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.
72 /* Until the key-gen callbacks are modified to use newer prototypes, we allow
73 * deprecated functions for openssl-internal code */
74 #ifdef OPENSSL_NO_DEPRECATED
75 #undef OPENSSL_NO_DEPRECATED
84 #include <openssl/bio.h>
85 #include <openssl/bn.h>
86 #include <openssl/rand.h>
87 #include <openssl/x509.h>
88 #include <openssl/err.h>
90 #ifdef OPENSSL_SYS_WINDOWS
91 #include "../bio/bss_file.c"
94 const int num0 = 100; /* number of tests */
95 const int num1 = 50; /* additional tests for some functions */
96 const int num2 = 5; /* number of tests for slow functions */
98 int test_add(BIO *bp);
99 int test_sub(BIO *bp);
100 int test_lshift1(BIO *bp);
101 int test_lshift(BIO *bp,BN_CTX *ctx,BIGNUM *a_);
102 int test_rshift1(BIO *bp);
103 int test_rshift(BIO *bp,BN_CTX *ctx);
104 int test_div(BIO *bp,BN_CTX *ctx);
105 int test_div_recp(BIO *bp,BN_CTX *ctx);
106 int test_mul(BIO *bp);
107 int test_sqr(BIO *bp,BN_CTX *ctx);
108 int test_mont(BIO *bp,BN_CTX *ctx);
109 int test_mod(BIO *bp,BN_CTX *ctx);
110 int test_mod_mul(BIO *bp,BN_CTX *ctx);
111 int test_mod_exp(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 #ifdef OPENSSL_NO_STDIO
129 #include "bss_file.c"
132 static unsigned char lst[]="\xC6\x4F\x43\x04\x2A\xEA\xCA\x6E\x58\x36\x80\x5B\xE8\xC9"
133 "\x9B\x04\x5D\x48\x36\xC2\xFD\x16\xC9\x64\xF0";
135 static const char rnd_seed[] = "string to make the random number generator think it has entropy";
137 static void message(BIO *out, char *m)
139 fprintf(stderr, "test %s\n", m);
140 BIO_puts(out, "print \"test ");
142 BIO_puts(out, "\\n\"\n");
145 int main(int argc, char *argv[])
153 RAND_seed(rnd_seed, sizeof rnd_seed); /* or BN_generate_prime may fail */
159 if (strcmp(*argv,"-results") == 0)
161 else if (strcmp(*argv,"-out") == 0)
163 if (--argc < 1) break;
172 if (ctx == NULL) EXIT(1);
174 out=BIO_new(BIO_s_file());
175 if (out == NULL) EXIT(1);
178 BIO_set_fp(out,stdout,BIO_NOCLOSE);
182 if (!BIO_write_filename(out,outfile))
190 BIO_puts(out,"obase=16\nibase=16\n");
192 message(out,"BN_add");
193 if (!test_add(out)) goto err;
196 message(out,"BN_sub");
197 if (!test_sub(out)) goto err;
200 message(out,"BN_lshift1");
201 if (!test_lshift1(out)) goto err;
204 message(out,"BN_lshift (fixed)");
205 if (!test_lshift(out,ctx,BN_bin2bn(lst,sizeof(lst)-1,NULL)))
209 message(out,"BN_lshift");
210 if (!test_lshift(out,ctx,NULL)) goto err;
213 message(out,"BN_rshift1");
214 if (!test_rshift1(out)) goto err;
217 message(out,"BN_rshift");
218 if (!test_rshift(out,ctx)) goto err;
221 message(out,"BN_sqr");
222 if (!test_sqr(out,ctx)) goto err;
225 message(out,"BN_mul");
226 if (!test_mul(out)) goto err;
229 message(out,"BN_div");
230 if (!test_div(out,ctx)) goto err;
233 message(out,"BN_div_recp");
234 if (!test_div_recp(out,ctx)) goto err;
237 message(out,"BN_mod");
238 if (!test_mod(out,ctx)) goto err;
241 message(out,"BN_mod_mul");
242 if (!test_mod_mul(out,ctx)) goto err;
245 message(out,"BN_mont");
246 if (!test_mont(out,ctx)) goto err;
249 message(out,"BN_mod_exp");
250 if (!test_mod_exp(out,ctx)) goto err;
253 message(out,"BN_exp");
254 if (!test_exp(out,ctx)) goto err;
257 message(out,"BN_kronecker");
258 if (!test_kron(out,ctx)) goto err;
261 message(out,"BN_mod_sqrt");
262 if (!test_sqrt(out,ctx)) goto err;
265 message(out,"BN_GF2m_add");
266 if (!test_gf2m_add(out)) goto err;
269 message(out,"BN_GF2m_mod");
270 if (!test_gf2m_mod(out)) goto err;
273 message(out,"BN_GF2m_mod_mul");
274 if (!test_gf2m_mod_mul(out,ctx)) goto err;
277 message(out,"BN_GF2m_mod_sqr");
278 if (!test_gf2m_mod_sqr(out,ctx)) goto err;
281 message(out,"BN_GF2m_mod_inv");
282 if (!test_gf2m_mod_inv(out,ctx)) goto err;
285 message(out,"BN_GF2m_mod_div");
286 if (!test_gf2m_mod_div(out,ctx)) goto err;
289 message(out,"BN_GF2m_mod_exp");
290 if (!test_gf2m_mod_exp(out,ctx)) goto err;
293 message(out,"BN_GF2m_mod_sqrt");
294 if (!test_gf2m_mod_sqrt(out,ctx)) goto err;
297 message(out,"BN_GF2m_mod_solve_quad");
298 if (!test_gf2m_mod_solve_quad(out,ctx)) goto err;
307 BIO_puts(out,"1\n"); /* make sure the Perl script fed by bc notices
308 * the failure, see test_bn in test/Makefile.ssl*/
310 ERR_load_crypto_strings();
311 ERR_print_errors_fp(stderr);
316 int test_add(BIO *bp)
325 BN_bntest_rand(&a,512,0,0);
326 for (i=0; i<num0; i++)
328 BN_bntest_rand(&b,450+i,0,0);
350 fprintf(stderr,"Add test failed!\n");
360 int test_sub(BIO *bp)
369 for (i=0; i<num0+num1; i++)
373 BN_bntest_rand(&a,512,0,0);
375 if (BN_set_bit(&a,i)==0) return(0);
380 BN_bntest_rand(&b,400+i-num1,0,0);
401 fprintf(stderr,"Subtract test failed!\n");
411 int test_div(BIO *bp, BN_CTX *ctx)
422 for (i=0; i<num0+num1; i++)
426 BN_bntest_rand(&a,400,0,0);
432 BN_bntest_rand(&b,50+3*(i-num1),0,0);
435 BN_div(&d,&c,&a,&b,ctx);
458 BN_mul(&e,&d,&b,ctx);
463 fprintf(stderr,"Division test failed!\n");
475 int test_div_recp(BIO *bp, BN_CTX *ctx)
481 BN_RECP_CTX_init(&recp);
488 for (i=0; i<num0+num1; i++)
492 BN_bntest_rand(&a,400,0,0);
498 BN_bntest_rand(&b,50+3*(i-num1),0,0);
501 BN_RECP_CTX_set(&recp,&b,ctx);
502 BN_div_recp(&d,&c,&a,&recp,ctx);
525 BN_mul(&e,&d,&b,ctx);
530 fprintf(stderr,"Reciprocal division test failed!\n");
531 fprintf(stderr,"a=");
532 BN_print_fp(stderr,&a);
533 fprintf(stderr,"\nb=");
534 BN_print_fp(stderr,&b);
535 fprintf(stderr,"\n");
544 BN_RECP_CTX_free(&recp);
548 int test_mul(BIO *bp)
555 if (ctx == NULL) EXIT(1);
563 for (i=0; i<num0+num1; i++)
567 BN_bntest_rand(&a,100,0,0);
568 BN_bntest_rand(&b,100,0,0);
571 BN_bntest_rand(&b,i-num1,0,0);
574 BN_mul(&c,&a,&b,ctx);
587 BN_div(&d,&e,&c,&a,ctx);
589 if(!BN_is_zero(&d) || !BN_is_zero(&e))
591 fprintf(stderr,"Multiplication test failed!\n");
604 int test_sqr(BIO *bp, BN_CTX *ctx)
614 for (i=0; i<num0; i++)
616 BN_bntest_rand(&a,40+i*10,0,0);
631 BN_div(&d,&e,&c,&a,ctx);
633 if(!BN_is_zero(&d) || !BN_is_zero(&e))
635 fprintf(stderr,"Square test failed!\n");
646 int test_mont(BIO *bp, BN_CTX *ctx)
661 mont=BN_MONT_CTX_new();
663 BN_bntest_rand(&a,100,0,0); /**/
664 BN_bntest_rand(&b,100,0,0); /**/
665 for (i=0; i<num2; i++)
667 int bits = (200*(i+1))/num2;
671 BN_bntest_rand(&n,bits,0,1);
672 BN_MONT_CTX_set(mont,&n,ctx);
674 BN_nnmod(&a,&a,&n,ctx);
675 BN_nnmod(&b,&b,&n,ctx);
677 BN_to_montgomery(&A,&a,mont,ctx);
678 BN_to_montgomery(&B,&b,mont,ctx);
680 BN_mod_mul_montgomery(&c,&A,&B,mont,ctx);/**/
681 BN_from_montgomery(&A,&c,mont,ctx);/**/
687 fprintf(stderr,"%d * %d %% %d\n",
690 BN_num_bits(mont->N));
696 BN_print(bp,&(mont->N));
702 BN_mod_mul(&d,&a,&b,&n,ctx);
706 fprintf(stderr,"Montgomery multiplication test failed!\n");
710 BN_MONT_CTX_free(mont);
721 int test_mod(BIO *bp, BN_CTX *ctx)
723 BIGNUM *a,*b,*c,*d,*e;
732 BN_bntest_rand(a,1024,0,0); /**/
733 for (i=0; i<num0; i++)
735 BN_bntest_rand(b,450+i*10,0,0); /**/
738 BN_mod(c,a,b,ctx);/**/
755 fprintf(stderr,"Modulo test failed!\n");
767 int test_mod_mul(BIO *bp, BN_CTX *ctx)
769 BIGNUM *a,*b,*c,*d,*e;
778 for (j=0; j<3; j++) {
779 BN_bntest_rand(c,1024,0,0); /**/
780 for (i=0; i<num0; i++)
782 BN_bntest_rand(a,475+i*10,0,0); /**/
783 BN_bntest_rand(b,425+i*11,0,0); /**/
786 if (!BN_mod_mul(e,a,b,c,ctx))
790 while ((l=ERR_get_error()))
791 fprintf(stderr,"ERROR:%s\n",
792 ERR_error_string(l,NULL));
804 if ((a->neg ^ b->neg) && !BN_is_zero(e))
806 /* If (a*b) % c is negative, c must be added
807 * in order to obtain the normalized remainder
808 * (new with OpenSSL 0.9.7, previous versions of
809 * BN_mod_mul could generate negative results)
824 fprintf(stderr,"Modulo multiply test failed!\n");
825 ERR_print_errors_fp(stderr);
838 int test_mod_exp(BIO *bp, BN_CTX *ctx)
840 BIGNUM *a,*b,*c,*d,*e;
849 BN_bntest_rand(c,30,0,1); /* must be odd for montgomery */
850 for (i=0; i<num2; i++)
852 BN_bntest_rand(a,20+i*5,0,0); /**/
853 BN_bntest_rand(b,2+i,0,0); /**/
855 if (!BN_mod_exp(d,a,b,c,ctx))
877 fprintf(stderr,"Modulo exponentiation test failed!\n");
889 int test_exp(BIO *bp, BN_CTX *ctx)
891 BIGNUM *a,*b,*d,*e,*one;
901 for (i=0; i<num2; i++)
903 BN_bntest_rand(a,20+i*5,0,0); /**/
904 BN_bntest_rand(b,2+i,0,0); /**/
906 if (!BN_exp(d,a,b,ctx))
922 for( ; !BN_is_zero(b) ; BN_sub(b,b,one))
927 fprintf(stderr,"Exponentiation test failed!\n");
939 int test_gf2m_add(BIO *bp)
948 for (i=0; i<num0; i++)
951 BN_copy(&b, BN_value_one());
954 BN_GF2m_add(&c,&a,&b);
955 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
969 /* Test that two added values have the correct parity. */
970 if((BN_is_odd(&a) && BN_is_odd(&c)) || (!BN_is_odd(&a) && !BN_is_odd(&c)))
972 fprintf(stderr,"GF(2^m) addition test (a) failed!\n");
975 BN_GF2m_add(&c,&c,&c);
976 /* Test that c + c = 0. */
979 fprintf(stderr,"GF(2^m) addition test (b) failed!\n");
991 int test_gf2m_mod(BIO *bp)
993 BIGNUM *a,*b[2],*c,*d,*e;
995 unsigned int p0[] = {163,7,6,3,0};
996 unsigned int p1[] = {193,15,0};
1005 BN_GF2m_arr2poly(p0, b[0]);
1006 BN_GF2m_arr2poly(p1, b[1]);
1008 for (i=0; i<num0; i++)
1010 BN_bntest_rand(a, 1024, 0, 0);
1011 for (j=0; j < 2; j++)
1013 BN_GF2m_mod(c, a, b[j]);
1014 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1028 BN_GF2m_add(d, a, c);
1029 BN_GF2m_mod(e, d, b[j]);
1030 /* Test that a + (a mod p) mod p == 0. */
1033 fprintf(stderr,"GF(2^m) modulo test failed!\n");
1049 int test_gf2m_mod_mul(BIO *bp,BN_CTX *ctx)
1051 BIGNUM *a,*b[2],*c,*d,*e,*f,*g,*h;
1053 unsigned int p0[] = {163,7,6,3,0};
1054 unsigned int p1[] = {193,15,0};
1066 BN_GF2m_arr2poly(p0, b[0]);
1067 BN_GF2m_arr2poly(p1, b[1]);
1069 for (i=0; i<num0; i++)
1071 BN_bntest_rand(a, 1024, 0, 0);
1072 BN_bntest_rand(c, 1024, 0, 0);
1073 BN_bntest_rand(d, 1024, 0, 0);
1074 for (j=0; j < 2; j++)
1076 BN_GF2m_mod_mul(e, a, c, b[j], ctx);
1077 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1093 BN_GF2m_add(f, a, d);
1094 BN_GF2m_mod_mul(g, f, c, b[j], ctx);
1095 BN_GF2m_mod_mul(h, d, c, b[j], ctx);
1096 BN_GF2m_add(f, e, g);
1097 BN_GF2m_add(f, f, h);
1098 /* Test that (a+d)*c = a*c + d*c. */
1101 fprintf(stderr,"GF(2^m) modular multiplication test failed!\n");
1120 int test_gf2m_mod_sqr(BIO *bp,BN_CTX *ctx)
1122 BIGNUM *a,*b[2],*c,*d;
1124 unsigned int p0[] = {163,7,6,3,0};
1125 unsigned int p1[] = {193,15,0};
1133 BN_GF2m_arr2poly(p0, b[0]);
1134 BN_GF2m_arr2poly(p1, b[1]);
1136 for (i=0; i<num0; i++)
1138 BN_bntest_rand(a, 1024, 0, 0);
1139 for (j=0; j < 2; j++)
1141 BN_GF2m_mod_sqr(c, a, b[j], ctx);
1143 BN_GF2m_mod_mul(d, a, d, b[j], ctx);
1144 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1150 BIO_puts(bp," ^ 2 % ");
1152 BIO_puts(bp, " = ");
1154 BIO_puts(bp,"; a * a = ");
1160 BN_GF2m_add(d, c, d);
1161 /* Test that a*a = a^2. */
1164 fprintf(stderr,"GF(2^m) modular squaring test failed!\n");
1179 int test_gf2m_mod_inv(BIO *bp,BN_CTX *ctx)
1181 BIGNUM *a,*b[2],*c,*d;
1183 unsigned int p0[] = {163,7,6,3,0};
1184 unsigned int p1[] = {193,15,0};
1192 BN_GF2m_arr2poly(p0, b[0]);
1193 BN_GF2m_arr2poly(p1, b[1]);
1195 for (i=0; i<num0; i++)
1197 BN_bntest_rand(a, 512, 0, 0);
1198 for (j=0; j < 2; j++)
1200 BN_GF2m_mod_inv(c, a, b[j], ctx);
1201 BN_GF2m_mod_mul(d, a, c, b[j], ctx);
1202 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1208 BIO_puts(bp, " * ");
1210 BIO_puts(bp," - 1 % ");
1216 /* Test that ((1/a)*a) = 1. */
1219 fprintf(stderr,"GF(2^m) modular inversion test failed!\n");
1234 int test_gf2m_mod_div(BIO *bp,BN_CTX *ctx)
1236 BIGNUM *a,*b[2],*c,*d,*e,*f;
1238 unsigned int p0[] = {163,7,6,3,0};
1239 unsigned int p1[] = {193,15,0};
1249 BN_GF2m_arr2poly(p0, b[0]);
1250 BN_GF2m_arr2poly(p1, b[1]);
1252 for (i=0; i<num0; i++)
1254 BN_bntest_rand(a, 512, 0, 0);
1255 BN_bntest_rand(c, 512, 0, 0);
1256 for (j=0; j < 2; j++)
1258 BN_GF2m_mod_div(d, a, c, b[j], ctx);
1259 BN_GF2m_mod_mul(e, d, c, b[j], ctx);
1260 BN_GF2m_mod_div(f, a, e, b[j], ctx);
1261 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1267 BIO_puts(bp, " = ");
1271 BIO_puts(bp, " % ");
1277 /* Test that ((a/c)*c)/a = 1. */
1280 fprintf(stderr,"GF(2^m) modular division test failed!\n");
1297 int test_gf2m_mod_exp(BIO *bp,BN_CTX *ctx)
1299 BIGNUM *a,*b[2],*c,*d,*e,*f;
1301 unsigned int p0[] = {163,7,6,3,0};
1302 unsigned int p1[] = {193,15,0};
1312 BN_GF2m_arr2poly(p0, b[0]);
1313 BN_GF2m_arr2poly(p1, b[1]);
1315 for (i=0; i<num0; i++)
1317 BN_bntest_rand(a, 512, 0, 0);
1318 BN_bntest_rand(c, 512, 0, 0);
1319 BN_bntest_rand(d, 512, 0, 0);
1320 for (j=0; j < 2; j++)
1322 BN_GF2m_mod_exp(e, a, c, b[j], ctx);
1323 BN_GF2m_mod_exp(f, a, d, b[j], ctx);
1324 BN_GF2m_mod_mul(e, e, f, b[j], ctx);
1326 BN_GF2m_mod_exp(f, a, f, b[j], ctx);
1327 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1333 BIO_puts(bp, " ^ (");
1337 BIO_puts(bp, ") = ");
1339 BIO_puts(bp, "; - ");
1341 BIO_puts(bp, " % ");
1347 BN_GF2m_add(f, e, f);
1348 /* Test that a^(c+d)=a^c*a^d. */
1351 fprintf(stderr,"GF(2^m) modular exponentiation test failed!\n");
1368 int test_gf2m_mod_sqrt(BIO *bp,BN_CTX *ctx)
1370 BIGNUM *a,*b[2],*c,*d,*e,*f;
1372 unsigned int p0[] = {163,7,6,3,0};
1373 unsigned int p1[] = {193,15,0};
1383 BN_GF2m_arr2poly(p0, b[0]);
1384 BN_GF2m_arr2poly(p1, b[1]);
1386 for (i=0; i<num0; i++)
1388 BN_bntest_rand(a, 512, 0, 0);
1389 for (j=0; j < 2; j++)
1391 BN_GF2m_mod(c, a, b[j]);
1392 BN_GF2m_mod_sqrt(d, a, b[j], ctx);
1393 BN_GF2m_mod_sqr(e, d, b[j], ctx);
1394 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1400 BIO_puts(bp, " ^ 2 - ");
1406 BN_GF2m_add(f, c, e);
1407 /* Test that d^2 = a, where d = sqrt(a). */
1410 fprintf(stderr,"GF(2^m) modular square root test failed!\n");
1427 int test_gf2m_mod_solve_quad(BIO *bp,BN_CTX *ctx)
1429 BIGNUM *a,*b[2],*c,*d,*e;
1430 int i, j, s = 0, t, ret = 0;
1431 unsigned int p0[] = {163,7,6,3,0};
1432 unsigned int p1[] = {193,15,0};
1441 BN_GF2m_arr2poly(p0, b[0]);
1442 BN_GF2m_arr2poly(p1, b[1]);
1444 for (i=0; i<num0; i++)
1446 BN_bntest_rand(a, 512, 0, 0);
1447 for (j=0; j < 2; j++)
1449 t = BN_GF2m_mod_solve_quad(c, a, b[j], ctx);
1453 BN_GF2m_mod_sqr(d, c, b[j], ctx);
1454 BN_GF2m_add(d, c, d);
1455 BN_GF2m_mod(e, a, b[j]);
1456 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1462 BIO_puts(bp, " is root of z^2 + z = ");
1464 BIO_puts(bp, " % ");
1470 BN_GF2m_add(e, e, d);
1471 /* Test that solution of quadratic c satisfies c^2 + c = a. */
1474 fprintf(stderr,"GF(2^m) modular solve quadratic test failed!\n");
1481 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1486 BIO_puts(bp, "There are no roots of z^2 + z = ");
1488 BIO_puts(bp, " % ");
1499 fprintf(stderr,"All %i tests of GF(2^m) modular solve quadratic resulted in no roots;\n", num0);
1500 fprintf(stderr,"this is very unlikely and probably indicates an error.\n");
1514 static void genprime_cb(int p, int n, void *arg)
1528 int test_kron(BIO *bp, BN_CTX *ctx)
1532 int legendre, kronecker;
1539 if (a == NULL || b == NULL || r == NULL || t == NULL) goto err;
1541 /* We test BN_kronecker(a, b, ctx) just for b odd (Jacobi symbol).
1542 * In this case we know that if b is prime, then BN_kronecker(a, b, ctx)
1543 * is congruent to $a^{(b-1)/2}$, modulo $b$ (Legendre symbol).
1544 * So we generate a random prime b and compare these values
1545 * for a number of random a's. (That is, we run the Solovay-Strassen
1546 * primality test to confirm that b is prime, except that we
1547 * don't want to test whether b is prime but whether BN_kronecker
1550 if (!BN_generate_prime(b, 512, 0, NULL, NULL, genprime_cb, NULL)) goto err;
1551 b->neg = rand_neg();
1554 for (i = 0; i < num0; i++)
1556 if (!BN_bntest_rand(a, 512, 0, 0)) goto err;
1557 a->neg = rand_neg();
1559 /* t := (|b|-1)/2 (note that b is odd) */
1560 if (!BN_copy(t, b)) goto err;
1562 if (!BN_sub_word(t, 1)) goto err;
1563 if (!BN_rshift1(t, t)) goto err;
1564 /* r := a^t mod b */
1567 if (!BN_mod_exp_recp(r, a, t, b, ctx)) goto err;
1570 if (BN_is_word(r, 1))
1572 else if (BN_is_zero(r))
1576 if (!BN_add_word(r, 1)) goto err;
1577 if (0 != BN_ucmp(r, b))
1579 fprintf(stderr, "Legendre symbol computation failed\n");
1585 kronecker = BN_kronecker(a, b, ctx);
1586 if (kronecker < -1) goto err;
1587 /* we actually need BN_kronecker(a, |b|) */
1588 if (a->neg && b->neg)
1589 kronecker = -kronecker;
1591 if (legendre != kronecker)
1593 fprintf(stderr, "legendre != kronecker; a = ");
1594 BN_print_fp(stderr, a);
1595 fprintf(stderr, ", b = ");
1596 BN_print_fp(stderr, b);
1597 fprintf(stderr, "\n");
1609 if (a != NULL) BN_free(a);
1610 if (b != NULL) BN_free(b);
1611 if (r != NULL) BN_free(r);
1612 if (t != NULL) BN_free(t);
1616 int test_sqrt(BIO *bp, BN_CTX *ctx)
1625 if (a == NULL || p == NULL || r == NULL) goto err;
1627 for (i = 0; i < 16; i++)
1631 unsigned primes[8] = { 2, 3, 5, 7, 11, 13, 17, 19 };
1633 if (!BN_set_word(p, primes[i])) goto err;
1637 if (!BN_set_word(a, 32)) goto err;
1638 if (!BN_set_word(r, 2*i + 1)) goto err;
1640 if (!BN_generate_prime(p, 256, 0, a, r, genprime_cb, NULL)) goto err;
1643 p->neg = rand_neg();
1645 for (j = 0; j < num2; j++)
1647 /* construct 'a' such that it is a square modulo p,
1648 * but in general not a proper square and not reduced modulo p */
1649 if (!BN_bntest_rand(r, 256, 0, 3)) goto err;
1650 if (!BN_nnmod(r, r, p, ctx)) goto err;
1651 if (!BN_mod_sqr(r, r, p, ctx)) goto err;
1652 if (!BN_bntest_rand(a, 256, 0, 3)) goto err;
1653 if (!BN_nnmod(a, a, p, ctx)) goto err;
1654 if (!BN_mod_sqr(a, a, p, ctx)) goto err;
1655 if (!BN_mul(a, a, r, ctx)) goto err;
1657 if (!BN_sub(a, a, p)) goto err;
1659 if (!BN_mod_sqrt(r, a, p, ctx)) goto err;
1660 if (!BN_mod_sqr(r, r, p, ctx)) goto err;
1662 if (!BN_nnmod(a, a, p, ctx)) goto err;
1664 if (BN_cmp(a, r) != 0)
1666 fprintf(stderr, "BN_mod_sqrt failed: a = ");
1667 BN_print_fp(stderr, a);
1668 fprintf(stderr, ", r = ");
1669 BN_print_fp(stderr, r);
1670 fprintf(stderr, ", p = ");
1671 BN_print_fp(stderr, p);
1672 fprintf(stderr, "\n");
1685 if (a != NULL) BN_free(a);
1686 if (p != NULL) BN_free(p);
1687 if (r != NULL) BN_free(r);
1691 int test_lshift(BIO *bp,BN_CTX *ctx,BIGNUM *a_)
1706 BN_bntest_rand(a,200,0,0); /**/
1709 for (i=0; i<num0; i++)
1729 fprintf(stderr,"Left shift test failed!\n");
1730 fprintf(stderr,"a=");
1731 BN_print_fp(stderr,a);
1732 fprintf(stderr,"\nb=");
1733 BN_print_fp(stderr,b);
1734 fprintf(stderr,"\nc=");
1735 BN_print_fp(stderr,c);
1736 fprintf(stderr,"\nd=");
1737 BN_print_fp(stderr,d);
1738 fprintf(stderr,"\n");
1749 int test_lshift1(BIO *bp)
1758 BN_bntest_rand(a,200,0,0); /**/
1760 for (i=0; i<num0; i++)
1768 BIO_puts(bp," * 2");
1778 fprintf(stderr,"Left shift one test failed!\n");
1790 int test_rshift(BIO *bp,BN_CTX *ctx)
1792 BIGNUM *a,*b,*c,*d,*e;
1802 BN_bntest_rand(a,200,0,0); /**/
1804 for (i=0; i<num0; i++)
1820 BN_div(d,e,a,c,ctx);
1824 fprintf(stderr,"Right shift test failed!\n");
1836 int test_rshift1(BIO *bp)
1845 BN_bntest_rand(a,200,0,0); /**/
1847 for (i=0; i<num0; i++)
1855 BIO_puts(bp," / 2");
1863 if(!BN_is_zero(c) && !BN_abs_is_word(c, 1))
1865 fprintf(stderr,"Right shift one test failed!\n");
1878 static unsigned int neg=0;
1879 static int sign[8]={0,0,0,1,1,0,1,1};
1881 return(sign[(neg++)%8]);