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 #include "../crypto/bn/bn_lcl.h"
92 const int num0 = 100; /* number of tests */
93 const int num1 = 50; /* additional tests for some functions */
94 const int num2 = 5; /* number of tests for slow functions */
96 int test_add(BIO *bp);
97 int test_sub(BIO *bp);
98 int test_lshift1(BIO *bp);
99 int test_lshift(BIO *bp,BN_CTX *ctx,BIGNUM *a_);
100 int test_rshift1(BIO *bp);
101 int test_rshift(BIO *bp,BN_CTX *ctx);
102 int test_div(BIO *bp,BN_CTX *ctx);
103 int test_div_word(BIO *bp);
104 int test_div_recp(BIO *bp,BN_CTX *ctx);
105 int test_mul(BIO *bp);
106 int test_sqr(BIO *bp,BN_CTX *ctx);
107 int test_mont(BIO *bp,BN_CTX *ctx);
108 int test_mod(BIO *bp,BN_CTX *ctx);
109 int test_mod_mul(BIO *bp,BN_CTX *ctx);
110 int test_mod_exp(BIO *bp,BN_CTX *ctx);
111 int test_mod_exp_mont_consttime(BIO *bp,BN_CTX *ctx);
112 int test_mod_exp_mont5(BIO *bp, BN_CTX *ctx);
113 int test_exp(BIO *bp,BN_CTX *ctx);
114 int test_gf2m_add(BIO *bp);
115 int test_gf2m_mod(BIO *bp);
116 int test_gf2m_mod_mul(BIO *bp,BN_CTX *ctx);
117 int test_gf2m_mod_sqr(BIO *bp,BN_CTX *ctx);
118 int test_gf2m_mod_inv(BIO *bp,BN_CTX *ctx);
119 int test_gf2m_mod_div(BIO *bp,BN_CTX *ctx);
120 int test_gf2m_mod_exp(BIO *bp,BN_CTX *ctx);
121 int test_gf2m_mod_sqrt(BIO *bp,BN_CTX *ctx);
122 int test_gf2m_mod_solve_quad(BIO *bp,BN_CTX *ctx);
123 int test_kron(BIO *bp,BN_CTX *ctx);
124 int test_sqrt(BIO *bp,BN_CTX *ctx);
125 int test_small_prime(BIO *bp,BN_CTX *ctx);
126 int test_probable_prime_coprime(BIO *bp,BN_CTX *ctx);
128 static int results=0;
130 static unsigned char lst[]="\xC6\x4F\x43\x04\x2A\xEA\xCA\x6E\x58\x36\x80\x5B\xE8\xC9"
131 "\x9B\x04\x5D\x48\x36\xC2\xFD\x16\xC9\x64\xF0";
133 static const char rnd_seed[] = "string to make the random number generator think it has entropy";
135 static void message(BIO *out, char *m)
137 fprintf(stderr, "test %s\n", m);
138 BIO_puts(out, "print \"test ");
140 BIO_puts(out, "\\n\"\n");
143 int main(int argc, char *argv[])
151 RAND_seed(rnd_seed, sizeof rnd_seed); /* or BN_generate_prime may fail */
157 if (strcmp(*argv,"-results") == 0)
159 else if (strcmp(*argv,"-out") == 0)
161 if (--argc < 1) break;
170 if (ctx == NULL) EXIT(1);
172 out=BIO_new(BIO_s_file());
173 if (out == NULL) EXIT(1);
176 BIO_set_fp(out,stdout,BIO_NOCLOSE);
180 if (!BIO_write_filename(out,outfile))
188 BIO_puts(out,"obase=16\nibase=16\n");
190 message(out,"BN_add");
191 if (!test_add(out)) goto err;
192 (void)BIO_flush(out);
194 message(out,"BN_sub");
195 if (!test_sub(out)) goto err;
196 (void)BIO_flush(out);
198 message(out,"BN_lshift1");
199 if (!test_lshift1(out)) goto err;
200 (void)BIO_flush(out);
202 message(out,"BN_lshift (fixed)");
203 if (!test_lshift(out,ctx,BN_bin2bn(lst,sizeof(lst)-1,NULL)))
205 (void)BIO_flush(out);
207 message(out,"BN_lshift");
208 if (!test_lshift(out,ctx,NULL)) goto err;
209 (void)BIO_flush(out);
211 message(out,"BN_rshift1");
212 if (!test_rshift1(out)) goto err;
213 (void)BIO_flush(out);
215 message(out,"BN_rshift");
216 if (!test_rshift(out,ctx)) goto err;
217 (void)BIO_flush(out);
219 message(out,"BN_sqr");
220 if (!test_sqr(out,ctx)) goto err;
221 (void)BIO_flush(out);
223 message(out,"BN_mul");
224 if (!test_mul(out)) goto err;
225 (void)BIO_flush(out);
227 message(out,"BN_div");
228 if (!test_div(out,ctx)) goto err;
229 (void)BIO_flush(out);
231 message(out,"BN_div_word");
232 if (!test_div_word(out)) goto err;
233 (void)BIO_flush(out);
235 message(out,"BN_div_recp");
236 if (!test_div_recp(out,ctx)) goto err;
237 (void)BIO_flush(out);
239 message(out,"BN_mod");
240 if (!test_mod(out,ctx)) goto err;
241 (void)BIO_flush(out);
243 message(out,"BN_mod_mul");
244 if (!test_mod_mul(out,ctx)) goto err;
245 (void)BIO_flush(out);
247 message(out,"BN_mont");
248 if (!test_mont(out,ctx)) goto err;
249 (void)BIO_flush(out);
251 message(out,"BN_mod_exp");
252 if (!test_mod_exp(out,ctx)) goto err;
253 (void)BIO_flush(out);
255 message(out,"BN_mod_exp_mont_consttime");
256 if (!test_mod_exp_mont_consttime(out,ctx)) goto err;
257 if (!test_mod_exp_mont5(out,ctx)) goto err;
258 (void)BIO_flush(out);
260 message(out,"BN_exp");
261 if (!test_exp(out,ctx)) goto err;
262 (void)BIO_flush(out);
264 message(out,"BN_kronecker");
265 if (!test_kron(out,ctx)) goto err;
266 (void)BIO_flush(out);
268 message(out,"BN_mod_sqrt");
269 if (!test_sqrt(out,ctx)) goto err;
270 (void)BIO_flush(out);
272 message(out,"Small prime generation");
273 if (!test_small_prime(out,ctx)) goto err;
274 (void)BIO_flush(out);
276 message(out,"Probable prime generation with coprimes");
277 if (!test_probable_prime_coprime(out,ctx)) goto err;
278 (void)BIO_flush(out);
280 #ifndef OPENSSL_NO_EC2M
281 message(out,"BN_GF2m_add");
282 if (!test_gf2m_add(out)) goto err;
283 (void)BIO_flush(out);
285 message(out,"BN_GF2m_mod");
286 if (!test_gf2m_mod(out)) goto err;
287 (void)BIO_flush(out);
289 message(out,"BN_GF2m_mod_mul");
290 if (!test_gf2m_mod_mul(out,ctx)) goto err;
291 (void)BIO_flush(out);
293 message(out,"BN_GF2m_mod_sqr");
294 if (!test_gf2m_mod_sqr(out,ctx)) goto err;
295 (void)BIO_flush(out);
297 message(out,"BN_GF2m_mod_inv");
298 if (!test_gf2m_mod_inv(out,ctx)) goto err;
299 (void)BIO_flush(out);
301 message(out,"BN_GF2m_mod_div");
302 if (!test_gf2m_mod_div(out,ctx)) goto err;
303 (void)BIO_flush(out);
305 message(out,"BN_GF2m_mod_exp");
306 if (!test_gf2m_mod_exp(out,ctx)) goto err;
307 (void)BIO_flush(out);
309 message(out,"BN_GF2m_mod_sqrt");
310 if (!test_gf2m_mod_sqrt(out,ctx)) goto err;
311 (void)BIO_flush(out);
313 message(out,"BN_GF2m_mod_solve_quad");
314 if (!test_gf2m_mod_solve_quad(out,ctx)) goto err;
315 (void)BIO_flush(out);
323 BIO_puts(out,"1\n"); /* make sure the Perl script fed by bc notices
324 * the failure, see test_bn in test/Makefile.ssl*/
325 (void)BIO_flush(out);
326 ERR_load_crypto_strings();
327 ERR_print_errors_fp(stderr);
332 int test_add(BIO *bp)
341 BN_bntest_rand(&a,512,0,0);
342 for (i=0; i<num0; i++)
344 BN_bntest_rand(&b,450+i,0,0);
366 fprintf(stderr,"Add test failed!\n");
376 int test_sub(BIO *bp)
385 for (i=0; i<num0+num1; i++)
389 BN_bntest_rand(&a,512,0,0);
391 if (BN_set_bit(&a,i)==0) return(0);
396 BN_bntest_rand(&b,400+i-num1,0,0);
417 fprintf(stderr,"Subtract test failed!\n");
427 int test_div(BIO *bp, BN_CTX *ctx)
438 for (i=0; i<num0+num1; i++)
442 BN_bntest_rand(&a,400,0,0);
448 BN_bntest_rand(&b,50+3*(i-num1),0,0);
451 BN_div(&d,&c,&a,&b,ctx);
474 BN_mul(&e,&d,&b,ctx);
479 fprintf(stderr,"Division test failed!\n");
491 static void print_word(BIO *bp,BN_ULONG w)
493 #ifdef SIXTY_FOUR_BIT
494 if (sizeof(w) > sizeof(unsigned long))
496 unsigned long h=(unsigned long)(w>>32),
497 l=(unsigned long)(w);
499 if (h) BIO_printf(bp,"%lX%08lX",h,l);
500 else BIO_printf(bp,"%lX",l);
504 BIO_printf(bp,BN_HEX_FMT1,w);
507 int test_div_word(BIO *bp)
516 for (i=0; i<num0; i++)
519 BN_bntest_rand(&a,512,-1,0);
520 BN_bntest_rand(&b,BN_BITS2,-1,0);
525 r = BN_div_word(&b, s);
554 fprintf(stderr,"Division (word) test failed!\n");
563 int test_div_recp(BIO *bp, BN_CTX *ctx)
569 BN_RECP_CTX_init(&recp);
576 for (i=0; i<num0+num1; i++)
580 BN_bntest_rand(&a,400,0,0);
586 BN_bntest_rand(&b,50+3*(i-num1),0,0);
589 BN_RECP_CTX_set(&recp,&b,ctx);
590 BN_div_recp(&d,&c,&a,&recp,ctx);
613 BN_mul(&e,&d,&b,ctx);
618 fprintf(stderr,"Reciprocal division test failed!\n");
619 fprintf(stderr,"a=");
620 BN_print_fp(stderr,&a);
621 fprintf(stderr,"\nb=");
622 BN_print_fp(stderr,&b);
623 fprintf(stderr,"\n");
632 BN_RECP_CTX_free(&recp);
636 int test_mul(BIO *bp)
643 if (ctx == NULL) EXIT(1);
651 for (i=0; i<num0+num1; i++)
655 BN_bntest_rand(&a,100,0,0);
656 BN_bntest_rand(&b,100,0,0);
659 BN_bntest_rand(&b,i-num1,0,0);
662 BN_mul(&c,&a,&b,ctx);
675 BN_div(&d,&e,&c,&a,ctx);
677 if(!BN_is_zero(&d) || !BN_is_zero(&e))
679 fprintf(stderr,"Multiplication test failed!\n");
692 int test_sqr(BIO *bp, BN_CTX *ctx)
702 for (i=0; i<num0; i++)
704 BN_bntest_rand(&a,40+i*10,0,0);
719 BN_div(&d,&e,&c,&a,ctx);
721 if(!BN_is_zero(&d) || !BN_is_zero(&e))
723 fprintf(stderr,"Square test failed!\n");
734 int test_mont(BIO *bp, BN_CTX *ctx)
749 mont=BN_MONT_CTX_new();
753 BN_bntest_rand(&a,100,0,0); /**/
754 BN_bntest_rand(&b,100,0,0); /**/
755 for (i=0; i<num2; i++)
757 int bits = (200*(i+1))/num2;
761 BN_bntest_rand(&n,bits,0,1);
762 BN_MONT_CTX_set(mont,&n,ctx);
764 BN_nnmod(&a,&a,&n,ctx);
765 BN_nnmod(&b,&b,&n,ctx);
767 BN_to_montgomery(&A,&a,mont,ctx);
768 BN_to_montgomery(&B,&b,mont,ctx);
770 BN_mod_mul_montgomery(&c,&A,&B,mont,ctx);/**/
771 BN_from_montgomery(&A,&c,mont,ctx);/**/
777 fprintf(stderr,"%d * %d %% %d\n",
780 BN_num_bits(mont->N));
786 BN_print(bp,&(mont->N));
792 BN_mod_mul(&d,&a,&b,&n,ctx);
796 fprintf(stderr,"Montgomery multiplication test failed!\n");
800 BN_MONT_CTX_free(mont);
811 int test_mod(BIO *bp, BN_CTX *ctx)
813 BIGNUM *a,*b,*c,*d,*e;
822 BN_bntest_rand(a,1024,0,0); /**/
823 for (i=0; i<num0; i++)
825 BN_bntest_rand(b,450+i*10,0,0); /**/
828 BN_mod(c,a,b,ctx);/**/
845 fprintf(stderr,"Modulo test failed!\n");
857 int test_mod_mul(BIO *bp, BN_CTX *ctx)
859 BIGNUM *a,*b,*c,*d,*e;
868 for (j=0; j<3; j++) {
869 BN_bntest_rand(c,1024,0,0); /**/
870 for (i=0; i<num0; i++)
872 BN_bntest_rand(a,475+i*10,0,0); /**/
873 BN_bntest_rand(b,425+i*11,0,0); /**/
876 if (!BN_mod_mul(e,a,b,c,ctx))
880 while ((l=ERR_get_error()))
881 fprintf(stderr,"ERROR:%s\n",
882 ERR_error_string(l,NULL));
894 if ((a->neg ^ b->neg) && !BN_is_zero(e))
896 /* If (a*b) % c is negative, c must be added
897 * in order to obtain the normalized remainder
898 * (new with OpenSSL 0.9.7, previous versions of
899 * BN_mod_mul could generate negative results)
914 fprintf(stderr,"Modulo multiply test failed!\n");
915 ERR_print_errors_fp(stderr);
928 int test_mod_exp(BIO *bp, BN_CTX *ctx)
930 BIGNUM *a,*b,*c,*d,*e;
939 BN_bntest_rand(c,30,0,1); /* must be odd for montgomery */
940 for (i=0; i<num2; i++)
942 BN_bntest_rand(a,20+i*5,0,0); /**/
943 BN_bntest_rand(b,2+i,0,0); /**/
945 if (!BN_mod_exp(d,a,b,c,ctx))
967 fprintf(stderr,"Modulo exponentiation test failed!\n");
979 int test_mod_exp_mont_consttime(BIO *bp, BN_CTX *ctx)
981 BIGNUM *a,*b,*c,*d,*e;
990 BN_bntest_rand(c,30,0,1); /* must be odd for montgomery */
991 for (i=0; i<num2; i++)
993 BN_bntest_rand(a,20+i*5,0,0); /**/
994 BN_bntest_rand(b,2+i,0,0); /**/
996 if (!BN_mod_exp_mont_consttime(d,a,b,c,ctx,NULL))
1015 BN_div(a,b,e,c,ctx);
1018 fprintf(stderr,"Modulo exponentiation test failed!\n");
1030 /* Test constant-time modular exponentiation with 1024-bit inputs,
1031 * which on x86_64 cause a different code branch to be taken.
1033 int test_mod_exp_mont5(BIO *bp, BN_CTX *ctx)
1035 BIGNUM *a,*p,*m,*d,*e;
1045 mont = BN_MONT_CTX_new();
1047 BN_bntest_rand(m,1024,0,1); /* must be odd for montgomery */
1049 BN_bntest_rand(a,1024,0,0);
1051 if(!BN_mod_exp_mont_consttime(d,a,p,m,ctx,NULL))
1055 fprintf(stderr, "Modular exponentiation test failed!\n");
1059 BN_bntest_rand(p,1024,0,0);
1061 if(!BN_mod_exp_mont_consttime(d,a,p,m,ctx,NULL))
1065 fprintf(stderr, "Modular exponentiation test failed!\n");
1068 /* Craft an input whose Montgomery representation is 1,
1069 * i.e., shorter than the modulus m, in order to test
1070 * the const time precomputation scattering/gathering.
1073 BN_MONT_CTX_set(mont,m,ctx);
1074 if(!BN_from_montgomery(e,a,mont,ctx))
1076 if(!BN_mod_exp_mont_consttime(d,e,p,m,ctx,NULL))
1078 if(!BN_mod_exp_simple(a,e,p,m,ctx))
1080 if(BN_cmp(a,d) != 0)
1082 fprintf(stderr,"Modular exponentiation test failed!\n");
1085 /* Finally, some regular test vectors. */
1086 BN_bntest_rand(e,1024,0,0);
1087 if(!BN_mod_exp_mont_consttime(d,e,p,m,ctx,NULL))
1089 if(!BN_mod_exp_simple(a,e,p,m,ctx))
1091 if(BN_cmp(a,d) != 0)
1093 fprintf(stderr,"Modular exponentiation test failed!\n");
1104 int test_exp(BIO *bp, BN_CTX *ctx)
1106 BIGNUM *a,*b,*d,*e,*one;
1116 for (i=0; i<num2; i++)
1118 BN_bntest_rand(a,20+i*5,0,0); /**/
1119 BN_bntest_rand(b,2+i,0,0); /**/
1121 if (BN_exp(d,a,b,ctx) <= 0)
1137 for( ; !BN_is_zero(b) ; BN_sub(b,b,one))
1142 fprintf(stderr,"Exponentiation test failed!\n");
1153 #ifndef OPENSSL_NO_EC2M
1154 int test_gf2m_add(BIO *bp)
1163 for (i=0; i<num0; i++)
1165 BN_rand(&a,512,0,0);
1166 BN_copy(&b, BN_value_one());
1169 BN_GF2m_add(&c,&a,&b);
1170 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1184 /* Test that two added values have the correct parity. */
1185 if((BN_is_odd(&a) && BN_is_odd(&c)) || (!BN_is_odd(&a) && !BN_is_odd(&c)))
1187 fprintf(stderr,"GF(2^m) addition test (a) failed!\n");
1190 BN_GF2m_add(&c,&c,&c);
1191 /* Test that c + c = 0. */
1194 fprintf(stderr,"GF(2^m) addition test (b) failed!\n");
1206 int test_gf2m_mod(BIO *bp)
1208 BIGNUM *a,*b[2],*c,*d,*e;
1210 int p0[] = {163,7,6,3,0,-1};
1211 int p1[] = {193,15,0,-1};
1220 BN_GF2m_arr2poly(p0, b[0]);
1221 BN_GF2m_arr2poly(p1, b[1]);
1223 for (i=0; i<num0; i++)
1225 BN_bntest_rand(a, 1024, 0, 0);
1226 for (j=0; j < 2; j++)
1228 BN_GF2m_mod(c, a, b[j]);
1229 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1243 BN_GF2m_add(d, a, c);
1244 BN_GF2m_mod(e, d, b[j]);
1245 /* Test that a + (a mod p) mod p == 0. */
1248 fprintf(stderr,"GF(2^m) modulo test failed!\n");
1264 int test_gf2m_mod_mul(BIO *bp,BN_CTX *ctx)
1266 BIGNUM *a,*b[2],*c,*d,*e,*f,*g,*h;
1268 int p0[] = {163,7,6,3,0,-1};
1269 int p1[] = {193,15,0,-1};
1281 BN_GF2m_arr2poly(p0, b[0]);
1282 BN_GF2m_arr2poly(p1, b[1]);
1284 for (i=0; i<num0; i++)
1286 BN_bntest_rand(a, 1024, 0, 0);
1287 BN_bntest_rand(c, 1024, 0, 0);
1288 BN_bntest_rand(d, 1024, 0, 0);
1289 for (j=0; j < 2; j++)
1291 BN_GF2m_mod_mul(e, a, c, b[j], ctx);
1292 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1308 BN_GF2m_add(f, a, d);
1309 BN_GF2m_mod_mul(g, f, c, b[j], ctx);
1310 BN_GF2m_mod_mul(h, d, c, b[j], ctx);
1311 BN_GF2m_add(f, e, g);
1312 BN_GF2m_add(f, f, h);
1313 /* Test that (a+d)*c = a*c + d*c. */
1316 fprintf(stderr,"GF(2^m) modular multiplication test failed!\n");
1335 int test_gf2m_mod_sqr(BIO *bp,BN_CTX *ctx)
1337 BIGNUM *a,*b[2],*c,*d;
1339 int p0[] = {163,7,6,3,0,-1};
1340 int p1[] = {193,15,0,-1};
1348 BN_GF2m_arr2poly(p0, b[0]);
1349 BN_GF2m_arr2poly(p1, b[1]);
1351 for (i=0; i<num0; i++)
1353 BN_bntest_rand(a, 1024, 0, 0);
1354 for (j=0; j < 2; j++)
1356 BN_GF2m_mod_sqr(c, a, b[j], ctx);
1358 BN_GF2m_mod_mul(d, a, d, b[j], ctx);
1359 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1365 BIO_puts(bp," ^ 2 % ");
1367 BIO_puts(bp, " = ");
1369 BIO_puts(bp,"; a * a = ");
1375 BN_GF2m_add(d, c, d);
1376 /* Test that a*a = a^2. */
1379 fprintf(stderr,"GF(2^m) modular squaring test failed!\n");
1394 int test_gf2m_mod_inv(BIO *bp,BN_CTX *ctx)
1396 BIGNUM *a,*b[2],*c,*d;
1398 int p0[] = {163,7,6,3,0,-1};
1399 int p1[] = {193,15,0,-1};
1407 BN_GF2m_arr2poly(p0, b[0]);
1408 BN_GF2m_arr2poly(p1, b[1]);
1410 for (i=0; i<num0; i++)
1412 BN_bntest_rand(a, 512, 0, 0);
1413 for (j=0; j < 2; j++)
1415 BN_GF2m_mod_inv(c, a, b[j], ctx);
1416 BN_GF2m_mod_mul(d, a, c, b[j], ctx);
1417 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1423 BIO_puts(bp, " * ");
1425 BIO_puts(bp," - 1 % ");
1431 /* Test that ((1/a)*a) = 1. */
1434 fprintf(stderr,"GF(2^m) modular inversion test failed!\n");
1449 int test_gf2m_mod_div(BIO *bp,BN_CTX *ctx)
1451 BIGNUM *a,*b[2],*c,*d,*e,*f;
1453 int p0[] = {163,7,6,3,0,-1};
1454 int p1[] = {193,15,0,-1};
1464 BN_GF2m_arr2poly(p0, b[0]);
1465 BN_GF2m_arr2poly(p1, b[1]);
1467 for (i=0; i<num0; i++)
1469 BN_bntest_rand(a, 512, 0, 0);
1470 BN_bntest_rand(c, 512, 0, 0);
1471 for (j=0; j < 2; j++)
1473 BN_GF2m_mod_div(d, a, c, b[j], ctx);
1474 BN_GF2m_mod_mul(e, d, c, b[j], ctx);
1475 BN_GF2m_mod_div(f, a, e, b[j], ctx);
1476 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1482 BIO_puts(bp, " = ");
1486 BIO_puts(bp, " % ");
1492 /* Test that ((a/c)*c)/a = 1. */
1495 fprintf(stderr,"GF(2^m) modular division test failed!\n");
1512 int test_gf2m_mod_exp(BIO *bp,BN_CTX *ctx)
1514 BIGNUM *a,*b[2],*c,*d,*e,*f;
1516 int p0[] = {163,7,6,3,0,-1};
1517 int p1[] = {193,15,0,-1};
1527 BN_GF2m_arr2poly(p0, b[0]);
1528 BN_GF2m_arr2poly(p1, b[1]);
1530 for (i=0; i<num0; i++)
1532 BN_bntest_rand(a, 512, 0, 0);
1533 BN_bntest_rand(c, 512, 0, 0);
1534 BN_bntest_rand(d, 512, 0, 0);
1535 for (j=0; j < 2; j++)
1537 BN_GF2m_mod_exp(e, a, c, b[j], ctx);
1538 BN_GF2m_mod_exp(f, a, d, b[j], ctx);
1539 BN_GF2m_mod_mul(e, e, f, b[j], ctx);
1541 BN_GF2m_mod_exp(f, a, f, b[j], ctx);
1542 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1548 BIO_puts(bp, " ^ (");
1552 BIO_puts(bp, ") = ");
1554 BIO_puts(bp, "; - ");
1556 BIO_puts(bp, " % ");
1562 BN_GF2m_add(f, e, f);
1563 /* Test that a^(c+d)=a^c*a^d. */
1566 fprintf(stderr,"GF(2^m) modular exponentiation test failed!\n");
1583 int test_gf2m_mod_sqrt(BIO *bp,BN_CTX *ctx)
1585 BIGNUM *a,*b[2],*c,*d,*e,*f;
1587 int p0[] = {163,7,6,3,0,-1};
1588 int p1[] = {193,15,0,-1};
1598 BN_GF2m_arr2poly(p0, b[0]);
1599 BN_GF2m_arr2poly(p1, b[1]);
1601 for (i=0; i<num0; i++)
1603 BN_bntest_rand(a, 512, 0, 0);
1604 for (j=0; j < 2; j++)
1606 BN_GF2m_mod(c, a, b[j]);
1607 BN_GF2m_mod_sqrt(d, a, b[j], ctx);
1608 BN_GF2m_mod_sqr(e, d, b[j], ctx);
1609 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1615 BIO_puts(bp, " ^ 2 - ");
1621 BN_GF2m_add(f, c, e);
1622 /* Test that d^2 = a, where d = sqrt(a). */
1625 fprintf(stderr,"GF(2^m) modular square root test failed!\n");
1642 int test_gf2m_mod_solve_quad(BIO *bp,BN_CTX *ctx)
1644 BIGNUM *a,*b[2],*c,*d,*e;
1645 int i, j, s = 0, t, ret = 0;
1646 int p0[] = {163,7,6,3,0,-1};
1647 int p1[] = {193,15,0,-1};
1656 BN_GF2m_arr2poly(p0, b[0]);
1657 BN_GF2m_arr2poly(p1, b[1]);
1659 for (i=0; i<num0; i++)
1661 BN_bntest_rand(a, 512, 0, 0);
1662 for (j=0; j < 2; j++)
1664 t = BN_GF2m_mod_solve_quad(c, a, b[j], ctx);
1668 BN_GF2m_mod_sqr(d, c, b[j], ctx);
1669 BN_GF2m_add(d, c, d);
1670 BN_GF2m_mod(e, a, b[j]);
1671 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1677 BIO_puts(bp, " is root of z^2 + z = ");
1679 BIO_puts(bp, " % ");
1685 BN_GF2m_add(e, e, d);
1686 /* Test that solution of quadratic c satisfies c^2 + c = a. */
1689 fprintf(stderr,"GF(2^m) modular solve quadratic test failed!\n");
1696 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1701 BIO_puts(bp, "There are no roots of z^2 + z = ");
1703 BIO_puts(bp, " % ");
1714 fprintf(stderr,"All %i tests of GF(2^m) modular solve quadratic resulted in no roots;\n", num0);
1715 fprintf(stderr,"this is very unlikely and probably indicates an error.\n");
1729 static int genprime_cb(int p, int n, BN_GENCB *arg)
1742 int test_kron(BIO *bp, BN_CTX *ctx)
1747 int legendre, kronecker;
1754 if (a == NULL || b == NULL || r == NULL || t == NULL) goto err;
1756 BN_GENCB_set(&cb, genprime_cb, NULL);
1758 /* We test BN_kronecker(a, b, ctx) just for b odd (Jacobi symbol).
1759 * In this case we know that if b is prime, then BN_kronecker(a, b, ctx)
1760 * is congruent to $a^{(b-1)/2}$, modulo $b$ (Legendre symbol).
1761 * So we generate a random prime b and compare these values
1762 * for a number of random a's. (That is, we run the Solovay-Strassen
1763 * primality test to confirm that b is prime, except that we
1764 * don't want to test whether b is prime but whether BN_kronecker
1767 if (!BN_generate_prime_ex(b, 512, 0, NULL, NULL, &cb)) goto err;
1768 b->neg = rand_neg();
1771 for (i = 0; i < num0; i++)
1773 if (!BN_bntest_rand(a, 512, 0, 0)) goto err;
1774 a->neg = rand_neg();
1776 /* t := (|b|-1)/2 (note that b is odd) */
1777 if (!BN_copy(t, b)) goto err;
1779 if (!BN_sub_word(t, 1)) goto err;
1780 if (!BN_rshift1(t, t)) goto err;
1781 /* r := a^t mod b */
1784 if (!BN_mod_exp_recp(r, a, t, b, ctx)) goto err;
1787 if (BN_is_word(r, 1))
1789 else if (BN_is_zero(r))
1793 if (!BN_add_word(r, 1)) goto err;
1794 if (0 != BN_ucmp(r, b))
1796 fprintf(stderr, "Legendre symbol computation failed\n");
1802 kronecker = BN_kronecker(a, b, ctx);
1803 if (kronecker < -1) goto err;
1804 /* we actually need BN_kronecker(a, |b|) */
1805 if (a->neg && b->neg)
1806 kronecker = -kronecker;
1808 if (legendre != kronecker)
1810 fprintf(stderr, "legendre != kronecker; a = ");
1811 BN_print_fp(stderr, a);
1812 fprintf(stderr, ", b = ");
1813 BN_print_fp(stderr, b);
1814 fprintf(stderr, "\n");
1826 if (a != NULL) BN_free(a);
1827 if (b != NULL) BN_free(b);
1828 if (r != NULL) BN_free(r);
1829 if (t != NULL) BN_free(t);
1833 int test_sqrt(BIO *bp, BN_CTX *ctx)
1843 if (a == NULL || p == NULL || r == NULL) goto err;
1845 BN_GENCB_set(&cb, genprime_cb, NULL);
1847 for (i = 0; i < 16; i++)
1851 unsigned primes[8] = { 2, 3, 5, 7, 11, 13, 17, 19 };
1853 if (!BN_set_word(p, primes[i])) goto err;
1857 if (!BN_set_word(a, 32)) goto err;
1858 if (!BN_set_word(r, 2*i + 1)) goto err;
1860 if (!BN_generate_prime_ex(p, 256, 0, a, r, &cb)) goto err;
1863 p->neg = rand_neg();
1865 for (j = 0; j < num2; j++)
1867 /* construct 'a' such that it is a square modulo p,
1868 * but in general not a proper square and not reduced modulo p */
1869 if (!BN_bntest_rand(r, 256, 0, 3)) goto err;
1870 if (!BN_nnmod(r, r, p, ctx)) goto err;
1871 if (!BN_mod_sqr(r, r, p, ctx)) goto err;
1872 if (!BN_bntest_rand(a, 256, 0, 3)) goto err;
1873 if (!BN_nnmod(a, a, p, ctx)) goto err;
1874 if (!BN_mod_sqr(a, a, p, ctx)) goto err;
1875 if (!BN_mul(a, a, r, ctx)) goto err;
1877 if (!BN_sub(a, a, p)) goto err;
1879 if (!BN_mod_sqrt(r, a, p, ctx)) goto err;
1880 if (!BN_mod_sqr(r, r, p, ctx)) goto err;
1882 if (!BN_nnmod(a, a, p, ctx)) goto err;
1884 if (BN_cmp(a, r) != 0)
1886 fprintf(stderr, "BN_mod_sqrt failed: a = ");
1887 BN_print_fp(stderr, a);
1888 fprintf(stderr, ", r = ");
1889 BN_print_fp(stderr, r);
1890 fprintf(stderr, ", p = ");
1891 BN_print_fp(stderr, p);
1892 fprintf(stderr, "\n");
1905 if (a != NULL) BN_free(a);
1906 if (p != NULL) BN_free(p);
1907 if (r != NULL) BN_free(r);
1911 int test_small_prime(BIO *bp,BN_CTX *ctx)
1913 static const int bits = 10;
1918 if (!BN_generate_prime_ex(&r, bits, 0, NULL, NULL, NULL))
1920 if (BN_num_bits(&r) != bits)
1922 BIO_printf(bp, "Expected %d bit prime, got %d bit number\n", bits, BN_num_bits(&r));
1933 int test_probable_prime_coprime(BIO *bp, BN_CTX *ctx)
1937 BN_ULONG primes[5] = { 2, 3, 5, 7, 11 };
1941 for (i = 0; i < 1000; i++)
1943 if (!bn_probable_prime_dh_coprime(&r, 1024, ctx)) goto err;
1945 for (j = 0; j < 5; j++)
1947 if (BN_mod_word(&r, primes[j]) == 0)
1949 BIO_printf(bp, "Number generated is not coprime to %ld:\n", primes[j]);
1950 BN_print_fp(stdout, &r);
1951 BIO_printf(bp, "\n");
1964 int test_lshift(BIO *bp,BN_CTX *ctx,BIGNUM *a_)
1979 BN_bntest_rand(a,200,0,0); /**/
1982 for (i=0; i<num0; i++)
2002 fprintf(stderr,"Left shift test failed!\n");
2003 fprintf(stderr,"a=");
2004 BN_print_fp(stderr,a);
2005 fprintf(stderr,"\nb=");
2006 BN_print_fp(stderr,b);
2007 fprintf(stderr,"\nc=");
2008 BN_print_fp(stderr,c);
2009 fprintf(stderr,"\nd=");
2010 BN_print_fp(stderr,d);
2011 fprintf(stderr,"\n");
2022 int test_lshift1(BIO *bp)
2031 BN_bntest_rand(a,200,0,0); /**/
2033 for (i=0; i<num0; i++)
2041 BIO_puts(bp," * 2");
2051 fprintf(stderr,"Left shift one test failed!\n");
2063 int test_rshift(BIO *bp,BN_CTX *ctx)
2065 BIGNUM *a,*b,*c,*d,*e;
2075 BN_bntest_rand(a,200,0,0); /**/
2077 for (i=0; i<num0; i++)
2093 BN_div(d,e,a,c,ctx);
2097 fprintf(stderr,"Right shift test failed!\n");
2109 int test_rshift1(BIO *bp)
2118 BN_bntest_rand(a,200,0,0); /**/
2120 for (i=0; i<num0; i++)
2128 BIO_puts(bp," / 2");
2136 if(!BN_is_zero(c) && !BN_abs_is_word(c, 1))
2138 fprintf(stderr,"Right shift one test failed!\n");
2151 static unsigned int neg=0;
2152 static int sign[8]={0,0,0,1,1,0,1,1};
2154 return(sign[(neg++)%8]);