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_word(BIO *bp);
102 int test_div_recp(BIO *bp,BN_CTX *ctx);
103 int test_mul(BIO *bp);
104 int test_sqr(BIO *bp,BN_CTX *ctx);
105 int test_mont(BIO *bp,BN_CTX *ctx);
106 int test_mod(BIO *bp,BN_CTX *ctx);
107 int test_mod_mul(BIO *bp,BN_CTX *ctx);
108 int test_mod_exp(BIO *bp,BN_CTX *ctx);
109 int test_exp(BIO *bp,BN_CTX *ctx);
110 int test_gf2m_add(BIO *bp);
111 int test_gf2m_mod(BIO *bp);
112 int test_gf2m_mod_mul(BIO *bp,BN_CTX *ctx);
113 int test_gf2m_mod_sqr(BIO *bp,BN_CTX *ctx);
114 int test_gf2m_mod_inv(BIO *bp,BN_CTX *ctx);
115 int test_gf2m_mod_div(BIO *bp,BN_CTX *ctx);
116 int test_gf2m_mod_exp(BIO *bp,BN_CTX *ctx);
117 int test_gf2m_mod_sqrt(BIO *bp,BN_CTX *ctx);
118 int test_gf2m_mod_solve_quad(BIO *bp,BN_CTX *ctx);
119 int test_kron(BIO *bp,BN_CTX *ctx);
120 int test_sqrt(BIO *bp,BN_CTX *ctx);
122 static int results=0;
124 static unsigned char lst[]="\xC6\x4F\x43\x04\x2A\xEA\xCA\x6E\x58\x36\x80\x5B\xE8\xC9"
125 "\x9B\x04\x5D\x48\x36\xC2\xFD\x16\xC9\x64\xF0";
127 static const char rnd_seed[] = "string to make the random number generator think it has entropy";
129 static void message(BIO *out, char *m)
131 fprintf(stderr, "test %s\n", m);
132 BIO_puts(out, "print \"test ");
134 BIO_puts(out, "\\n\"\n");
137 int main(int argc, char *argv[])
145 RAND_seed(rnd_seed, sizeof rnd_seed); /* or BN_generate_prime may fail */
151 if (strcmp(*argv,"-results") == 0)
153 else if (strcmp(*argv,"-out") == 0)
155 if (--argc < 1) break;
164 if (ctx == NULL) EXIT(1);
166 out=BIO_new(BIO_s_file());
167 if (out == NULL) EXIT(1);
170 BIO_set_fp(out,stdout,BIO_NOCLOSE);
174 if (!BIO_write_filename(out,outfile))
182 BIO_puts(out,"obase=16\nibase=16\n");
184 message(out,"BN_add");
185 if (!test_add(out)) goto err;
188 message(out,"BN_sub");
189 if (!test_sub(out)) goto err;
192 message(out,"BN_lshift1");
193 if (!test_lshift1(out)) goto err;
196 message(out,"BN_lshift (fixed)");
197 if (!test_lshift(out,ctx,BN_bin2bn(lst,sizeof(lst)-1,NULL)))
201 message(out,"BN_lshift");
202 if (!test_lshift(out,ctx,NULL)) goto err;
205 message(out,"BN_rshift1");
206 if (!test_rshift1(out)) goto err;
209 message(out,"BN_rshift");
210 if (!test_rshift(out,ctx)) goto err;
213 message(out,"BN_sqr");
214 if (!test_sqr(out,ctx)) goto err;
217 message(out,"BN_mul");
218 if (!test_mul(out)) goto err;
221 message(out,"BN_div");
222 if (!test_div(out,ctx)) goto err;
225 message(out,"BN_div_word");
226 if (!test_div_word(out)) goto err;
229 message(out,"BN_div_recp");
230 if (!test_div_recp(out,ctx)) goto err;
233 message(out,"BN_mod");
234 if (!test_mod(out,ctx)) goto err;
237 message(out,"BN_mod_mul");
238 if (!test_mod_mul(out,ctx)) goto err;
241 message(out,"BN_mont");
242 if (!test_mont(out,ctx)) goto err;
245 message(out,"BN_mod_exp");
246 if (!test_mod_exp(out,ctx)) goto err;
249 message(out,"BN_exp");
250 if (!test_exp(out,ctx)) goto err;
253 message(out,"BN_kronecker");
254 if (!test_kron(out,ctx)) goto err;
257 message(out,"BN_mod_sqrt");
258 if (!test_sqrt(out,ctx)) goto err;
261 message(out,"BN_GF2m_add");
262 if (!test_gf2m_add(out)) goto err;
265 message(out,"BN_GF2m_mod");
266 if (!test_gf2m_mod(out)) goto err;
269 message(out,"BN_GF2m_mod_mul");
270 if (!test_gf2m_mod_mul(out,ctx)) goto err;
273 message(out,"BN_GF2m_mod_sqr");
274 if (!test_gf2m_mod_sqr(out,ctx)) goto err;
277 message(out,"BN_GF2m_mod_inv");
278 if (!test_gf2m_mod_inv(out,ctx)) goto err;
281 message(out,"BN_GF2m_mod_div");
282 if (!test_gf2m_mod_div(out,ctx)) goto err;
285 message(out,"BN_GF2m_mod_exp");
286 if (!test_gf2m_mod_exp(out,ctx)) goto err;
289 message(out,"BN_GF2m_mod_sqrt");
290 if (!test_gf2m_mod_sqrt(out,ctx)) goto err;
293 message(out,"BN_GF2m_mod_solve_quad");
294 if (!test_gf2m_mod_solve_quad(out,ctx)) goto err;
303 BIO_puts(out,"1\n"); /* make sure the Perl script fed by bc notices
304 * the failure, see test_bn in test/Makefile.ssl*/
306 ERR_load_crypto_strings();
307 ERR_print_errors_fp(stderr);
312 int test_add(BIO *bp)
321 BN_bntest_rand(&a,512,0,0);
322 for (i=0; i<num0; i++)
324 BN_bntest_rand(&b,450+i,0,0);
346 fprintf(stderr,"Add test failed!\n");
356 int test_sub(BIO *bp)
365 for (i=0; i<num0+num1; i++)
369 BN_bntest_rand(&a,512,0,0);
371 if (BN_set_bit(&a,i)==0) return(0);
376 BN_bntest_rand(&b,400+i-num1,0,0);
397 fprintf(stderr,"Subtract test failed!\n");
407 int test_div(BIO *bp, BN_CTX *ctx)
418 for (i=0; i<num0+num1; i++)
422 BN_bntest_rand(&a,400,0,0);
428 BN_bntest_rand(&b,50+3*(i-num1),0,0);
431 BN_div(&d,&c,&a,&b,ctx);
454 BN_mul(&e,&d,&b,ctx);
459 fprintf(stderr,"Division test failed!\n");
471 int test_div_word(BIO *bp)
480 for (i=0; i<num0; i++)
483 BN_bntest_rand(&a,512,-1,0);
484 BN_bntest_rand(&b,BN_BITS2,-1,0);
489 r = BN_div_word(&b, s);
497 BIO_printf(bp,"%lX",s);
507 BIO_printf(bp,"%lX",s);
510 BIO_printf(bp,"%lX",r);
518 fprintf(stderr,"Division (word) test failed!\n");
527 int test_div_recp(BIO *bp, BN_CTX *ctx)
533 BN_RECP_CTX_init(&recp);
540 for (i=0; i<num0+num1; i++)
544 BN_bntest_rand(&a,400,0,0);
550 BN_bntest_rand(&b,50+3*(i-num1),0,0);
553 BN_RECP_CTX_set(&recp,&b,ctx);
554 BN_div_recp(&d,&c,&a,&recp,ctx);
577 BN_mul(&e,&d,&b,ctx);
582 fprintf(stderr,"Reciprocal division test failed!\n");
583 fprintf(stderr,"a=");
584 BN_print_fp(stderr,&a);
585 fprintf(stderr,"\nb=");
586 BN_print_fp(stderr,&b);
587 fprintf(stderr,"\n");
596 BN_RECP_CTX_free(&recp);
600 int test_mul(BIO *bp)
607 if (ctx == NULL) EXIT(1);
615 for (i=0; i<num0+num1; i++)
619 BN_bntest_rand(&a,100,0,0);
620 BN_bntest_rand(&b,100,0,0);
623 BN_bntest_rand(&b,i-num1,0,0);
626 BN_mul(&c,&a,&b,ctx);
639 BN_div(&d,&e,&c,&a,ctx);
641 if(!BN_is_zero(&d) || !BN_is_zero(&e))
643 fprintf(stderr,"Multiplication test failed!\n");
656 int test_sqr(BIO *bp, BN_CTX *ctx)
666 for (i=0; i<num0; i++)
668 BN_bntest_rand(&a,40+i*10,0,0);
683 BN_div(&d,&e,&c,&a,ctx);
685 if(!BN_is_zero(&d) || !BN_is_zero(&e))
687 fprintf(stderr,"Square test failed!\n");
698 int test_mont(BIO *bp, BN_CTX *ctx)
713 mont=BN_MONT_CTX_new();
715 BN_bntest_rand(&a,100,0,0); /**/
716 BN_bntest_rand(&b,100,0,0); /**/
717 for (i=0; i<num2; i++)
719 int bits = (200*(i+1))/num2;
723 BN_bntest_rand(&n,bits,0,1);
724 BN_MONT_CTX_set(mont,&n,ctx);
726 BN_nnmod(&a,&a,&n,ctx);
727 BN_nnmod(&b,&b,&n,ctx);
729 BN_to_montgomery(&A,&a,mont,ctx);
730 BN_to_montgomery(&B,&b,mont,ctx);
732 BN_mod_mul_montgomery(&c,&A,&B,mont,ctx);/**/
733 BN_from_montgomery(&A,&c,mont,ctx);/**/
739 fprintf(stderr,"%d * %d %% %d\n",
742 BN_num_bits(mont->N));
748 BN_print(bp,&(mont->N));
754 BN_mod_mul(&d,&a,&b,&n,ctx);
758 fprintf(stderr,"Montgomery multiplication test failed!\n");
762 BN_MONT_CTX_free(mont);
773 int test_mod(BIO *bp, BN_CTX *ctx)
775 BIGNUM *a,*b,*c,*d,*e;
784 BN_bntest_rand(a,1024,0,0); /**/
785 for (i=0; i<num0; i++)
787 BN_bntest_rand(b,450+i*10,0,0); /**/
790 BN_mod(c,a,b,ctx);/**/
807 fprintf(stderr,"Modulo test failed!\n");
819 int test_mod_mul(BIO *bp, BN_CTX *ctx)
821 BIGNUM *a,*b,*c,*d,*e;
830 for (j=0; j<3; j++) {
831 BN_bntest_rand(c,1024,0,0); /**/
832 for (i=0; i<num0; i++)
834 BN_bntest_rand(a,475+i*10,0,0); /**/
835 BN_bntest_rand(b,425+i*11,0,0); /**/
838 if (!BN_mod_mul(e,a,b,c,ctx))
842 while ((l=ERR_get_error()))
843 fprintf(stderr,"ERROR:%s\n",
844 ERR_error_string(l,NULL));
856 if ((a->neg ^ b->neg) && !BN_is_zero(e))
858 /* If (a*b) % c is negative, c must be added
859 * in order to obtain the normalized remainder
860 * (new with OpenSSL 0.9.7, previous versions of
861 * BN_mod_mul could generate negative results)
876 fprintf(stderr,"Modulo multiply test failed!\n");
877 ERR_print_errors_fp(stderr);
890 int test_mod_exp(BIO *bp, BN_CTX *ctx)
892 BIGNUM *a,*b,*c,*d,*e;
901 BN_bntest_rand(c,30,0,1); /* must be odd for montgomery */
902 for (i=0; i<num2; i++)
904 BN_bntest_rand(a,20+i*5,0,0); /**/
905 BN_bntest_rand(b,2+i,0,0); /**/
907 if (!BN_mod_exp(d,a,b,c,ctx))
929 fprintf(stderr,"Modulo exponentiation test failed!\n");
941 int test_exp(BIO *bp, BN_CTX *ctx)
943 BIGNUM *a,*b,*d,*e,*one;
953 for (i=0; i<num2; i++)
955 BN_bntest_rand(a,20+i*5,0,0); /**/
956 BN_bntest_rand(b,2+i,0,0); /**/
958 if (!BN_exp(d,a,b,ctx))
974 for( ; !BN_is_zero(b) ; BN_sub(b,b,one))
979 fprintf(stderr,"Exponentiation test failed!\n");
991 int test_gf2m_add(BIO *bp)
1000 for (i=0; i<num0; i++)
1002 BN_rand(&a,512,0,0);
1003 BN_copy(&b, BN_value_one());
1006 BN_GF2m_add(&c,&a,&b);
1007 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1021 /* Test that two added values have the correct parity. */
1022 if((BN_is_odd(&a) && BN_is_odd(&c)) || (!BN_is_odd(&a) && !BN_is_odd(&c)))
1024 fprintf(stderr,"GF(2^m) addition test (a) failed!\n");
1027 BN_GF2m_add(&c,&c,&c);
1028 /* Test that c + c = 0. */
1031 fprintf(stderr,"GF(2^m) addition test (b) failed!\n");
1043 int test_gf2m_mod(BIO *bp)
1045 BIGNUM *a,*b[2],*c,*d,*e;
1047 unsigned int p0[] = {163,7,6,3,0};
1048 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 for (j=0; j < 2; j++)
1065 BN_GF2m_mod(c, a, b[j]);
1066 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1080 BN_GF2m_add(d, a, c);
1081 BN_GF2m_mod(e, d, b[j]);
1082 /* Test that a + (a mod p) mod p == 0. */
1085 fprintf(stderr,"GF(2^m) modulo test failed!\n");
1101 int test_gf2m_mod_mul(BIO *bp,BN_CTX *ctx)
1103 BIGNUM *a,*b[2],*c,*d,*e,*f,*g,*h;
1105 unsigned int p0[] = {163,7,6,3,0};
1106 unsigned int p1[] = {193,15,0};
1118 BN_GF2m_arr2poly(p0, b[0]);
1119 BN_GF2m_arr2poly(p1, b[1]);
1121 for (i=0; i<num0; i++)
1123 BN_bntest_rand(a, 1024, 0, 0);
1124 BN_bntest_rand(c, 1024, 0, 0);
1125 BN_bntest_rand(d, 1024, 0, 0);
1126 for (j=0; j < 2; j++)
1128 BN_GF2m_mod_mul(e, a, c, b[j], ctx);
1129 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1145 BN_GF2m_add(f, a, d);
1146 BN_GF2m_mod_mul(g, f, c, b[j], ctx);
1147 BN_GF2m_mod_mul(h, d, c, b[j], ctx);
1148 BN_GF2m_add(f, e, g);
1149 BN_GF2m_add(f, f, h);
1150 /* Test that (a+d)*c = a*c + d*c. */
1153 fprintf(stderr,"GF(2^m) modular multiplication test failed!\n");
1172 int test_gf2m_mod_sqr(BIO *bp,BN_CTX *ctx)
1174 BIGNUM *a,*b[2],*c,*d;
1176 unsigned int p0[] = {163,7,6,3,0};
1177 unsigned int p1[] = {193,15,0};
1185 BN_GF2m_arr2poly(p0, b[0]);
1186 BN_GF2m_arr2poly(p1, b[1]);
1188 for (i=0; i<num0; i++)
1190 BN_bntest_rand(a, 1024, 0, 0);
1191 for (j=0; j < 2; j++)
1193 BN_GF2m_mod_sqr(c, a, b[j], ctx);
1195 BN_GF2m_mod_mul(d, a, d, b[j], ctx);
1196 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1202 BIO_puts(bp," ^ 2 % ");
1204 BIO_puts(bp, " = ");
1206 BIO_puts(bp,"; a * a = ");
1212 BN_GF2m_add(d, c, d);
1213 /* Test that a*a = a^2. */
1216 fprintf(stderr,"GF(2^m) modular squaring test failed!\n");
1231 int test_gf2m_mod_inv(BIO *bp,BN_CTX *ctx)
1233 BIGNUM *a,*b[2],*c,*d;
1235 unsigned int p0[] = {163,7,6,3,0};
1236 unsigned int p1[] = {193,15,0};
1244 BN_GF2m_arr2poly(p0, b[0]);
1245 BN_GF2m_arr2poly(p1, b[1]);
1247 for (i=0; i<num0; i++)
1249 BN_bntest_rand(a, 512, 0, 0);
1250 for (j=0; j < 2; j++)
1252 BN_GF2m_mod_inv(c, a, b[j], ctx);
1253 BN_GF2m_mod_mul(d, a, c, b[j], ctx);
1254 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1260 BIO_puts(bp, " * ");
1262 BIO_puts(bp," - 1 % ");
1268 /* Test that ((1/a)*a) = 1. */
1271 fprintf(stderr,"GF(2^m) modular inversion test failed!\n");
1286 int test_gf2m_mod_div(BIO *bp,BN_CTX *ctx)
1288 BIGNUM *a,*b[2],*c,*d,*e,*f;
1290 unsigned int p0[] = {163,7,6,3,0};
1291 unsigned int p1[] = {193,15,0};
1301 BN_GF2m_arr2poly(p0, b[0]);
1302 BN_GF2m_arr2poly(p1, b[1]);
1304 for (i=0; i<num0; i++)
1306 BN_bntest_rand(a, 512, 0, 0);
1307 BN_bntest_rand(c, 512, 0, 0);
1308 for (j=0; j < 2; j++)
1310 BN_GF2m_mod_div(d, a, c, b[j], ctx);
1311 BN_GF2m_mod_mul(e, d, c, b[j], ctx);
1312 BN_GF2m_mod_div(f, a, e, b[j], ctx);
1313 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1319 BIO_puts(bp, " = ");
1323 BIO_puts(bp, " % ");
1329 /* Test that ((a/c)*c)/a = 1. */
1332 fprintf(stderr,"GF(2^m) modular division test failed!\n");
1349 int test_gf2m_mod_exp(BIO *bp,BN_CTX *ctx)
1351 BIGNUM *a,*b[2],*c,*d,*e,*f;
1353 unsigned int p0[] = {163,7,6,3,0};
1354 unsigned int p1[] = {193,15,0};
1364 BN_GF2m_arr2poly(p0, b[0]);
1365 BN_GF2m_arr2poly(p1, b[1]);
1367 for (i=0; i<num0; i++)
1369 BN_bntest_rand(a, 512, 0, 0);
1370 BN_bntest_rand(c, 512, 0, 0);
1371 BN_bntest_rand(d, 512, 0, 0);
1372 for (j=0; j < 2; j++)
1374 BN_GF2m_mod_exp(e, a, c, b[j], ctx);
1375 BN_GF2m_mod_exp(f, a, d, b[j], ctx);
1376 BN_GF2m_mod_mul(e, e, f, b[j], ctx);
1378 BN_GF2m_mod_exp(f, a, f, b[j], ctx);
1379 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1385 BIO_puts(bp, " ^ (");
1389 BIO_puts(bp, ") = ");
1391 BIO_puts(bp, "; - ");
1393 BIO_puts(bp, " % ");
1399 BN_GF2m_add(f, e, f);
1400 /* Test that a^(c+d)=a^c*a^d. */
1403 fprintf(stderr,"GF(2^m) modular exponentiation test failed!\n");
1420 int test_gf2m_mod_sqrt(BIO *bp,BN_CTX *ctx)
1422 BIGNUM *a,*b[2],*c,*d,*e,*f;
1424 unsigned int p0[] = {163,7,6,3,0};
1425 unsigned int p1[] = {193,15,0};
1435 BN_GF2m_arr2poly(p0, b[0]);
1436 BN_GF2m_arr2poly(p1, b[1]);
1438 for (i=0; i<num0; i++)
1440 BN_bntest_rand(a, 512, 0, 0);
1441 for (j=0; j < 2; j++)
1443 BN_GF2m_mod(c, a, b[j]);
1444 BN_GF2m_mod_sqrt(d, a, b[j], ctx);
1445 BN_GF2m_mod_sqr(e, d, b[j], ctx);
1446 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1452 BIO_puts(bp, " ^ 2 - ");
1458 BN_GF2m_add(f, c, e);
1459 /* Test that d^2 = a, where d = sqrt(a). */
1462 fprintf(stderr,"GF(2^m) modular square root test failed!\n");
1479 int test_gf2m_mod_solve_quad(BIO *bp,BN_CTX *ctx)
1481 BIGNUM *a,*b[2],*c,*d,*e;
1482 int i, j, s = 0, t, ret = 0;
1483 unsigned int p0[] = {163,7,6,3,0};
1484 unsigned int p1[] = {193,15,0};
1493 BN_GF2m_arr2poly(p0, b[0]);
1494 BN_GF2m_arr2poly(p1, b[1]);
1496 for (i=0; i<num0; i++)
1498 BN_bntest_rand(a, 512, 0, 0);
1499 for (j=0; j < 2; j++)
1501 t = BN_GF2m_mod_solve_quad(c, a, b[j], ctx);
1505 BN_GF2m_mod_sqr(d, c, b[j], ctx);
1506 BN_GF2m_add(d, c, d);
1507 BN_GF2m_mod(e, a, b[j]);
1508 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1514 BIO_puts(bp, " is root of z^2 + z = ");
1516 BIO_puts(bp, " % ");
1522 BN_GF2m_add(e, e, d);
1523 /* Test that solution of quadratic c satisfies c^2 + c = a. */
1526 fprintf(stderr,"GF(2^m) modular solve quadratic test failed!\n");
1533 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1538 BIO_puts(bp, "There are no roots of z^2 + z = ");
1540 BIO_puts(bp, " % ");
1551 fprintf(stderr,"All %i tests of GF(2^m) modular solve quadratic resulted in no roots;\n", num0);
1552 fprintf(stderr,"this is very unlikely and probably indicates an error.\n");
1566 static int genprime_cb(int p, int n, BN_GENCB *arg)
1579 int test_kron(BIO *bp, BN_CTX *ctx)
1584 int legendre, kronecker;
1591 if (a == NULL || b == NULL || r == NULL || t == NULL) goto err;
1593 BN_GENCB_set(&cb, genprime_cb, NULL);
1595 /* We test BN_kronecker(a, b, ctx) just for b odd (Jacobi symbol).
1596 * In this case we know that if b is prime, then BN_kronecker(a, b, ctx)
1597 * is congruent to $a^{(b-1)/2}$, modulo $b$ (Legendre symbol).
1598 * So we generate a random prime b and compare these values
1599 * for a number of random a's. (That is, we run the Solovay-Strassen
1600 * primality test to confirm that b is prime, except that we
1601 * don't want to test whether b is prime but whether BN_kronecker
1604 if (!BN_generate_prime_ex(b, 512, 0, NULL, NULL, &cb)) goto err;
1605 b->neg = rand_neg();
1608 for (i = 0; i < num0; i++)
1610 if (!BN_bntest_rand(a, 512, 0, 0)) goto err;
1611 a->neg = rand_neg();
1613 /* t := (|b|-1)/2 (note that b is odd) */
1614 if (!BN_copy(t, b)) goto err;
1616 if (!BN_sub_word(t, 1)) goto err;
1617 if (!BN_rshift1(t, t)) goto err;
1618 /* r := a^t mod b */
1621 if (!BN_mod_exp_recp(r, a, t, b, ctx)) goto err;
1624 if (BN_is_word(r, 1))
1626 else if (BN_is_zero(r))
1630 if (!BN_add_word(r, 1)) goto err;
1631 if (0 != BN_ucmp(r, b))
1633 fprintf(stderr, "Legendre symbol computation failed\n");
1639 kronecker = BN_kronecker(a, b, ctx);
1640 if (kronecker < -1) goto err;
1641 /* we actually need BN_kronecker(a, |b|) */
1642 if (a->neg && b->neg)
1643 kronecker = -kronecker;
1645 if (legendre != kronecker)
1647 fprintf(stderr, "legendre != kronecker; a = ");
1648 BN_print_fp(stderr, a);
1649 fprintf(stderr, ", b = ");
1650 BN_print_fp(stderr, b);
1651 fprintf(stderr, "\n");
1663 if (a != NULL) BN_free(a);
1664 if (b != NULL) BN_free(b);
1665 if (r != NULL) BN_free(r);
1666 if (t != NULL) BN_free(t);
1670 int test_sqrt(BIO *bp, BN_CTX *ctx)
1680 if (a == NULL || p == NULL || r == NULL) goto err;
1682 BN_GENCB_set(&cb, genprime_cb, NULL);
1684 for (i = 0; i < 16; i++)
1688 unsigned primes[8] = { 2, 3, 5, 7, 11, 13, 17, 19 };
1690 if (!BN_set_word(p, primes[i])) goto err;
1694 if (!BN_set_word(a, 32)) goto err;
1695 if (!BN_set_word(r, 2*i + 1)) goto err;
1697 if (!BN_generate_prime_ex(p, 256, 0, a, r, &cb)) goto err;
1700 p->neg = rand_neg();
1702 for (j = 0; j < num2; j++)
1704 /* construct 'a' such that it is a square modulo p,
1705 * but in general not a proper square and not reduced modulo p */
1706 if (!BN_bntest_rand(r, 256, 0, 3)) goto err;
1707 if (!BN_nnmod(r, r, p, ctx)) goto err;
1708 if (!BN_mod_sqr(r, r, p, ctx)) goto err;
1709 if (!BN_bntest_rand(a, 256, 0, 3)) goto err;
1710 if (!BN_nnmod(a, a, p, ctx)) goto err;
1711 if (!BN_mod_sqr(a, a, p, ctx)) goto err;
1712 if (!BN_mul(a, a, r, ctx)) goto err;
1714 if (!BN_sub(a, a, p)) goto err;
1716 if (!BN_mod_sqrt(r, a, p, ctx)) goto err;
1717 if (!BN_mod_sqr(r, r, p, ctx)) goto err;
1719 if (!BN_nnmod(a, a, p, ctx)) goto err;
1721 if (BN_cmp(a, r) != 0)
1723 fprintf(stderr, "BN_mod_sqrt failed: a = ");
1724 BN_print_fp(stderr, a);
1725 fprintf(stderr, ", r = ");
1726 BN_print_fp(stderr, r);
1727 fprintf(stderr, ", p = ");
1728 BN_print_fp(stderr, p);
1729 fprintf(stderr, "\n");
1742 if (a != NULL) BN_free(a);
1743 if (p != NULL) BN_free(p);
1744 if (r != NULL) BN_free(r);
1748 int test_lshift(BIO *bp,BN_CTX *ctx,BIGNUM *a_)
1763 BN_bntest_rand(a,200,0,0); /**/
1766 for (i=0; i<num0; i++)
1786 fprintf(stderr,"Left shift test failed!\n");
1787 fprintf(stderr,"a=");
1788 BN_print_fp(stderr,a);
1789 fprintf(stderr,"\nb=");
1790 BN_print_fp(stderr,b);
1791 fprintf(stderr,"\nc=");
1792 BN_print_fp(stderr,c);
1793 fprintf(stderr,"\nd=");
1794 BN_print_fp(stderr,d);
1795 fprintf(stderr,"\n");
1806 int test_lshift1(BIO *bp)
1815 BN_bntest_rand(a,200,0,0); /**/
1817 for (i=0; i<num0; i++)
1825 BIO_puts(bp," * 2");
1835 fprintf(stderr,"Left shift one test failed!\n");
1847 int test_rshift(BIO *bp,BN_CTX *ctx)
1849 BIGNUM *a,*b,*c,*d,*e;
1859 BN_bntest_rand(a,200,0,0); /**/
1861 for (i=0; i<num0; i++)
1877 BN_div(d,e,a,c,ctx);
1881 fprintf(stderr,"Right shift test failed!\n");
1893 int test_rshift1(BIO *bp)
1902 BN_bntest_rand(a,200,0,0); /**/
1904 for (i=0; i<num0; i++)
1912 BIO_puts(bp," / 2");
1920 if(!BN_is_zero(c) && !BN_abs_is_word(c, 1))
1922 fprintf(stderr,"Right shift one test failed!\n");
1935 static unsigned int neg=0;
1936 static int sign[8]={0,0,0,1,1,0,1,1};
1938 return(sign[(neg++)%8]);