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_mod_exp_mont5(BIO *bp, BN_CTX *ctx);
111 int test_exp(BIO *bp,BN_CTX *ctx);
112 int test_gf2m_add(BIO *bp);
113 int test_gf2m_mod(BIO *bp);
114 int test_gf2m_mod_mul(BIO *bp,BN_CTX *ctx);
115 int test_gf2m_mod_sqr(BIO *bp,BN_CTX *ctx);
116 int test_gf2m_mod_inv(BIO *bp,BN_CTX *ctx);
117 int test_gf2m_mod_div(BIO *bp,BN_CTX *ctx);
118 int test_gf2m_mod_exp(BIO *bp,BN_CTX *ctx);
119 int test_gf2m_mod_sqrt(BIO *bp,BN_CTX *ctx);
120 int test_gf2m_mod_solve_quad(BIO *bp,BN_CTX *ctx);
121 int test_kron(BIO *bp,BN_CTX *ctx);
122 int test_sqrt(BIO *bp,BN_CTX *ctx);
124 static int results=0;
126 static unsigned char lst[]="\xC6\x4F\x43\x04\x2A\xEA\xCA\x6E\x58\x36\x80\x5B\xE8\xC9"
127 "\x9B\x04\x5D\x48\x36\xC2\xFD\x16\xC9\x64\xF0";
129 static const char rnd_seed[] = "string to make the random number generator think it has entropy";
131 static void message(BIO *out, char *m)
133 fprintf(stderr, "test %s\n", m);
134 BIO_puts(out, "print \"test ");
136 BIO_puts(out, "\\n\"\n");
139 int main(int argc, char *argv[])
147 RAND_seed(rnd_seed, sizeof rnd_seed); /* or BN_generate_prime may fail */
153 if (strcmp(*argv,"-results") == 0)
155 else if (strcmp(*argv,"-out") == 0)
157 if (--argc < 1) break;
166 if (ctx == NULL) EXIT(1);
168 out=BIO_new(BIO_s_file());
169 if (out == NULL) EXIT(1);
172 BIO_set_fp(out,stdout,BIO_NOCLOSE);
176 if (!BIO_write_filename(out,outfile))
184 BIO_puts(out,"obase=16\nibase=16\n");
186 message(out,"BN_add");
187 if (!test_add(out)) goto err;
188 (void)BIO_flush(out);
190 message(out,"BN_sub");
191 if (!test_sub(out)) goto err;
192 (void)BIO_flush(out);
194 message(out,"BN_lshift1");
195 if (!test_lshift1(out)) goto err;
196 (void)BIO_flush(out);
198 message(out,"BN_lshift (fixed)");
199 if (!test_lshift(out,ctx,BN_bin2bn(lst,sizeof(lst)-1,NULL)))
201 (void)BIO_flush(out);
203 message(out,"BN_lshift");
204 if (!test_lshift(out,ctx,NULL)) goto err;
205 (void)BIO_flush(out);
207 message(out,"BN_rshift1");
208 if (!test_rshift1(out)) goto err;
209 (void)BIO_flush(out);
211 message(out,"BN_rshift");
212 if (!test_rshift(out,ctx)) goto err;
213 (void)BIO_flush(out);
215 message(out,"BN_sqr");
216 if (!test_sqr(out,ctx)) goto err;
217 (void)BIO_flush(out);
219 message(out,"BN_mul");
220 if (!test_mul(out)) goto err;
221 (void)BIO_flush(out);
223 message(out,"BN_div");
224 if (!test_div(out,ctx)) goto err;
225 (void)BIO_flush(out);
227 message(out,"BN_div_word");
228 if (!test_div_word(out)) goto err;
229 (void)BIO_flush(out);
231 message(out,"BN_div_recp");
232 if (!test_div_recp(out,ctx)) goto err;
233 (void)BIO_flush(out);
235 message(out,"BN_mod");
236 if (!test_mod(out,ctx)) goto err;
237 (void)BIO_flush(out);
239 message(out,"BN_mod_mul");
240 if (!test_mod_mul(out,ctx)) goto err;
241 (void)BIO_flush(out);
243 message(out,"BN_mont");
244 if (!test_mont(out,ctx)) goto err;
245 (void)BIO_flush(out);
247 message(out,"BN_mod_exp");
248 if (!test_mod_exp(out,ctx)) goto err;
249 (void)BIO_flush(out);
251 message(out,"BN_mod_exp_mont_consttime");
252 if (!test_mod_exp_mont_consttime(out,ctx)) goto err;
253 if (!test_mod_exp_mont5(out,ctx)) goto err;
254 (void)BIO_flush(out);
256 message(out,"BN_exp");
257 if (!test_exp(out,ctx)) goto err;
258 (void)BIO_flush(out);
260 message(out,"BN_kronecker");
261 if (!test_kron(out,ctx)) goto err;
262 (void)BIO_flush(out);
264 message(out,"BN_mod_sqrt");
265 if (!test_sqrt(out,ctx)) goto err;
266 (void)BIO_flush(out);
267 #ifndef OPENSSL_NO_EC2M
268 message(out,"BN_GF2m_add");
269 if (!test_gf2m_add(out)) goto err;
270 (void)BIO_flush(out);
272 message(out,"BN_GF2m_mod");
273 if (!test_gf2m_mod(out)) goto err;
274 (void)BIO_flush(out);
276 message(out,"BN_GF2m_mod_mul");
277 if (!test_gf2m_mod_mul(out,ctx)) goto err;
278 (void)BIO_flush(out);
280 message(out,"BN_GF2m_mod_sqr");
281 if (!test_gf2m_mod_sqr(out,ctx)) goto err;
282 (void)BIO_flush(out);
284 message(out,"BN_GF2m_mod_inv");
285 if (!test_gf2m_mod_inv(out,ctx)) goto err;
286 (void)BIO_flush(out);
288 message(out,"BN_GF2m_mod_div");
289 if (!test_gf2m_mod_div(out,ctx)) goto err;
290 (void)BIO_flush(out);
292 message(out,"BN_GF2m_mod_exp");
293 if (!test_gf2m_mod_exp(out,ctx)) goto err;
294 (void)BIO_flush(out);
296 message(out,"BN_GF2m_mod_sqrt");
297 if (!test_gf2m_mod_sqrt(out,ctx)) goto err;
298 (void)BIO_flush(out);
300 message(out,"BN_GF2m_mod_solve_quad");
301 if (!test_gf2m_mod_solve_quad(out,ctx)) goto err;
302 (void)BIO_flush(out);
310 BIO_puts(out,"1\n"); /* make sure the Perl script fed by bc notices
311 * the failure, see test_bn in test/Makefile.ssl*/
312 (void)BIO_flush(out);
313 ERR_load_crypto_strings();
314 ERR_print_errors_fp(stderr);
319 int test_add(BIO *bp)
328 BN_bntest_rand(&a,512,0,0);
329 for (i=0; i<num0; i++)
331 BN_bntest_rand(&b,450+i,0,0);
353 fprintf(stderr,"Add test failed!\n");
363 int test_sub(BIO *bp)
372 for (i=0; i<num0+num1; i++)
376 BN_bntest_rand(&a,512,0,0);
378 if (BN_set_bit(&a,i)==0) return(0);
383 BN_bntest_rand(&b,400+i-num1,0,0);
404 fprintf(stderr,"Subtract test failed!\n");
414 int test_div(BIO *bp, BN_CTX *ctx)
425 for (i=0; i<num0+num1; i++)
429 BN_bntest_rand(&a,400,0,0);
435 BN_bntest_rand(&b,50+3*(i-num1),0,0);
438 BN_div(&d,&c,&a,&b,ctx);
461 BN_mul(&e,&d,&b,ctx);
466 fprintf(stderr,"Division test failed!\n");
478 static void print_word(BIO *bp,BN_ULONG w)
480 #ifdef SIXTY_FOUR_BIT
481 if (sizeof(w) > sizeof(unsigned long))
483 unsigned long h=(unsigned long)(w>>32),
484 l=(unsigned long)(w);
486 if (h) BIO_printf(bp,"%lX%08lX",h,l);
487 else BIO_printf(bp,"%lX",l);
491 BIO_printf(bp,BN_HEX_FMT1,w);
494 int test_div_word(BIO *bp)
503 for (i=0; i<num0; i++)
506 BN_bntest_rand(&a,512,-1,0);
507 BN_bntest_rand(&b,BN_BITS2,-1,0);
512 r = BN_div_word(&b, s);
541 fprintf(stderr,"Division (word) test failed!\n");
550 int test_div_recp(BIO *bp, BN_CTX *ctx)
556 BN_RECP_CTX_init(&recp);
563 for (i=0; i<num0+num1; i++)
567 BN_bntest_rand(&a,400,0,0);
573 BN_bntest_rand(&b,50+3*(i-num1),0,0);
576 BN_RECP_CTX_set(&recp,&b,ctx);
577 BN_div_recp(&d,&c,&a,&recp,ctx);
600 BN_mul(&e,&d,&b,ctx);
605 fprintf(stderr,"Reciprocal division test failed!\n");
606 fprintf(stderr,"a=");
607 BN_print_fp(stderr,&a);
608 fprintf(stderr,"\nb=");
609 BN_print_fp(stderr,&b);
610 fprintf(stderr,"\n");
619 BN_RECP_CTX_free(&recp);
623 int test_mul(BIO *bp)
630 if (ctx == NULL) EXIT(1);
638 for (i=0; i<num0+num1; i++)
642 BN_bntest_rand(&a,100,0,0);
643 BN_bntest_rand(&b,100,0,0);
646 BN_bntest_rand(&b,i-num1,0,0);
649 BN_mul(&c,&a,&b,ctx);
662 BN_div(&d,&e,&c,&a,ctx);
664 if(!BN_is_zero(&d) || !BN_is_zero(&e))
666 fprintf(stderr,"Multiplication test failed!\n");
679 int test_sqr(BIO *bp, BN_CTX *ctx)
688 if (a == NULL || c == NULL || d == NULL || e == NULL)
693 for (i=0; i<num0; i++)
695 BN_bntest_rand(a,40+i*10,0,0);
712 if(!BN_is_zero(d) || !BN_is_zero(e))
714 fprintf(stderr,"Square test failed!\n");
719 /* Regression test for a BN_sqr overflow bug. */
721 "80000000000000008000000000000001FFFFFFFFFFFFFFFE0000000000000000");
735 BN_mul(d, a, a, ctx);
738 fprintf(stderr, "Square test failed: BN_sqr and BN_mul produce "
739 "different results!\n");
743 /* Regression test for a BN_sqr overflow bug. */
745 "80000000000000000000000080000001FFFFFFFE000000000000000000000000");
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();
794 BN_bntest_rand(&a,100,0,0); /**/
795 BN_bntest_rand(&b,100,0,0); /**/
796 for (i=0; i<num2; i++)
798 int bits = (200*(i+1))/num2;
802 BN_bntest_rand(&n,bits,0,1);
803 BN_MONT_CTX_set(mont,&n,ctx);
805 BN_nnmod(&a,&a,&n,ctx);
806 BN_nnmod(&b,&b,&n,ctx);
808 BN_to_montgomery(&A,&a,mont,ctx);
809 BN_to_montgomery(&B,&b,mont,ctx);
811 BN_mod_mul_montgomery(&c,&A,&B,mont,ctx);/**/
812 BN_from_montgomery(&A,&c,mont,ctx);/**/
818 fprintf(stderr,"%d * %d %% %d\n",
821 BN_num_bits(mont->N));
827 BN_print(bp,&(mont->N));
833 BN_mod_mul(&d,&a,&b,&n,ctx);
837 fprintf(stderr,"Montgomery multiplication test failed!\n");
841 BN_MONT_CTX_free(mont);
852 int test_mod(BIO *bp, BN_CTX *ctx)
854 BIGNUM *a,*b,*c,*d,*e;
863 BN_bntest_rand(a,1024,0,0); /**/
864 for (i=0; i<num0; i++)
866 BN_bntest_rand(b,450+i*10,0,0); /**/
869 BN_mod(c,a,b,ctx);/**/
886 fprintf(stderr,"Modulo test failed!\n");
898 int test_mod_mul(BIO *bp, BN_CTX *ctx)
900 BIGNUM *a,*b,*c,*d,*e;
909 for (j=0; j<3; j++) {
910 BN_bntest_rand(c,1024,0,0); /**/
911 for (i=0; i<num0; i++)
913 BN_bntest_rand(a,475+i*10,0,0); /**/
914 BN_bntest_rand(b,425+i*11,0,0); /**/
917 if (!BN_mod_mul(e,a,b,c,ctx))
921 while ((l=ERR_get_error()))
922 fprintf(stderr,"ERROR:%s\n",
923 ERR_error_string(l,NULL));
935 if ((a->neg ^ b->neg) && !BN_is_zero(e))
937 /* If (a*b) % c is negative, c must be added
938 * in order to obtain the normalized remainder
939 * (new with OpenSSL 0.9.7, previous versions of
940 * BN_mod_mul could generate negative results)
955 fprintf(stderr,"Modulo multiply test failed!\n");
956 ERR_print_errors_fp(stderr);
969 int test_mod_exp(BIO *bp, BN_CTX *ctx)
971 BIGNUM *a,*b,*c,*d,*e;
980 BN_bntest_rand(c,30,0,1); /* must be odd for montgomery */
981 for (i=0; i<num2; i++)
983 BN_bntest_rand(a,20+i*5,0,0); /**/
984 BN_bntest_rand(b,2+i,0,0); /**/
986 if (!BN_mod_exp(d,a,b,c,ctx))
1005 BN_div(a,b,e,c,ctx);
1008 fprintf(stderr,"Modulo exponentiation test failed!\n");
1020 int test_mod_exp_mont_consttime(BIO *bp, BN_CTX *ctx)
1022 BIGNUM *a,*b,*c,*d,*e;
1031 BN_bntest_rand(c,30,0,1); /* must be odd for montgomery */
1032 for (i=0; i<num2; i++)
1034 BN_bntest_rand(a,20+i*5,0,0); /**/
1035 BN_bntest_rand(b,2+i,0,0); /**/
1037 if (!BN_mod_exp_mont_consttime(d,a,b,c,ctx,NULL))
1056 BN_div(a,b,e,c,ctx);
1059 fprintf(stderr,"Modulo exponentiation test failed!\n");
1071 /* Test constant-time modular exponentiation with 1024-bit inputs,
1072 * which on x86_64 cause a different code branch to be taken.
1074 int test_mod_exp_mont5(BIO *bp, BN_CTX *ctx)
1076 BIGNUM *a,*p,*m,*d,*e;
1086 mont = BN_MONT_CTX_new();
1088 BN_bntest_rand(m,1024,0,1); /* must be odd for montgomery */
1090 BN_bntest_rand(a,1024,0,0);
1092 if(!BN_mod_exp_mont_consttime(d,a,p,m,ctx,NULL))
1096 fprintf(stderr, "Modular exponentiation test failed!\n");
1100 BN_bntest_rand(p,1024,0,0);
1102 if(!BN_mod_exp_mont_consttime(d,a,p,m,ctx,NULL))
1106 fprintf(stderr, "Modular exponentiation test failed!\n");
1109 /* Craft an input whose Montgomery representation is 1,
1110 * i.e., shorter than the modulus m, in order to test
1111 * the const time precomputation scattering/gathering.
1114 BN_MONT_CTX_set(mont,m,ctx);
1115 if(!BN_from_montgomery(e,a,mont,ctx))
1117 if(!BN_mod_exp_mont_consttime(d,e,p,m,ctx,NULL))
1119 if(!BN_mod_exp_simple(a,e,p,m,ctx))
1121 if(BN_cmp(a,d) != 0)
1123 fprintf(stderr,"Modular exponentiation test failed!\n");
1126 /* Finally, some regular test vectors. */
1127 BN_bntest_rand(e,1024,0,0);
1128 if(!BN_mod_exp_mont_consttime(d,e,p,m,ctx,NULL))
1130 if(!BN_mod_exp_simple(a,e,p,m,ctx))
1132 if(BN_cmp(a,d) != 0)
1134 fprintf(stderr,"Modular exponentiation test failed!\n");
1145 int test_exp(BIO *bp, BN_CTX *ctx)
1147 BIGNUM *a,*b,*d,*e,*one;
1157 for (i=0; i<num2; i++)
1159 BN_bntest_rand(a,20+i*5,0,0); /**/
1160 BN_bntest_rand(b,2+i,0,0); /**/
1162 if (BN_exp(d,a,b,ctx) <= 0)
1178 for( ; !BN_is_zero(b) ; BN_sub(b,b,one))
1183 fprintf(stderr,"Exponentiation test failed!\n");
1194 #ifndef OPENSSL_NO_EC2M
1195 int test_gf2m_add(BIO *bp)
1204 for (i=0; i<num0; i++)
1206 BN_rand(&a,512,0,0);
1207 BN_copy(&b, BN_value_one());
1210 BN_GF2m_add(&c,&a,&b);
1211 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1225 /* Test that two added values have the correct parity. */
1226 if((BN_is_odd(&a) && BN_is_odd(&c)) || (!BN_is_odd(&a) && !BN_is_odd(&c)))
1228 fprintf(stderr,"GF(2^m) addition test (a) failed!\n");
1231 BN_GF2m_add(&c,&c,&c);
1232 /* Test that c + c = 0. */
1235 fprintf(stderr,"GF(2^m) addition test (b) failed!\n");
1247 int test_gf2m_mod(BIO *bp)
1249 BIGNUM *a,*b[2],*c,*d,*e;
1251 int p0[] = {163,7,6,3,0,-1};
1252 int p1[] = {193,15,0,-1};
1261 BN_GF2m_arr2poly(p0, b[0]);
1262 BN_GF2m_arr2poly(p1, b[1]);
1264 for (i=0; i<num0; i++)
1266 BN_bntest_rand(a, 1024, 0, 0);
1267 for (j=0; j < 2; j++)
1269 BN_GF2m_mod(c, a, b[j]);
1270 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1284 BN_GF2m_add(d, a, c);
1285 BN_GF2m_mod(e, d, b[j]);
1286 /* Test that a + (a mod p) mod p == 0. */
1289 fprintf(stderr,"GF(2^m) modulo test failed!\n");
1305 int test_gf2m_mod_mul(BIO *bp,BN_CTX *ctx)
1307 BIGNUM *a,*b[2],*c,*d,*e,*f,*g,*h;
1309 int p0[] = {163,7,6,3,0,-1};
1310 int p1[] = {193,15,0,-1};
1322 BN_GF2m_arr2poly(p0, b[0]);
1323 BN_GF2m_arr2poly(p1, b[1]);
1325 for (i=0; i<num0; i++)
1327 BN_bntest_rand(a, 1024, 0, 0);
1328 BN_bntest_rand(c, 1024, 0, 0);
1329 BN_bntest_rand(d, 1024, 0, 0);
1330 for (j=0; j < 2; j++)
1332 BN_GF2m_mod_mul(e, a, c, b[j], ctx);
1333 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1349 BN_GF2m_add(f, a, d);
1350 BN_GF2m_mod_mul(g, f, c, b[j], ctx);
1351 BN_GF2m_mod_mul(h, d, c, b[j], ctx);
1352 BN_GF2m_add(f, e, g);
1353 BN_GF2m_add(f, f, h);
1354 /* Test that (a+d)*c = a*c + d*c. */
1357 fprintf(stderr,"GF(2^m) modular multiplication test failed!\n");
1376 int test_gf2m_mod_sqr(BIO *bp,BN_CTX *ctx)
1378 BIGNUM *a,*b[2],*c,*d;
1380 int p0[] = {163,7,6,3,0,-1};
1381 int p1[] = {193,15,0,-1};
1389 BN_GF2m_arr2poly(p0, b[0]);
1390 BN_GF2m_arr2poly(p1, b[1]);
1392 for (i=0; i<num0; i++)
1394 BN_bntest_rand(a, 1024, 0, 0);
1395 for (j=0; j < 2; j++)
1397 BN_GF2m_mod_sqr(c, a, b[j], ctx);
1399 BN_GF2m_mod_mul(d, a, d, b[j], ctx);
1400 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1406 BIO_puts(bp," ^ 2 % ");
1408 BIO_puts(bp, " = ");
1410 BIO_puts(bp,"; a * a = ");
1416 BN_GF2m_add(d, c, d);
1417 /* Test that a*a = a^2. */
1420 fprintf(stderr,"GF(2^m) modular squaring test failed!\n");
1435 int test_gf2m_mod_inv(BIO *bp,BN_CTX *ctx)
1437 BIGNUM *a,*b[2],*c,*d;
1439 int p0[] = {163,7,6,3,0,-1};
1440 int p1[] = {193,15,0,-1};
1448 BN_GF2m_arr2poly(p0, b[0]);
1449 BN_GF2m_arr2poly(p1, b[1]);
1451 for (i=0; i<num0; i++)
1453 BN_bntest_rand(a, 512, 0, 0);
1454 for (j=0; j < 2; j++)
1456 BN_GF2m_mod_inv(c, a, b[j], ctx);
1457 BN_GF2m_mod_mul(d, a, c, b[j], ctx);
1458 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1464 BIO_puts(bp, " * ");
1466 BIO_puts(bp," - 1 % ");
1472 /* Test that ((1/a)*a) = 1. */
1475 fprintf(stderr,"GF(2^m) modular inversion test failed!\n");
1490 int test_gf2m_mod_div(BIO *bp,BN_CTX *ctx)
1492 BIGNUM *a,*b[2],*c,*d,*e,*f;
1494 int p0[] = {163,7,6,3,0,-1};
1495 int p1[] = {193,15,0,-1};
1505 BN_GF2m_arr2poly(p0, b[0]);
1506 BN_GF2m_arr2poly(p1, b[1]);
1508 for (i=0; i<num0; i++)
1510 BN_bntest_rand(a, 512, 0, 0);
1511 BN_bntest_rand(c, 512, 0, 0);
1512 for (j=0; j < 2; j++)
1514 BN_GF2m_mod_div(d, a, c, b[j], ctx);
1515 BN_GF2m_mod_mul(e, d, c, b[j], ctx);
1516 BN_GF2m_mod_div(f, a, e, b[j], ctx);
1517 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1523 BIO_puts(bp, " = ");
1527 BIO_puts(bp, " % ");
1533 /* Test that ((a/c)*c)/a = 1. */
1536 fprintf(stderr,"GF(2^m) modular division test failed!\n");
1553 int test_gf2m_mod_exp(BIO *bp,BN_CTX *ctx)
1555 BIGNUM *a,*b[2],*c,*d,*e,*f;
1557 int p0[] = {163,7,6,3,0,-1};
1558 int p1[] = {193,15,0,-1};
1568 BN_GF2m_arr2poly(p0, b[0]);
1569 BN_GF2m_arr2poly(p1, b[1]);
1571 for (i=0; i<num0; i++)
1573 BN_bntest_rand(a, 512, 0, 0);
1574 BN_bntest_rand(c, 512, 0, 0);
1575 BN_bntest_rand(d, 512, 0, 0);
1576 for (j=0; j < 2; j++)
1578 BN_GF2m_mod_exp(e, a, c, b[j], ctx);
1579 BN_GF2m_mod_exp(f, a, d, b[j], ctx);
1580 BN_GF2m_mod_mul(e, e, f, b[j], ctx);
1582 BN_GF2m_mod_exp(f, a, f, b[j], ctx);
1583 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1589 BIO_puts(bp, " ^ (");
1593 BIO_puts(bp, ") = ");
1595 BIO_puts(bp, "; - ");
1597 BIO_puts(bp, " % ");
1603 BN_GF2m_add(f, e, f);
1604 /* Test that a^(c+d)=a^c*a^d. */
1607 fprintf(stderr,"GF(2^m) modular exponentiation test failed!\n");
1624 int test_gf2m_mod_sqrt(BIO *bp,BN_CTX *ctx)
1626 BIGNUM *a,*b[2],*c,*d,*e,*f;
1628 int p0[] = {163,7,6,3,0,-1};
1629 int p1[] = {193,15,0,-1};
1639 BN_GF2m_arr2poly(p0, b[0]);
1640 BN_GF2m_arr2poly(p1, b[1]);
1642 for (i=0; i<num0; i++)
1644 BN_bntest_rand(a, 512, 0, 0);
1645 for (j=0; j < 2; j++)
1647 BN_GF2m_mod(c, a, b[j]);
1648 BN_GF2m_mod_sqrt(d, a, b[j], ctx);
1649 BN_GF2m_mod_sqr(e, d, b[j], ctx);
1650 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1656 BIO_puts(bp, " ^ 2 - ");
1662 BN_GF2m_add(f, c, e);
1663 /* Test that d^2 = a, where d = sqrt(a). */
1666 fprintf(stderr,"GF(2^m) modular square root test failed!\n");
1683 int test_gf2m_mod_solve_quad(BIO *bp,BN_CTX *ctx)
1685 BIGNUM *a,*b[2],*c,*d,*e;
1686 int i, j, s = 0, t, ret = 0;
1687 int p0[] = {163,7,6,3,0,-1};
1688 int p1[] = {193,15,0,-1};
1697 BN_GF2m_arr2poly(p0, b[0]);
1698 BN_GF2m_arr2poly(p1, b[1]);
1700 for (i=0; i<num0; i++)
1702 BN_bntest_rand(a, 512, 0, 0);
1703 for (j=0; j < 2; j++)
1705 t = BN_GF2m_mod_solve_quad(c, a, b[j], ctx);
1709 BN_GF2m_mod_sqr(d, c, b[j], ctx);
1710 BN_GF2m_add(d, c, d);
1711 BN_GF2m_mod(e, a, b[j]);
1712 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1718 BIO_puts(bp, " is root of z^2 + z = ");
1720 BIO_puts(bp, " % ");
1726 BN_GF2m_add(e, e, d);
1727 /* Test that solution of quadratic c satisfies c^2 + c = a. */
1730 fprintf(stderr,"GF(2^m) modular solve quadratic test failed!\n");
1737 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1742 BIO_puts(bp, "There are no roots of z^2 + z = ");
1744 BIO_puts(bp, " % ");
1755 fprintf(stderr,"All %i tests of GF(2^m) modular solve quadratic resulted in no roots;\n", num0);
1756 fprintf(stderr,"this is very unlikely and probably indicates an error.\n");
1770 static int genprime_cb(int p, int n, BN_GENCB *arg)
1783 int test_kron(BIO *bp, BN_CTX *ctx)
1788 int legendre, kronecker;
1795 if (a == NULL || b == NULL || r == NULL || t == NULL) goto err;
1797 BN_GENCB_set(&cb, genprime_cb, NULL);
1799 /* We test BN_kronecker(a, b, ctx) just for b odd (Jacobi symbol).
1800 * In this case we know that if b is prime, then BN_kronecker(a, b, ctx)
1801 * is congruent to $a^{(b-1)/2}$, modulo $b$ (Legendre symbol).
1802 * So we generate a random prime b and compare these values
1803 * for a number of random a's. (That is, we run the Solovay-Strassen
1804 * primality test to confirm that b is prime, except that we
1805 * don't want to test whether b is prime but whether BN_kronecker
1808 if (!BN_generate_prime_ex(b, 512, 0, NULL, NULL, &cb)) goto err;
1809 b->neg = rand_neg();
1812 for (i = 0; i < num0; i++)
1814 if (!BN_bntest_rand(a, 512, 0, 0)) goto err;
1815 a->neg = rand_neg();
1817 /* t := (|b|-1)/2 (note that b is odd) */
1818 if (!BN_copy(t, b)) goto err;
1820 if (!BN_sub_word(t, 1)) goto err;
1821 if (!BN_rshift1(t, t)) goto err;
1822 /* r := a^t mod b */
1825 if (!BN_mod_exp_recp(r, a, t, b, ctx)) goto err;
1828 if (BN_is_word(r, 1))
1830 else if (BN_is_zero(r))
1834 if (!BN_add_word(r, 1)) goto err;
1835 if (0 != BN_ucmp(r, b))
1837 fprintf(stderr, "Legendre symbol computation failed\n");
1843 kronecker = BN_kronecker(a, b, ctx);
1844 if (kronecker < -1) goto err;
1845 /* we actually need BN_kronecker(a, |b|) */
1846 if (a->neg && b->neg)
1847 kronecker = -kronecker;
1849 if (legendre != kronecker)
1851 fprintf(stderr, "legendre != kronecker; a = ");
1852 BN_print_fp(stderr, a);
1853 fprintf(stderr, ", b = ");
1854 BN_print_fp(stderr, b);
1855 fprintf(stderr, "\n");
1867 if (a != NULL) BN_free(a);
1868 if (b != NULL) BN_free(b);
1869 if (r != NULL) BN_free(r);
1870 if (t != NULL) BN_free(t);
1874 int test_sqrt(BIO *bp, BN_CTX *ctx)
1884 if (a == NULL || p == NULL || r == NULL) goto err;
1886 BN_GENCB_set(&cb, genprime_cb, NULL);
1888 for (i = 0; i < 16; i++)
1892 unsigned primes[8] = { 2, 3, 5, 7, 11, 13, 17, 19 };
1894 if (!BN_set_word(p, primes[i])) goto err;
1898 if (!BN_set_word(a, 32)) goto err;
1899 if (!BN_set_word(r, 2*i + 1)) goto err;
1901 if (!BN_generate_prime_ex(p, 256, 0, a, r, &cb)) goto err;
1904 p->neg = rand_neg();
1906 for (j = 0; j < num2; j++)
1908 /* construct 'a' such that it is a square modulo p,
1909 * but in general not a proper square and not reduced modulo p */
1910 if (!BN_bntest_rand(r, 256, 0, 3)) goto err;
1911 if (!BN_nnmod(r, r, p, ctx)) goto err;
1912 if (!BN_mod_sqr(r, r, p, ctx)) goto err;
1913 if (!BN_bntest_rand(a, 256, 0, 3)) goto err;
1914 if (!BN_nnmod(a, a, p, ctx)) goto err;
1915 if (!BN_mod_sqr(a, a, p, ctx)) goto err;
1916 if (!BN_mul(a, a, r, ctx)) goto err;
1918 if (!BN_sub(a, a, p)) goto err;
1920 if (!BN_mod_sqrt(r, a, p, ctx)) goto err;
1921 if (!BN_mod_sqr(r, r, p, ctx)) goto err;
1923 if (!BN_nnmod(a, a, p, ctx)) goto err;
1925 if (BN_cmp(a, r) != 0)
1927 fprintf(stderr, "BN_mod_sqrt failed: a = ");
1928 BN_print_fp(stderr, a);
1929 fprintf(stderr, ", r = ");
1930 BN_print_fp(stderr, r);
1931 fprintf(stderr, ", p = ");
1932 BN_print_fp(stderr, p);
1933 fprintf(stderr, "\n");
1946 if (a != NULL) BN_free(a);
1947 if (p != NULL) BN_free(p);
1948 if (r != NULL) BN_free(r);
1952 int test_lshift(BIO *bp,BN_CTX *ctx,BIGNUM *a_)
1967 BN_bntest_rand(a,200,0,0); /**/
1970 for (i=0; i<num0; i++)
1990 fprintf(stderr,"Left shift test failed!\n");
1991 fprintf(stderr,"a=");
1992 BN_print_fp(stderr,a);
1993 fprintf(stderr,"\nb=");
1994 BN_print_fp(stderr,b);
1995 fprintf(stderr,"\nc=");
1996 BN_print_fp(stderr,c);
1997 fprintf(stderr,"\nd=");
1998 BN_print_fp(stderr,d);
1999 fprintf(stderr,"\n");
2010 int test_lshift1(BIO *bp)
2019 BN_bntest_rand(a,200,0,0); /**/
2021 for (i=0; i<num0; i++)
2029 BIO_puts(bp," * 2");
2039 fprintf(stderr,"Left shift one test failed!\n");
2051 int test_rshift(BIO *bp,BN_CTX *ctx)
2053 BIGNUM *a,*b,*c,*d,*e;
2063 BN_bntest_rand(a,200,0,0); /**/
2065 for (i=0; i<num0; i++)
2081 BN_div(d,e,a,c,ctx);
2085 fprintf(stderr,"Right shift test failed!\n");
2097 int test_rshift1(BIO *bp)
2106 BN_bntest_rand(a,200,0,0); /**/
2108 for (i=0; i<num0; i++)
2116 BIO_puts(bp," / 2");
2124 if(!BN_is_zero(c) && !BN_abs_is_word(c, 1))
2126 fprintf(stderr,"Right shift one test failed!\n");
2139 static unsigned int neg=0;
2140 static int sign[8]={0,0,0,1,1,0,1,1};
2142 return(sign[(neg++)%8]);