
1184 BIGNUM
*a
, *b
[2], *c
, *d
, *e
, *f
, *g
, *h
;
1186 unsigned int p0
[] = { 163, 7, 6, 3, 0 };
1187 unsigned int p1
[] = { 193, 15, 0 };
1199 BN_GF2m_arr2poly(p0
, b
[0]);
1200 BN_GF2m_arr2poly(p1
, b
[1]);
1202 for (i
= 0; i
< num0
; i
++) {
1203 BN_bntest_rand(a
, 1024, 0, 0);
1204 BN_bntest_rand(c
, 1024, 0, 0);
1205 BN_bntest_rand(d
, 1024, 0, 0);
1206 for (j
= 0; j
< 2; j
++) {
1207 BN_GF2m_mod_mul(e
, a
, c
, b
[j
], ctx
);
1208 #if 0 /* make test uses ouput in bc but bc can't
1209 * handle GF(2^m) arithmetic */
1213 BIO_puts(bp
, " * ");
1215 BIO_puts(bp
, " % ");
1217 BIO_puts(bp
, " - ");
1223 BN_GF2m_add(f
, a
, d
);
1224 BN_GF2m_mod_mul(g
, f
, c
, b
[j
], ctx
);
1225 BN_GF2m_mod_mul(h
, d
, c
, b
[j
], ctx
);
1226 BN_GF2m_add(f
, e
, g
);
1227 BN_GF2m_add(f
, f
, h
);
1228 /* Test that (a+d)*c = a*c + d*c. */
1229 if (!BN_is_zero(f
)) {
1231 "GF(2^m) modular multiplication test failed!\n");
1250 int test_gf2m_mod_sqr(BIO
*bp
, BN_CTX
*ctx
)
1252 BIGNUM
*a
, *b
[2], *c
, *d
;
1254 unsigned int p0
[] = { 163, 7, 6, 3, 0 };
1255 unsigned int p1
[] = { 193, 15, 0 };
1263 BN_GF2m_arr2poly(p0
, b
[0]);
1264 BN_GF2m_arr2poly(p1
, b
[1]);
1266 for (i
= 0; i
< num0
; i
++) {
1267 BN_bntest_rand(a
, 1024, 0, 0);
1268 for (j
= 0; j
< 2; j
++) {
1269 BN_GF2m_mod_sqr(c
, a
, b
[j
], ctx
);
1271 BN_GF2m_mod_mul(d
, a
, d
, b
[j
], ctx
);
1272 #if 0 /* make test uses ouput in bc but bc can't
1273 * handle GF(2^m) arithmetic */
1277 BIO_puts(bp
, " ^ 2 % ");
1279 BIO_puts(bp
, " = ");
1281 BIO_puts(bp
, "; a * a = ");
1287 BN_GF2m_add(d
, c
, d
);
1288 /* Test that a*a = a^2. */
1289 if (!BN_is_zero(d
)) {
1290 fprintf(stderr
, "GF(2^m) modular squaring test failed!\n");
1305 int test_gf2m_mod_inv(BIO
*bp
, BN_CTX
*ctx
)
1307 BIGNUM
*a
, *b
[2], *c
, *d
;
1309 unsigned int p0
[] = { 163, 7, 6, 3, 0 };
1310 unsigned int p1
[] = { 193, 15, 0 };
1318 BN_GF2m_arr2poly(p0
, b
[0]);
1319 BN_GF2m_arr2poly(p1
, b
[1]);
1321 for (i
= 0; i
< num0
; i
++) {
1322 BN_bntest_rand(a
, 512, 0, 0);
1323 for (j
= 0; j
< 2; j
++) {
1324 BN_GF2m_mod_inv(c
, a
, b
[j
], ctx
);
1325 BN_GF2m_mod_mul(d
, a
, c
, b
[j
], ctx
);
1326 #if 0 /* make test uses ouput in bc but bc can't
1327 * handle GF(2^m) arithmetic */
1331 BIO_puts(bp
, " * ");
1333 BIO_puts(bp
, " - 1 % ");
1339 /* Test that ((1/a)*a) = 1. */
1340 if (!BN_is_one(d
)) {
1341 fprintf(stderr
, "GF(2^m) modular inversion test failed!\n");
1356 int test_gf2m_mod_div(BIO
*bp
, BN_CTX
*ctx
)
1358 BIGNUM
*a
, *b
[2], *c
, *d
, *e
, *f
;
1360 unsigned int p0
[] = { 163, 7, 6, 3, 0 };
1361 unsigned int p1
[] = { 193, 15, 0 };
1371 BN_GF2m_arr2poly(p0
, b
[0]);
1372 BN_GF2m_arr2poly(p1
, b
[1]);
1374 for (i
= 0; i
< num0
; i
++) {
1375 BN_bntest_rand(a
, 512, 0, 0);
1376 BN_bntest_rand(c
, 512, 0, 0);
1377 for (j
= 0; j
< 2; j
++) {
1378 BN_GF2m_mod_div(d
, a
, c
, b
[j
], ctx
);
1379 BN_GF2m_mod_mul(e
, d
, c
, b
[j
], ctx
);
1380 BN_GF2m_mod_div(f
, a
, e
, b
[j
], ctx
);
1381 #if 0 /* make test uses ouput in bc but bc can't
1382 * handle GF(2^m) arithmetic */
1386 BIO_puts(bp
, " = ");
1388 BIO_puts(bp
, " * ");
1390 BIO_puts(bp
, " % ");
1396 /* Test that ((a/c)*c)/a = 1. */
1397 if (!BN_is_one(f
)) {
1398 fprintf(stderr
, "GF(2^m) modular division test failed!\n");
1415 int test_gf2m_mod_exp(BIO
*bp
, BN_CTX
*ctx
)
1417 BIGNUM
*a
, *b
[2], *c
, *d
, *e
, *f
;
1419 unsigned int p0
[] = { 163, 7, 6, 3, 0 };
1420 unsigned int p1
[] = { 193, 15, 0 };
1430 BN_GF2m_arr2poly(p0
, b
[0]);
1431 BN_GF2m_arr2poly(p1
, b
[1]);
1433 for (i
= 0; i
< num0
; i
++) {
1434 BN_bntest_rand(a
, 512, 0, 0);
1435 BN_bntest_rand(c
, 512, 0, 0);
1436 BN_bntest_rand(d
, 512, 0, 0);
1437 for (j
= 0; j
< 2; j
++) {
1438 BN_GF2m_mod_exp(e
, a
, c
, b
[j
], ctx
);
1439 BN_GF2m_mod_exp(f
, a
, d
, b
[j
], ctx
);
1440 BN_GF2m_mod_mul(e
, e
, f
, b
[j
], ctx
);
1442 BN_GF2m_mod_exp(f
, a
, f
, b
[j
], ctx
);
1443 #if 0 /* make test uses ouput in bc but bc can't
1444 * handle GF(2^m) arithmetic */
1448 BIO_puts(bp
, " ^ (");
1450 BIO_puts(bp
, " + ");
1452 BIO_puts(bp
, ") = ");
1454 BIO_puts(bp
, "; - ");
1456 BIO_puts(bp
, " % ");
1462 BN_GF2m_add(f
, e
, f
);
1463 /* Test that a^(c+d)=a^c*a^d. */
1464 if (!BN_is_zero(f
)) {
1466 "GF(2^m) modular exponentiation test failed!\n");
1483 int test_gf2m_mod_sqrt(BIO
*bp
, BN_CTX
*ctx
)
1485 BIGNUM
*a
, *b
[2], *c
, *d
, *e
, *f
;
1487 unsigned int p0
[] = { 163, 7, 6, 3, 0 };
1488 unsigned int p1
[] = { 193, 15, 0 };
1498 BN_GF2m_arr2poly(p0
, b
[0]);
1499 BN_GF2m_arr2poly(p1
, b
[1]);
1501 for (i
= 0; i
< num0
; i
++) {
1502 BN_bntest_rand(a
, 512, 0, 0);
1503 for (j
= 0; j
< 2; j
++) {
1504 BN_GF2m_mod(c
, a
, b
[j
]);
1505 BN_GF2m_mod_sqrt(d
, a
, b
[j
], ctx
);
1506 BN_GF2m_mod_sqr(e
, d
, b
[j
], ctx
);
1507 #if 0 /* make test uses ouput in bc but bc can't
1508 * handle GF(2^m) arithmetic */
1512 BIO_puts(bp
, " ^ 2 - ");
1518 BN_GF2m_add(f
, c
, e
);
1519 /* Test that d^2 = a, where d = sqrt(a). */
1520 if (!BN_is_zero(f
)) {
1521 fprintf(stderr
, "GF(2^m) modular square root test failed!\n");
1538 int test_gf2m_mod_solve_quad(BIO
*bp
, BN_CTX
*ctx
)
1540 BIGNUM
*a
, *b
[2], *c
, *d
, *e
;
1541 int i
, j
, s
= 0, t
, ret
= 0;
1542 unsigned int p0
[] = { 163, 7, 6, 3, 0 };
1543 unsigned int p1
[] = { 193, 15, 0 };
1552 BN_GF2m_arr2poly(p0
, b
[0]);
1553 BN_GF2m_arr2poly(p1
, b
[1]);
1555 for (i
= 0; i
< num0
; i
++) {
1556 BN_bntest_rand(a
, 512, 0, 0);
1557 for (j
= 0; j
< 2; j
++) {
1558 t
= BN_GF2m_mod_solve_quad(c
, a
, b
[j
], ctx
);
1561 BN_GF2m_mod_sqr(d
, c
, b
[j
], ctx
);
1562 BN_GF2m_add(d
, c
, d
);
1563 BN_GF2m_mod(e
, a
, b
[j
]);
1564 #if 0 /* make test uses ouput in bc but bc can't
1565 * handle GF(2^m) arithmetic */
1569 BIO_puts(bp
, " is root of z^2 + z = ");
1571 BIO_puts(bp
, " % ");
1577 BN_GF2m_add(e
, e
, d
);
1579 * Test that solution of quadratic c satisfies c^2 + c = a.
1581 if (!BN_is_zero(e
)) {
1583 "GF(2^m) modular solve quadratic test failed!\n");
1588 #if 0 /* make test uses ouput in bc but bc can't
1589 * handle GF(2^m) arithmetic */
1592 BIO_puts(bp
, "There are no roots of z^2 + z = ");
1594 BIO_puts(bp
, " % ");
1605 "All %i tests of GF(2^m) modular solve quadratic resulted in no roots;\n",
1608 "this is very unlikely and probably indicates an error.\n");
1622 static int genprime_cb(int p
, int n
, BN_GENCB
*arg
)
1639 int test_kron(BIO
*bp
, BN_CTX
*ctx
)
1642 BIGNUM
*a
, *b
, *r
, *t
;
1644 int legendre
, kronecker
;
1651 if (a
== NULL
|| b
== NULL
|| r
== NULL
|| t
== NULL
)
1654 BN_GENCB_set(&cb
, genprime_cb
, NULL
);
1657 * We test BN_kronecker(a, b, ctx) just for b odd (Jacobi symbol). In
1658 * this case we know that if b is prime, then BN_kronecker(a, b, ctx) is
1659 * congruent to $a^{(b-1)/2}$, modulo $b$ (Legendre symbol). So we
1660 * generate a random prime b and compare these values for a number of
1661 * random a's. (That is, we run the Solovay-Strassen primality test to
1662 * confirm that b is prime, except that we don't want to test whether b
1663 * is prime but whether BN_kronecker works.)
1666 if (!BN_generate_prime_ex(b
, 512, 0, NULL
, NULL
, &cb
))
1668 b
->neg
= rand_neg();
1671 for (i
= 0; i
< num0
; i
++) {
1672 if (!BN_bntest_rand(a
, 512, 0, 0))
1674 a
->neg
= rand_neg();
1676 /* t := (|b|-1)/2 (note that b is odd) */
1680 if (!BN_sub_word(t
, 1))
1682 if (!BN_rshift1(t
, t
))
1684 /* r := a^t mod b */
1687 if (!BN_mod_exp_recp(r
, a
, t
, b
, ctx
))
1691 if (BN_is_word(r
, 1))
1693 else if (BN_is_zero(r
))
1696 if (!BN_add_word(r
, 1))
1698 if (0 != BN_ucmp(r
, b
)) {
1699 fprintf(stderr
, "Legendre symbol computation failed\n");
1705 kronecker
= BN_kronecker(a
, b
, ctx
);
1708 /* we actually need BN_kronecker(a, |b|) */
1709 if (a
->neg
&& b
->neg
)
1710 kronecker
= -kronecker
;
1712 if (legendre
!= kronecker
) {
1713 fprintf(stderr
, "legendre != kronecker; a = ");
1714 BN_print_fp(stderr
, a
);
1715 fprintf(stderr
, ", b = ");
1716 BN_print_fp(stderr
, b
);
1717 fprintf(stderr
, "\n");
1740 int test_sqrt(BIO
*bp
, BN_CTX
*ctx
)
1750 if (a
== NULL
|| p
== NULL
|| r
== NULL
)
1753 BN_GENCB_set(&cb
, genprime_cb
, NULL
);
1755 for (i
= 0; i
< 16; i
++) {
1757 unsigned primes
[8] = { 2, 3, 5, 7, 11, 13, 17, 19 };
1759 if (!BN_set_word(p
, primes
[i
]))
1762 if (!BN_set_word(a
, 32))
1764 if (!BN_set_word(r
, 2 * i
+ 1))
1767 if (!BN_generate_prime_ex(p
, 256, 0, a
, r
, &cb
))
1771 p
->neg
= rand_neg();
1773 for (j
= 0; j
< num2
; j
++) {
1775 * construct 'a' such that it is a square modulo p, but in
1776 * general not a proper square and not reduced modulo p
1778 if (!BN_bntest_rand(r
, 256, 0, 3))
1780 if (!BN_nnmod(r
, r
, p
, ctx
))
1782 if (!BN_mod_sqr(r
, r
, p
, ctx
))
1784 if (!BN_bntest_rand(a
, 256, 0, 3))
1786 if (!BN_nnmod(a
, a
, p
, ctx
))
1788 if (!BN_mod_sqr(a
, a
, p
, ctx
))
1790 if (!BN_mul(a
, a
, r
, ctx
))
1793 if (!BN_sub(a
, a
, p
))
1796 if (!BN_mod_sqrt(r
, a
, p
, ctx
))
1798 if (!BN_mod_sqr(r
, r
, p
, ctx
))
1801 if (!BN_nnmod(a
, a
, p
, ctx
))
1804 if (BN_cmp(a
, r
) != 0) {
1805 fprintf(stderr
, "BN_mod_sqrt failed: a = ");
1806 BN_print_fp(stderr
, a
);
1807 fprintf(stderr
, ", r = ");
1808 BN_print_fp(stderr
, r
);
1809 fprintf(stderr
, ", p = ");
1810 BN_print_fp(stderr
, p
);
1811 fprintf(stderr
, "\n");
1833 int test_lshift(BIO
*bp
, BN_CTX
*ctx
, BIGNUM
*a_
)
1835 BIGNUM
*a
, *b
, *c
, *d
;
1847 BN_bntest_rand(a
, 200, 0, 0);
1848 a
->neg
= rand_neg();
1850 for (i
= 0; i
< num0
; i
++) {
1851 BN_lshift(b
, a
, i
+ 1);
1856 BIO_puts(bp
, " * ");
1858 BIO_puts(bp
, " - ");
1863 BN_mul(d
, a
, c
, ctx
);
1865 if (!BN_is_zero(d
)) {
1866 fprintf(stderr
, "Left shift test failed!\n");
1867 fprintf(stderr
, "a=");
1868 BN_print_fp(stderr
, a
);
1869 fprintf(stderr
, "\nb=");
1870 BN_print_fp(stderr
, b
);
1871 fprintf(stderr
, "\nc=");
1872 BN_print_fp(stderr
, c
);
1873 fprintf(stderr
, "\nd=");
1874 BN_print_fp(stderr
, d
);
1875 fprintf(stderr
, "\n");
1886 int test_lshift1(BIO
*bp
)
1895 BN_bntest_rand(a
, 200, 0, 0);
1896 a
->neg
= rand_neg();
1897 for (i
= 0; i
< num0
; i
++) {
1902 BIO_puts(bp
, " * 2");
1903 BIO_puts(bp
, " - ");
1910 if (!BN_is_zero(a
)) {
1911 fprintf(stderr
, "Left shift one test failed!\n");
1923 int test_rshift(BIO
*bp
, BN_CTX
*ctx
)
1925 BIGNUM
*a
, *b
, *c
, *d
, *e
;
1935 BN_bntest_rand(a
, 200, 0, 0);
1936 a
->neg
= rand_neg();
1937 for (i
= 0; i
< num0
; i
++) {
1938 BN_rshift(b
, a
, i
+ 1);
1943 BIO_puts(bp
, " / ");
1945 BIO_puts(bp
, " - ");
1950 BN_div(d
, e
, a
, c
, ctx
);
1952 if (!BN_is_zero(d
)) {
1953 fprintf(stderr
, "Right shift test failed!\n");
1965 int test_rshift1(BIO
*bp
)
1974 BN_bntest_rand(a
, 200, 0, 0);
1975 a
->neg
= rand_neg();
1976 for (i
= 0; i
< num0
; i
++) {
1981 BIO_puts(bp
, " / 2");
1982 BIO_puts(bp
, " - ");
1989 if (!BN_is_zero(c
) && !BN_abs_is_word(c
, 1)) {
1990 fprintf(stderr
, "Right shift one test failed!\n");
2003 static unsigned int neg
= 0;
2004 static int sign
[8] = { 0, 0, 0, 1, 1, 0, 1, 1 };
2006 return (sign
[(neg
++) % 8]);