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_mod_exp_mont_consttime(BIO *bp,BN_CTX *ctx);
110 int test_exp(BIO *bp,BN_CTX *ctx);
111 int test_gf2m_add(BIO *bp);
112 int test_gf2m_mod(BIO *bp);
113 int test_gf2m_mod_mul(BIO *bp,BN_CTX *ctx);
114 int test_gf2m_mod_sqr(BIO *bp,BN_CTX *ctx);
115 int test_gf2m_mod_inv(BIO *bp,BN_CTX *ctx);
116 int test_gf2m_mod_div(BIO *bp,BN_CTX *ctx);
117 int test_gf2m_mod_exp(BIO *bp,BN_CTX *ctx);
118 int test_gf2m_mod_sqrt(BIO *bp,BN_CTX *ctx);
119 int test_gf2m_mod_solve_quad(BIO *bp,BN_CTX *ctx);
120 int test_kron(BIO *bp,BN_CTX *ctx);
121 int test_sqrt(BIO *bp,BN_CTX *ctx);
123 static int results=0;
125 static unsigned char lst[]="\xC6\x4F\x43\x04\x2A\xEA\xCA\x6E\x58\x36\x80\x5B\xE8\xC9"
126 "\x9B\x04\x5D\x48\x36\xC2\xFD\x16\xC9\x64\xF0";
128 static const char rnd_seed[] = "string to make the random number generator think it has entropy";
130 static void message(BIO *out, char *m)
132 fprintf(stderr, "test %s\n", m);
133 BIO_puts(out, "print \"test ");
135 BIO_puts(out, "\\n\"\n");
138 int main(int argc, char *argv[])
146 RAND_seed(rnd_seed, sizeof rnd_seed); /* or BN_generate_prime may fail */
152 if (strcmp(*argv,"-results") == 0)
154 else if (strcmp(*argv,"-out") == 0)
156 if (--argc < 1) break;
165 if (ctx == NULL) EXIT(1);
167 out=BIO_new(BIO_s_file());
168 if (out == NULL) EXIT(1);
171 BIO_set_fp(out,stdout,BIO_NOCLOSE);
175 if (!BIO_write_filename(out,outfile))
183 BIO_puts(out,"obase=16\nibase=16\n");
185 message(out,"BN_add");
186 if (!test_add(out)) goto err;
187 (void)BIO_flush(out);
189 message(out,"BN_sub");
190 if (!test_sub(out)) goto err;
191 (void)BIO_flush(out);
193 message(out,"BN_lshift1");
194 if (!test_lshift1(out)) goto err;
195 (void)BIO_flush(out);
197 message(out,"BN_lshift (fixed)");
198 if (!test_lshift(out,ctx,BN_bin2bn(lst,sizeof(lst)-1,NULL)))
200 (void)BIO_flush(out);
202 message(out,"BN_lshift");
203 if (!test_lshift(out,ctx,NULL)) goto err;
204 (void)BIO_flush(out);
206 message(out,"BN_rshift1");
207 if (!test_rshift1(out)) goto err;
208 (void)BIO_flush(out);
210 message(out,"BN_rshift");
211 if (!test_rshift(out,ctx)) goto err;
212 (void)BIO_flush(out);
214 message(out,"BN_sqr");
215 if (!test_sqr(out,ctx)) goto err;
216 (void)BIO_flush(out);
218 message(out,"BN_mul");
219 if (!test_mul(out)) goto err;
220 (void)BIO_flush(out);
222 message(out,"BN_div");
223 if (!test_div(out,ctx)) goto err;
224 (void)BIO_flush(out);
226 message(out,"BN_div_word");
227 if (!test_div_word(out)) goto err;
228 (void)BIO_flush(out);
230 message(out,"BN_div_recp");
231 if (!test_div_recp(out,ctx)) goto err;
232 (void)BIO_flush(out);
234 message(out,"BN_mod");
235 if (!test_mod(out,ctx)) goto err;
236 (void)BIO_flush(out);
238 message(out,"BN_mod_mul");
239 if (!test_mod_mul(out,ctx)) goto err;
240 (void)BIO_flush(out);
242 message(out,"BN_mont");
243 if (!test_mont(out,ctx)) goto err;
244 (void)BIO_flush(out);
246 message(out,"BN_mod_exp");
247 if (!test_mod_exp(out,ctx)) goto err;
248 (void)BIO_flush(out);
250 message(out,"BN_mod_exp_mont_consttime");
251 if (!test_mod_exp_mont_consttime(out,ctx)) goto err;
252 (void)BIO_flush(out);
254 message(out,"BN_exp");
255 if (!test_exp(out,ctx)) goto err;
256 (void)BIO_flush(out);
258 message(out,"BN_kronecker");
259 if (!test_kron(out,ctx)) goto err;
260 (void)BIO_flush(out);
262 message(out,"BN_mod_sqrt");
263 if (!test_sqrt(out,ctx)) goto err;
264 (void)BIO_flush(out);
265 #ifndef OPENSSL_NO_EC2M
266 message(out,"BN_GF2m_add");
267 if (!test_gf2m_add(out)) goto err;
268 (void)BIO_flush(out);
270 message(out,"BN_GF2m_mod");
271 if (!test_gf2m_mod(out)) goto err;
272 (void)BIO_flush(out);
274 message(out,"BN_GF2m_mod_mul");
275 if (!test_gf2m_mod_mul(out,ctx)) goto err;
276 (void)BIO_flush(out);
278 message(out,"BN_GF2m_mod_sqr");
279 if (!test_gf2m_mod_sqr(out,ctx)) goto err;
280 (void)BIO_flush(out);
282 message(out,"BN_GF2m_mod_inv");
283 if (!test_gf2m_mod_inv(out,ctx)) goto err;
284 (void)BIO_flush(out);
286 message(out,"BN_GF2m_mod_div");
287 if (!test_gf2m_mod_div(out,ctx)) goto err;
288 (void)BIO_flush(out);
290 message(out,"BN_GF2m_mod_exp");
291 if (!test_gf2m_mod_exp(out,ctx)) goto err;
292 (void)BIO_flush(out);
294 message(out,"BN_GF2m_mod_sqrt");
295 if (!test_gf2m_mod_sqrt(out,ctx)) goto err;
296 (void)BIO_flush(out);
298 message(out,"BN_GF2m_mod_solve_quad");
299 if (!test_gf2m_mod_solve_quad(out,ctx)) goto err;
300 (void)BIO_flush(out);
308 BIO_puts(out,"1\n"); /* make sure the Perl script fed by bc notices
309 * the failure, see test_bn in test/Makefile.ssl*/
310 (void)BIO_flush(out);
311 ERR_load_crypto_strings();
312 ERR_print_errors_fp(stderr);
317 int test_add(BIO *bp)
326 BN_bntest_rand(&a,512,0,0);
327 for (i=0; i<num0; i++)
329 BN_bntest_rand(&b,450+i,0,0);
351 fprintf(stderr,"Add test failed!\n");
361 int test_sub(BIO *bp)
370 for (i=0; i<num0+num1; i++)
374 BN_bntest_rand(&a,512,0,0);
376 if (BN_set_bit(&a,i)==0) return(0);
381 BN_bntest_rand(&b,400+i-num1,0,0);
402 fprintf(stderr,"Subtract test failed!\n");
412 int test_div(BIO *bp, BN_CTX *ctx)
423 for (i=0; i<num0+num1; i++)
427 BN_bntest_rand(&a,400,0,0);
433 BN_bntest_rand(&b,50+3*(i-num1),0,0);
436 BN_div(&d,&c,&a,&b,ctx);
459 BN_mul(&e,&d,&b,ctx);
464 fprintf(stderr,"Division test failed!\n");
476 static void print_word(BIO *bp,BN_ULONG w)
478 #ifdef SIXTY_FOUR_BIT
479 if (sizeof(w) > sizeof(unsigned long))
481 unsigned long h=(unsigned long)(w>>32),
482 l=(unsigned long)(w);
484 if (h) BIO_printf(bp,"%lX%08lX",h,l);
485 else BIO_printf(bp,"%lX",l);
489 BIO_printf(bp,BN_HEX_FMT1,w);
492 int test_div_word(BIO *bp)
501 for (i=0; i<num0; i++)
504 BN_bntest_rand(&a,512,-1,0);
505 BN_bntest_rand(&b,BN_BITS2,-1,0);
510 r = BN_div_word(&b, s);
539 fprintf(stderr,"Division (word) test failed!\n");
548 int test_div_recp(BIO *bp, BN_CTX *ctx)
554 BN_RECP_CTX_init(&recp);
561 for (i=0; i<num0+num1; i++)
565 BN_bntest_rand(&a,400,0,0);
571 BN_bntest_rand(&b,50+3*(i-num1),0,0);
574 BN_RECP_CTX_set(&recp,&b,ctx);
575 BN_div_recp(&d,&c,&a,&recp,ctx);
598 BN_mul(&e,&d,&b,ctx);
603 fprintf(stderr,"Reciprocal division test failed!\n");
604 fprintf(stderr,"a=");
605 BN_print_fp(stderr,&a);
606 fprintf(stderr,"\nb=");
607 BN_print_fp(stderr,&b);
608 fprintf(stderr,"\n");
617 BN_RECP_CTX_free(&recp);
621 int test_mul(BIO *bp)
628 if (ctx == NULL) EXIT(1);
636 for (i=0; i<num0+num1; i++)
640 BN_bntest_rand(&a,100,0,0);
641 BN_bntest_rand(&b,100,0,0);
644 BN_bntest_rand(&b,i-num1,0,0);
647 BN_mul(&c,&a,&b,ctx);
660 BN_div(&d,&e,&c,&a,ctx);
662 if(!BN_is_zero(&d) || !BN_is_zero(&e))
664 fprintf(stderr,"Multiplication test failed!\n");
677 int test_sqr(BIO *bp, BN_CTX *ctx)
687 for (i=0; i<num0; i++)
689 BN_bntest_rand(&a,40+i*10,0,0);
704 BN_div(&d,&e,&c,&a,ctx);
706 if(!BN_is_zero(&d) || !BN_is_zero(&e))
708 fprintf(stderr,"Square test failed!\n");
719 int test_mont(BIO *bp, BN_CTX *ctx)
734 mont=BN_MONT_CTX_new();
738 BN_bntest_rand(&a,100,0,0); /**/
739 BN_bntest_rand(&b,100,0,0); /**/
740 for (i=0; i<num2; i++)
742 int bits = (200*(i+1))/num2;
746 BN_bntest_rand(&n,bits,0,1);
747 BN_MONT_CTX_set(mont,&n,ctx);
749 BN_nnmod(&a,&a,&n,ctx);
750 BN_nnmod(&b,&b,&n,ctx);
752 BN_to_montgomery(&A,&a,mont,ctx);
753 BN_to_montgomery(&B,&b,mont,ctx);
755 BN_mod_mul_montgomery(&c,&A,&B,mont,ctx);/**/
756 BN_from_montgomery(&A,&c,mont,ctx);/**/
762 fprintf(stderr,"%d * %d %% %d\n",
765 BN_num_bits(mont->N));
771 BN_print(bp,&(mont->N));
777 BN_mod_mul(&d,&a,&b,&n,ctx);
781 fprintf(stderr,"Montgomery multiplication test failed!\n");
785 BN_MONT_CTX_free(mont);
796 int test_mod(BIO *bp, BN_CTX *ctx)
798 BIGNUM *a,*b,*c,*d,*e;
807 BN_bntest_rand(a,1024,0,0); /**/
808 for (i=0; i<num0; i++)
810 BN_bntest_rand(b,450+i*10,0,0); /**/
813 BN_mod(c,a,b,ctx);/**/
830 fprintf(stderr,"Modulo test failed!\n");
842 int test_mod_mul(BIO *bp, BN_CTX *ctx)
844 BIGNUM *a,*b,*c,*d,*e;
853 for (j=0; j<3; j++) {
854 BN_bntest_rand(c,1024,0,0); /**/
855 for (i=0; i<num0; i++)
857 BN_bntest_rand(a,475+i*10,0,0); /**/
858 BN_bntest_rand(b,425+i*11,0,0); /**/
861 if (!BN_mod_mul(e,a,b,c,ctx))
865 while ((l=ERR_get_error()))
866 fprintf(stderr,"ERROR:%s\n",
867 ERR_error_string(l,NULL));
879 if ((a->neg ^ b->neg) && !BN_is_zero(e))
881 /* If (a*b) % c is negative, c must be added
882 * in order to obtain the normalized remainder
883 * (new with OpenSSL 0.9.7, previous versions of
884 * BN_mod_mul could generate negative results)
899 fprintf(stderr,"Modulo multiply test failed!\n");
900 ERR_print_errors_fp(stderr);
913 int test_mod_exp(BIO *bp, BN_CTX *ctx)
915 BIGNUM *a,*b,*c,*d,*e;
924 BN_bntest_rand(c,30,0,1); /* must be odd for montgomery */
925 for (i=0; i<num2; i++)
927 BN_bntest_rand(a,20+i*5,0,0); /**/
928 BN_bntest_rand(b,2+i,0,0); /**/
930 if (!BN_mod_exp(d,a,b,c,ctx))
952 fprintf(stderr,"Modulo exponentiation test failed!\n");
964 int test_mod_exp_mont_consttime(BIO *bp, BN_CTX *ctx)
966 BIGNUM *a,*b,*c,*d,*e;
975 BN_bntest_rand(c,30,0,1); /* must be odd for montgomery */
976 for (i=0; i<num2; i++)
978 BN_bntest_rand(a,20+i*5,0,0); /**/
979 BN_bntest_rand(b,2+i,0,0); /**/
981 if (!BN_mod_exp_mont_consttime(d,a,b,c,ctx,NULL))
1000 BN_div(a,b,e,c,ctx);
1003 fprintf(stderr,"Modulo exponentiation test failed!\n");
1015 int test_exp(BIO *bp, BN_CTX *ctx)
1017 BIGNUM *a,*b,*d,*e,*one;
1027 for (i=0; i<num2; i++)
1029 BN_bntest_rand(a,20+i*5,0,0); /**/
1030 BN_bntest_rand(b,2+i,0,0); /**/
1032 if (BN_exp(d,a,b,ctx) <= 0)
1048 for( ; !BN_is_zero(b) ; BN_sub(b,b,one))
1053 fprintf(stderr,"Exponentiation test failed!\n");
1064 #ifndef OPENSSL_NO_EC2M
1065 int test_gf2m_add(BIO *bp)
1074 for (i=0; i<num0; i++)
1076 BN_rand(&a,512,0,0);
1077 BN_copy(&b, BN_value_one());
1080 BN_GF2m_add(&c,&a,&b);
1081 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1095 /* Test that two added values have the correct parity. */
1096 if((BN_is_odd(&a) && BN_is_odd(&c)) || (!BN_is_odd(&a) && !BN_is_odd(&c)))
1098 fprintf(stderr,"GF(2^m) addition test (a) failed!\n");
1101 BN_GF2m_add(&c,&c,&c);
1102 /* Test that c + c = 0. */
1105 fprintf(stderr,"GF(2^m) addition test (b) failed!\n");
1117 int test_gf2m_mod(BIO *bp)
1119 BIGNUM *a,*b[2],*c,*d,*e;
1121 int p0[] = {163,7,6,3,0,-1};
1122 int p1[] = {193,15,0,-1};
1131 BN_GF2m_arr2poly(p0, b[0]);
1132 BN_GF2m_arr2poly(p1, b[1]);
1134 for (i=0; i<num0; i++)
1136 BN_bntest_rand(a, 1024, 0, 0);
1137 for (j=0; j < 2; j++)
1139 BN_GF2m_mod(c, a, b[j]);
1140 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1154 BN_GF2m_add(d, a, c);
1155 BN_GF2m_mod(e, d, b[j]);
1156 /* Test that a + (a mod p) mod p == 0. */
1159 fprintf(stderr,"GF(2^m) modulo test failed!\n");
1175 int test_gf2m_mod_mul(BIO *bp,BN_CTX *ctx)
1177 BIGNUM *a,*b[2],*c,*d,*e,*f,*g,*h;
1179 int p0[] = {163,7,6,3,0,-1};
1180 int p1[] = {193,15,0,-1};
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, 1024, 0, 0);
1198 BN_bntest_rand(c, 1024, 0, 0);
1199 BN_bntest_rand(d, 1024, 0, 0);
1200 for (j=0; j < 2; j++)
1202 BN_GF2m_mod_mul(e, a, c, b[j], ctx);
1203 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1219 BN_GF2m_add(f, a, d);
1220 BN_GF2m_mod_mul(g, f, c, b[j], ctx);
1221 BN_GF2m_mod_mul(h, d, c, b[j], ctx);
1222 BN_GF2m_add(f, e, g);
1223 BN_GF2m_add(f, f, h);
1224 /* Test that (a+d)*c = a*c + d*c. */
1227 fprintf(stderr,"GF(2^m) modular multiplication test failed!\n");
1246 int test_gf2m_mod_sqr(BIO *bp,BN_CTX *ctx)
1248 BIGNUM *a,*b[2],*c,*d;
1250 int p0[] = {163,7,6,3,0,-1};
1251 int p1[] = {193,15,0,-1};
1259 BN_GF2m_arr2poly(p0, b[0]);
1260 BN_GF2m_arr2poly(p1, b[1]);
1262 for (i=0; i<num0; i++)
1264 BN_bntest_rand(a, 1024, 0, 0);
1265 for (j=0; j < 2; j++)
1267 BN_GF2m_mod_sqr(c, a, b[j], ctx);
1269 BN_GF2m_mod_mul(d, a, d, b[j], ctx);
1270 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1276 BIO_puts(bp," ^ 2 % ");
1278 BIO_puts(bp, " = ");
1280 BIO_puts(bp,"; a * a = ");
1286 BN_GF2m_add(d, c, d);
1287 /* Test that a*a = a^2. */
1290 fprintf(stderr,"GF(2^m) modular squaring test failed!\n");
1305 int test_gf2m_mod_inv(BIO *bp,BN_CTX *ctx)
1307 BIGNUM *a,*b[2],*c,*d;
1309 int p0[] = {163,7,6,3,0,-1};
1310 int p1[] = {193,15,0,-1};
1318 BN_GF2m_arr2poly(p0, b[0]);
1319 BN_GF2m_arr2poly(p1, b[1]);
1321 for (i=0; i<num0; i++)
1323 BN_bntest_rand(a, 512, 0, 0);
1324 for (j=0; j < 2; j++)
1326 BN_GF2m_mod_inv(c, a, b[j], ctx);
1327 BN_GF2m_mod_mul(d, a, c, b[j], ctx);
1328 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1334 BIO_puts(bp, " * ");
1336 BIO_puts(bp," - 1 % ");
1342 /* Test that ((1/a)*a) = 1. */
1345 fprintf(stderr,"GF(2^m) modular inversion test failed!\n");
1360 int test_gf2m_mod_div(BIO *bp,BN_CTX *ctx)
1362 BIGNUM *a,*b[2],*c,*d,*e,*f;
1364 int p0[] = {163,7,6,3,0,-1};
1365 int p1[] = {193,15,0,-1};
1375 BN_GF2m_arr2poly(p0, b[0]);
1376 BN_GF2m_arr2poly(p1, b[1]);
1378 for (i=0; i<num0; i++)
1380 BN_bntest_rand(a, 512, 0, 0);
1381 BN_bntest_rand(c, 512, 0, 0);
1382 for (j=0; j < 2; j++)
1384 BN_GF2m_mod_div(d, a, c, b[j], ctx);
1385 BN_GF2m_mod_mul(e, d, c, b[j], ctx);
1386 BN_GF2m_mod_div(f, a, e, b[j], ctx);
1387 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1393 BIO_puts(bp, " = ");
1397 BIO_puts(bp, " % ");
1403 /* Test that ((a/c)*c)/a = 1. */
1406 fprintf(stderr,"GF(2^m) modular division test failed!\n");
1423 int test_gf2m_mod_exp(BIO *bp,BN_CTX *ctx)
1425 BIGNUM *a,*b[2],*c,*d,*e,*f;
1427 int p0[] = {163,7,6,3,0,-1};
1428 int p1[] = {193,15,0,-1};
1438 BN_GF2m_arr2poly(p0, b[0]);
1439 BN_GF2m_arr2poly(p1, b[1]);
1441 for (i=0; i<num0; i++)
1443 BN_bntest_rand(a, 512, 0, 0);
1444 BN_bntest_rand(c, 512, 0, 0);
1445 BN_bntest_rand(d, 512, 0, 0);
1446 for (j=0; j < 2; j++)
1448 BN_GF2m_mod_exp(e, a, c, b[j], ctx);
1449 BN_GF2m_mod_exp(f, a, d, b[j], ctx);
1450 BN_GF2m_mod_mul(e, e, f, b[j], ctx);
1452 BN_GF2m_mod_exp(f, a, f, b[j], ctx);
1453 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1459 BIO_puts(bp, " ^ (");
1463 BIO_puts(bp, ") = ");
1465 BIO_puts(bp, "; - ");
1467 BIO_puts(bp, " % ");
1473 BN_GF2m_add(f, e, f);
1474 /* Test that a^(c+d)=a^c*a^d. */
1477 fprintf(stderr,"GF(2^m) modular exponentiation test failed!\n");
1494 int test_gf2m_mod_sqrt(BIO *bp,BN_CTX *ctx)
1496 BIGNUM *a,*b[2],*c,*d,*e,*f;
1498 int p0[] = {163,7,6,3,0,-1};
1499 int p1[] = {193,15,0,-1};
1509 BN_GF2m_arr2poly(p0, b[0]);
1510 BN_GF2m_arr2poly(p1, b[1]);
1512 for (i=0; i<num0; i++)
1514 BN_bntest_rand(a, 512, 0, 0);
1515 for (j=0; j < 2; j++)
1517 BN_GF2m_mod(c, a, b[j]);
1518 BN_GF2m_mod_sqrt(d, a, b[j], ctx);
1519 BN_GF2m_mod_sqr(e, d, b[j], ctx);
1520 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1526 BIO_puts(bp, " ^ 2 - ");
1532 BN_GF2m_add(f, c, e);
1533 /* Test that d^2 = a, where d = sqrt(a). */
1536 fprintf(stderr,"GF(2^m) modular square root test failed!\n");
1553 int test_gf2m_mod_solve_quad(BIO *bp,BN_CTX *ctx)
1555 BIGNUM *a,*b[2],*c,*d,*e;
1556 int i, j, s = 0, t, ret = 0;
1557 int p0[] = {163,7,6,3,0,-1};
1558 int p1[] = {193,15,0,-1};
1567 BN_GF2m_arr2poly(p0, b[0]);
1568 BN_GF2m_arr2poly(p1, b[1]);
1570 for (i=0; i<num0; i++)
1572 BN_bntest_rand(a, 512, 0, 0);
1573 for (j=0; j < 2; j++)
1575 t = BN_GF2m_mod_solve_quad(c, a, b[j], ctx);
1579 BN_GF2m_mod_sqr(d, c, b[j], ctx);
1580 BN_GF2m_add(d, c, d);
1581 BN_GF2m_mod(e, a, b[j]);
1582 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1588 BIO_puts(bp, " is root of z^2 + z = ");
1590 BIO_puts(bp, " % ");
1596 BN_GF2m_add(e, e, d);
1597 /* Test that solution of quadratic c satisfies c^2 + c = a. */
1600 fprintf(stderr,"GF(2^m) modular solve quadratic test failed!\n");
1607 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1612 BIO_puts(bp, "There are no roots of z^2 + z = ");
1614 BIO_puts(bp, " % ");
1625 fprintf(stderr,"All %i tests of GF(2^m) modular solve quadratic resulted in no roots;\n", num0);
1626 fprintf(stderr,"this is very unlikely and probably indicates an error.\n");
1640 static int genprime_cb(int p, int n, BN_GENCB *arg)
1653 int test_kron(BIO *bp, BN_CTX *ctx)
1658 int legendre, kronecker;
1665 if (a == NULL || b == NULL || r == NULL || t == NULL) goto err;
1667 BN_GENCB_set(&cb, genprime_cb, NULL);
1669 /* We test BN_kronecker(a, b, ctx) just for b odd (Jacobi symbol).
1670 * In this case we know that if b is prime, then BN_kronecker(a, b, ctx)
1671 * is congruent to $a^{(b-1)/2}$, modulo $b$ (Legendre symbol).
1672 * So we generate a random prime b and compare these values
1673 * for a number of random a's. (That is, we run the Solovay-Strassen
1674 * primality test to confirm that b is prime, except that we
1675 * don't want to test whether b is prime but whether BN_kronecker
1678 if (!BN_generate_prime_ex(b, 512, 0, NULL, NULL, &cb)) goto err;
1679 b->neg = rand_neg();
1682 for (i = 0; i < num0; i++)
1684 if (!BN_bntest_rand(a, 512, 0, 0)) goto err;
1685 a->neg = rand_neg();
1687 /* t := (|b|-1)/2 (note that b is odd) */
1688 if (!BN_copy(t, b)) goto err;
1690 if (!BN_sub_word(t, 1)) goto err;
1691 if (!BN_rshift1(t, t)) goto err;
1692 /* r := a^t mod b */
1695 if (!BN_mod_exp_recp(r, a, t, b, ctx)) goto err;
1698 if (BN_is_word(r, 1))
1700 else if (BN_is_zero(r))
1704 if (!BN_add_word(r, 1)) goto err;
1705 if (0 != BN_ucmp(r, b))
1707 fprintf(stderr, "Legendre symbol computation failed\n");
1713 kronecker = BN_kronecker(a, b, ctx);
1714 if (kronecker < -1) goto err;
1715 /* we actually need BN_kronecker(a, |b|) */
1716 if (a->neg && b->neg)
1717 kronecker = -kronecker;
1719 if (legendre != kronecker)
1721 fprintf(stderr, "legendre != kronecker; a = ");
1722 BN_print_fp(stderr, a);
1723 fprintf(stderr, ", b = ");
1724 BN_print_fp(stderr, b);
1725 fprintf(stderr, "\n");
1737 if (a != NULL) BN_free(a);
1738 if (b != NULL) BN_free(b);
1739 if (r != NULL) BN_free(r);
1740 if (t != NULL) BN_free(t);
1744 int test_sqrt(BIO *bp, BN_CTX *ctx)
1754 if (a == NULL || p == NULL || r == NULL) goto err;
1756 BN_GENCB_set(&cb, genprime_cb, NULL);
1758 for (i = 0; i < 16; i++)
1762 unsigned primes[8] = { 2, 3, 5, 7, 11, 13, 17, 19 };
1764 if (!BN_set_word(p, primes[i])) goto err;
1768 if (!BN_set_word(a, 32)) goto err;
1769 if (!BN_set_word(r, 2*i + 1)) goto err;
1771 if (!BN_generate_prime_ex(p, 256, 0, a, r, &cb)) goto err;
1774 p->neg = rand_neg();
1776 for (j = 0; j < num2; j++)
1778 /* construct 'a' such that it is a square modulo p,
1779 * but in general not a proper square and not reduced modulo p */
1780 if (!BN_bntest_rand(r, 256, 0, 3)) goto err;
1781 if (!BN_nnmod(r, r, p, ctx)) goto err;
1782 if (!BN_mod_sqr(r, r, p, ctx)) goto err;
1783 if (!BN_bntest_rand(a, 256, 0, 3)) goto err;
1784 if (!BN_nnmod(a, a, p, ctx)) goto err;
1785 if (!BN_mod_sqr(a, a, p, ctx)) goto err;
1786 if (!BN_mul(a, a, r, ctx)) goto err;
1788 if (!BN_sub(a, a, p)) goto err;
1790 if (!BN_mod_sqrt(r, a, p, ctx)) goto err;
1791 if (!BN_mod_sqr(r, r, p, ctx)) goto err;
1793 if (!BN_nnmod(a, a, p, ctx)) goto err;
1795 if (BN_cmp(a, r) != 0)
1797 fprintf(stderr, "BN_mod_sqrt failed: a = ");
1798 BN_print_fp(stderr, a);
1799 fprintf(stderr, ", r = ");
1800 BN_print_fp(stderr, r);
1801 fprintf(stderr, ", p = ");
1802 BN_print_fp(stderr, p);
1803 fprintf(stderr, "\n");
1816 if (a != NULL) BN_free(a);
1817 if (p != NULL) BN_free(p);
1818 if (r != NULL) BN_free(r);
1822 int test_lshift(BIO *bp,BN_CTX *ctx,BIGNUM *a_)
1837 BN_bntest_rand(a,200,0,0); /**/
1840 for (i=0; i<num0; i++)
1860 fprintf(stderr,"Left shift test failed!\n");
1861 fprintf(stderr,"a=");
1862 BN_print_fp(stderr,a);
1863 fprintf(stderr,"\nb=");
1864 BN_print_fp(stderr,b);
1865 fprintf(stderr,"\nc=");
1866 BN_print_fp(stderr,c);
1867 fprintf(stderr,"\nd=");
1868 BN_print_fp(stderr,d);
1869 fprintf(stderr,"\n");
1880 int test_lshift1(BIO *bp)
1889 BN_bntest_rand(a,200,0,0); /**/
1891 for (i=0; i<num0; i++)
1899 BIO_puts(bp," * 2");
1909 fprintf(stderr,"Left shift one test failed!\n");
1921 int test_rshift(BIO *bp,BN_CTX *ctx)
1923 BIGNUM *a,*b,*c,*d,*e;
1933 BN_bntest_rand(a,200,0,0); /**/
1935 for (i=0; i<num0; i++)
1951 BN_div(d,e,a,c,ctx);
1955 fprintf(stderr,"Right shift test failed!\n");
1967 int test_rshift1(BIO *bp)
1976 BN_bntest_rand(a,200,0,0); /**/
1978 for (i=0; i<num0; i++)
1986 BIO_puts(bp," / 2");
1994 if(!BN_is_zero(c) && !BN_abs_is_word(c, 1))
1996 fprintf(stderr,"Right shift one test failed!\n");
2009 static unsigned int neg=0;
2010 static int sign[8]={0,0,0,1,1,0,1,1};
2012 return(sign[(neg++)%8]);