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);
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);
307 BIO_puts(out,"1\n"); /* make sure the Perl script fed by bc notices
308 * the failure, see test_bn in test/Makefile.ssl
310 (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,"%lX",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)
686 if (a == NULL || c == NULL || d == NULL || e == NULL)
691 for (i=0; i<num0; i++)
693 BN_bntest_rand(a,40+i*10,0,0);
710 if(!BN_is_zero(d) || !BN_is_zero(e))
712 fprintf(stderr,"Square test failed!\n");
717 /* Regression test for a BN_sqr overflow bug. */
719 "80000000000000008000000000000001"
720 "FFFFFFFFFFFFFFFE0000000000000000");
734 BN_mul(d, a, a, ctx);
737 fprintf(stderr, "Square test failed: BN_sqr and BN_mul produce "
738 "different results!\n");
742 /* Regression test for a BN_sqr overflow bug. */
744 "80000000000000000000000080000001"
745 "FFFFFFFE000000000000000000000000");
759 BN_mul(d, a, a, ctx);
762 fprintf(stderr, "Square test failed: BN_sqr and BN_mul produce "
763 "different results!\n");
768 if (a != NULL) BN_free(a);
769 if (c != NULL) BN_free(c);
770 if (d != NULL) BN_free(d);
771 if (e != NULL) BN_free(e);
775 int test_mont(BIO *bp, BN_CTX *ctx)
790 mont=BN_MONT_CTX_new();
792 BN_bntest_rand(&a,100,0,0);
793 BN_bntest_rand(&b,100,0,0);
794 for (i=0; i<num2; i++)
796 int bits = (200*(i+1))/num2;
800 BN_bntest_rand(&n,bits,0,1);
801 BN_MONT_CTX_set(mont,&n,ctx);
803 BN_nnmod(&a,&a,&n,ctx);
804 BN_nnmod(&b,&b,&n,ctx);
806 BN_to_montgomery(&A,&a,mont,ctx);
807 BN_to_montgomery(&B,&b,mont,ctx);
809 BN_mod_mul_montgomery(&c,&A,&B,mont,ctx);
810 BN_from_montgomery(&A,&c,mont,ctx);
816 fprintf(stderr,"%d * %d %% %d\n",
819 BN_num_bits(mont->N));
825 BN_print(bp,&(mont->N));
831 BN_mod_mul(&d,&a,&b,&n,ctx);
835 fprintf(stderr,"Montgomery multiplication test failed!\n");
839 BN_MONT_CTX_free(mont);
850 int test_mod(BIO *bp, BN_CTX *ctx)
852 BIGNUM *a,*b,*c,*d,*e;
861 BN_bntest_rand(a,1024,0,0);
862 for (i=0; i<num0; i++)
864 BN_bntest_rand(b,450+i*10,0,0);
884 fprintf(stderr,"Modulo test failed!\n");
896 int test_mod_mul(BIO *bp, BN_CTX *ctx)
898 BIGNUM *a,*b,*c,*d,*e;
907 for (j=0; j<3; j++) {
908 BN_bntest_rand(c,1024,0,0);
909 for (i=0; i<num0; i++)
911 BN_bntest_rand(a,475+i*10,0,0);
912 BN_bntest_rand(b,425+i*11,0,0);
915 if (!BN_mod_mul(e,a,b,c,ctx))
919 while ((l=ERR_get_error()))
920 fprintf(stderr,"ERROR:%s\n",
921 ERR_error_string(l,NULL));
933 if ((a->neg ^ b->neg) && !BN_is_zero(e))
935 /* If (a*b) % c is negative, c must be added
936 * in order to obtain the normalized remainder
937 * (new with OpenSSL 0.9.7, previous versions of
938 * BN_mod_mul could generate negative results)
953 fprintf(stderr,"Modulo multiply test failed!\n");
954 ERR_print_errors_fp(stderr);
967 int test_mod_exp(BIO *bp, BN_CTX *ctx)
969 BIGNUM *a,*b,*c,*d,*e;
978 BN_bntest_rand(c,30,0,1); /* must be odd for montgomery */
979 for (i=0; i<num2; i++)
981 BN_bntest_rand(a,20+i*5,0,0);
982 BN_bntest_rand(b,2+i,0,0);
984 if (!BN_mod_exp(d,a,b,c,ctx))
1003 BN_div(a,b,e,c,ctx);
1006 fprintf(stderr,"Modulo exponentiation test failed!\n");
1018 int test_mod_exp_mont_consttime(BIO *bp, BN_CTX *ctx)
1020 BIGNUM *a,*b,*c,*d,*e;
1029 BN_bntest_rand(c,30,0,1); /* must be odd for montgomery */
1030 for (i=0; i<num2; i++)
1032 BN_bntest_rand(a,20+i*5,0,0);
1033 BN_bntest_rand(b,2+i,0,0);
1035 if (!BN_mod_exp_mont_consttime(d,a,b,c,ctx,NULL))
1054 BN_div(a,b,e,c,ctx);
1057 fprintf(stderr,"Modulo exponentiation test failed!\n");
1069 int test_exp(BIO *bp, BN_CTX *ctx)
1071 BIGNUM *a,*b,*d,*e,*one;
1081 for (i=0; i<num2; i++)
1083 BN_bntest_rand(a,20+i*5,0,0);
1084 BN_bntest_rand(b,2+i,0,0);
1086 if (BN_exp(d,a,b,ctx) <= 0)
1102 for( ; !BN_is_zero(b) ; BN_sub(b,b,one))
1107 fprintf(stderr,"Exponentiation test failed!\n");
1119 int test_gf2m_add(BIO *bp)
1128 for (i=0; i<num0; i++)
1130 BN_rand(&a,512,0,0);
1131 BN_copy(&b, BN_value_one());
1134 BN_GF2m_add(&c,&a,&b);
1135 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1149 /* Test that two added values have the correct parity. */
1150 if((BN_is_odd(&a) && BN_is_odd(&c)) || (!BN_is_odd(&a) && !BN_is_odd(&c)))
1152 fprintf(stderr,"GF(2^m) addition test (a) failed!\n");
1155 BN_GF2m_add(&c,&c,&c);
1156 /* Test that c + c = 0. */
1159 fprintf(stderr,"GF(2^m) addition test (b) failed!\n");
1171 int test_gf2m_mod(BIO *bp)
1173 BIGNUM *a,*b[2],*c,*d,*e;
1175 unsigned int p0[] = {163,7,6,3,0};
1176 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(c, a, b[j]);
1194 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1208 BN_GF2m_add(d, a, c);
1209 BN_GF2m_mod(e, d, b[j]);
1210 /* Test that a + (a mod p) mod p == 0. */
1213 fprintf(stderr,"GF(2^m) modulo test failed!\n");
1229 int test_gf2m_mod_mul(BIO *bp,BN_CTX *ctx)
1231 BIGNUM *a,*b[2],*c,*d,*e,*f,*g,*h;
1233 unsigned int p0[] = {163,7,6,3,0};
1234 unsigned int p1[] = {193,15,0};
1246 BN_GF2m_arr2poly(p0, b[0]);
1247 BN_GF2m_arr2poly(p1, b[1]);
1249 for (i=0; i<num0; i++)
1251 BN_bntest_rand(a, 1024, 0, 0);
1252 BN_bntest_rand(c, 1024, 0, 0);
1253 BN_bntest_rand(d, 1024, 0, 0);
1254 for (j=0; j < 2; j++)
1256 BN_GF2m_mod_mul(e, a, c, b[j], ctx);
1257 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1273 BN_GF2m_add(f, a, d);
1274 BN_GF2m_mod_mul(g, f, c, b[j], ctx);
1275 BN_GF2m_mod_mul(h, d, c, b[j], ctx);
1276 BN_GF2m_add(f, e, g);
1277 BN_GF2m_add(f, f, h);
1278 /* Test that (a+d)*c = a*c + d*c. */
1281 fprintf(stderr,"GF(2^m) modular multiplication test failed!\n");
1300 int test_gf2m_mod_sqr(BIO *bp,BN_CTX *ctx)
1302 BIGNUM *a,*b[2],*c,*d;
1304 unsigned int p0[] = {163,7,6,3,0};
1305 unsigned int p1[] = {193,15,0};
1313 BN_GF2m_arr2poly(p0, b[0]);
1314 BN_GF2m_arr2poly(p1, b[1]);
1316 for (i=0; i<num0; i++)
1318 BN_bntest_rand(a, 1024, 0, 0);
1319 for (j=0; j < 2; j++)
1321 BN_GF2m_mod_sqr(c, a, b[j], ctx);
1323 BN_GF2m_mod_mul(d, a, d, b[j], ctx);
1324 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1330 BIO_puts(bp," ^ 2 % ");
1332 BIO_puts(bp, " = ");
1334 BIO_puts(bp,"; a * a = ");
1340 BN_GF2m_add(d, c, d);
1341 /* Test that a*a = a^2. */
1344 fprintf(stderr,"GF(2^m) modular squaring test failed!\n");
1359 int test_gf2m_mod_inv(BIO *bp,BN_CTX *ctx)
1361 BIGNUM *a,*b[2],*c,*d;
1363 unsigned int p0[] = {163,7,6,3,0};
1364 unsigned int p1[] = {193,15,0};
1372 BN_GF2m_arr2poly(p0, b[0]);
1373 BN_GF2m_arr2poly(p1, b[1]);
1375 for (i=0; i<num0; i++)
1377 BN_bntest_rand(a, 512, 0, 0);
1378 for (j=0; j < 2; j++)
1380 BN_GF2m_mod_inv(c, a, b[j], ctx);
1381 BN_GF2m_mod_mul(d, a, c, b[j], ctx);
1382 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1388 BIO_puts(bp, " * ");
1390 BIO_puts(bp," - 1 % ");
1396 /* Test that ((1/a)*a) = 1. */
1399 fprintf(stderr,"GF(2^m) modular inversion test failed!\n");
1414 int test_gf2m_mod_div(BIO *bp,BN_CTX *ctx)
1416 BIGNUM *a,*b[2],*c,*d,*e,*f;
1418 unsigned int p0[] = {163,7,6,3,0};
1419 unsigned int p1[] = {193,15,0};
1429 BN_GF2m_arr2poly(p0, b[0]);
1430 BN_GF2m_arr2poly(p1, b[1]);
1432 for (i=0; i<num0; i++)
1434 BN_bntest_rand(a, 512, 0, 0);
1435 BN_bntest_rand(c, 512, 0, 0);
1436 for (j=0; j < 2; j++)
1438 BN_GF2m_mod_div(d, a, c, b[j], ctx);
1439 BN_GF2m_mod_mul(e, d, c, b[j], ctx);
1440 BN_GF2m_mod_div(f, a, e, b[j], ctx);
1441 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1447 BIO_puts(bp, " = ");
1451 BIO_puts(bp, " % ");
1457 /* Test that ((a/c)*c)/a = 1. */
1460 fprintf(stderr,"GF(2^m) modular division test failed!\n");
1477 int test_gf2m_mod_exp(BIO *bp,BN_CTX *ctx)
1479 BIGNUM *a,*b[2],*c,*d,*e,*f;
1481 unsigned int p0[] = {163,7,6,3,0};
1482 unsigned int p1[] = {193,15,0};
1492 BN_GF2m_arr2poly(p0, b[0]);
1493 BN_GF2m_arr2poly(p1, b[1]);
1495 for (i=0; i<num0; i++)
1497 BN_bntest_rand(a, 512, 0, 0);
1498 BN_bntest_rand(c, 512, 0, 0);
1499 BN_bntest_rand(d, 512, 0, 0);
1500 for (j=0; j < 2; j++)
1502 BN_GF2m_mod_exp(e, a, c, b[j], ctx);
1503 BN_GF2m_mod_exp(f, a, d, b[j], ctx);
1504 BN_GF2m_mod_mul(e, e, f, b[j], ctx);
1506 BN_GF2m_mod_exp(f, a, f, b[j], ctx);
1507 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1513 BIO_puts(bp, " ^ (");
1517 BIO_puts(bp, ") = ");
1519 BIO_puts(bp, "; - ");
1521 BIO_puts(bp, " % ");
1527 BN_GF2m_add(f, e, f);
1528 /* Test that a^(c+d)=a^c*a^d. */
1531 fprintf(stderr,"GF(2^m) modular exponentiation test failed!\n");
1548 int test_gf2m_mod_sqrt(BIO *bp,BN_CTX *ctx)
1550 BIGNUM *a,*b[2],*c,*d,*e,*f;
1552 unsigned int p0[] = {163,7,6,3,0};
1553 unsigned int p1[] = {193,15,0};
1563 BN_GF2m_arr2poly(p0, b[0]);
1564 BN_GF2m_arr2poly(p1, b[1]);
1566 for (i=0; i<num0; i++)
1568 BN_bntest_rand(a, 512, 0, 0);
1569 for (j=0; j < 2; j++)
1571 BN_GF2m_mod(c, a, b[j]);
1572 BN_GF2m_mod_sqrt(d, a, b[j], ctx);
1573 BN_GF2m_mod_sqr(e, d, b[j], ctx);
1574 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1580 BIO_puts(bp, " ^ 2 - ");
1586 BN_GF2m_add(f, c, e);
1587 /* Test that d^2 = a, where d = sqrt(a). */
1590 fprintf(stderr,"GF(2^m) modular square root test failed!\n");
1607 int test_gf2m_mod_solve_quad(BIO *bp,BN_CTX *ctx)
1609 BIGNUM *a,*b[2],*c,*d,*e;
1610 int i, j, s = 0, t, ret = 0;
1611 unsigned int p0[] = {163,7,6,3,0};
1612 unsigned int p1[] = {193,15,0};
1621 BN_GF2m_arr2poly(p0, b[0]);
1622 BN_GF2m_arr2poly(p1, b[1]);
1624 for (i=0; i<num0; i++)
1626 BN_bntest_rand(a, 512, 0, 0);
1627 for (j=0; j < 2; j++)
1629 t = BN_GF2m_mod_solve_quad(c, a, b[j], ctx);
1633 BN_GF2m_mod_sqr(d, c, b[j], ctx);
1634 BN_GF2m_add(d, c, d);
1635 BN_GF2m_mod(e, a, b[j]);
1636 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1642 BIO_puts(bp, " is root of z^2 + z = ");
1644 BIO_puts(bp, " % ");
1650 BN_GF2m_add(e, e, d);
1651 /* Test that solution of quadratic c satisfies c^2 + c = a. */
1654 fprintf(stderr,"GF(2^m) modular solve quadratic test failed!\n");
1661 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1666 BIO_puts(bp, "There are no roots of z^2 + z = ");
1668 BIO_puts(bp, " % ");
1679 fprintf(stderr,"All %i tests of GF(2^m) modular solve quadratic resulted in no roots;\n", num0);
1680 fprintf(stderr,"this is very unlikely and probably indicates an error.\n");
1694 static int genprime_cb(int p, int n, BN_GENCB *arg)
1707 int test_kron(BIO *bp, BN_CTX *ctx)
1712 int legendre, kronecker;
1719 if (a == NULL || b == NULL || r == NULL || t == NULL) goto err;
1721 BN_GENCB_set(&cb, genprime_cb, NULL);
1723 /* We test BN_kronecker(a, b, ctx) just for b odd (Jacobi symbol).
1724 * In this case we know that if b is prime, then BN_kronecker(a, b, ctx)
1725 * is congruent to $a^{(b-1)/2}$, modulo $b$ (Legendre symbol).
1726 * So we generate a random prime b and compare these values
1727 * for a number of random a's. (That is, we run the Solovay-Strassen
1728 * primality test to confirm that b is prime, except that we
1729 * don't want to test whether b is prime but whether BN_kronecker
1732 if (!BN_generate_prime_ex(b, 512, 0, NULL, NULL, &cb)) goto err;
1733 b->neg = rand_neg();
1736 for (i = 0; i < num0; i++)
1738 if (!BN_bntest_rand(a, 512, 0, 0)) goto err;
1739 a->neg = rand_neg();
1741 /* t := (|b|-1)/2 (note that b is odd) */
1742 if (!BN_copy(t, b)) goto err;
1744 if (!BN_sub_word(t, 1)) goto err;
1745 if (!BN_rshift1(t, t)) goto err;
1746 /* r := a^t mod b */
1749 if (!BN_mod_exp_recp(r, a, t, b, ctx)) goto err;
1752 if (BN_is_word(r, 1))
1754 else if (BN_is_zero(r))
1758 if (!BN_add_word(r, 1)) goto err;
1759 if (0 != BN_ucmp(r, b))
1761 fprintf(stderr, "Legendre symbol computation failed\n");
1767 kronecker = BN_kronecker(a, b, ctx);
1768 if (kronecker < -1) goto err;
1769 /* we actually need BN_kronecker(a, |b|) */
1770 if (a->neg && b->neg)
1771 kronecker = -kronecker;
1773 if (legendre != kronecker)
1775 fprintf(stderr, "legendre != kronecker; a = ");
1776 BN_print_fp(stderr, a);
1777 fprintf(stderr, ", b = ");
1778 BN_print_fp(stderr, b);
1779 fprintf(stderr, "\n");
1791 if (a != NULL) BN_free(a);
1792 if (b != NULL) BN_free(b);
1793 if (r != NULL) BN_free(r);
1794 if (t != NULL) BN_free(t);
1798 int test_sqrt(BIO *bp, BN_CTX *ctx)
1808 if (a == NULL || p == NULL || r == NULL) goto err;
1810 BN_GENCB_set(&cb, genprime_cb, NULL);
1812 for (i = 0; i < 16; i++)
1816 unsigned primes[8] = { 2, 3, 5, 7, 11, 13, 17, 19 };
1818 if (!BN_set_word(p, primes[i])) goto err;
1822 if (!BN_set_word(a, 32)) goto err;
1823 if (!BN_set_word(r, 2*i + 1)) goto err;
1825 if (!BN_generate_prime_ex(p, 256, 0, a, r, &cb)) goto err;
1828 p->neg = rand_neg();
1830 for (j = 0; j < num2; j++)
1832 /* construct 'a' such that it is a square modulo p,
1833 * but in general not a proper square and not reduced modulo p */
1834 if (!BN_bntest_rand(r, 256, 0, 3)) goto err;
1835 if (!BN_nnmod(r, r, p, ctx)) goto err;
1836 if (!BN_mod_sqr(r, r, p, ctx)) goto err;
1837 if (!BN_bntest_rand(a, 256, 0, 3)) goto err;
1838 if (!BN_nnmod(a, a, p, ctx)) goto err;
1839 if (!BN_mod_sqr(a, a, p, ctx)) goto err;
1840 if (!BN_mul(a, a, r, ctx)) goto err;
1842 if (!BN_sub(a, a, p)) goto err;
1844 if (!BN_mod_sqrt(r, a, p, ctx)) goto err;
1845 if (!BN_mod_sqr(r, r, p, ctx)) goto err;
1847 if (!BN_nnmod(a, a, p, ctx)) goto err;
1849 if (BN_cmp(a, r) != 0)
1851 fprintf(stderr, "BN_mod_sqrt failed: a = ");
1852 BN_print_fp(stderr, a);
1853 fprintf(stderr, ", r = ");
1854 BN_print_fp(stderr, r);
1855 fprintf(stderr, ", p = ");
1856 BN_print_fp(stderr, p);
1857 fprintf(stderr, "\n");
1870 if (a != NULL) BN_free(a);
1871 if (p != NULL) BN_free(p);
1872 if (r != NULL) BN_free(r);
1876 int test_lshift(BIO *bp,BN_CTX *ctx,BIGNUM *a_)
1891 BN_bntest_rand(a,200,0,0);
1894 for (i=0; i<num0; i++)
1914 fprintf(stderr,"Left shift test failed!\n");
1915 fprintf(stderr,"a=");
1916 BN_print_fp(stderr,a);
1917 fprintf(stderr,"\nb=");
1918 BN_print_fp(stderr,b);
1919 fprintf(stderr,"\nc=");
1920 BN_print_fp(stderr,c);
1921 fprintf(stderr,"\nd=");
1922 BN_print_fp(stderr,d);
1923 fprintf(stderr,"\n");
1934 int test_lshift1(BIO *bp)
1943 BN_bntest_rand(a,200,0,0);
1945 for (i=0; i<num0; i++)
1953 BIO_puts(bp," * 2");
1963 fprintf(stderr,"Left shift one test failed!\n");
1975 int test_rshift(BIO *bp,BN_CTX *ctx)
1977 BIGNUM *a,*b,*c,*d,*e;
1987 BN_bntest_rand(a,200,0,0);
1989 for (i=0; i<num0; i++)
2005 BN_div(d,e,a,c,ctx);
2009 fprintf(stderr,"Right shift test failed!\n");
2021 int test_rshift1(BIO *bp)
2030 BN_bntest_rand(a,200,0,0);
2032 for (i=0; i<num0; i++)
2040 BIO_puts(bp," / 2");
2048 if(!BN_is_zero(c) && !BN_abs_is_word(c, 1))
2050 fprintf(stderr,"Right shift one test failed!\n");
2063 static unsigned int neg=0;
2064 static int sign[8]={0,0,0,1,1,0,1,1};
2066 return(sign[(neg++)%8]);