c885300a669fc10a0189fa062b44c8beeac2c947
[openssl.git] / crypto / bn / bntest.c
1 /* crypto/bn/bntest.c */
2 /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
3  * All rights reserved.
4  *
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.
8  * 
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).
15  * 
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.
22  * 
23  * Redistribution and use in source and binary forms, with or without
24  * modification, are permitted provided that the following conditions
25  * are met:
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)"
40  * 
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
51  * SUCH DAMAGE.
52  * 
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.]
57  */
58 /* ====================================================================
59  * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
60  *
61  * Portions of the attached software ("Contribution") are developed by 
62  * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
63  *
64  * The Contribution is licensed pursuant to the Eric Young open source
65  * license provided above.
66  *
67  * The binary polynomial arithmetic software is originally written by 
68  * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
69  *
70  */
71
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
76 #endif
77
78 #include <stdio.h>
79 #include <stdlib.h>
80 #include <string.h>
81
82 #include "e_os.h"
83
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>
89
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 */
93
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);
122 int rand_neg(void);
123 static int results=0;
124
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";
127
128 static const char rnd_seed[] = "string to make the random number generator think it has entropy";
129
130 static void message(BIO *out, char *m)
131         {
132         fprintf(stderr, "test %s\n", m);
133         BIO_puts(out, "print \"test ");
134         BIO_puts(out, m);
135         BIO_puts(out, "\\n\"\n");
136         }
137
138 int main(int argc, char *argv[])
139         {
140         BN_CTX *ctx;
141         BIO *out;
142         char *outfile=NULL;
143
144         results = 0;
145
146         RAND_seed(rnd_seed, sizeof rnd_seed); /* or BN_generate_prime may fail */
147
148         argc--;
149         argv++;
150         while (argc >= 1)
151                 {
152                 if (strcmp(*argv,"-results") == 0)
153                         results=1;
154                 else if (strcmp(*argv,"-out") == 0)
155                         {
156                         if (--argc < 1) break;
157                         outfile= *(++argv);
158                         }
159                 argc--;
160                 argv++;
161                 }
162
163
164         ctx=BN_CTX_new();
165         if (ctx == NULL) EXIT(1);
166
167         out=BIO_new(BIO_s_file());
168         if (out == NULL) EXIT(1);
169         if (outfile == NULL)
170                 {
171                 BIO_set_fp(out,stdout,BIO_NOCLOSE);
172                 }
173         else
174                 {
175                 if (!BIO_write_filename(out,outfile))
176                         {
177                         perror(outfile);
178                         EXIT(1);
179                         }
180                 }
181
182         if (!results)
183                 BIO_puts(out,"obase=16\nibase=16\n");
184
185         message(out,"BN_add");
186         if (!test_add(out)) goto err;
187         BIO_flush(out);
188
189         message(out,"BN_sub");
190         if (!test_sub(out)) goto err;
191         BIO_flush(out);
192
193         message(out,"BN_lshift1");
194         if (!test_lshift1(out)) goto err;
195         BIO_flush(out);
196
197         message(out,"BN_lshift (fixed)");
198         if (!test_lshift(out,ctx,BN_bin2bn(lst,sizeof(lst)-1,NULL)))
199             goto err;
200         BIO_flush(out);
201
202         message(out,"BN_lshift");
203         if (!test_lshift(out,ctx,NULL)) goto err;
204         BIO_flush(out);
205
206         message(out,"BN_rshift1");
207         if (!test_rshift1(out)) goto err;
208         BIO_flush(out);
209
210         message(out,"BN_rshift");
211         if (!test_rshift(out,ctx)) goto err;
212         BIO_flush(out);
213
214         message(out,"BN_sqr");
215         if (!test_sqr(out,ctx)) goto err;
216         BIO_flush(out);
217
218         message(out,"BN_mul");
219         if (!test_mul(out)) goto err;
220         BIO_flush(out);
221
222         message(out,"BN_div");
223         if (!test_div(out,ctx)) goto err;
224         BIO_flush(out);
225
226         message(out,"BN_div_word");
227         if (!test_div_word(out)) goto err;
228         BIO_flush(out);
229
230         message(out,"BN_div_recp");
231         if (!test_div_recp(out,ctx)) goto err;
232         BIO_flush(out);
233
234         message(out,"BN_mod");
235         if (!test_mod(out,ctx)) goto err;
236         BIO_flush(out);
237
238         message(out,"BN_mod_mul");
239         if (!test_mod_mul(out,ctx)) goto err;
240         BIO_flush(out);
241
242         message(out,"BN_mont");
243         if (!test_mont(out,ctx)) goto err;
244         BIO_flush(out);
245
246         message(out,"BN_mod_exp");
247         if (!test_mod_exp(out,ctx)) goto err;
248         BIO_flush(out);
249
250         message(out,"BN_mod_exp_mont_consttime");
251         if (!test_mod_exp_mont_consttime(out,ctx)) goto err;
252         BIO_flush(out);
253
254         message(out,"BN_exp");
255         if (!test_exp(out,ctx)) goto err;
256         BIO_flush(out);
257
258         message(out,"BN_kronecker");
259         if (!test_kron(out,ctx)) goto err;
260         BIO_flush(out);
261
262         message(out,"BN_mod_sqrt");
263         if (!test_sqrt(out,ctx)) goto err;
264         BIO_flush(out);
265
266         message(out,"BN_GF2m_add");
267         if (!test_gf2m_add(out)) goto err;
268         BIO_flush(out);
269
270         message(out,"BN_GF2m_mod");
271         if (!test_gf2m_mod(out)) goto err;
272         BIO_flush(out);
273
274         message(out,"BN_GF2m_mod_mul");
275         if (!test_gf2m_mod_mul(out,ctx)) goto err;
276         BIO_flush(out);
277
278         message(out,"BN_GF2m_mod_sqr");
279         if (!test_gf2m_mod_sqr(out,ctx)) goto err;
280         BIO_flush(out);
281
282         message(out,"BN_GF2m_mod_inv");
283         if (!test_gf2m_mod_inv(out,ctx)) goto err;
284         BIO_flush(out);
285
286         message(out,"BN_GF2m_mod_div");
287         if (!test_gf2m_mod_div(out,ctx)) goto err;
288         BIO_flush(out);
289
290         message(out,"BN_GF2m_mod_exp");
291         if (!test_gf2m_mod_exp(out,ctx)) goto err;
292         BIO_flush(out);
293
294         message(out,"BN_GF2m_mod_sqrt");
295         if (!test_gf2m_mod_sqrt(out,ctx)) goto err;
296         BIO_flush(out);
297
298         message(out,"BN_GF2m_mod_solve_quad");
299         if (!test_gf2m_mod_solve_quad(out,ctx)) goto err;
300         BIO_flush(out);
301
302         BN_CTX_free(ctx);
303         BIO_free(out);
304
305 /**/
306         EXIT(0);
307 err:
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         BIO_flush(out);
311         ERR_load_crypto_strings();
312         ERR_print_errors_fp(stderr);
313         EXIT(1);
314         return(1);
315         }
316
317 int test_add(BIO *bp)
318         {
319         BIGNUM a,b,c;
320         int i;
321
322         BN_init(&a);
323         BN_init(&b);
324         BN_init(&c);
325
326         BN_bntest_rand(&a,512,0,0);
327         for (i=0; i<num0; i++)
328                 {
329                 BN_bntest_rand(&b,450+i,0,0);
330                 a.neg=rand_neg();
331                 b.neg=rand_neg();
332                 BN_add(&c,&a,&b);
333                 if (bp != NULL)
334                         {
335                         if (!results)
336                                 {
337                                 BN_print(bp,&a);
338                                 BIO_puts(bp," + ");
339                                 BN_print(bp,&b);
340                                 BIO_puts(bp," - ");
341                                 }
342                         BN_print(bp,&c);
343                         BIO_puts(bp,"\n");
344                         }
345                 a.neg=!a.neg;
346                 b.neg=!b.neg;
347                 BN_add(&c,&c,&b);
348                 BN_add(&c,&c,&a);
349                 if(!BN_is_zero(&c))
350                     {
351                     fprintf(stderr,"Add test failed!\n");
352                     return 0;
353                     }
354                 }
355         BN_free(&a);
356         BN_free(&b);
357         BN_free(&c);
358         return(1);
359         }
360
361 int test_sub(BIO *bp)
362         {
363         BIGNUM a,b,c;
364         int i;
365
366         BN_init(&a);
367         BN_init(&b);
368         BN_init(&c);
369
370         for (i=0; i<num0+num1; i++)
371                 {
372                 if (i < num1)
373                         {
374                         BN_bntest_rand(&a,512,0,0);
375                         BN_copy(&b,&a);
376                         if (BN_set_bit(&a,i)==0) return(0);
377                         BN_add_word(&b,i);
378                         }
379                 else
380                         {
381                         BN_bntest_rand(&b,400+i-num1,0,0);
382                         a.neg=rand_neg();
383                         b.neg=rand_neg();
384                         }
385                 BN_sub(&c,&a,&b);
386                 if (bp != NULL)
387                         {
388                         if (!results)
389                                 {
390                                 BN_print(bp,&a);
391                                 BIO_puts(bp," - ");
392                                 BN_print(bp,&b);
393                                 BIO_puts(bp," - ");
394                                 }
395                         BN_print(bp,&c);
396                         BIO_puts(bp,"\n");
397                         }
398                 BN_add(&c,&c,&b);
399                 BN_sub(&c,&c,&a);
400                 if(!BN_is_zero(&c))
401                     {
402                     fprintf(stderr,"Subtract test failed!\n");
403                     return 0;
404                     }
405                 }
406         BN_free(&a);
407         BN_free(&b);
408         BN_free(&c);
409         return(1);
410         }
411
412 int test_div(BIO *bp, BN_CTX *ctx)
413         {
414         BIGNUM a,b,c,d,e;
415         int i;
416
417         BN_init(&a);
418         BN_init(&b);
419         BN_init(&c);
420         BN_init(&d);
421         BN_init(&e);
422
423         for (i=0; i<num0+num1; i++)
424                 {
425                 if (i < num1)
426                         {
427                         BN_bntest_rand(&a,400,0,0);
428                         BN_copy(&b,&a);
429                         BN_lshift(&a,&a,i);
430                         BN_add_word(&a,i);
431                         }
432                 else
433                         BN_bntest_rand(&b,50+3*(i-num1),0,0);
434                 a.neg=rand_neg();
435                 b.neg=rand_neg();
436                 BN_div(&d,&c,&a,&b,ctx);
437                 if (bp != NULL)
438                         {
439                         if (!results)
440                                 {
441                                 BN_print(bp,&a);
442                                 BIO_puts(bp," / ");
443                                 BN_print(bp,&b);
444                                 BIO_puts(bp," - ");
445                                 }
446                         BN_print(bp,&d);
447                         BIO_puts(bp,"\n");
448
449                         if (!results)
450                                 {
451                                 BN_print(bp,&a);
452                                 BIO_puts(bp," % ");
453                                 BN_print(bp,&b);
454                                 BIO_puts(bp," - ");
455                                 }
456                         BN_print(bp,&c);
457                         BIO_puts(bp,"\n");
458                         }
459                 BN_mul(&e,&d,&b,ctx);
460                 BN_add(&d,&e,&c);
461                 BN_sub(&d,&d,&a);
462                 if(!BN_is_zero(&d))
463                     {
464                     fprintf(stderr,"Division test failed!\n");
465                     return 0;
466                     }
467                 }
468         BN_free(&a);
469         BN_free(&b);
470         BN_free(&c);
471         BN_free(&d);
472         BN_free(&e);
473         return(1);
474         }
475
476 static void print_word(BIO *bp,BN_ULONG w)
477         {
478 #ifdef SIXTY_FOUR_BIT
479         if (sizeof(w) > sizeof(unsigned long))
480                 {
481                 unsigned long   h=(unsigned long)(w>>32),
482                                 l=(unsigned long)(w);
483
484                 if (h)  BIO_printf(bp,"%lX%08lX",h,l);
485                 else    BIO_printf(bp,"%lX",l);
486                 return;
487                 }
488 #endif
489         BIO_printf(bp,"%lX",w);
490         }
491
492 int test_div_word(BIO *bp)
493         {
494         BIGNUM   a,b;
495         BN_ULONG r,s;
496         int i;
497
498         BN_init(&a);
499         BN_init(&b);
500
501         for (i=0; i<num0; i++)
502                 {
503                 do {
504                         BN_bntest_rand(&a,512,-1,0);
505                         BN_bntest_rand(&b,BN_BITS2,-1,0);
506                         s = b.d[0];
507                 } while (!s);
508
509                 BN_copy(&b, &a);
510                 r = BN_div_word(&b, s);
511
512                 if (bp != NULL)
513                         {
514                         if (!results)
515                                 {
516                                 BN_print(bp,&a);
517                                 BIO_puts(bp," / ");
518                                 print_word(bp,s);
519                                 BIO_puts(bp," - ");
520                                 }
521                         BN_print(bp,&b);
522                         BIO_puts(bp,"\n");
523
524                         if (!results)
525                                 {
526                                 BN_print(bp,&a);
527                                 BIO_puts(bp," % ");
528                                 print_word(bp,s);
529                                 BIO_puts(bp," - ");
530                                 }
531                         print_word(bp,r);
532                         BIO_puts(bp,"\n");
533                         }
534                 BN_mul_word(&b,s);
535                 BN_add_word(&b,r);
536                 BN_sub(&b,&a,&b);
537                 if(!BN_is_zero(&b))
538                     {
539                     fprintf(stderr,"Division (word) test failed!\n");
540                     return 0;
541                     }
542                 }
543         BN_free(&a);
544         BN_free(&b);
545         return(1);
546         }
547
548 int test_div_recp(BIO *bp, BN_CTX *ctx)
549         {
550         BIGNUM a,b,c,d,e;
551         BN_RECP_CTX recp;
552         int i;
553
554         BN_RECP_CTX_init(&recp);
555         BN_init(&a);
556         BN_init(&b);
557         BN_init(&c);
558         BN_init(&d);
559         BN_init(&e);
560
561         for (i=0; i<num0+num1; i++)
562                 {
563                 if (i < num1)
564                         {
565                         BN_bntest_rand(&a,400,0,0);
566                         BN_copy(&b,&a);
567                         BN_lshift(&a,&a,i);
568                         BN_add_word(&a,i);
569                         }
570                 else
571                         BN_bntest_rand(&b,50+3*(i-num1),0,0);
572                 a.neg=rand_neg();
573                 b.neg=rand_neg();
574                 BN_RECP_CTX_set(&recp,&b,ctx);
575                 BN_div_recp(&d,&c,&a,&recp,ctx);
576                 if (bp != NULL)
577                         {
578                         if (!results)
579                                 {
580                                 BN_print(bp,&a);
581                                 BIO_puts(bp," / ");
582                                 BN_print(bp,&b);
583                                 BIO_puts(bp," - ");
584                                 }
585                         BN_print(bp,&d);
586                         BIO_puts(bp,"\n");
587
588                         if (!results)
589                                 {
590                                 BN_print(bp,&a);
591                                 BIO_puts(bp," % ");
592                                 BN_print(bp,&b);
593                                 BIO_puts(bp," - ");
594                                 }
595                         BN_print(bp,&c);
596                         BIO_puts(bp,"\n");
597                         }
598                 BN_mul(&e,&d,&b,ctx);
599                 BN_add(&d,&e,&c);
600                 BN_sub(&d,&d,&a);
601                 if(!BN_is_zero(&d))
602                     {
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");
609                     return 0;
610                     }
611                 }
612         BN_free(&a);
613         BN_free(&b);
614         BN_free(&c);
615         BN_free(&d);
616         BN_free(&e);
617         BN_RECP_CTX_free(&recp);
618         return(1);
619         }
620
621 int test_mul(BIO *bp)
622         {
623         BIGNUM a,b,c,d,e;
624         int i;
625         BN_CTX *ctx;
626
627         ctx = BN_CTX_new();
628         if (ctx == NULL) EXIT(1);
629         
630         BN_init(&a);
631         BN_init(&b);
632         BN_init(&c);
633         BN_init(&d);
634         BN_init(&e);
635
636         for (i=0; i<num0+num1; i++)
637                 {
638                 if (i <= num1)
639                         {
640                         BN_bntest_rand(&a,100,0,0);
641                         BN_bntest_rand(&b,100,0,0);
642                         }
643                 else
644                         BN_bntest_rand(&b,i-num1,0,0);
645                 a.neg=rand_neg();
646                 b.neg=rand_neg();
647                 BN_mul(&c,&a,&b,ctx);
648                 if (bp != NULL)
649                         {
650                         if (!results)
651                                 {
652                                 BN_print(bp,&a);
653                                 BIO_puts(bp," * ");
654                                 BN_print(bp,&b);
655                                 BIO_puts(bp," - ");
656                                 }
657                         BN_print(bp,&c);
658                         BIO_puts(bp,"\n");
659                         }
660                 BN_div(&d,&e,&c,&a,ctx);
661                 BN_sub(&d,&d,&b);
662                 if(!BN_is_zero(&d) || !BN_is_zero(&e))
663                     {
664                     fprintf(stderr,"Multiplication test failed!\n");
665                     return 0;
666                     }
667                 }
668         BN_free(&a);
669         BN_free(&b);
670         BN_free(&c);
671         BN_free(&d);
672         BN_free(&e);
673         BN_CTX_free(ctx);
674         return(1);
675         }
676
677 int test_sqr(BIO *bp, BN_CTX *ctx)
678         {
679         BIGNUM a,c,d,e;
680         int i;
681
682         BN_init(&a);
683         BN_init(&c);
684         BN_init(&d);
685         BN_init(&e);
686
687         for (i=0; i<num0; i++)
688                 {
689                 BN_bntest_rand(&a,40+i*10,0,0);
690                 a.neg=rand_neg();
691                 BN_sqr(&c,&a,ctx);
692                 if (bp != NULL)
693                         {
694                         if (!results)
695                                 {
696                                 BN_print(bp,&a);
697                                 BIO_puts(bp," * ");
698                                 BN_print(bp,&a);
699                                 BIO_puts(bp," - ");
700                                 }
701                         BN_print(bp,&c);
702                         BIO_puts(bp,"\n");
703                         }
704                 BN_div(&d,&e,&c,&a,ctx);
705                 BN_sub(&d,&d,&a);
706                 if(!BN_is_zero(&d) || !BN_is_zero(&e))
707                     {
708                     fprintf(stderr,"Square test failed!\n");
709                     return 0;
710                     }
711                 }
712         BN_free(&a);
713         BN_free(&c);
714         BN_free(&d);
715         BN_free(&e);
716         return(1);
717         }
718
719 int test_mont(BIO *bp, BN_CTX *ctx)
720         {
721         BIGNUM a,b,c,d,A,B;
722         BIGNUM n;
723         int i;
724         BN_MONT_CTX *mont;
725
726         BN_init(&a);
727         BN_init(&b);
728         BN_init(&c);
729         BN_init(&d);
730         BN_init(&A);
731         BN_init(&B);
732         BN_init(&n);
733
734         mont=BN_MONT_CTX_new();
735
736         BN_bntest_rand(&a,100,0,0); /**/
737         BN_bntest_rand(&b,100,0,0); /**/
738         for (i=0; i<num2; i++)
739                 {
740                 int bits = (200*(i+1))/num2;
741
742                 if (bits == 0)
743                         continue;
744                 BN_bntest_rand(&n,bits,0,1);
745                 BN_MONT_CTX_set(mont,&n,ctx);
746
747                 BN_nnmod(&a,&a,&n,ctx);
748                 BN_nnmod(&b,&b,&n,ctx);
749
750                 BN_to_montgomery(&A,&a,mont,ctx);
751                 BN_to_montgomery(&B,&b,mont,ctx);
752
753                 BN_mod_mul_montgomery(&c,&A,&B,mont,ctx);/**/
754                 BN_from_montgomery(&A,&c,mont,ctx);/**/
755                 if (bp != NULL)
756                         {
757                         if (!results)
758                                 {
759 #ifdef undef
760 fprintf(stderr,"%d * %d %% %d\n",
761 BN_num_bits(&a),
762 BN_num_bits(&b),
763 BN_num_bits(mont->N));
764 #endif
765                                 BN_print(bp,&a);
766                                 BIO_puts(bp," * ");
767                                 BN_print(bp,&b);
768                                 BIO_puts(bp," % ");
769                                 BN_print(bp,&(mont->N));
770                                 BIO_puts(bp," - ");
771                                 }
772                         BN_print(bp,&A);
773                         BIO_puts(bp,"\n");
774                         }
775                 BN_mod_mul(&d,&a,&b,&n,ctx);
776                 BN_sub(&d,&d,&A);
777                 if(!BN_is_zero(&d))
778                     {
779                     fprintf(stderr,"Montgomery multiplication test failed!\n");
780                     return 0;
781                     }
782                 }
783         BN_MONT_CTX_free(mont);
784         BN_free(&a);
785         BN_free(&b);
786         BN_free(&c);
787         BN_free(&d);
788         BN_free(&A);
789         BN_free(&B);
790         BN_free(&n);
791         return(1);
792         }
793
794 int test_mod(BIO *bp, BN_CTX *ctx)
795         {
796         BIGNUM *a,*b,*c,*d,*e;
797         int i;
798
799         a=BN_new();
800         b=BN_new();
801         c=BN_new();
802         d=BN_new();
803         e=BN_new();
804
805         BN_bntest_rand(a,1024,0,0); /**/
806         for (i=0; i<num0; i++)
807                 {
808                 BN_bntest_rand(b,450+i*10,0,0); /**/
809                 a->neg=rand_neg();
810                 b->neg=rand_neg();
811                 BN_mod(c,a,b,ctx);/**/
812                 if (bp != NULL)
813                         {
814                         if (!results)
815                                 {
816                                 BN_print(bp,a);
817                                 BIO_puts(bp," % ");
818                                 BN_print(bp,b);
819                                 BIO_puts(bp," - ");
820                                 }
821                         BN_print(bp,c);
822                         BIO_puts(bp,"\n");
823                         }
824                 BN_div(d,e,a,b,ctx);
825                 BN_sub(e,e,c);
826                 if(!BN_is_zero(e))
827                     {
828                     fprintf(stderr,"Modulo test failed!\n");
829                     return 0;
830                     }
831                 }
832         BN_free(a);
833         BN_free(b);
834         BN_free(c);
835         BN_free(d);
836         BN_free(e);
837         return(1);
838         }
839
840 int test_mod_mul(BIO *bp, BN_CTX *ctx)
841         {
842         BIGNUM *a,*b,*c,*d,*e;
843         int i,j;
844
845         a=BN_new();
846         b=BN_new();
847         c=BN_new();
848         d=BN_new();
849         e=BN_new();
850
851         for (j=0; j<3; j++) {
852         BN_bntest_rand(c,1024,0,0); /**/
853         for (i=0; i<num0; i++)
854                 {
855                 BN_bntest_rand(a,475+i*10,0,0); /**/
856                 BN_bntest_rand(b,425+i*11,0,0); /**/
857                 a->neg=rand_neg();
858                 b->neg=rand_neg();
859                 if (!BN_mod_mul(e,a,b,c,ctx))
860                         {
861                         unsigned long l;
862
863                         while ((l=ERR_get_error()))
864                                 fprintf(stderr,"ERROR:%s\n",
865                                         ERR_error_string(l,NULL));
866                         EXIT(1);
867                         }
868                 if (bp != NULL)
869                         {
870                         if (!results)
871                                 {
872                                 BN_print(bp,a);
873                                 BIO_puts(bp," * ");
874                                 BN_print(bp,b);
875                                 BIO_puts(bp," % ");
876                                 BN_print(bp,c);
877                                 if ((a->neg ^ b->neg) && !BN_is_zero(e))
878                                         {
879                                         /* If  (a*b) % c  is negative,  c  must be added
880                                          * in order to obtain the normalized remainder
881                                          * (new with OpenSSL 0.9.7, previous versions of
882                                          * BN_mod_mul could generate negative results)
883                                          */
884                                         BIO_puts(bp," + ");
885                                         BN_print(bp,c);
886                                         }
887                                 BIO_puts(bp," - ");
888                                 }
889                         BN_print(bp,e);
890                         BIO_puts(bp,"\n");
891                         }
892                 BN_mul(d,a,b,ctx);
893                 BN_sub(d,d,e);
894                 BN_div(a,b,d,c,ctx);
895                 if(!BN_is_zero(b))
896                     {
897                     fprintf(stderr,"Modulo multiply test failed!\n");
898                     ERR_print_errors_fp(stderr);
899                     return 0;
900                     }
901                 }
902         }
903         BN_free(a);
904         BN_free(b);
905         BN_free(c);
906         BN_free(d);
907         BN_free(e);
908         return(1);
909         }
910
911 int test_mod_exp(BIO *bp, BN_CTX *ctx)
912         {
913         BIGNUM *a,*b,*c,*d,*e;
914         int i;
915
916         a=BN_new();
917         b=BN_new();
918         c=BN_new();
919         d=BN_new();
920         e=BN_new();
921
922         BN_bntest_rand(c,30,0,1); /* must be odd for montgomery */
923         for (i=0; i<num2; i++)
924                 {
925                 BN_bntest_rand(a,20+i*5,0,0); /**/
926                 BN_bntest_rand(b,2+i,0,0); /**/
927
928                 if (!BN_mod_exp(d,a,b,c,ctx))
929                         return(00);
930
931                 if (bp != NULL)
932                         {
933                         if (!results)
934                                 {
935                                 BN_print(bp,a);
936                                 BIO_puts(bp," ^ ");
937                                 BN_print(bp,b);
938                                 BIO_puts(bp," % ");
939                                 BN_print(bp,c);
940                                 BIO_puts(bp," - ");
941                                 }
942                         BN_print(bp,d);
943                         BIO_puts(bp,"\n");
944                         }
945                 BN_exp(e,a,b,ctx);
946                 BN_sub(e,e,d);
947                 BN_div(a,b,e,c,ctx);
948                 if(!BN_is_zero(b))
949                     {
950                     fprintf(stderr,"Modulo exponentiation test failed!\n");
951                     return 0;
952                     }
953                 }
954         BN_free(a);
955         BN_free(b);
956         BN_free(c);
957         BN_free(d);
958         BN_free(e);
959         return(1);
960         }
961
962 int test_mod_exp_mont_consttime(BIO *bp, BN_CTX *ctx)
963         {
964         BIGNUM *a,*b,*c,*d,*e;
965         int i;
966
967         a=BN_new();
968         b=BN_new();
969         c=BN_new();
970         d=BN_new();
971         e=BN_new();
972
973         BN_bntest_rand(c,30,0,1); /* must be odd for montgomery */
974         for (i=0; i<num2; i++)
975                 {
976                 BN_bntest_rand(a,20+i*5,0,0); /**/
977                 BN_bntest_rand(b,2+i,0,0); /**/
978
979                 if (!BN_mod_exp_mont_consttime(d,a,b,c,ctx,NULL))
980                         return(00);
981
982                 if (bp != NULL)
983                         {
984                         if (!results)
985                                 {
986                                 BN_print(bp,a);
987                                 BIO_puts(bp," ^ ");
988                                 BN_print(bp,b);
989                                 BIO_puts(bp," % ");
990                                 BN_print(bp,c);
991                                 BIO_puts(bp," - ");
992                                 }
993                         BN_print(bp,d);
994                         BIO_puts(bp,"\n");
995                         }
996                 BN_exp(e,a,b,ctx);
997                 BN_sub(e,e,d);
998                 BN_div(a,b,e,c,ctx);
999                 if(!BN_is_zero(b))
1000                     {
1001                     fprintf(stderr,"Modulo exponentiation test failed!\n");
1002                     return 0;
1003                     }
1004                 }
1005         BN_free(a);
1006         BN_free(b);
1007         BN_free(c);
1008         BN_free(d);
1009         BN_free(e);
1010         return(1);
1011         }
1012
1013 int test_exp(BIO *bp, BN_CTX *ctx)
1014         {
1015         BIGNUM *a,*b,*d,*e,*one;
1016         int i;
1017
1018         a=BN_new();
1019         b=BN_new();
1020         d=BN_new();
1021         e=BN_new();
1022         one=BN_new();
1023         BN_one(one);
1024
1025         for (i=0; i<num2; i++)
1026                 {
1027                 BN_bntest_rand(a,20+i*5,0,0); /**/
1028                 BN_bntest_rand(b,2+i,0,0); /**/
1029
1030                 if (!BN_exp(d,a,b,ctx))
1031                         return(00);
1032
1033                 if (bp != NULL)
1034                         {
1035                         if (!results)
1036                                 {
1037                                 BN_print(bp,a);
1038                                 BIO_puts(bp," ^ ");
1039                                 BN_print(bp,b);
1040                                 BIO_puts(bp," - ");
1041                                 }
1042                         BN_print(bp,d);
1043                         BIO_puts(bp,"\n");
1044                         }
1045                 BN_one(e);
1046                 for( ; !BN_is_zero(b) ; BN_sub(b,b,one))
1047                     BN_mul(e,e,a,ctx);
1048                 BN_sub(e,e,d);
1049                 if(!BN_is_zero(e))
1050                     {
1051                     fprintf(stderr,"Exponentiation test failed!\n");
1052                     return 0;
1053                     }
1054                 }
1055         BN_free(a);
1056         BN_free(b);
1057         BN_free(d);
1058         BN_free(e);
1059         BN_free(one);
1060         return(1);
1061         }
1062
1063 int test_gf2m_add(BIO *bp)
1064         {
1065         BIGNUM a,b,c;
1066         int i, ret = 0;
1067
1068         BN_init(&a);
1069         BN_init(&b);
1070         BN_init(&c);
1071
1072         for (i=0; i<num0; i++)
1073                 {
1074                 BN_rand(&a,512,0,0);
1075                 BN_copy(&b, BN_value_one());
1076                 a.neg=rand_neg();
1077                 b.neg=rand_neg();
1078                 BN_GF2m_add(&c,&a,&b);
1079 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1080                 if (bp != NULL)
1081                         {
1082                         if (!results)
1083                                 {
1084                                 BN_print(bp,&a);
1085                                 BIO_puts(bp," ^ ");
1086                                 BN_print(bp,&b);
1087                                 BIO_puts(bp," = ");
1088                                 }
1089                         BN_print(bp,&c);
1090                         BIO_puts(bp,"\n");
1091                         }
1092 #endif
1093                 /* Test that two added values have the correct parity. */
1094                 if((BN_is_odd(&a) && BN_is_odd(&c)) || (!BN_is_odd(&a) && !BN_is_odd(&c)))
1095                         {
1096                     fprintf(stderr,"GF(2^m) addition test (a) failed!\n");
1097                         goto err;
1098                         }
1099                 BN_GF2m_add(&c,&c,&c);
1100                 /* Test that c + c = 0. */
1101                 if(!BN_is_zero(&c))
1102                     {
1103                     fprintf(stderr,"GF(2^m) addition test (b) failed!\n");
1104                         goto err;
1105                     }
1106                 }
1107         ret = 1;
1108   err:
1109         BN_free(&a);
1110         BN_free(&b);
1111         BN_free(&c);
1112         return ret;
1113         }
1114
1115 int test_gf2m_mod(BIO *bp)
1116         {
1117         BIGNUM *a,*b[2],*c,*d,*e;
1118         int i, j, ret = 0;
1119         unsigned int p0[] = {163,7,6,3,0};
1120         unsigned int p1[] = {193,15,0};
1121
1122         a=BN_new();
1123         b[0]=BN_new();
1124         b[1]=BN_new();
1125         c=BN_new();
1126         d=BN_new();
1127         e=BN_new();
1128
1129         BN_GF2m_arr2poly(p0, b[0]);
1130         BN_GF2m_arr2poly(p1, b[1]);
1131
1132         for (i=0; i<num0; i++)
1133                 {
1134                 BN_bntest_rand(a, 1024, 0, 0);
1135                 for (j=0; j < 2; j++)
1136                         {
1137                         BN_GF2m_mod(c, a, b[j]);
1138 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1139                         if (bp != NULL)
1140                                 {
1141                                 if (!results)
1142                                         {
1143                                         BN_print(bp,a);
1144                                         BIO_puts(bp," % ");
1145                                         BN_print(bp,b[j]);
1146                                         BIO_puts(bp," - ");
1147                                         BN_print(bp,c);
1148                                         BIO_puts(bp,"\n");
1149                                         }
1150                                 }
1151 #endif
1152                         BN_GF2m_add(d, a, c);
1153                         BN_GF2m_mod(e, d, b[j]);
1154                         /* Test that a + (a mod p) mod p == 0. */
1155                         if(!BN_is_zero(e))
1156                                 {
1157                                 fprintf(stderr,"GF(2^m) modulo test failed!\n");
1158                                 goto err;
1159                                 }
1160                         }
1161                 }
1162         ret = 1;
1163   err:
1164         BN_free(a);
1165         BN_free(b[0]);
1166         BN_free(b[1]);
1167         BN_free(c);
1168         BN_free(d);
1169         BN_free(e);
1170         return ret;
1171         }
1172
1173 int test_gf2m_mod_mul(BIO *bp,BN_CTX *ctx)
1174         {
1175         BIGNUM *a,*b[2],*c,*d,*e,*f,*g,*h;
1176         int i, j, ret = 0;
1177         unsigned int p0[] = {163,7,6,3,0};
1178         unsigned int p1[] = {193,15,0};
1179
1180         a=BN_new();
1181         b[0]=BN_new();
1182         b[1]=BN_new();
1183         c=BN_new();
1184         d=BN_new();
1185         e=BN_new();
1186         f=BN_new();
1187         g=BN_new();
1188         h=BN_new();
1189
1190         BN_GF2m_arr2poly(p0, b[0]);
1191         BN_GF2m_arr2poly(p1, b[1]);
1192
1193         for (i=0; i<num0; i++)
1194                 {
1195                 BN_bntest_rand(a, 1024, 0, 0);
1196                 BN_bntest_rand(c, 1024, 0, 0);
1197                 BN_bntest_rand(d, 1024, 0, 0);
1198                 for (j=0; j < 2; j++)
1199                         {
1200                         BN_GF2m_mod_mul(e, a, c, b[j], ctx);
1201 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1202                         if (bp != NULL)
1203                                 {
1204                                 if (!results)
1205                                         {
1206                                         BN_print(bp,a);
1207                                         BIO_puts(bp," * ");
1208                                         BN_print(bp,c);
1209                                         BIO_puts(bp," % ");
1210                                         BN_print(bp,b[j]);
1211                                         BIO_puts(bp," - ");
1212                                         BN_print(bp,e);
1213                                         BIO_puts(bp,"\n");
1214                                         }
1215                                 }
1216 #endif
1217                         BN_GF2m_add(f, a, d);
1218                         BN_GF2m_mod_mul(g, f, c, b[j], ctx);
1219                         BN_GF2m_mod_mul(h, d, c, b[j], ctx);
1220                         BN_GF2m_add(f, e, g);
1221                         BN_GF2m_add(f, f, h);
1222                         /* Test that (a+d)*c = a*c + d*c. */
1223                         if(!BN_is_zero(f))
1224                                 {
1225                                 fprintf(stderr,"GF(2^m) modular multiplication test failed!\n");
1226                                 goto err;
1227                                 }
1228                         }
1229                 }
1230         ret = 1;
1231   err:
1232         BN_free(a);
1233         BN_free(b[0]);
1234         BN_free(b[1]);
1235         BN_free(c);
1236         BN_free(d);
1237         BN_free(e);
1238         BN_free(f);
1239         BN_free(g);
1240         BN_free(h);
1241         return ret;
1242         }
1243
1244 int test_gf2m_mod_sqr(BIO *bp,BN_CTX *ctx)
1245         {
1246         BIGNUM *a,*b[2],*c,*d;
1247         int i, j, ret = 0;
1248         unsigned int p0[] = {163,7,6,3,0};
1249         unsigned int p1[] = {193,15,0};
1250
1251         a=BN_new();
1252         b[0]=BN_new();
1253         b[1]=BN_new();
1254         c=BN_new();
1255         d=BN_new();
1256
1257         BN_GF2m_arr2poly(p0, b[0]);
1258         BN_GF2m_arr2poly(p1, b[1]);
1259
1260         for (i=0; i<num0; i++)
1261                 {
1262                 BN_bntest_rand(a, 1024, 0, 0);
1263                 for (j=0; j < 2; j++)
1264                         {
1265                         BN_GF2m_mod_sqr(c, a, b[j], ctx);
1266                         BN_copy(d, a);
1267                         BN_GF2m_mod_mul(d, a, d, b[j], ctx);
1268 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1269                         if (bp != NULL)
1270                                 {
1271                                 if (!results)
1272                                         {
1273                                         BN_print(bp,a);
1274                                         BIO_puts(bp," ^ 2 % ");
1275                                         BN_print(bp,b[j]);
1276                                         BIO_puts(bp, " = ");
1277                                         BN_print(bp,c);
1278                                         BIO_puts(bp,"; a * a = ");
1279                                         BN_print(bp,d);
1280                                         BIO_puts(bp,"\n");
1281                                         }
1282                                 }
1283 #endif
1284                         BN_GF2m_add(d, c, d);
1285                         /* Test that a*a = a^2. */
1286                         if(!BN_is_zero(d))
1287                                 {
1288                                 fprintf(stderr,"GF(2^m) modular squaring test failed!\n");
1289                                 goto err;
1290                                 }
1291                         }
1292                 }
1293         ret = 1;
1294   err:
1295         BN_free(a);
1296         BN_free(b[0]);
1297         BN_free(b[1]);
1298         BN_free(c);
1299         BN_free(d);
1300         return ret;
1301         }
1302
1303 int test_gf2m_mod_inv(BIO *bp,BN_CTX *ctx)
1304         {
1305         BIGNUM *a,*b[2],*c,*d;
1306         int i, j, ret = 0;
1307         unsigned int p0[] = {163,7,6,3,0};
1308         unsigned int p1[] = {193,15,0};
1309
1310         a=BN_new();
1311         b[0]=BN_new();
1312         b[1]=BN_new();
1313         c=BN_new();
1314         d=BN_new();
1315
1316         BN_GF2m_arr2poly(p0, b[0]);
1317         BN_GF2m_arr2poly(p1, b[1]);
1318
1319         for (i=0; i<num0; i++)
1320                 {
1321                 BN_bntest_rand(a, 512, 0, 0); 
1322                 for (j=0; j < 2; j++)
1323                         {
1324                         BN_GF2m_mod_inv(c, a, b[j], ctx);
1325                         BN_GF2m_mod_mul(d, a, c, b[j], ctx);
1326 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1327                         if (bp != NULL)
1328                                 {
1329                                 if (!results)
1330                                         {
1331                                         BN_print(bp,a);
1332                                         BIO_puts(bp, " * ");
1333                                         BN_print(bp,c);
1334                                         BIO_puts(bp," - 1 % ");
1335                                         BN_print(bp,b[j]);
1336                                         BIO_puts(bp,"\n");
1337                                         }
1338                                 }
1339 #endif
1340                         /* Test that ((1/a)*a) = 1. */
1341                         if(!BN_is_one(d))
1342                                 {
1343                                 fprintf(stderr,"GF(2^m) modular inversion test failed!\n");
1344                                 goto err;
1345                                 }
1346                         }
1347                 }
1348         ret = 1;
1349   err:
1350         BN_free(a);
1351         BN_free(b[0]);
1352         BN_free(b[1]);
1353         BN_free(c);
1354         BN_free(d);
1355         return ret;
1356         }
1357
1358 int test_gf2m_mod_div(BIO *bp,BN_CTX *ctx)
1359         {
1360         BIGNUM *a,*b[2],*c,*d,*e,*f;
1361         int i, j, ret = 0;
1362         unsigned int p0[] = {163,7,6,3,0};
1363         unsigned int p1[] = {193,15,0};
1364
1365         a=BN_new();
1366         b[0]=BN_new();
1367         b[1]=BN_new();
1368         c=BN_new();
1369         d=BN_new();
1370         e=BN_new();
1371         f=BN_new();
1372
1373         BN_GF2m_arr2poly(p0, b[0]);
1374         BN_GF2m_arr2poly(p1, b[1]);
1375
1376         for (i=0; i<num0; i++)
1377                 {
1378                 BN_bntest_rand(a, 512, 0, 0); 
1379                 BN_bntest_rand(c, 512, 0, 0);
1380                 for (j=0; j < 2; j++)
1381                         {
1382                         BN_GF2m_mod_div(d, a, c, b[j], ctx);
1383                         BN_GF2m_mod_mul(e, d, c, b[j], ctx);
1384                         BN_GF2m_mod_div(f, a, e, b[j], ctx);
1385 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1386                         if (bp != NULL)
1387                                 {
1388                                 if (!results)
1389                                         {
1390                                         BN_print(bp,a);
1391                                         BIO_puts(bp, " = ");
1392                                         BN_print(bp,c);
1393                                         BIO_puts(bp," * ");
1394                                         BN_print(bp,d);
1395                                         BIO_puts(bp, " % ");
1396                                         BN_print(bp,b[j]);
1397                                         BIO_puts(bp,"\n");
1398                                         }
1399                                 }
1400 #endif
1401                         /* Test that ((a/c)*c)/a = 1. */
1402                         if(!BN_is_one(f))
1403                                 {
1404                                 fprintf(stderr,"GF(2^m) modular division test failed!\n");
1405                                 goto err;
1406                                 }
1407                         }
1408                 }
1409         ret = 1;
1410   err:
1411         BN_free(a);
1412         BN_free(b[0]);
1413         BN_free(b[1]);
1414         BN_free(c);
1415         BN_free(d);
1416         BN_free(e);
1417         BN_free(f);
1418         return ret;
1419         }
1420
1421 int test_gf2m_mod_exp(BIO *bp,BN_CTX *ctx)
1422         {
1423         BIGNUM *a,*b[2],*c,*d,*e,*f;
1424         int i, j, ret = 0;
1425         unsigned int p0[] = {163,7,6,3,0};
1426         unsigned int p1[] = {193,15,0};
1427
1428         a=BN_new();
1429         b[0]=BN_new();
1430         b[1]=BN_new();
1431         c=BN_new();
1432         d=BN_new();
1433         e=BN_new();
1434         f=BN_new();
1435
1436         BN_GF2m_arr2poly(p0, b[0]);
1437         BN_GF2m_arr2poly(p1, b[1]);
1438
1439         for (i=0; i<num0; i++)
1440                 {
1441                 BN_bntest_rand(a, 512, 0, 0);
1442                 BN_bntest_rand(c, 512, 0, 0);
1443                 BN_bntest_rand(d, 512, 0, 0);
1444                 for (j=0; j < 2; j++)
1445                         {
1446                         BN_GF2m_mod_exp(e, a, c, b[j], ctx);
1447                         BN_GF2m_mod_exp(f, a, d, b[j], ctx);
1448                         BN_GF2m_mod_mul(e, e, f, b[j], ctx);
1449                         BN_add(f, c, d);
1450                         BN_GF2m_mod_exp(f, a, f, b[j], ctx);
1451 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1452                         if (bp != NULL)
1453                                 {
1454                                 if (!results)
1455                                         {
1456                                         BN_print(bp,a);
1457                                         BIO_puts(bp, " ^ (");
1458                                         BN_print(bp,c);
1459                                         BIO_puts(bp," + ");
1460                                         BN_print(bp,d);
1461                                         BIO_puts(bp, ") = ");
1462                                         BN_print(bp,e);
1463                                         BIO_puts(bp, "; - ");
1464                                         BN_print(bp,f);
1465                                         BIO_puts(bp, " % ");
1466                                         BN_print(bp,b[j]);
1467                                         BIO_puts(bp,"\n");
1468                                         }
1469                                 }
1470 #endif
1471                         BN_GF2m_add(f, e, f);
1472                         /* Test that a^(c+d)=a^c*a^d. */
1473                         if(!BN_is_zero(f))
1474                                 {
1475                                 fprintf(stderr,"GF(2^m) modular exponentiation test failed!\n");
1476                                 goto err;
1477                                 }
1478                         }
1479                 }
1480         ret = 1;
1481   err:
1482         BN_free(a);
1483         BN_free(b[0]);
1484         BN_free(b[1]);
1485         BN_free(c);
1486         BN_free(d);
1487         BN_free(e);
1488         BN_free(f);
1489         return ret;
1490         }
1491
1492 int test_gf2m_mod_sqrt(BIO *bp,BN_CTX *ctx)
1493         {
1494         BIGNUM *a,*b[2],*c,*d,*e,*f;
1495         int i, j, ret = 0;
1496         unsigned int p0[] = {163,7,6,3,0};
1497         unsigned int p1[] = {193,15,0};
1498
1499         a=BN_new();
1500         b[0]=BN_new();
1501         b[1]=BN_new();
1502         c=BN_new();
1503         d=BN_new();
1504         e=BN_new();
1505         f=BN_new();
1506
1507         BN_GF2m_arr2poly(p0, b[0]);
1508         BN_GF2m_arr2poly(p1, b[1]);
1509
1510         for (i=0; i<num0; i++)
1511                 {
1512                 BN_bntest_rand(a, 512, 0, 0);
1513                 for (j=0; j < 2; j++)
1514                         {
1515                         BN_GF2m_mod(c, a, b[j]);
1516                         BN_GF2m_mod_sqrt(d, a, b[j], ctx);
1517                         BN_GF2m_mod_sqr(e, d, b[j], ctx);
1518 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1519                         if (bp != NULL)
1520                                 {
1521                                 if (!results)
1522                                         {
1523                                         BN_print(bp,d);
1524                                         BIO_puts(bp, " ^ 2 - ");
1525                                         BN_print(bp,a);
1526                                         BIO_puts(bp,"\n");
1527                                         }
1528                                 }
1529 #endif
1530                         BN_GF2m_add(f, c, e);
1531                         /* Test that d^2 = a, where d = sqrt(a). */
1532                         if(!BN_is_zero(f))
1533                                 {
1534                                 fprintf(stderr,"GF(2^m) modular square root test failed!\n");
1535                                 goto err;
1536                                 }
1537                         }
1538                 }
1539         ret = 1;
1540   err:
1541         BN_free(a);
1542         BN_free(b[0]);
1543         BN_free(b[1]);
1544         BN_free(c);
1545         BN_free(d);
1546         BN_free(e);
1547         BN_free(f);
1548         return ret;
1549         }
1550
1551 int test_gf2m_mod_solve_quad(BIO *bp,BN_CTX *ctx)
1552         {
1553         BIGNUM *a,*b[2],*c,*d,*e;
1554         int i, j, s = 0, t, ret = 0;
1555         unsigned int p0[] = {163,7,6,3,0};
1556         unsigned int p1[] = {193,15,0};
1557
1558         a=BN_new();
1559         b[0]=BN_new();
1560         b[1]=BN_new();
1561         c=BN_new();
1562         d=BN_new();
1563         e=BN_new();
1564
1565         BN_GF2m_arr2poly(p0, b[0]);
1566         BN_GF2m_arr2poly(p1, b[1]);
1567
1568         for (i=0; i<num0; i++)
1569                 {
1570                 BN_bntest_rand(a, 512, 0, 0);
1571                 for (j=0; j < 2; j++)
1572                         {
1573                         t = BN_GF2m_mod_solve_quad(c, a, b[j], ctx);
1574                         if (t)
1575                                 {
1576                                 s++;
1577                                 BN_GF2m_mod_sqr(d, c, b[j], ctx);
1578                                 BN_GF2m_add(d, c, d);
1579                                 BN_GF2m_mod(e, a, b[j]);
1580 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1581                                 if (bp != NULL)
1582                                         {
1583                                         if (!results)
1584                                                 {
1585                                                 BN_print(bp,c);
1586                                                 BIO_puts(bp, " is root of z^2 + z = ");
1587                                                 BN_print(bp,a);
1588                                                 BIO_puts(bp, " % ");
1589                                                 BN_print(bp,b[j]);
1590                                                 BIO_puts(bp, "\n");
1591                                                 }
1592                                         }
1593 #endif
1594                                 BN_GF2m_add(e, e, d);
1595                                 /* Test that solution of quadratic c satisfies c^2 + c = a. */
1596                                 if(!BN_is_zero(e))
1597                                         {
1598                                         fprintf(stderr,"GF(2^m) modular solve quadratic test failed!\n");
1599                                         goto err;
1600                                         }
1601
1602                                 }
1603                         else 
1604                                 {
1605 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1606                                 if (bp != NULL)
1607                                         {
1608                                         if (!results)
1609                                                 {
1610                                                 BIO_puts(bp, "There are no roots of z^2 + z = ");
1611                                                 BN_print(bp,a);
1612                                                 BIO_puts(bp, " % ");
1613                                                 BN_print(bp,b[j]);
1614                                                 BIO_puts(bp, "\n");
1615                                                 }
1616                                         }
1617 #endif
1618                                 }
1619                         }
1620                 }
1621         if (s == 0)
1622                 {       
1623                 fprintf(stderr,"All %i tests of GF(2^m) modular solve quadratic resulted in no roots;\n", num0);
1624                 fprintf(stderr,"this is very unlikely and probably indicates an error.\n");
1625                 goto err;
1626                 }
1627         ret = 1;
1628   err:
1629         BN_free(a);
1630         BN_free(b[0]);
1631         BN_free(b[1]);
1632         BN_free(c);
1633         BN_free(d);
1634         BN_free(e);
1635         return ret;
1636         }
1637
1638 static int genprime_cb(int p, int n, BN_GENCB *arg)
1639         {
1640         char c='*';
1641
1642         if (p == 0) c='.';
1643         if (p == 1) c='+';
1644         if (p == 2) c='*';
1645         if (p == 3) c='\n';
1646         putc(c, stderr);
1647         fflush(stderr);
1648         return 1;
1649         }
1650
1651 int test_kron(BIO *bp, BN_CTX *ctx)
1652         {
1653         BN_GENCB cb;
1654         BIGNUM *a,*b,*r,*t;
1655         int i;
1656         int legendre, kronecker;
1657         int ret = 0;
1658
1659         a = BN_new();
1660         b = BN_new();
1661         r = BN_new();
1662         t = BN_new();
1663         if (a == NULL || b == NULL || r == NULL || t == NULL) goto err;
1664
1665         BN_GENCB_set(&cb, genprime_cb, NULL);
1666         
1667         /* We test BN_kronecker(a, b, ctx) just for  b  odd (Jacobi symbol).
1668          * In this case we know that if  b  is prime, then BN_kronecker(a, b, ctx)
1669          * is congruent to $a^{(b-1)/2}$, modulo $b$ (Legendre symbol).
1670          * So we generate a random prime  b  and compare these values
1671          * for a number of random  a's.  (That is, we run the Solovay-Strassen
1672          * primality test to confirm that  b  is prime, except that we
1673          * don't want to test whether  b  is prime but whether BN_kronecker
1674          * works.) */
1675
1676         if (!BN_generate_prime_ex(b, 512, 0, NULL, NULL, &cb)) goto err;
1677         b->neg = rand_neg();
1678         putc('\n', stderr);
1679
1680         for (i = 0; i < num0; i++)
1681                 {
1682                 if (!BN_bntest_rand(a, 512, 0, 0)) goto err;
1683                 a->neg = rand_neg();
1684
1685                 /* t := (|b|-1)/2  (note that b is odd) */
1686                 if (!BN_copy(t, b)) goto err;
1687                 t->neg = 0;
1688                 if (!BN_sub_word(t, 1)) goto err;
1689                 if (!BN_rshift1(t, t)) goto err;
1690                 /* r := a^t mod b */
1691                 b->neg=0;
1692                 
1693                 if (!BN_mod_exp_recp(r, a, t, b, ctx)) goto err;
1694                 b->neg=1;
1695
1696                 if (BN_is_word(r, 1))
1697                         legendre = 1;
1698                 else if (BN_is_zero(r))
1699                         legendre = 0;
1700                 else
1701                         {
1702                         if (!BN_add_word(r, 1)) goto err;
1703                         if (0 != BN_ucmp(r, b))
1704                                 {
1705                                 fprintf(stderr, "Legendre symbol computation failed\n");
1706                                 goto err;
1707                                 }
1708                         legendre = -1;
1709                         }
1710                 
1711                 kronecker = BN_kronecker(a, b, ctx);
1712                 if (kronecker < -1) goto err;
1713                 /* we actually need BN_kronecker(a, |b|) */
1714                 if (a->neg && b->neg)
1715                         kronecker = -kronecker;
1716                 
1717                 if (legendre != kronecker)
1718                         {
1719                         fprintf(stderr, "legendre != kronecker; a = ");
1720                         BN_print_fp(stderr, a);
1721                         fprintf(stderr, ", b = ");
1722                         BN_print_fp(stderr, b);
1723                         fprintf(stderr, "\n");
1724                         goto err;
1725                         }
1726
1727                 putc('.', stderr);
1728                 fflush(stderr);
1729                 }
1730
1731         putc('\n', stderr);
1732         fflush(stderr);
1733         ret = 1;
1734  err:
1735         if (a != NULL) BN_free(a);
1736         if (b != NULL) BN_free(b);
1737         if (r != NULL) BN_free(r);
1738         if (t != NULL) BN_free(t);
1739         return ret;
1740         }
1741
1742 int test_sqrt(BIO *bp, BN_CTX *ctx)
1743         {
1744         BN_GENCB cb;
1745         BIGNUM *a,*p,*r;
1746         int i, j;
1747         int ret = 0;
1748
1749         a = BN_new();
1750         p = BN_new();
1751         r = BN_new();
1752         if (a == NULL || p == NULL || r == NULL) goto err;
1753
1754         BN_GENCB_set(&cb, genprime_cb, NULL);
1755
1756         for (i = 0; i < 16; i++)
1757                 {
1758                 if (i < 8)
1759                         {
1760                         unsigned primes[8] = { 2, 3, 5, 7, 11, 13, 17, 19 };
1761                         
1762                         if (!BN_set_word(p, primes[i])) goto err;
1763                         }
1764                 else
1765                         {
1766                         if (!BN_set_word(a, 32)) goto err;
1767                         if (!BN_set_word(r, 2*i + 1)) goto err;
1768                 
1769                         if (!BN_generate_prime_ex(p, 256, 0, a, r, &cb)) goto err;
1770                         putc('\n', stderr);
1771                         }
1772                 p->neg = rand_neg();
1773
1774                 for (j = 0; j < num2; j++)
1775                         {
1776                         /* construct 'a' such that it is a square modulo p,
1777                          * but in general not a proper square and not reduced modulo p */
1778                         if (!BN_bntest_rand(r, 256, 0, 3)) goto err;
1779                         if (!BN_nnmod(r, r, p, ctx)) goto err;
1780                         if (!BN_mod_sqr(r, r, p, ctx)) goto err;
1781                         if (!BN_bntest_rand(a, 256, 0, 3)) goto err;
1782                         if (!BN_nnmod(a, a, p, ctx)) goto err;
1783                         if (!BN_mod_sqr(a, a, p, ctx)) goto err;
1784                         if (!BN_mul(a, a, r, ctx)) goto err;
1785                         if (rand_neg())
1786                                 if (!BN_sub(a, a, p)) goto err;
1787
1788                         if (!BN_mod_sqrt(r, a, p, ctx)) goto err;
1789                         if (!BN_mod_sqr(r, r, p, ctx)) goto err;
1790
1791                         if (!BN_nnmod(a, a, p, ctx)) goto err;
1792
1793                         if (BN_cmp(a, r) != 0)
1794                                 {
1795                                 fprintf(stderr, "BN_mod_sqrt failed: a = ");
1796                                 BN_print_fp(stderr, a);
1797                                 fprintf(stderr, ", r = ");
1798                                 BN_print_fp(stderr, r);
1799                                 fprintf(stderr, ", p = ");
1800                                 BN_print_fp(stderr, p);
1801                                 fprintf(stderr, "\n");
1802                                 goto err;
1803                                 }
1804
1805                         putc('.', stderr);
1806                         fflush(stderr);
1807                         }
1808                 
1809                 putc('\n', stderr);
1810                 fflush(stderr);
1811                 }
1812         ret = 1;
1813  err:
1814         if (a != NULL) BN_free(a);
1815         if (p != NULL) BN_free(p);
1816         if (r != NULL) BN_free(r);
1817         return ret;
1818         }
1819
1820 int test_lshift(BIO *bp,BN_CTX *ctx,BIGNUM *a_)
1821         {
1822         BIGNUM *a,*b,*c,*d;
1823         int i;
1824
1825         b=BN_new();
1826         c=BN_new();
1827         d=BN_new();
1828         BN_one(c);
1829
1830         if(a_)
1831             a=a_;
1832         else
1833             {
1834             a=BN_new();
1835             BN_bntest_rand(a,200,0,0); /**/
1836             a->neg=rand_neg();
1837             }
1838         for (i=0; i<num0; i++)
1839                 {
1840                 BN_lshift(b,a,i+1);
1841                 BN_add(c,c,c);
1842                 if (bp != NULL)
1843                         {
1844                         if (!results)
1845                                 {
1846                                 BN_print(bp,a);
1847                                 BIO_puts(bp," * ");
1848                                 BN_print(bp,c);
1849                                 BIO_puts(bp," - ");
1850                                 }
1851                         BN_print(bp,b);
1852                         BIO_puts(bp,"\n");
1853                         }
1854                 BN_mul(d,a,c,ctx);
1855                 BN_sub(d,d,b);
1856                 if(!BN_is_zero(d))
1857                     {
1858                     fprintf(stderr,"Left shift test failed!\n");
1859                     fprintf(stderr,"a=");
1860                     BN_print_fp(stderr,a);
1861                     fprintf(stderr,"\nb=");
1862                     BN_print_fp(stderr,b);
1863                     fprintf(stderr,"\nc=");
1864                     BN_print_fp(stderr,c);
1865                     fprintf(stderr,"\nd=");
1866                     BN_print_fp(stderr,d);
1867                     fprintf(stderr,"\n");
1868                     return 0;
1869                     }
1870                 }
1871         BN_free(a);
1872         BN_free(b);
1873         BN_free(c);
1874         BN_free(d);
1875         return(1);
1876         }
1877
1878 int test_lshift1(BIO *bp)
1879         {
1880         BIGNUM *a,*b,*c;
1881         int i;
1882
1883         a=BN_new();
1884         b=BN_new();
1885         c=BN_new();
1886
1887         BN_bntest_rand(a,200,0,0); /**/
1888         a->neg=rand_neg();
1889         for (i=0; i<num0; i++)
1890                 {
1891                 BN_lshift1(b,a);
1892                 if (bp != NULL)
1893                         {
1894                         if (!results)
1895                                 {
1896                                 BN_print(bp,a);
1897                                 BIO_puts(bp," * 2");
1898                                 BIO_puts(bp," - ");
1899                                 }
1900                         BN_print(bp,b);
1901                         BIO_puts(bp,"\n");
1902                         }
1903                 BN_add(c,a,a);
1904                 BN_sub(a,b,c);
1905                 if(!BN_is_zero(a))
1906                     {
1907                     fprintf(stderr,"Left shift one test failed!\n");
1908                     return 0;
1909                     }
1910                 
1911                 BN_copy(a,b);
1912                 }
1913         BN_free(a);
1914         BN_free(b);
1915         BN_free(c);
1916         return(1);
1917         }
1918
1919 int test_rshift(BIO *bp,BN_CTX *ctx)
1920         {
1921         BIGNUM *a,*b,*c,*d,*e;
1922         int i;
1923
1924         a=BN_new();
1925         b=BN_new();
1926         c=BN_new();
1927         d=BN_new();
1928         e=BN_new();
1929         BN_one(c);
1930
1931         BN_bntest_rand(a,200,0,0); /**/
1932         a->neg=rand_neg();
1933         for (i=0; i<num0; i++)
1934                 {
1935                 BN_rshift(b,a,i+1);
1936                 BN_add(c,c,c);
1937                 if (bp != NULL)
1938                         {
1939                         if (!results)
1940                                 {
1941                                 BN_print(bp,a);
1942                                 BIO_puts(bp," / ");
1943                                 BN_print(bp,c);
1944                                 BIO_puts(bp," - ");
1945                                 }
1946                         BN_print(bp,b);
1947                         BIO_puts(bp,"\n");
1948                         }
1949                 BN_div(d,e,a,c,ctx);
1950                 BN_sub(d,d,b);
1951                 if(!BN_is_zero(d))
1952                     {
1953                     fprintf(stderr,"Right shift test failed!\n");
1954                     return 0;
1955                     }
1956                 }
1957         BN_free(a);
1958         BN_free(b);
1959         BN_free(c);
1960         BN_free(d);
1961         BN_free(e);
1962         return(1);
1963         }
1964
1965 int test_rshift1(BIO *bp)
1966         {
1967         BIGNUM *a,*b,*c;
1968         int i;
1969
1970         a=BN_new();
1971         b=BN_new();
1972         c=BN_new();
1973
1974         BN_bntest_rand(a,200,0,0); /**/
1975         a->neg=rand_neg();
1976         for (i=0; i<num0; i++)
1977                 {
1978                 BN_rshift1(b,a);
1979                 if (bp != NULL)
1980                         {
1981                         if (!results)
1982                                 {
1983                                 BN_print(bp,a);
1984                                 BIO_puts(bp," / 2");
1985                                 BIO_puts(bp," - ");
1986                                 }
1987                         BN_print(bp,b);
1988                         BIO_puts(bp,"\n");
1989                         }
1990                 BN_sub(c,a,b);
1991                 BN_sub(c,c,b);
1992                 if(!BN_is_zero(c) && !BN_abs_is_word(c, 1))
1993                     {
1994                     fprintf(stderr,"Right shift one test failed!\n");
1995                     return 0;
1996                     }
1997                 BN_copy(a,b);
1998                 }
1999         BN_free(a);
2000         BN_free(b);
2001         BN_free(c);
2002         return(1);
2003         }
2004
2005 int rand_neg(void)
2006         {
2007         static unsigned int neg=0;
2008         static int sign[8]={0,0,0,1,1,0,1,1};
2009
2010         return(sign[(neg++)%8]);
2011         }