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2013 lines
39 KiB
2013 lines
39 KiB
/* crypto/bn/bntest.c */
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/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
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* All rights reserved.
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*
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* This package is an SSL implementation written
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* by Eric Young (eay@cryptsoft.com).
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* The implementation was written so as to conform with Netscapes SSL.
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*
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* This library is free for commercial and non-commercial use as long as
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* the following conditions are aheared to. The following conditions
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* apply to all code found in this distribution, be it the RC4, RSA,
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* lhash, DES, etc., code; not just the SSL code. The SSL documentation
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* included with this distribution is covered by the same copyright terms
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* except that the holder is Tim Hudson (tjh@cryptsoft.com).
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*
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* Copyright remains Eric Young's, and as such any Copyright notices in
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* the code are not to be removed.
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* If this package is used in a product, Eric Young should be given attribution
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* as the author of the parts of the library used.
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* This can be in the form of a textual message at program startup or
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* in documentation (online or textual) provided with the package.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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* 3. All advertising materials mentioning features or use of this software
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* must display the following acknowledgement:
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* "This product includes cryptographic software written by
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* Eric Young (eay@cryptsoft.com)"
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* The word 'cryptographic' can be left out if the rouines from the library
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* being used are not cryptographic related :-).
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* 4. If you include any Windows specific code (or a derivative thereof) from
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* the apps directory (application code) you must include an acknowledgement:
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* "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
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*
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* THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*
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* The licence and distribution terms for any publically available version or
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* derivative of this code cannot be changed. i.e. this code cannot simply be
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* copied and put under another distribution licence
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* [including the GNU Public Licence.]
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*/
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/* ====================================================================
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* Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
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*
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* Portions of the attached software ("Contribution") are developed by
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* SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
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*
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* The Contribution is licensed pursuant to the Eric Young open source
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* license provided above.
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*
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* The binary polynomial arithmetic software is originally written by
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* Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
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*
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*/
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/* Until the key-gen callbacks are modified to use newer prototypes, we allow
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* deprecated functions for openssl-internal code */
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#ifdef OPENSSL_NO_DEPRECATED
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#undef OPENSSL_NO_DEPRECATED
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#endif
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#include <stdio.h>
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#include <stdlib.h>
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#include <string.h>
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#include "e_os.h"
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#include <openssl/bio.h>
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#include <openssl/bn.h>
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#include <openssl/rand.h>
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#include <openssl/x509.h>
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#include <openssl/err.h>
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const int num0 = 100; /* number of tests */
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const int num1 = 50; /* additional tests for some functions */
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const int num2 = 5; /* number of tests for slow functions */
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int test_add(BIO *bp);
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int test_sub(BIO *bp);
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int test_lshift1(BIO *bp);
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int test_lshift(BIO *bp,BN_CTX *ctx,BIGNUM *a_);
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int test_rshift1(BIO *bp);
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int test_rshift(BIO *bp,BN_CTX *ctx);
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int test_div(BIO *bp,BN_CTX *ctx);
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int test_div_word(BIO *bp);
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int test_div_recp(BIO *bp,BN_CTX *ctx);
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int test_mul(BIO *bp);
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int test_sqr(BIO *bp,BN_CTX *ctx);
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int test_mont(BIO *bp,BN_CTX *ctx);
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int test_mod(BIO *bp,BN_CTX *ctx);
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int test_mod_mul(BIO *bp,BN_CTX *ctx);
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int test_mod_exp(BIO *bp,BN_CTX *ctx);
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int test_mod_exp_mont_consttime(BIO *bp,BN_CTX *ctx);
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int test_exp(BIO *bp,BN_CTX *ctx);
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int test_gf2m_add(BIO *bp);
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int test_gf2m_mod(BIO *bp);
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int test_gf2m_mod_mul(BIO *bp,BN_CTX *ctx);
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int test_gf2m_mod_sqr(BIO *bp,BN_CTX *ctx);
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int test_gf2m_mod_inv(BIO *bp,BN_CTX *ctx);
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int test_gf2m_mod_div(BIO *bp,BN_CTX *ctx);
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int test_gf2m_mod_exp(BIO *bp,BN_CTX *ctx);
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int test_gf2m_mod_sqrt(BIO *bp,BN_CTX *ctx);
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int test_gf2m_mod_solve_quad(BIO *bp,BN_CTX *ctx);
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int test_kron(BIO *bp,BN_CTX *ctx);
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int test_sqrt(BIO *bp,BN_CTX *ctx);
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int rand_neg(void);
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static int results=0;
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static unsigned char lst[]="\xC6\x4F\x43\x04\x2A\xEA\xCA\x6E\x58\x36\x80\x5B\xE8\xC9"
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"\x9B\x04\x5D\x48\x36\xC2\xFD\x16\xC9\x64\xF0";
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static const char rnd_seed[] = "string to make the random number generator think it has entropy";
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static void message(BIO *out, char *m)
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{
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fprintf(stderr, "test %s\n", m);
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BIO_puts(out, "print \"test ");
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BIO_puts(out, m);
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BIO_puts(out, "\\n\"\n");
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}
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int main(int argc, char *argv[])
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{
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BN_CTX *ctx;
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BIO *out;
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char *outfile=NULL;
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results = 0;
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RAND_seed(rnd_seed, sizeof rnd_seed); /* or BN_generate_prime may fail */
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argc--;
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argv++;
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while (argc >= 1)
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{
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if (strcmp(*argv,"-results") == 0)
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results=1;
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else if (strcmp(*argv,"-out") == 0)
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{
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if (--argc < 1) break;
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outfile= *(++argv);
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}
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argc--;
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argv++;
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}
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ctx=BN_CTX_new();
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if (ctx == NULL) EXIT(1);
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out=BIO_new(BIO_s_file());
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if (out == NULL) EXIT(1);
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if (outfile == NULL)
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{
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BIO_set_fp(out,stdout,BIO_NOCLOSE);
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}
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else
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{
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if (!BIO_write_filename(out,outfile))
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{
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perror(outfile);
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EXIT(1);
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}
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}
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if (!results)
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BIO_puts(out,"obase=16\nibase=16\n");
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message(out,"BN_add");
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if (!test_add(out)) goto err;
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(void)BIO_flush(out);
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message(out,"BN_sub");
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if (!test_sub(out)) goto err;
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(void)BIO_flush(out);
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message(out,"BN_lshift1");
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if (!test_lshift1(out)) goto err;
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(void)BIO_flush(out);
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message(out,"BN_lshift (fixed)");
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if (!test_lshift(out,ctx,BN_bin2bn(lst,sizeof(lst)-1,NULL)))
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goto err;
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(void)BIO_flush(out);
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message(out,"BN_lshift");
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if (!test_lshift(out,ctx,NULL)) goto err;
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(void)BIO_flush(out);
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message(out,"BN_rshift1");
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if (!test_rshift1(out)) goto err;
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(void)BIO_flush(out);
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message(out,"BN_rshift");
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if (!test_rshift(out,ctx)) goto err;
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(void)BIO_flush(out);
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message(out,"BN_sqr");
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if (!test_sqr(out,ctx)) goto err;
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(void)BIO_flush(out);
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message(out,"BN_mul");
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if (!test_mul(out)) goto err;
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(void)BIO_flush(out);
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message(out,"BN_div");
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if (!test_div(out,ctx)) goto err;
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(void)BIO_flush(out);
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message(out,"BN_div_word");
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if (!test_div_word(out)) goto err;
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(void)BIO_flush(out);
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message(out,"BN_div_recp");
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if (!test_div_recp(out,ctx)) goto err;
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(void)BIO_flush(out);
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message(out,"BN_mod");
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if (!test_mod(out,ctx)) goto err;
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(void)BIO_flush(out);
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message(out,"BN_mod_mul");
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if (!test_mod_mul(out,ctx)) goto err;
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(void)BIO_flush(out);
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message(out,"BN_mont");
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if (!test_mont(out,ctx)) goto err;
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(void)BIO_flush(out);
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message(out,"BN_mod_exp");
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if (!test_mod_exp(out,ctx)) goto err;
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(void)BIO_flush(out);
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message(out,"BN_mod_exp_mont_consttime");
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if (!test_mod_exp_mont_consttime(out,ctx)) goto err;
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(void)BIO_flush(out);
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message(out,"BN_exp");
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if (!test_exp(out,ctx)) goto err;
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(void)BIO_flush(out);
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message(out,"BN_kronecker");
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if (!test_kron(out,ctx)) goto err;
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(void)BIO_flush(out);
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message(out,"BN_mod_sqrt");
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if (!test_sqrt(out,ctx)) goto err;
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(void)BIO_flush(out);
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message(out,"BN_GF2m_add");
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if (!test_gf2m_add(out)) goto err;
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(void)BIO_flush(out);
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message(out,"BN_GF2m_mod");
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if (!test_gf2m_mod(out)) goto err;
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(void)BIO_flush(out);
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message(out,"BN_GF2m_mod_mul");
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if (!test_gf2m_mod_mul(out,ctx)) goto err;
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(void)BIO_flush(out);
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message(out,"BN_GF2m_mod_sqr");
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if (!test_gf2m_mod_sqr(out,ctx)) goto err;
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(void)BIO_flush(out);
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message(out,"BN_GF2m_mod_inv");
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if (!test_gf2m_mod_inv(out,ctx)) goto err;
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(void)BIO_flush(out);
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message(out,"BN_GF2m_mod_div");
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if (!test_gf2m_mod_div(out,ctx)) goto err;
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(void)BIO_flush(out);
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message(out,"BN_GF2m_mod_exp");
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if (!test_gf2m_mod_exp(out,ctx)) goto err;
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(void)BIO_flush(out);
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message(out,"BN_GF2m_mod_sqrt");
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if (!test_gf2m_mod_sqrt(out,ctx)) goto err;
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(void)BIO_flush(out);
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message(out,"BN_GF2m_mod_solve_quad");
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if (!test_gf2m_mod_solve_quad(out,ctx)) goto err;
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(void)BIO_flush(out);
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BN_CTX_free(ctx);
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BIO_free(out);
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/**/
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EXIT(0);
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err:
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BIO_puts(out,"1\n"); /* make sure the Perl script fed by bc notices
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* the failure, see test_bn in test/Makefile.ssl*/
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(void)BIO_flush(out);
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ERR_load_crypto_strings();
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ERR_print_errors_fp(stderr);
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EXIT(1);
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return(1);
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}
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int test_add(BIO *bp)
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{
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BIGNUM a,b,c;
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int i;
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BN_init(&a);
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BN_init(&b);
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BN_init(&c);
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BN_bntest_rand(&a,512,0,0);
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for (i=0; i<num0; i++)
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{
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BN_bntest_rand(&b,450+i,0,0);
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a.neg=rand_neg();
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b.neg=rand_neg();
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BN_add(&c,&a,&b);
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if (bp != NULL)
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{
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if (!results)
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{
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BN_print(bp,&a);
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BIO_puts(bp," + ");
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BN_print(bp,&b);
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BIO_puts(bp," - ");
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}
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BN_print(bp,&c);
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BIO_puts(bp,"\n");
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}
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a.neg=!a.neg;
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b.neg=!b.neg;
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BN_add(&c,&c,&b);
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BN_add(&c,&c,&a);
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if(!BN_is_zero(&c))
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{
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fprintf(stderr,"Add test failed!\n");
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return 0;
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}
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}
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BN_free(&a);
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BN_free(&b);
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BN_free(&c);
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return(1);
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}
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int test_sub(BIO *bp)
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{
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BIGNUM a,b,c;
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int i;
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BN_init(&a);
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BN_init(&b);
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BN_init(&c);
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for (i=0; i<num0+num1; i++)
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{
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if (i < num1)
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{
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BN_bntest_rand(&a,512,0,0);
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BN_copy(&b,&a);
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if (BN_set_bit(&a,i)==0) return(0);
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BN_add_word(&b,i);
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}
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else
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{
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BN_bntest_rand(&b,400+i-num1,0,0);
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a.neg=rand_neg();
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b.neg=rand_neg();
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}
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BN_sub(&c,&a,&b);
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if (bp != NULL)
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{
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if (!results)
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{
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BN_print(bp,&a);
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BIO_puts(bp," - ");
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BN_print(bp,&b);
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BIO_puts(bp," - ");
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}
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BN_print(bp,&c);
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BIO_puts(bp,"\n");
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}
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BN_add(&c,&c,&b);
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BN_sub(&c,&c,&a);
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if(!BN_is_zero(&c))
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{
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fprintf(stderr,"Subtract test failed!\n");
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return 0;
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}
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}
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BN_free(&a);
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BN_free(&b);
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BN_free(&c);
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return(1);
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}
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int test_div(BIO *bp, BN_CTX *ctx)
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{
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BIGNUM a,b,c,d,e;
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int i;
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BN_init(&a);
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BN_init(&b);
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BN_init(&c);
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BN_init(&d);
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BN_init(&e);
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for (i=0; i<num0+num1; i++)
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{
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if (i < num1)
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{
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BN_bntest_rand(&a,400,0,0);
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BN_copy(&b,&a);
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BN_lshift(&a,&a,i);
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BN_add_word(&a,i);
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}
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else
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BN_bntest_rand(&b,50+3*(i-num1),0,0);
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a.neg=rand_neg();
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b.neg=rand_neg();
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BN_div(&d,&c,&a,&b,ctx);
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if (bp != NULL)
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{
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if (!results)
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{
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BN_print(bp,&a);
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BIO_puts(bp," / ");
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BN_print(bp,&b);
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BIO_puts(bp," - ");
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}
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BN_print(bp,&d);
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BIO_puts(bp,"\n");
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if (!results)
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{
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BN_print(bp,&a);
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BIO_puts(bp," % ");
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BN_print(bp,&b);
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BIO_puts(bp," - ");
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}
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BN_print(bp,&c);
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BIO_puts(bp,"\n");
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}
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BN_mul(&e,&d,&b,ctx);
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BN_add(&d,&e,&c);
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BN_sub(&d,&d,&a);
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if(!BN_is_zero(&d))
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{
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fprintf(stderr,"Division test failed!\n");
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return 0;
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}
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}
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BN_free(&a);
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BN_free(&b);
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BN_free(&c);
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BN_free(&d);
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BN_free(&e);
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return(1);
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}
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static void print_word(BIO *bp,BN_ULONG w)
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{
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#ifdef SIXTY_FOUR_BIT
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if (sizeof(w) > sizeof(unsigned long))
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{
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unsigned long h=(unsigned long)(w>>32),
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l=(unsigned long)(w);
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if (h) BIO_printf(bp,"%lX%08lX",h,l);
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else BIO_printf(bp,"%lX",l);
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return;
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}
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#endif
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BIO_printf(bp,BN_HEX_FMT1,w);
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}
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int test_div_word(BIO *bp)
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{
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BIGNUM a,b;
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BN_ULONG r,s;
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int i;
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BN_init(&a);
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BN_init(&b);
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for (i=0; i<num0; i++)
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{
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do {
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BN_bntest_rand(&a,512,-1,0);
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BN_bntest_rand(&b,BN_BITS2,-1,0);
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s = b.d[0];
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} while (!s);
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BN_copy(&b, &a);
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r = BN_div_word(&b, s);
|
|
|
|
if (bp != NULL)
|
|
{
|
|
if (!results)
|
|
{
|
|
BN_print(bp,&a);
|
|
BIO_puts(bp," / ");
|
|
print_word(bp,s);
|
|
BIO_puts(bp," - ");
|
|
}
|
|
BN_print(bp,&b);
|
|
BIO_puts(bp,"\n");
|
|
|
|
if (!results)
|
|
{
|
|
BN_print(bp,&a);
|
|
BIO_puts(bp," % ");
|
|
print_word(bp,s);
|
|
BIO_puts(bp," - ");
|
|
}
|
|
print_word(bp,r);
|
|
BIO_puts(bp,"\n");
|
|
}
|
|
BN_mul_word(&b,s);
|
|
BN_add_word(&b,r);
|
|
BN_sub(&b,&a,&b);
|
|
if(!BN_is_zero(&b))
|
|
{
|
|
fprintf(stderr,"Division (word) test failed!\n");
|
|
return 0;
|
|
}
|
|
}
|
|
BN_free(&a);
|
|
BN_free(&b);
|
|
return(1);
|
|
}
|
|
|
|
int test_div_recp(BIO *bp, BN_CTX *ctx)
|
|
{
|
|
BIGNUM a,b,c,d,e;
|
|
BN_RECP_CTX recp;
|
|
int i;
|
|
|
|
BN_RECP_CTX_init(&recp);
|
|
BN_init(&a);
|
|
BN_init(&b);
|
|
BN_init(&c);
|
|
BN_init(&d);
|
|
BN_init(&e);
|
|
|
|
for (i=0; i<num0+num1; i++)
|
|
{
|
|
if (i < num1)
|
|
{
|
|
BN_bntest_rand(&a,400,0,0);
|
|
BN_copy(&b,&a);
|
|
BN_lshift(&a,&a,i);
|
|
BN_add_word(&a,i);
|
|
}
|
|
else
|
|
BN_bntest_rand(&b,50+3*(i-num1),0,0);
|
|
a.neg=rand_neg();
|
|
b.neg=rand_neg();
|
|
BN_RECP_CTX_set(&recp,&b,ctx);
|
|
BN_div_recp(&d,&c,&a,&recp,ctx);
|
|
if (bp != NULL)
|
|
{
|
|
if (!results)
|
|
{
|
|
BN_print(bp,&a);
|
|
BIO_puts(bp," / ");
|
|
BN_print(bp,&b);
|
|
BIO_puts(bp," - ");
|
|
}
|
|
BN_print(bp,&d);
|
|
BIO_puts(bp,"\n");
|
|
|
|
if (!results)
|
|
{
|
|
BN_print(bp,&a);
|
|
BIO_puts(bp," % ");
|
|
BN_print(bp,&b);
|
|
BIO_puts(bp," - ");
|
|
}
|
|
BN_print(bp,&c);
|
|
BIO_puts(bp,"\n");
|
|
}
|
|
BN_mul(&e,&d,&b,ctx);
|
|
BN_add(&d,&e,&c);
|
|
BN_sub(&d,&d,&a);
|
|
if(!BN_is_zero(&d))
|
|
{
|
|
fprintf(stderr,"Reciprocal division test failed!\n");
|
|
fprintf(stderr,"a=");
|
|
BN_print_fp(stderr,&a);
|
|
fprintf(stderr,"\nb=");
|
|
BN_print_fp(stderr,&b);
|
|
fprintf(stderr,"\n");
|
|
return 0;
|
|
}
|
|
}
|
|
BN_free(&a);
|
|
BN_free(&b);
|
|
BN_free(&c);
|
|
BN_free(&d);
|
|
BN_free(&e);
|
|
BN_RECP_CTX_free(&recp);
|
|
return(1);
|
|
}
|
|
|
|
int test_mul(BIO *bp)
|
|
{
|
|
BIGNUM a,b,c,d,e;
|
|
int i;
|
|
BN_CTX *ctx;
|
|
|
|
ctx = BN_CTX_new();
|
|
if (ctx == NULL) EXIT(1);
|
|
|
|
BN_init(&a);
|
|
BN_init(&b);
|
|
BN_init(&c);
|
|
BN_init(&d);
|
|
BN_init(&e);
|
|
|
|
for (i=0; i<num0+num1; i++)
|
|
{
|
|
if (i <= num1)
|
|
{
|
|
BN_bntest_rand(&a,100,0,0);
|
|
BN_bntest_rand(&b,100,0,0);
|
|
}
|
|
else
|
|
BN_bntest_rand(&b,i-num1,0,0);
|
|
a.neg=rand_neg();
|
|
b.neg=rand_neg();
|
|
BN_mul(&c,&a,&b,ctx);
|
|
if (bp != NULL)
|
|
{
|
|
if (!results)
|
|
{
|
|
BN_print(bp,&a);
|
|
BIO_puts(bp," * ");
|
|
BN_print(bp,&b);
|
|
BIO_puts(bp," - ");
|
|
}
|
|
BN_print(bp,&c);
|
|
BIO_puts(bp,"\n");
|
|
}
|
|
BN_div(&d,&e,&c,&a,ctx);
|
|
BN_sub(&d,&d,&b);
|
|
if(!BN_is_zero(&d) || !BN_is_zero(&e))
|
|
{
|
|
fprintf(stderr,"Multiplication test failed!\n");
|
|
return 0;
|
|
}
|
|
}
|
|
BN_free(&a);
|
|
BN_free(&b);
|
|
BN_free(&c);
|
|
BN_free(&d);
|
|
BN_free(&e);
|
|
BN_CTX_free(ctx);
|
|
return(1);
|
|
}
|
|
|
|
int test_sqr(BIO *bp, BN_CTX *ctx)
|
|
{
|
|
BIGNUM a,c,d,e;
|
|
int i;
|
|
|
|
BN_init(&a);
|
|
BN_init(&c);
|
|
BN_init(&d);
|
|
BN_init(&e);
|
|
|
|
for (i=0; i<num0; i++)
|
|
{
|
|
BN_bntest_rand(&a,40+i*10,0,0);
|
|
a.neg=rand_neg();
|
|
BN_sqr(&c,&a,ctx);
|
|
if (bp != NULL)
|
|
{
|
|
if (!results)
|
|
{
|
|
BN_print(bp,&a);
|
|
BIO_puts(bp," * ");
|
|
BN_print(bp,&a);
|
|
BIO_puts(bp," - ");
|
|
}
|
|
BN_print(bp,&c);
|
|
BIO_puts(bp,"\n");
|
|
}
|
|
BN_div(&d,&e,&c,&a,ctx);
|
|
BN_sub(&d,&d,&a);
|
|
if(!BN_is_zero(&d) || !BN_is_zero(&e))
|
|
{
|
|
fprintf(stderr,"Square test failed!\n");
|
|
return 0;
|
|
}
|
|
}
|
|
BN_free(&a);
|
|
BN_free(&c);
|
|
BN_free(&d);
|
|
BN_free(&e);
|
|
return(1);
|
|
}
|
|
|
|
int test_mont(BIO *bp, BN_CTX *ctx)
|
|
{
|
|
BIGNUM a,b,c,d,A,B;
|
|
BIGNUM n;
|
|
int i;
|
|
BN_MONT_CTX *mont;
|
|
|
|
BN_init(&a);
|
|
BN_init(&b);
|
|
BN_init(&c);
|
|
BN_init(&d);
|
|
BN_init(&A);
|
|
BN_init(&B);
|
|
BN_init(&n);
|
|
|
|
mont=BN_MONT_CTX_new();
|
|
if (mont == NULL)
|
|
return 0;
|
|
|
|
BN_bntest_rand(&a,100,0,0); /**/
|
|
BN_bntest_rand(&b,100,0,0); /**/
|
|
for (i=0; i<num2; i++)
|
|
{
|
|
int bits = (200*(i+1))/num2;
|
|
|
|
if (bits == 0)
|
|
continue;
|
|
BN_bntest_rand(&n,bits,0,1);
|
|
BN_MONT_CTX_set(mont,&n,ctx);
|
|
|
|
BN_nnmod(&a,&a,&n,ctx);
|
|
BN_nnmod(&b,&b,&n,ctx);
|
|
|
|
BN_to_montgomery(&A,&a,mont,ctx);
|
|
BN_to_montgomery(&B,&b,mont,ctx);
|
|
|
|
BN_mod_mul_montgomery(&c,&A,&B,mont,ctx);/**/
|
|
BN_from_montgomery(&A,&c,mont,ctx);/**/
|
|
if (bp != NULL)
|
|
{
|
|
if (!results)
|
|
{
|
|
#ifdef undef
|
|
fprintf(stderr,"%d * %d %% %d\n",
|
|
BN_num_bits(&a),
|
|
BN_num_bits(&b),
|
|
BN_num_bits(mont->N));
|
|
#endif
|
|
BN_print(bp,&a);
|
|
BIO_puts(bp," * ");
|
|
BN_print(bp,&b);
|
|
BIO_puts(bp," % ");
|
|
BN_print(bp,&(mont->N));
|
|
BIO_puts(bp," - ");
|
|
}
|
|
BN_print(bp,&A);
|
|
BIO_puts(bp,"\n");
|
|
}
|
|
BN_mod_mul(&d,&a,&b,&n,ctx);
|
|
BN_sub(&d,&d,&A);
|
|
if(!BN_is_zero(&d))
|
|
{
|
|
fprintf(stderr,"Montgomery multiplication test failed!\n");
|
|
return 0;
|
|
}
|
|
}
|
|
BN_MONT_CTX_free(mont);
|
|
BN_free(&a);
|
|
BN_free(&b);
|
|
BN_free(&c);
|
|
BN_free(&d);
|
|
BN_free(&A);
|
|
BN_free(&B);
|
|
BN_free(&n);
|
|
return(1);
|
|
}
|
|
|
|
int test_mod(BIO *bp, BN_CTX *ctx)
|
|
{
|
|
BIGNUM *a,*b,*c,*d,*e;
|
|
int i;
|
|
|
|
a=BN_new();
|
|
b=BN_new();
|
|
c=BN_new();
|
|
d=BN_new();
|
|
e=BN_new();
|
|
|
|
BN_bntest_rand(a,1024,0,0); /**/
|
|
for (i=0; i<num0; i++)
|
|
{
|
|
BN_bntest_rand(b,450+i*10,0,0); /**/
|
|
a->neg=rand_neg();
|
|
b->neg=rand_neg();
|
|
BN_mod(c,a,b,ctx);/**/
|
|
if (bp != NULL)
|
|
{
|
|
if (!results)
|
|
{
|
|
BN_print(bp,a);
|
|
BIO_puts(bp," % ");
|
|
BN_print(bp,b);
|
|
BIO_puts(bp," - ");
|
|
}
|
|
BN_print(bp,c);
|
|
BIO_puts(bp,"\n");
|
|
}
|
|
BN_div(d,e,a,b,ctx);
|
|
BN_sub(e,e,c);
|
|
if(!BN_is_zero(e))
|
|
{
|
|
fprintf(stderr,"Modulo test failed!\n");
|
|
return 0;
|
|
}
|
|
}
|
|
BN_free(a);
|
|
BN_free(b);
|
|
BN_free(c);
|
|
BN_free(d);
|
|
BN_free(e);
|
|
return(1);
|
|
}
|
|
|
|
int test_mod_mul(BIO *bp, BN_CTX *ctx)
|
|
{
|
|
BIGNUM *a,*b,*c,*d,*e;
|
|
int i,j;
|
|
|
|
a=BN_new();
|
|
b=BN_new();
|
|
c=BN_new();
|
|
d=BN_new();
|
|
e=BN_new();
|
|
|
|
for (j=0; j<3; j++) {
|
|
BN_bntest_rand(c,1024,0,0); /**/
|
|
for (i=0; i<num0; i++)
|
|
{
|
|
BN_bntest_rand(a,475+i*10,0,0); /**/
|
|
BN_bntest_rand(b,425+i*11,0,0); /**/
|
|
a->neg=rand_neg();
|
|
b->neg=rand_neg();
|
|
if (!BN_mod_mul(e,a,b,c,ctx))
|
|
{
|
|
unsigned long l;
|
|
|
|
while ((l=ERR_get_error()))
|
|
fprintf(stderr,"ERROR:%s\n",
|
|
ERR_error_string(l,NULL));
|
|
EXIT(1);
|
|
}
|
|
if (bp != NULL)
|
|
{
|
|
if (!results)
|
|
{
|
|
BN_print(bp,a);
|
|
BIO_puts(bp," * ");
|
|
BN_print(bp,b);
|
|
BIO_puts(bp," % ");
|
|
BN_print(bp,c);
|
|
if ((a->neg ^ b->neg) && !BN_is_zero(e))
|
|
{
|
|
/* If (a*b) % c is negative, c must be added
|
|
* in order to obtain the normalized remainder
|
|
* (new with OpenSSL 0.9.7, previous versions of
|
|
* BN_mod_mul could generate negative results)
|
|
*/
|
|
BIO_puts(bp," + ");
|
|
BN_print(bp,c);
|
|
}
|
|
BIO_puts(bp," - ");
|
|
}
|
|
BN_print(bp,e);
|
|
BIO_puts(bp,"\n");
|
|
}
|
|
BN_mul(d,a,b,ctx);
|
|
BN_sub(d,d,e);
|
|
BN_div(a,b,d,c,ctx);
|
|
if(!BN_is_zero(b))
|
|
{
|
|
fprintf(stderr,"Modulo multiply test failed!\n");
|
|
ERR_print_errors_fp(stderr);
|
|
return 0;
|
|
}
|
|
}
|
|
}
|
|
BN_free(a);
|
|
BN_free(b);
|
|
BN_free(c);
|
|
BN_free(d);
|
|
BN_free(e);
|
|
return(1);
|
|
}
|
|
|
|
int test_mod_exp(BIO *bp, BN_CTX *ctx)
|
|
{
|
|
BIGNUM *a,*b,*c,*d,*e;
|
|
int i;
|
|
|
|
a=BN_new();
|
|
b=BN_new();
|
|
c=BN_new();
|
|
d=BN_new();
|
|
e=BN_new();
|
|
|
|
BN_bntest_rand(c,30,0,1); /* must be odd for montgomery */
|
|
for (i=0; i<num2; i++)
|
|
{
|
|
BN_bntest_rand(a,20+i*5,0,0); /**/
|
|
BN_bntest_rand(b,2+i,0,0); /**/
|
|
|
|
if (!BN_mod_exp(d,a,b,c,ctx))
|
|
return(0);
|
|
|
|
if (bp != NULL)
|
|
{
|
|
if (!results)
|
|
{
|
|
BN_print(bp,a);
|
|
BIO_puts(bp," ^ ");
|
|
BN_print(bp,b);
|
|
BIO_puts(bp," % ");
|
|
BN_print(bp,c);
|
|
BIO_puts(bp," - ");
|
|
}
|
|
BN_print(bp,d);
|
|
BIO_puts(bp,"\n");
|
|
}
|
|
BN_exp(e,a,b,ctx);
|
|
BN_sub(e,e,d);
|
|
BN_div(a,b,e,c,ctx);
|
|
if(!BN_is_zero(b))
|
|
{
|
|
fprintf(stderr,"Modulo exponentiation test failed!\n");
|
|
return 0;
|
|
}
|
|
}
|
|
BN_free(a);
|
|
BN_free(b);
|
|
BN_free(c);
|
|
BN_free(d);
|
|
BN_free(e);
|
|
return(1);
|
|
}
|
|
|
|
int test_mod_exp_mont_consttime(BIO *bp, BN_CTX *ctx)
|
|
{
|
|
BIGNUM *a,*b,*c,*d,*e;
|
|
int i;
|
|
|
|
a=BN_new();
|
|
b=BN_new();
|
|
c=BN_new();
|
|
d=BN_new();
|
|
e=BN_new();
|
|
|
|
BN_bntest_rand(c,30,0,1); /* must be odd for montgomery */
|
|
for (i=0; i<num2; i++)
|
|
{
|
|
BN_bntest_rand(a,20+i*5,0,0); /**/
|
|
BN_bntest_rand(b,2+i,0,0); /**/
|
|
|
|
if (!BN_mod_exp_mont_consttime(d,a,b,c,ctx,NULL))
|
|
return(00);
|
|
|
|
if (bp != NULL)
|
|
{
|
|
if (!results)
|
|
{
|
|
BN_print(bp,a);
|
|
BIO_puts(bp," ^ ");
|
|
BN_print(bp,b);
|
|
BIO_puts(bp," % ");
|
|
BN_print(bp,c);
|
|
BIO_puts(bp," - ");
|
|
}
|
|
BN_print(bp,d);
|
|
BIO_puts(bp,"\n");
|
|
}
|
|
BN_exp(e,a,b,ctx);
|
|
BN_sub(e,e,d);
|
|
BN_div(a,b,e,c,ctx);
|
|
if(!BN_is_zero(b))
|
|
{
|
|
fprintf(stderr,"Modulo exponentiation test failed!\n");
|
|
return 0;
|
|
}
|
|
}
|
|
BN_free(a);
|
|
BN_free(b);
|
|
BN_free(c);
|
|
BN_free(d);
|
|
BN_free(e);
|
|
return(1);
|
|
}
|
|
|
|
int test_exp(BIO *bp, BN_CTX *ctx)
|
|
{
|
|
BIGNUM *a,*b,*d,*e,*one;
|
|
int i;
|
|
|
|
a=BN_new();
|
|
b=BN_new();
|
|
d=BN_new();
|
|
e=BN_new();
|
|
one=BN_new();
|
|
BN_one(one);
|
|
|
|
for (i=0; i<num2; i++)
|
|
{
|
|
BN_bntest_rand(a,20+i*5,0,0); /**/
|
|
BN_bntest_rand(b,2+i,0,0); /**/
|
|
|
|
if (BN_exp(d,a,b,ctx) <= 0)
|
|
return(0);
|
|
|
|
if (bp != NULL)
|
|
{
|
|
if (!results)
|
|
{
|
|
BN_print(bp,a);
|
|
BIO_puts(bp," ^ ");
|
|
BN_print(bp,b);
|
|
BIO_puts(bp," - ");
|
|
}
|
|
BN_print(bp,d);
|
|
BIO_puts(bp,"\n");
|
|
}
|
|
BN_one(e);
|
|
for( ; !BN_is_zero(b) ; BN_sub(b,b,one))
|
|
BN_mul(e,e,a,ctx);
|
|
BN_sub(e,e,d);
|
|
if(!BN_is_zero(e))
|
|
{
|
|
fprintf(stderr,"Exponentiation test failed!\n");
|
|
return 0;
|
|
}
|
|
}
|
|
BN_free(a);
|
|
BN_free(b);
|
|
BN_free(d);
|
|
BN_free(e);
|
|
BN_free(one);
|
|
return(1);
|
|
}
|
|
|
|
int test_gf2m_add(BIO *bp)
|
|
{
|
|
BIGNUM a,b,c;
|
|
int i, ret = 0;
|
|
|
|
BN_init(&a);
|
|
BN_init(&b);
|
|
BN_init(&c);
|
|
|
|
for (i=0; i<num0; i++)
|
|
{
|
|
BN_rand(&a,512,0,0);
|
|
BN_copy(&b, BN_value_one());
|
|
a.neg=rand_neg();
|
|
b.neg=rand_neg();
|
|
BN_GF2m_add(&c,&a,&b);
|
|
#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
|
|
if (bp != NULL)
|
|
{
|
|
if (!results)
|
|
{
|
|
BN_print(bp,&a);
|
|
BIO_puts(bp," ^ ");
|
|
BN_print(bp,&b);
|
|
BIO_puts(bp," = ");
|
|
}
|
|
BN_print(bp,&c);
|
|
BIO_puts(bp,"\n");
|
|
}
|
|
#endif
|
|
/* Test that two added values have the correct parity. */
|
|
if((BN_is_odd(&a) && BN_is_odd(&c)) || (!BN_is_odd(&a) && !BN_is_odd(&c)))
|
|
{
|
|
fprintf(stderr,"GF(2^m) addition test (a) failed!\n");
|
|
goto err;
|
|
}
|
|
BN_GF2m_add(&c,&c,&c);
|
|
/* Test that c + c = 0. */
|
|
if(!BN_is_zero(&c))
|
|
{
|
|
fprintf(stderr,"GF(2^m) addition test (b) failed!\n");
|
|
goto err;
|
|
}
|
|
}
|
|
ret = 1;
|
|
err:
|
|
BN_free(&a);
|
|
BN_free(&b);
|
|
BN_free(&c);
|
|
return ret;
|
|
}
|
|
|
|
int test_gf2m_mod(BIO *bp)
|
|
{
|
|
BIGNUM *a,*b[2],*c,*d,*e;
|
|
int i, j, ret = 0;
|
|
int p0[] = {163,7,6,3,0,-1};
|
|
int p1[] = {193,15,0,-1};
|
|
|
|
a=BN_new();
|
|
b[0]=BN_new();
|
|
b[1]=BN_new();
|
|
c=BN_new();
|
|
d=BN_new();
|
|
e=BN_new();
|
|
|
|
BN_GF2m_arr2poly(p0, b[0]);
|
|
BN_GF2m_arr2poly(p1, b[1]);
|
|
|
|
for (i=0; i<num0; i++)
|
|
{
|
|
BN_bntest_rand(a, 1024, 0, 0);
|
|
for (j=0; j < 2; j++)
|
|
{
|
|
BN_GF2m_mod(c, a, b[j]);
|
|
#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
|
|
if (bp != NULL)
|
|
{
|
|
if (!results)
|
|
{
|
|
BN_print(bp,a);
|
|
BIO_puts(bp," % ");
|
|
BN_print(bp,b[j]);
|
|
BIO_puts(bp," - ");
|
|
BN_print(bp,c);
|
|
BIO_puts(bp,"\n");
|
|
}
|
|
}
|
|
#endif
|
|
BN_GF2m_add(d, a, c);
|
|
BN_GF2m_mod(e, d, b[j]);
|
|
/* Test that a + (a mod p) mod p == 0. */
|
|
if(!BN_is_zero(e))
|
|
{
|
|
fprintf(stderr,"GF(2^m) modulo test failed!\n");
|
|
goto err;
|
|
}
|
|
}
|
|
}
|
|
ret = 1;
|
|
err:
|
|
BN_free(a);
|
|
BN_free(b[0]);
|
|
BN_free(b[1]);
|
|
BN_free(c);
|
|
BN_free(d);
|
|
BN_free(e);
|
|
return ret;
|
|
}
|
|
|
|
int test_gf2m_mod_mul(BIO *bp,BN_CTX *ctx)
|
|
{
|
|
BIGNUM *a,*b[2],*c,*d,*e,*f,*g,*h;
|
|
int i, j, ret = 0;
|
|
int p0[] = {163,7,6,3,0,-1};
|
|
int p1[] = {193,15,0,-1};
|
|
|
|
a=BN_new();
|
|
b[0]=BN_new();
|
|
b[1]=BN_new();
|
|
c=BN_new();
|
|
d=BN_new();
|
|
e=BN_new();
|
|
f=BN_new();
|
|
g=BN_new();
|
|
h=BN_new();
|
|
|
|
BN_GF2m_arr2poly(p0, b[0]);
|
|
BN_GF2m_arr2poly(p1, b[1]);
|
|
|
|
for (i=0; i<num0; i++)
|
|
{
|
|
BN_bntest_rand(a, 1024, 0, 0);
|
|
BN_bntest_rand(c, 1024, 0, 0);
|
|
BN_bntest_rand(d, 1024, 0, 0);
|
|
for (j=0; j < 2; j++)
|
|
{
|
|
BN_GF2m_mod_mul(e, a, c, b[j], ctx);
|
|
#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
|
|
if (bp != NULL)
|
|
{
|
|
if (!results)
|
|
{
|
|
BN_print(bp,a);
|
|
BIO_puts(bp," * ");
|
|
BN_print(bp,c);
|
|
BIO_puts(bp," % ");
|
|
BN_print(bp,b[j]);
|
|
BIO_puts(bp," - ");
|
|
BN_print(bp,e);
|
|
BIO_puts(bp,"\n");
|
|
}
|
|
}
|
|
#endif
|
|
BN_GF2m_add(f, a, d);
|
|
BN_GF2m_mod_mul(g, f, c, b[j], ctx);
|
|
BN_GF2m_mod_mul(h, d, c, b[j], ctx);
|
|
BN_GF2m_add(f, e, g);
|
|
BN_GF2m_add(f, f, h);
|
|
/* Test that (a+d)*c = a*c + d*c. */
|
|
if(!BN_is_zero(f))
|
|
{
|
|
fprintf(stderr,"GF(2^m) modular multiplication test failed!\n");
|
|
goto err;
|
|
}
|
|
}
|
|
}
|
|
ret = 1;
|
|
err:
|
|
BN_free(a);
|
|
BN_free(b[0]);
|
|
BN_free(b[1]);
|
|
BN_free(c);
|
|
BN_free(d);
|
|
BN_free(e);
|
|
BN_free(f);
|
|
BN_free(g);
|
|
BN_free(h);
|
|
return ret;
|
|
}
|
|
|
|
int test_gf2m_mod_sqr(BIO *bp,BN_CTX *ctx)
|
|
{
|
|
BIGNUM *a,*b[2],*c,*d;
|
|
int i, j, ret = 0;
|
|
int p0[] = {163,7,6,3,0,-1};
|
|
int p1[] = {193,15,0,-1};
|
|
|
|
a=BN_new();
|
|
b[0]=BN_new();
|
|
b[1]=BN_new();
|
|
c=BN_new();
|
|
d=BN_new();
|
|
|
|
BN_GF2m_arr2poly(p0, b[0]);
|
|
BN_GF2m_arr2poly(p1, b[1]);
|
|
|
|
for (i=0; i<num0; i++)
|
|
{
|
|
BN_bntest_rand(a, 1024, 0, 0);
|
|
for (j=0; j < 2; j++)
|
|
{
|
|
BN_GF2m_mod_sqr(c, a, b[j], ctx);
|
|
BN_copy(d, a);
|
|
BN_GF2m_mod_mul(d, a, d, b[j], ctx);
|
|
#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
|
|
if (bp != NULL)
|
|
{
|
|
if (!results)
|
|
{
|
|
BN_print(bp,a);
|
|
BIO_puts(bp," ^ 2 % ");
|
|
BN_print(bp,b[j]);
|
|
BIO_puts(bp, " = ");
|
|
BN_print(bp,c);
|
|
BIO_puts(bp,"; a * a = ");
|
|
BN_print(bp,d);
|
|
BIO_puts(bp,"\n");
|
|
}
|
|
}
|
|
#endif
|
|
BN_GF2m_add(d, c, d);
|
|
/* Test that a*a = a^2. */
|
|
if(!BN_is_zero(d))
|
|
{
|
|
fprintf(stderr,"GF(2^m) modular squaring test failed!\n");
|
|
goto err;
|
|
}
|
|
}
|
|
}
|
|
ret = 1;
|
|
err:
|
|
BN_free(a);
|
|
BN_free(b[0]);
|
|
BN_free(b[1]);
|
|
BN_free(c);
|
|
BN_free(d);
|
|
return ret;
|
|
}
|
|
|
|
int test_gf2m_mod_inv(BIO *bp,BN_CTX *ctx)
|
|
{
|
|
BIGNUM *a,*b[2],*c,*d;
|
|
int i, j, ret = 0;
|
|
int p0[] = {163,7,6,3,0,-1};
|
|
int p1[] = {193,15,0,-1};
|
|
|
|
a=BN_new();
|
|
b[0]=BN_new();
|
|
b[1]=BN_new();
|
|
c=BN_new();
|
|
d=BN_new();
|
|
|
|
BN_GF2m_arr2poly(p0, b[0]);
|
|
BN_GF2m_arr2poly(p1, b[1]);
|
|
|
|
for (i=0; i<num0; i++)
|
|
{
|
|
BN_bntest_rand(a, 512, 0, 0);
|
|
for (j=0; j < 2; j++)
|
|
{
|
|
BN_GF2m_mod_inv(c, a, b[j], ctx);
|
|
BN_GF2m_mod_mul(d, a, c, b[j], ctx);
|
|
#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
|
|
if (bp != NULL)
|
|
{
|
|
if (!results)
|
|
{
|
|
BN_print(bp,a);
|
|
BIO_puts(bp, " * ");
|
|
BN_print(bp,c);
|
|
BIO_puts(bp," - 1 % ");
|
|
BN_print(bp,b[j]);
|
|
BIO_puts(bp,"\n");
|
|
}
|
|
}
|
|
#endif
|
|
/* Test that ((1/a)*a) = 1. */
|
|
if(!BN_is_one(d))
|
|
{
|
|
fprintf(stderr,"GF(2^m) modular inversion test failed!\n");
|
|
goto err;
|
|
}
|
|
}
|
|
}
|
|
ret = 1;
|
|
err:
|
|
BN_free(a);
|
|
BN_free(b[0]);
|
|
BN_free(b[1]);
|
|
BN_free(c);
|
|
BN_free(d);
|
|
return ret;
|
|
}
|
|
|
|
int test_gf2m_mod_div(BIO *bp,BN_CTX *ctx)
|
|
{
|
|
BIGNUM *a,*b[2],*c,*d,*e,*f;
|
|
int i, j, ret = 0;
|
|
int p0[] = {163,7,6,3,0,-1};
|
|
int p1[] = {193,15,0,-1};
|
|
|
|
a=BN_new();
|
|
b[0]=BN_new();
|
|
b[1]=BN_new();
|
|
c=BN_new();
|
|
d=BN_new();
|
|
e=BN_new();
|
|
f=BN_new();
|
|
|
|
BN_GF2m_arr2poly(p0, b[0]);
|
|
BN_GF2m_arr2poly(p1, b[1]);
|
|
|
|
for (i=0; i<num0; i++)
|
|
{
|
|
BN_bntest_rand(a, 512, 0, 0);
|
|
BN_bntest_rand(c, 512, 0, 0);
|
|
for (j=0; j < 2; j++)
|
|
{
|
|
BN_GF2m_mod_div(d, a, c, b[j], ctx);
|
|
BN_GF2m_mod_mul(e, d, c, b[j], ctx);
|
|
BN_GF2m_mod_div(f, a, e, b[j], ctx);
|
|
#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
|
|
if (bp != NULL)
|
|
{
|
|
if (!results)
|
|
{
|
|
BN_print(bp,a);
|
|
BIO_puts(bp, " = ");
|
|
BN_print(bp,c);
|
|
BIO_puts(bp," * ");
|
|
BN_print(bp,d);
|
|
BIO_puts(bp, " % ");
|
|
BN_print(bp,b[j]);
|
|
BIO_puts(bp,"\n");
|
|
}
|
|
}
|
|
#endif
|
|
/* Test that ((a/c)*c)/a = 1. */
|
|
if(!BN_is_one(f))
|
|
{
|
|
fprintf(stderr,"GF(2^m) modular division test failed!\n");
|
|
goto err;
|
|
}
|
|
}
|
|
}
|
|
ret = 1;
|
|
err:
|
|
BN_free(a);
|
|
BN_free(b[0]);
|
|
BN_free(b[1]);
|
|
BN_free(c);
|
|
BN_free(d);
|
|
BN_free(e);
|
|
BN_free(f);
|
|
return ret;
|
|
}
|
|
|
|
int test_gf2m_mod_exp(BIO *bp,BN_CTX *ctx)
|
|
{
|
|
BIGNUM *a,*b[2],*c,*d,*e,*f;
|
|
int i, j, ret = 0;
|
|
int p0[] = {163,7,6,3,0,-1};
|
|
int p1[] = {193,15,0,-1};
|
|
|
|
a=BN_new();
|
|
b[0]=BN_new();
|
|
b[1]=BN_new();
|
|
c=BN_new();
|
|
d=BN_new();
|
|
e=BN_new();
|
|
f=BN_new();
|
|
|
|
BN_GF2m_arr2poly(p0, b[0]);
|
|
BN_GF2m_arr2poly(p1, b[1]);
|
|
|
|
for (i=0; i<num0; i++)
|
|
{
|
|
BN_bntest_rand(a, 512, 0, 0);
|
|
BN_bntest_rand(c, 512, 0, 0);
|
|
BN_bntest_rand(d, 512, 0, 0);
|
|
for (j=0; j < 2; j++)
|
|
{
|
|
BN_GF2m_mod_exp(e, a, c, b[j], ctx);
|
|
BN_GF2m_mod_exp(f, a, d, b[j], ctx);
|
|
BN_GF2m_mod_mul(e, e, f, b[j], ctx);
|
|
BN_add(f, c, d);
|
|
BN_GF2m_mod_exp(f, a, f, b[j], ctx);
|
|
#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
|
|
if (bp != NULL)
|
|
{
|
|
if (!results)
|
|
{
|
|
BN_print(bp,a);
|
|
BIO_puts(bp, " ^ (");
|
|
BN_print(bp,c);
|
|
BIO_puts(bp," + ");
|
|
BN_print(bp,d);
|
|
BIO_puts(bp, ") = ");
|
|
BN_print(bp,e);
|
|
BIO_puts(bp, "; - ");
|
|
BN_print(bp,f);
|
|
BIO_puts(bp, " % ");
|
|
BN_print(bp,b[j]);
|
|
BIO_puts(bp,"\n");
|
|
}
|
|
}
|
|
#endif
|
|
BN_GF2m_add(f, e, f);
|
|
/* Test that a^(c+d)=a^c*a^d. */
|
|
if(!BN_is_zero(f))
|
|
{
|
|
fprintf(stderr,"GF(2^m) modular exponentiation test failed!\n");
|
|
goto err;
|
|
}
|
|
}
|
|
}
|
|
ret = 1;
|
|
err:
|
|
BN_free(a);
|
|
BN_free(b[0]);
|
|
BN_free(b[1]);
|
|
BN_free(c);
|
|
BN_free(d);
|
|
BN_free(e);
|
|
BN_free(f);
|
|
return ret;
|
|
}
|
|
|
|
int test_gf2m_mod_sqrt(BIO *bp,BN_CTX *ctx)
|
|
{
|
|
BIGNUM *a,*b[2],*c,*d,*e,*f;
|
|
int i, j, ret = 0;
|
|
int p0[] = {163,7,6,3,0,-1};
|
|
int p1[] = {193,15,0,-1};
|
|
|
|
a=BN_new();
|
|
b[0]=BN_new();
|
|
b[1]=BN_new();
|
|
c=BN_new();
|
|
d=BN_new();
|
|
e=BN_new();
|
|
f=BN_new();
|
|
|
|
BN_GF2m_arr2poly(p0, b[0]);
|
|
BN_GF2m_arr2poly(p1, b[1]);
|
|
|
|
for (i=0; i<num0; i++)
|
|
{
|
|
BN_bntest_rand(a, 512, 0, 0);
|
|
for (j=0; j < 2; j++)
|
|
{
|
|
BN_GF2m_mod(c, a, b[j]);
|
|
BN_GF2m_mod_sqrt(d, a, b[j], ctx);
|
|
BN_GF2m_mod_sqr(e, d, b[j], ctx);
|
|
#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
|
|
if (bp != NULL)
|
|
{
|
|
if (!results)
|
|
{
|
|
BN_print(bp,d);
|
|
BIO_puts(bp, " ^ 2 - ");
|
|
BN_print(bp,a);
|
|
BIO_puts(bp,"\n");
|
|
}
|
|
}
|
|
#endif
|
|
BN_GF2m_add(f, c, e);
|
|
/* Test that d^2 = a, where d = sqrt(a). */
|
|
if(!BN_is_zero(f))
|
|
{
|
|
fprintf(stderr,"GF(2^m) modular square root test failed!\n");
|
|
goto err;
|
|
}
|
|
}
|
|
}
|
|
ret = 1;
|
|
err:
|
|
BN_free(a);
|
|
BN_free(b[0]);
|
|
BN_free(b[1]);
|
|
BN_free(c);
|
|
BN_free(d);
|
|
BN_free(e);
|
|
BN_free(f);
|
|
return ret;
|
|
}
|
|
|
|
int test_gf2m_mod_solve_quad(BIO *bp,BN_CTX *ctx)
|
|
{
|
|
BIGNUM *a,*b[2],*c,*d,*e;
|
|
int i, j, s = 0, t, ret = 0;
|
|
int p0[] = {163,7,6,3,0,-1};
|
|
int p1[] = {193,15,0,-1};
|
|
|
|
a=BN_new();
|
|
b[0]=BN_new();
|
|
b[1]=BN_new();
|
|
c=BN_new();
|
|
d=BN_new();
|
|
e=BN_new();
|
|
|
|
BN_GF2m_arr2poly(p0, b[0]);
|
|
BN_GF2m_arr2poly(p1, b[1]);
|
|
|
|
for (i=0; i<num0; i++)
|
|
{
|
|
BN_bntest_rand(a, 512, 0, 0);
|
|
for (j=0; j < 2; j++)
|
|
{
|
|
t = BN_GF2m_mod_solve_quad(c, a, b[j], ctx);
|
|
if (t)
|
|
{
|
|
s++;
|
|
BN_GF2m_mod_sqr(d, c, b[j], ctx);
|
|
BN_GF2m_add(d, c, d);
|
|
BN_GF2m_mod(e, a, b[j]);
|
|
#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
|
|
if (bp != NULL)
|
|
{
|
|
if (!results)
|
|
{
|
|
BN_print(bp,c);
|
|
BIO_puts(bp, " is root of z^2 + z = ");
|
|
BN_print(bp,a);
|
|
BIO_puts(bp, " % ");
|
|
BN_print(bp,b[j]);
|
|
BIO_puts(bp, "\n");
|
|
}
|
|
}
|
|
#endif
|
|
BN_GF2m_add(e, e, d);
|
|
/* Test that solution of quadratic c satisfies c^2 + c = a. */
|
|
if(!BN_is_zero(e))
|
|
{
|
|
fprintf(stderr,"GF(2^m) modular solve quadratic test failed!\n");
|
|
goto err;
|
|
}
|
|
|
|
}
|
|
else
|
|
{
|
|
#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
|
|
if (bp != NULL)
|
|
{
|
|
if (!results)
|
|
{
|
|
BIO_puts(bp, "There are no roots of z^2 + z = ");
|
|
BN_print(bp,a);
|
|
BIO_puts(bp, " % ");
|
|
BN_print(bp,b[j]);
|
|
BIO_puts(bp, "\n");
|
|
}
|
|
}
|
|
#endif
|
|
}
|
|
}
|
|
}
|
|
if (s == 0)
|
|
{
|
|
fprintf(stderr,"All %i tests of GF(2^m) modular solve quadratic resulted in no roots;\n", num0);
|
|
fprintf(stderr,"this is very unlikely and probably indicates an error.\n");
|
|
goto err;
|
|
}
|
|
ret = 1;
|
|
err:
|
|
BN_free(a);
|
|
BN_free(b[0]);
|
|
BN_free(b[1]);
|
|
BN_free(c);
|
|
BN_free(d);
|
|
BN_free(e);
|
|
return ret;
|
|
}
|
|
|
|
static int genprime_cb(int p, int n, BN_GENCB *arg)
|
|
{
|
|
char c='*';
|
|
|
|
if (p == 0) c='.';
|
|
if (p == 1) c='+';
|
|
if (p == 2) c='*';
|
|
if (p == 3) c='\n';
|
|
putc(c, stderr);
|
|
fflush(stderr);
|
|
return 1;
|
|
}
|
|
|
|
int test_kron(BIO *bp, BN_CTX *ctx)
|
|
{
|
|
BN_GENCB cb;
|
|
BIGNUM *a,*b,*r,*t;
|
|
int i;
|
|
int legendre, kronecker;
|
|
int ret = 0;
|
|
|
|
a = BN_new();
|
|
b = BN_new();
|
|
r = BN_new();
|
|
t = BN_new();
|
|
if (a == NULL || b == NULL || r == NULL || t == NULL) goto err;
|
|
|
|
BN_GENCB_set(&cb, genprime_cb, NULL);
|
|
|
|
/* We test BN_kronecker(a, b, ctx) just for b odd (Jacobi symbol).
|
|
* In this case we know that if b is prime, then BN_kronecker(a, b, ctx)
|
|
* is congruent to $a^{(b-1)/2}$, modulo $b$ (Legendre symbol).
|
|
* So we generate a random prime b and compare these values
|
|
* for a number of random a's. (That is, we run the Solovay-Strassen
|
|
* primality test to confirm that b is prime, except that we
|
|
* don't want to test whether b is prime but whether BN_kronecker
|
|
* works.) */
|
|
|
|
if (!BN_generate_prime_ex(b, 512, 0, NULL, NULL, &cb)) goto err;
|
|
b->neg = rand_neg();
|
|
putc('\n', stderr);
|
|
|
|
for (i = 0; i < num0; i++)
|
|
{
|
|
if (!BN_bntest_rand(a, 512, 0, 0)) goto err;
|
|
a->neg = rand_neg();
|
|
|
|
/* t := (|b|-1)/2 (note that b is odd) */
|
|
if (!BN_copy(t, b)) goto err;
|
|
t->neg = 0;
|
|
if (!BN_sub_word(t, 1)) goto err;
|
|
if (!BN_rshift1(t, t)) goto err;
|
|
/* r := a^t mod b */
|
|
b->neg=0;
|
|
|
|
if (!BN_mod_exp_recp(r, a, t, b, ctx)) goto err;
|
|
b->neg=1;
|
|
|
|
if (BN_is_word(r, 1))
|
|
legendre = 1;
|
|
else if (BN_is_zero(r))
|
|
legendre = 0;
|
|
else
|
|
{
|
|
if (!BN_add_word(r, 1)) goto err;
|
|
if (0 != BN_ucmp(r, b))
|
|
{
|
|
fprintf(stderr, "Legendre symbol computation failed\n");
|
|
goto err;
|
|
}
|
|
legendre = -1;
|
|
}
|
|
|
|
kronecker = BN_kronecker(a, b, ctx);
|
|
if (kronecker < -1) goto err;
|
|
/* we actually need BN_kronecker(a, |b|) */
|
|
if (a->neg && b->neg)
|
|
kronecker = -kronecker;
|
|
|
|
if (legendre != kronecker)
|
|
{
|
|
fprintf(stderr, "legendre != kronecker; a = ");
|
|
BN_print_fp(stderr, a);
|
|
fprintf(stderr, ", b = ");
|
|
BN_print_fp(stderr, b);
|
|
fprintf(stderr, "\n");
|
|
goto err;
|
|
}
|
|
|
|
putc('.', stderr);
|
|
fflush(stderr);
|
|
}
|
|
|
|
putc('\n', stderr);
|
|
fflush(stderr);
|
|
ret = 1;
|
|
err:
|
|
if (a != NULL) BN_free(a);
|
|
if (b != NULL) BN_free(b);
|
|
if (r != NULL) BN_free(r);
|
|
if (t != NULL) BN_free(t);
|
|
return ret;
|
|
}
|
|
|
|
int test_sqrt(BIO *bp, BN_CTX *ctx)
|
|
{
|
|
BN_GENCB cb;
|
|
BIGNUM *a,*p,*r;
|
|
int i, j;
|
|
int ret = 0;
|
|
|
|
a = BN_new();
|
|
p = BN_new();
|
|
r = BN_new();
|
|
if (a == NULL || p == NULL || r == NULL) goto err;
|
|
|
|
BN_GENCB_set(&cb, genprime_cb, NULL);
|
|
|
|
for (i = 0; i < 16; i++)
|
|
{
|
|
if (i < 8)
|
|
{
|
|
unsigned primes[8] = { 2, 3, 5, 7, 11, 13, 17, 19 };
|
|
|
|
if (!BN_set_word(p, primes[i])) goto err;
|
|
}
|
|
else
|
|
{
|
|
if (!BN_set_word(a, 32)) goto err;
|
|
if (!BN_set_word(r, 2*i + 1)) goto err;
|
|
|
|
if (!BN_generate_prime_ex(p, 256, 0, a, r, &cb)) goto err;
|
|
putc('\n', stderr);
|
|
}
|
|
p->neg = rand_neg();
|
|
|
|
for (j = 0; j < num2; j++)
|
|
{
|
|
/* construct 'a' such that it is a square modulo p,
|
|
* but in general not a proper square and not reduced modulo p */
|
|
if (!BN_bntest_rand(r, 256, 0, 3)) goto err;
|
|
if (!BN_nnmod(r, r, p, ctx)) goto err;
|
|
if (!BN_mod_sqr(r, r, p, ctx)) goto err;
|
|
if (!BN_bntest_rand(a, 256, 0, 3)) goto err;
|
|
if (!BN_nnmod(a, a, p, ctx)) goto err;
|
|
if (!BN_mod_sqr(a, a, p, ctx)) goto err;
|
|
if (!BN_mul(a, a, r, ctx)) goto err;
|
|
if (rand_neg())
|
|
if (!BN_sub(a, a, p)) goto err;
|
|
|
|
if (!BN_mod_sqrt(r, a, p, ctx)) goto err;
|
|
if (!BN_mod_sqr(r, r, p, ctx)) goto err;
|
|
|
|
if (!BN_nnmod(a, a, p, ctx)) goto err;
|
|
|
|
if (BN_cmp(a, r) != 0)
|
|
{
|
|
fprintf(stderr, "BN_mod_sqrt failed: a = ");
|
|
BN_print_fp(stderr, a);
|
|
fprintf(stderr, ", r = ");
|
|
BN_print_fp(stderr, r);
|
|
fprintf(stderr, ", p = ");
|
|
BN_print_fp(stderr, p);
|
|
fprintf(stderr, "\n");
|
|
goto err;
|
|
}
|
|
|
|
putc('.', stderr);
|
|
fflush(stderr);
|
|
}
|
|
|
|
putc('\n', stderr);
|
|
fflush(stderr);
|
|
}
|
|
ret = 1;
|
|
err:
|
|
if (a != NULL) BN_free(a);
|
|
if (p != NULL) BN_free(p);
|
|
if (r != NULL) BN_free(r);
|
|
return ret;
|
|
}
|
|
|
|
int test_lshift(BIO *bp,BN_CTX *ctx,BIGNUM *a_)
|
|
{
|
|
BIGNUM *a,*b,*c,*d;
|
|
int i;
|
|
|
|
b=BN_new();
|
|
c=BN_new();
|
|
d=BN_new();
|
|
BN_one(c);
|
|
|
|
if(a_)
|
|
a=a_;
|
|
else
|
|
{
|
|
a=BN_new();
|
|
BN_bntest_rand(a,200,0,0); /**/
|
|
a->neg=rand_neg();
|
|
}
|
|
for (i=0; i<num0; i++)
|
|
{
|
|
BN_lshift(b,a,i+1);
|
|
BN_add(c,c,c);
|
|
if (bp != NULL)
|
|
{
|
|
if (!results)
|
|
{
|
|
BN_print(bp,a);
|
|
BIO_puts(bp," * ");
|
|
BN_print(bp,c);
|
|
BIO_puts(bp," - ");
|
|
}
|
|
BN_print(bp,b);
|
|
BIO_puts(bp,"\n");
|
|
}
|
|
BN_mul(d,a,c,ctx);
|
|
BN_sub(d,d,b);
|
|
if(!BN_is_zero(d))
|
|
{
|
|
fprintf(stderr,"Left shift test failed!\n");
|
|
fprintf(stderr,"a=");
|
|
BN_print_fp(stderr,a);
|
|
fprintf(stderr,"\nb=");
|
|
BN_print_fp(stderr,b);
|
|
fprintf(stderr,"\nc=");
|
|
BN_print_fp(stderr,c);
|
|
fprintf(stderr,"\nd=");
|
|
BN_print_fp(stderr,d);
|
|
fprintf(stderr,"\n");
|
|
return 0;
|
|
}
|
|
}
|
|
BN_free(a);
|
|
BN_free(b);
|
|
BN_free(c);
|
|
BN_free(d);
|
|
return(1);
|
|
}
|
|
|
|
int test_lshift1(BIO *bp)
|
|
{
|
|
BIGNUM *a,*b,*c;
|
|
int i;
|
|
|
|
a=BN_new();
|
|
b=BN_new();
|
|
c=BN_new();
|
|
|
|
BN_bntest_rand(a,200,0,0); /**/
|
|
a->neg=rand_neg();
|
|
for (i=0; i<num0; i++)
|
|
{
|
|
BN_lshift1(b,a);
|
|
if (bp != NULL)
|
|
{
|
|
if (!results)
|
|
{
|
|
BN_print(bp,a);
|
|
BIO_puts(bp," * 2");
|
|
BIO_puts(bp," - ");
|
|
}
|
|
BN_print(bp,b);
|
|
BIO_puts(bp,"\n");
|
|
}
|
|
BN_add(c,a,a);
|
|
BN_sub(a,b,c);
|
|
if(!BN_is_zero(a))
|
|
{
|
|
fprintf(stderr,"Left shift one test failed!\n");
|
|
return 0;
|
|
}
|
|
|
|
BN_copy(a,b);
|
|
}
|
|
BN_free(a);
|
|
BN_free(b);
|
|
BN_free(c);
|
|
return(1);
|
|
}
|
|
|
|
int test_rshift(BIO *bp,BN_CTX *ctx)
|
|
{
|
|
BIGNUM *a,*b,*c,*d,*e;
|
|
int i;
|
|
|
|
a=BN_new();
|
|
b=BN_new();
|
|
c=BN_new();
|
|
d=BN_new();
|
|
e=BN_new();
|
|
BN_one(c);
|
|
|
|
BN_bntest_rand(a,200,0,0); /**/
|
|
a->neg=rand_neg();
|
|
for (i=0; i<num0; i++)
|
|
{
|
|
BN_rshift(b,a,i+1);
|
|
BN_add(c,c,c);
|
|
if (bp != NULL)
|
|
{
|
|
if (!results)
|
|
{
|
|
BN_print(bp,a);
|
|
BIO_puts(bp," / ");
|
|
BN_print(bp,c);
|
|
BIO_puts(bp," - ");
|
|
}
|
|
BN_print(bp,b);
|
|
BIO_puts(bp,"\n");
|
|
}
|
|
BN_div(d,e,a,c,ctx);
|
|
BN_sub(d,d,b);
|
|
if(!BN_is_zero(d))
|
|
{
|
|
fprintf(stderr,"Right shift test failed!\n");
|
|
return 0;
|
|
}
|
|
}
|
|
BN_free(a);
|
|
BN_free(b);
|
|
BN_free(c);
|
|
BN_free(d);
|
|
BN_free(e);
|
|
return(1);
|
|
}
|
|
|
|
int test_rshift1(BIO *bp)
|
|
{
|
|
BIGNUM *a,*b,*c;
|
|
int i;
|
|
|
|
a=BN_new();
|
|
b=BN_new();
|
|
c=BN_new();
|
|
|
|
BN_bntest_rand(a,200,0,0); /**/
|
|
a->neg=rand_neg();
|
|
for (i=0; i<num0; i++)
|
|
{
|
|
BN_rshift1(b,a);
|
|
if (bp != NULL)
|
|
{
|
|
if (!results)
|
|
{
|
|
BN_print(bp,a);
|
|
BIO_puts(bp," / 2");
|
|
BIO_puts(bp," - ");
|
|
}
|
|
BN_print(bp,b);
|
|
BIO_puts(bp,"\n");
|
|
}
|
|
BN_sub(c,a,b);
|
|
BN_sub(c,c,b);
|
|
if(!BN_is_zero(c) && !BN_abs_is_word(c, 1))
|
|
{
|
|
fprintf(stderr,"Right shift one test failed!\n");
|
|
return 0;
|
|
}
|
|
BN_copy(a,b);
|
|
}
|
|
BN_free(a);
|
|
BN_free(b);
|
|
BN_free(c);
|
|
return(1);
|
|
}
|
|
|
|
int rand_neg(void)
|
|
{
|
|
static unsigned int neg=0;
|
|
static int sign[8]={0,0,0,1,1,0,1,1};
|
|
|
|
return(sign[(neg++)%8]);
|
|
}
|
|
|