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 const int num0 = 100; /* number of tests */
91 const int num1 = 50; /* additional tests for some functions */
92 const int num2 = 5; /* number of tests for slow functions */
94 int test_add(BIO *bp);
95 int test_sub(BIO *bp);
96 int test_lshift1(BIO *bp);
97 int test_lshift(BIO *bp,BN_CTX *ctx,BIGNUM *a_);
98 int test_rshift1(BIO *bp);
99 int test_rshift(BIO *bp,BN_CTX *ctx);
100 int test_div(BIO *bp,BN_CTX *ctx);
101 int test_div_recp(BIO *bp,BN_CTX *ctx);
102 int test_mul(BIO *bp);
103 int test_sqr(BIO *bp,BN_CTX *ctx);
104 int test_mont(BIO *bp,BN_CTX *ctx);
105 int test_mod(BIO *bp,BN_CTX *ctx);
106 int test_mod_mul(BIO *bp,BN_CTX *ctx);
107 int test_mod_exp(BIO *bp,BN_CTX *ctx);
108 int test_exp(BIO *bp,BN_CTX *ctx);
109 int test_gf2m_add(BIO *bp);
110 int test_gf2m_mod(BIO *bp);
111 int test_gf2m_mod_mul(BIO *bp,BN_CTX *ctx);
112 int test_gf2m_mod_sqr(BIO *bp,BN_CTX *ctx);
113 int test_gf2m_mod_inv(BIO *bp,BN_CTX *ctx);
114 int test_gf2m_mod_div(BIO *bp,BN_CTX *ctx);
115 int test_gf2m_mod_exp(BIO *bp,BN_CTX *ctx);
116 int test_gf2m_mod_sqrt(BIO *bp,BN_CTX *ctx);
117 int test_gf2m_mod_solve_quad(BIO *bp,BN_CTX *ctx);
118 int test_kron(BIO *bp,BN_CTX *ctx);
119 int test_sqrt(BIO *bp,BN_CTX *ctx);
121 static int results=0;
123 static unsigned char lst[]="\xC6\x4F\x43\x04\x2A\xEA\xCA\x6E\x58\x36\x80\x5B\xE8\xC9"
124 "\x9B\x04\x5D\x48\x36\xC2\xFD\x16\xC9\x64\xF0";
126 static const char rnd_seed[] = "string to make the random number generator think it has entropy";
128 static void message(BIO *out, char *m)
130 fprintf(stderr, "test %s\n", m);
131 BIO_puts(out, "print \"test ");
133 BIO_puts(out, "\\n\"\n");
136 int main(int argc, char *argv[])
144 RAND_seed(rnd_seed, sizeof rnd_seed); /* or BN_generate_prime may fail */
150 if (strcmp(*argv,"-results") == 0)
152 else if (strcmp(*argv,"-out") == 0)
154 if (--argc < 1) break;
163 if (ctx == NULL) EXIT(1);
165 out=BIO_new(BIO_s_file());
166 if (out == NULL) EXIT(1);
169 BIO_set_fp(out,stdout,BIO_NOCLOSE);
173 if (!BIO_write_filename(out,outfile))
181 BIO_puts(out,"obase=16\nibase=16\n");
183 message(out,"BN_add");
184 if (!test_add(out)) goto err;
187 message(out,"BN_sub");
188 if (!test_sub(out)) goto err;
191 message(out,"BN_lshift1");
192 if (!test_lshift1(out)) goto err;
195 message(out,"BN_lshift (fixed)");
196 if (!test_lshift(out,ctx,BN_bin2bn(lst,sizeof(lst)-1,NULL)))
200 message(out,"BN_lshift");
201 if (!test_lshift(out,ctx,NULL)) goto err;
204 message(out,"BN_rshift1");
205 if (!test_rshift1(out)) goto err;
208 message(out,"BN_rshift");
209 if (!test_rshift(out,ctx)) goto err;
212 message(out,"BN_sqr");
213 if (!test_sqr(out,ctx)) goto err;
216 message(out,"BN_mul");
217 if (!test_mul(out)) goto err;
220 message(out,"BN_div");
221 if (!test_div(out,ctx)) goto err;
224 message(out,"BN_div_recp");
225 if (!test_div_recp(out,ctx)) goto err;
228 message(out,"BN_mod");
229 if (!test_mod(out,ctx)) goto err;
232 message(out,"BN_mod_mul");
233 if (!test_mod_mul(out,ctx)) goto err;
236 message(out,"BN_mont");
237 if (!test_mont(out,ctx)) goto err;
240 message(out,"BN_mod_exp");
241 if (!test_mod_exp(out,ctx)) goto err;
244 message(out,"BN_exp");
245 if (!test_exp(out,ctx)) goto err;
248 message(out,"BN_kronecker");
249 if (!test_kron(out,ctx)) goto err;
252 message(out,"BN_mod_sqrt");
253 if (!test_sqrt(out,ctx)) goto err;
256 message(out,"BN_GF2m_add");
257 if (!test_gf2m_add(out)) goto err;
260 message(out,"BN_GF2m_mod");
261 if (!test_gf2m_mod(out)) goto err;
264 message(out,"BN_GF2m_mod_mul");
265 if (!test_gf2m_mod_mul(out,ctx)) goto err;
268 message(out,"BN_GF2m_mod_sqr");
269 if (!test_gf2m_mod_sqr(out,ctx)) goto err;
272 message(out,"BN_GF2m_mod_inv");
273 if (!test_gf2m_mod_inv(out,ctx)) goto err;
276 message(out,"BN_GF2m_mod_div");
277 if (!test_gf2m_mod_div(out,ctx)) goto err;
280 message(out,"BN_GF2m_mod_exp");
281 if (!test_gf2m_mod_exp(out,ctx)) goto err;
284 message(out,"BN_GF2m_mod_sqrt");
285 if (!test_gf2m_mod_sqrt(out,ctx)) goto err;
288 message(out,"BN_GF2m_mod_solve_quad");
289 if (!test_gf2m_mod_solve_quad(out,ctx)) goto err;
298 BIO_puts(out,"1\n"); /* make sure the Perl script fed by bc notices
299 * the failure, see test_bn in test/Makefile.ssl*/
301 ERR_load_crypto_strings();
302 ERR_print_errors_fp(stderr);
307 int test_add(BIO *bp)
316 BN_bntest_rand(&a,512,0,0);
317 for (i=0; i<num0; i++)
319 BN_bntest_rand(&b,450+i,0,0);
341 fprintf(stderr,"Add test failed!\n");
351 int test_sub(BIO *bp)
360 for (i=0; i<num0+num1; i++)
364 BN_bntest_rand(&a,512,0,0);
366 if (BN_set_bit(&a,i)==0) return(0);
371 BN_bntest_rand(&b,400+i-num1,0,0);
392 fprintf(stderr,"Subtract test failed!\n");
402 int test_div(BIO *bp, BN_CTX *ctx)
413 for (i=0; i<num0+num1; i++)
417 BN_bntest_rand(&a,400,0,0);
423 BN_bntest_rand(&b,50+3*(i-num1),0,0);
426 BN_div(&d,&c,&a,&b,ctx);
449 BN_mul(&e,&d,&b,ctx);
454 fprintf(stderr,"Division test failed!\n");
466 int test_div_recp(BIO *bp, BN_CTX *ctx)
472 BN_RECP_CTX_init(&recp);
479 for (i=0; i<num0+num1; i++)
483 BN_bntest_rand(&a,400,0,0);
489 BN_bntest_rand(&b,50+3*(i-num1),0,0);
492 BN_RECP_CTX_set(&recp,&b,ctx);
493 BN_div_recp(&d,&c,&a,&recp,ctx);
516 BN_mul(&e,&d,&b,ctx);
521 fprintf(stderr,"Reciprocal division test failed!\n");
522 fprintf(stderr,"a=");
523 BN_print_fp(stderr,&a);
524 fprintf(stderr,"\nb=");
525 BN_print_fp(stderr,&b);
526 fprintf(stderr,"\n");
535 BN_RECP_CTX_free(&recp);
539 int test_mul(BIO *bp)
546 if (ctx == NULL) EXIT(1);
554 for (i=0; i<num0+num1; i++)
558 BN_bntest_rand(&a,100,0,0);
559 BN_bntest_rand(&b,100,0,0);
562 BN_bntest_rand(&b,i-num1,0,0);
565 BN_mul(&c,&a,&b,ctx);
578 BN_div(&d,&e,&c,&a,ctx);
580 if(!BN_is_zero(&d) || !BN_is_zero(&e))
582 fprintf(stderr,"Multiplication test failed!\n");
595 int test_sqr(BIO *bp, BN_CTX *ctx)
605 for (i=0; i<num0; i++)
607 BN_bntest_rand(&a,40+i*10,0,0);
622 BN_div(&d,&e,&c,&a,ctx);
624 if(!BN_is_zero(&d) || !BN_is_zero(&e))
626 fprintf(stderr,"Square test failed!\n");
637 int test_mont(BIO *bp, BN_CTX *ctx)
652 mont=BN_MONT_CTX_new();
654 BN_bntest_rand(&a,100,0,0); /**/
655 BN_bntest_rand(&b,100,0,0); /**/
656 for (i=0; i<num2; i++)
658 int bits = (200*(i+1))/num2;
662 BN_bntest_rand(&n,bits,0,1);
663 BN_MONT_CTX_set(mont,&n,ctx);
665 BN_nnmod(&a,&a,&n,ctx);
666 BN_nnmod(&b,&b,&n,ctx);
668 BN_to_montgomery(&A,&a,mont,ctx);
669 BN_to_montgomery(&B,&b,mont,ctx);
671 BN_mod_mul_montgomery(&c,&A,&B,mont,ctx);/**/
672 BN_from_montgomery(&A,&c,mont,ctx);/**/
678 fprintf(stderr,"%d * %d %% %d\n",
681 BN_num_bits(mont->N));
687 BN_print(bp,&(mont->N));
693 BN_mod_mul(&d,&a,&b,&n,ctx);
697 fprintf(stderr,"Montgomery multiplication test failed!\n");
701 BN_MONT_CTX_free(mont);
712 int test_mod(BIO *bp, BN_CTX *ctx)
714 BIGNUM *a,*b,*c,*d,*e;
723 BN_bntest_rand(a,1024,0,0); /**/
724 for (i=0; i<num0; i++)
726 BN_bntest_rand(b,450+i*10,0,0); /**/
729 BN_mod(c,a,b,ctx);/**/
746 fprintf(stderr,"Modulo test failed!\n");
758 int test_mod_mul(BIO *bp, BN_CTX *ctx)
760 BIGNUM *a,*b,*c,*d,*e;
769 for (j=0; j<3; j++) {
770 BN_bntest_rand(c,1024,0,0); /**/
771 for (i=0; i<num0; i++)
773 BN_bntest_rand(a,475+i*10,0,0); /**/
774 BN_bntest_rand(b,425+i*11,0,0); /**/
777 if (!BN_mod_mul(e,a,b,c,ctx))
781 while ((l=ERR_get_error()))
782 fprintf(stderr,"ERROR:%s\n",
783 ERR_error_string(l,NULL));
795 if ((a->neg ^ b->neg) && !BN_is_zero(e))
797 /* If (a*b) % c is negative, c must be added
798 * in order to obtain the normalized remainder
799 * (new with OpenSSL 0.9.7, previous versions of
800 * BN_mod_mul could generate negative results)
815 fprintf(stderr,"Modulo multiply test failed!\n");
816 ERR_print_errors_fp(stderr);
829 int test_mod_exp(BIO *bp, BN_CTX *ctx)
831 BIGNUM *a,*b,*c,*d,*e;
840 BN_bntest_rand(c,30,0,1); /* must be odd for montgomery */
841 for (i=0; i<num2; i++)
843 BN_bntest_rand(a,20+i*5,0,0); /**/
844 BN_bntest_rand(b,2+i,0,0); /**/
846 if (!BN_mod_exp(d,a,b,c,ctx))
868 fprintf(stderr,"Modulo exponentiation test failed!\n");
880 int test_exp(BIO *bp, BN_CTX *ctx)
882 BIGNUM *a,*b,*d,*e,*one;
892 for (i=0; i<num2; i++)
894 BN_bntest_rand(a,20+i*5,0,0); /**/
895 BN_bntest_rand(b,2+i,0,0); /**/
897 if (!BN_exp(d,a,b,ctx))
913 for( ; !BN_is_zero(b) ; BN_sub(b,b,one))
918 fprintf(stderr,"Exponentiation test failed!\n");
930 int test_gf2m_add(BIO *bp)
939 for (i=0; i<num0; i++)
942 BN_copy(&b, BN_value_one());
945 BN_GF2m_add(&c,&a,&b);
946 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
960 /* Test that two added values have the correct parity. */
961 if((BN_is_odd(&a) && BN_is_odd(&c)) || (!BN_is_odd(&a) && !BN_is_odd(&c)))
963 fprintf(stderr,"GF(2^m) addition test (a) failed!\n");
966 BN_GF2m_add(&c,&c,&c);
967 /* Test that c + c = 0. */
970 fprintf(stderr,"GF(2^m) addition test (b) failed!\n");
982 int test_gf2m_mod(BIO *bp)
984 BIGNUM *a,*b[2],*c,*d,*e;
986 unsigned int p0[] = {163,7,6,3,0};
987 unsigned int p1[] = {193,15,0};
996 BN_GF2m_arr2poly(p0, b[0]);
997 BN_GF2m_arr2poly(p1, b[1]);
999 for (i=0; i<num0; i++)
1001 BN_bntest_rand(a, 1024, 0, 0);
1002 for (j=0; j < 2; j++)
1004 BN_GF2m_mod(c, a, b[j]);
1005 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1019 BN_GF2m_add(d, a, c);
1020 BN_GF2m_mod(e, d, b[j]);
1021 /* Test that a + (a mod p) mod p == 0. */
1024 fprintf(stderr,"GF(2^m) modulo test failed!\n");
1040 int test_gf2m_mod_mul(BIO *bp,BN_CTX *ctx)
1042 BIGNUM *a,*b[2],*c,*d,*e,*f,*g,*h;
1044 unsigned int p0[] = {163,7,6,3,0};
1045 unsigned int p1[] = {193,15,0};
1057 BN_GF2m_arr2poly(p0, b[0]);
1058 BN_GF2m_arr2poly(p1, b[1]);
1060 for (i=0; i<num0; i++)
1062 BN_bntest_rand(a, 1024, 0, 0);
1063 BN_bntest_rand(c, 1024, 0, 0);
1064 BN_bntest_rand(d, 1024, 0, 0);
1065 for (j=0; j < 2; j++)
1067 BN_GF2m_mod_mul(e, a, c, b[j], ctx);
1068 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1084 BN_GF2m_add(f, a, d);
1085 BN_GF2m_mod_mul(g, f, c, b[j], ctx);
1086 BN_GF2m_mod_mul(h, d, c, b[j], ctx);
1087 BN_GF2m_add(f, e, g);
1088 BN_GF2m_add(f, f, h);
1089 /* Test that (a+d)*c = a*c + d*c. */
1092 fprintf(stderr,"GF(2^m) modular multiplication test failed!\n");
1111 int test_gf2m_mod_sqr(BIO *bp,BN_CTX *ctx)
1113 BIGNUM *a,*b[2],*c,*d;
1115 unsigned int p0[] = {163,7,6,3,0};
1116 unsigned int p1[] = {193,15,0};
1124 BN_GF2m_arr2poly(p0, b[0]);
1125 BN_GF2m_arr2poly(p1, b[1]);
1127 for (i=0; i<num0; i++)
1129 BN_bntest_rand(a, 1024, 0, 0);
1130 for (j=0; j < 2; j++)
1132 BN_GF2m_mod_sqr(c, a, b[j], ctx);
1134 BN_GF2m_mod_mul(d, a, d, b[j], ctx);
1135 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1141 BIO_puts(bp," ^ 2 % ");
1143 BIO_puts(bp, " = ");
1145 BIO_puts(bp,"; a * a = ");
1151 BN_GF2m_add(d, c, d);
1152 /* Test that a*a = a^2. */
1155 fprintf(stderr,"GF(2^m) modular squaring test failed!\n");
1170 int test_gf2m_mod_inv(BIO *bp,BN_CTX *ctx)
1172 BIGNUM *a,*b[2],*c,*d;
1174 unsigned int p0[] = {163,7,6,3,0};
1175 unsigned int p1[] = {193,15,0};
1183 BN_GF2m_arr2poly(p0, b[0]);
1184 BN_GF2m_arr2poly(p1, b[1]);
1186 for (i=0; i<num0; i++)
1188 BN_bntest_rand(a, 512, 0, 0);
1189 for (j=0; j < 2; j++)
1191 BN_GF2m_mod_inv(c, a, b[j], ctx);
1192 BN_GF2m_mod_mul(d, a, c, b[j], ctx);
1193 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1199 BIO_puts(bp, " * ");
1201 BIO_puts(bp," - 1 % ");
1207 /* Test that ((1/a)*a) = 1. */
1210 fprintf(stderr,"GF(2^m) modular inversion test failed!\n");
1225 int test_gf2m_mod_div(BIO *bp,BN_CTX *ctx)
1227 BIGNUM *a,*b[2],*c,*d,*e,*f;
1229 unsigned int p0[] = {163,7,6,3,0};
1230 unsigned int p1[] = {193,15,0};
1240 BN_GF2m_arr2poly(p0, b[0]);
1241 BN_GF2m_arr2poly(p1, b[1]);
1243 for (i=0; i<num0; i++)
1245 BN_bntest_rand(a, 512, 0, 0);
1246 BN_bntest_rand(c, 512, 0, 0);
1247 for (j=0; j < 2; j++)
1249 BN_GF2m_mod_div(d, a, c, b[j], ctx);
1250 BN_GF2m_mod_mul(e, d, c, b[j], ctx);
1251 BN_GF2m_mod_div(f, a, e, b[j], ctx);
1252 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1258 BIO_puts(bp, " = ");
1262 BIO_puts(bp, " % ");
1268 /* Test that ((a/c)*c)/a = 1. */
1271 fprintf(stderr,"GF(2^m) modular division test failed!\n");
1288 int test_gf2m_mod_exp(BIO *bp,BN_CTX *ctx)
1290 BIGNUM *a,*b[2],*c,*d,*e,*f;
1292 unsigned int p0[] = {163,7,6,3,0};
1293 unsigned int p1[] = {193,15,0};
1303 BN_GF2m_arr2poly(p0, b[0]);
1304 BN_GF2m_arr2poly(p1, b[1]);
1306 for (i=0; i<num0; i++)
1308 BN_bntest_rand(a, 512, 0, 0);
1309 BN_bntest_rand(c, 512, 0, 0);
1310 BN_bntest_rand(d, 512, 0, 0);
1311 for (j=0; j < 2; j++)
1313 BN_GF2m_mod_exp(e, a, c, b[j], ctx);
1314 BN_GF2m_mod_exp(f, a, d, b[j], ctx);
1315 BN_GF2m_mod_mul(e, e, f, b[j], ctx);
1317 BN_GF2m_mod_exp(f, a, f, b[j], ctx);
1318 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1324 BIO_puts(bp, " ^ (");
1328 BIO_puts(bp, ") = ");
1330 BIO_puts(bp, "; - ");
1332 BIO_puts(bp, " % ");
1338 BN_GF2m_add(f, e, f);
1339 /* Test that a^(c+d)=a^c*a^d. */
1342 fprintf(stderr,"GF(2^m) modular exponentiation test failed!\n");
1359 int test_gf2m_mod_sqrt(BIO *bp,BN_CTX *ctx)
1361 BIGNUM *a,*b[2],*c,*d,*e,*f;
1363 unsigned int p0[] = {163,7,6,3,0};
1364 unsigned int p1[] = {193,15,0};
1374 BN_GF2m_arr2poly(p0, b[0]);
1375 BN_GF2m_arr2poly(p1, b[1]);
1377 for (i=0; i<num0; i++)
1379 BN_bntest_rand(a, 512, 0, 0);
1380 for (j=0; j < 2; j++)
1382 BN_GF2m_mod(c, a, b[j]);
1383 BN_GF2m_mod_sqrt(d, a, b[j], ctx);
1384 BN_GF2m_mod_sqr(e, d, b[j], ctx);
1385 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1391 BIO_puts(bp, " ^ 2 - ");
1397 BN_GF2m_add(f, c, e);
1398 /* Test that d^2 = a, where d = sqrt(a). */
1401 fprintf(stderr,"GF(2^m) modular square root test failed!\n");
1418 int test_gf2m_mod_solve_quad(BIO *bp,BN_CTX *ctx)
1420 BIGNUM *a,*b[2],*c,*d,*e;
1421 int i, j, s = 0, t, ret = 0;
1422 unsigned int p0[] = {163,7,6,3,0};
1423 unsigned int p1[] = {193,15,0};
1432 BN_GF2m_arr2poly(p0, b[0]);
1433 BN_GF2m_arr2poly(p1, b[1]);
1435 for (i=0; i<num0; i++)
1437 BN_bntest_rand(a, 512, 0, 0);
1438 for (j=0; j < 2; j++)
1440 t = BN_GF2m_mod_solve_quad(c, a, b[j], ctx);
1444 BN_GF2m_mod_sqr(d, c, b[j], ctx);
1445 BN_GF2m_add(d, c, d);
1446 BN_GF2m_mod(e, a, b[j]);
1447 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1453 BIO_puts(bp, " is root of z^2 + z = ");
1455 BIO_puts(bp, " % ");
1461 BN_GF2m_add(e, e, d);
1462 /* Test that solution of quadratic c satisfies c^2 + c = a. */
1465 fprintf(stderr,"GF(2^m) modular solve quadratic test failed!\n");
1472 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1477 BIO_puts(bp, "There are no roots of z^2 + z = ");
1479 BIO_puts(bp, " % ");
1490 fprintf(stderr,"All %i tests of GF(2^m) modular solve quadratic resulted in no roots;\n", num0);
1491 fprintf(stderr,"this is very unlikely and probably indicates an error.\n");
1505 static void genprime_cb(int p, int n, void *arg)
1519 int test_kron(BIO *bp, BN_CTX *ctx)
1523 int legendre, kronecker;
1530 if (a == NULL || b == NULL || r == NULL || t == NULL) goto err;
1532 /* We test BN_kronecker(a, b, ctx) just for b odd (Jacobi symbol).
1533 * In this case we know that if b is prime, then BN_kronecker(a, b, ctx)
1534 * is congruent to $a^{(b-1)/2}$, modulo $b$ (Legendre symbol).
1535 * So we generate a random prime b and compare these values
1536 * for a number of random a's. (That is, we run the Solovay-Strassen
1537 * primality test to confirm that b is prime, except that we
1538 * don't want to test whether b is prime but whether BN_kronecker
1541 if (!BN_generate_prime(b, 512, 0, NULL, NULL, genprime_cb, NULL)) goto err;
1542 b->neg = rand_neg();
1545 for (i = 0; i < num0; i++)
1547 if (!BN_bntest_rand(a, 512, 0, 0)) goto err;
1548 a->neg = rand_neg();
1550 /* t := (|b|-1)/2 (note that b is odd) */
1551 if (!BN_copy(t, b)) goto err;
1553 if (!BN_sub_word(t, 1)) goto err;
1554 if (!BN_rshift1(t, t)) goto err;
1555 /* r := a^t mod b */
1558 if (!BN_mod_exp_recp(r, a, t, b, ctx)) goto err;
1561 if (BN_is_word(r, 1))
1563 else if (BN_is_zero(r))
1567 if (!BN_add_word(r, 1)) goto err;
1568 if (0 != BN_ucmp(r, b))
1570 fprintf(stderr, "Legendre symbol computation failed\n");
1576 kronecker = BN_kronecker(a, b, ctx);
1577 if (kronecker < -1) goto err;
1578 /* we actually need BN_kronecker(a, |b|) */
1579 if (a->neg && b->neg)
1580 kronecker = -kronecker;
1582 if (legendre != kronecker)
1584 fprintf(stderr, "legendre != kronecker; a = ");
1585 BN_print_fp(stderr, a);
1586 fprintf(stderr, ", b = ");
1587 BN_print_fp(stderr, b);
1588 fprintf(stderr, "\n");
1600 if (a != NULL) BN_free(a);
1601 if (b != NULL) BN_free(b);
1602 if (r != NULL) BN_free(r);
1603 if (t != NULL) BN_free(t);
1607 int test_sqrt(BIO *bp, BN_CTX *ctx)
1616 if (a == NULL || p == NULL || r == NULL) goto err;
1618 for (i = 0; i < 16; i++)
1622 unsigned primes[8] = { 2, 3, 5, 7, 11, 13, 17, 19 };
1624 if (!BN_set_word(p, primes[i])) goto err;
1628 if (!BN_set_word(a, 32)) goto err;
1629 if (!BN_set_word(r, 2*i + 1)) goto err;
1631 if (!BN_generate_prime(p, 256, 0, a, r, genprime_cb, NULL)) goto err;
1634 p->neg = rand_neg();
1636 for (j = 0; j < num2; j++)
1638 /* construct 'a' such that it is a square modulo p,
1639 * but in general not a proper square and not reduced modulo p */
1640 if (!BN_bntest_rand(r, 256, 0, 3)) goto err;
1641 if (!BN_nnmod(r, r, p, ctx)) goto err;
1642 if (!BN_mod_sqr(r, r, p, ctx)) goto err;
1643 if (!BN_bntest_rand(a, 256, 0, 3)) goto err;
1644 if (!BN_nnmod(a, a, p, ctx)) goto err;
1645 if (!BN_mod_sqr(a, a, p, ctx)) goto err;
1646 if (!BN_mul(a, a, r, ctx)) goto err;
1648 if (!BN_sub(a, a, p)) goto err;
1650 if (!BN_mod_sqrt(r, a, p, ctx)) goto err;
1651 if (!BN_mod_sqr(r, r, p, ctx)) goto err;
1653 if (!BN_nnmod(a, a, p, ctx)) goto err;
1655 if (BN_cmp(a, r) != 0)
1657 fprintf(stderr, "BN_mod_sqrt failed: a = ");
1658 BN_print_fp(stderr, a);
1659 fprintf(stderr, ", r = ");
1660 BN_print_fp(stderr, r);
1661 fprintf(stderr, ", p = ");
1662 BN_print_fp(stderr, p);
1663 fprintf(stderr, "\n");
1676 if (a != NULL) BN_free(a);
1677 if (p != NULL) BN_free(p);
1678 if (r != NULL) BN_free(r);
1682 int test_lshift(BIO *bp,BN_CTX *ctx,BIGNUM *a_)
1697 BN_bntest_rand(a,200,0,0); /**/
1700 for (i=0; i<num0; i++)
1720 fprintf(stderr,"Left shift test failed!\n");
1721 fprintf(stderr,"a=");
1722 BN_print_fp(stderr,a);
1723 fprintf(stderr,"\nb=");
1724 BN_print_fp(stderr,b);
1725 fprintf(stderr,"\nc=");
1726 BN_print_fp(stderr,c);
1727 fprintf(stderr,"\nd=");
1728 BN_print_fp(stderr,d);
1729 fprintf(stderr,"\n");
1740 int test_lshift1(BIO *bp)
1749 BN_bntest_rand(a,200,0,0); /**/
1751 for (i=0; i<num0; i++)
1759 BIO_puts(bp," * 2");
1769 fprintf(stderr,"Left shift one test failed!\n");
1781 int test_rshift(BIO *bp,BN_CTX *ctx)
1783 BIGNUM *a,*b,*c,*d,*e;
1793 BN_bntest_rand(a,200,0,0); /**/
1795 for (i=0; i<num0; i++)
1811 BN_div(d,e,a,c,ctx);
1815 fprintf(stderr,"Right shift test failed!\n");
1827 int test_rshift1(BIO *bp)
1836 BN_bntest_rand(a,200,0,0); /**/
1838 for (i=0; i<num0; i++)
1846 BIO_puts(bp," / 2");
1854 if(!BN_is_zero(c) && !BN_abs_is_word(c, 1))
1856 fprintf(stderr,"Right shift one test failed!\n");
1869 static unsigned int neg=0;
1870 static int sign[8]={0,0,0,1,1,0,1,1};
1872 return(sign[(neg++)%8]);