2015 lines
51 KiB
C
2015 lines
51 KiB
C
/* 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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/*
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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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*/
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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[] =
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"\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[] =
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"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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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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if (--argc < 1)
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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)
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EXIT(1);
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out = BIO_new(BIO_s_file());
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if (out == NULL)
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EXIT(1);
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if (outfile == NULL) {
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BIO_set_fp(out, stdout, BIO_NOCLOSE);
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} else {
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if (!BIO_write_filename(out, outfile)) {
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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))
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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))
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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))
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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))
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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))
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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))
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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))
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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))
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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))
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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))
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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))
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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))
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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))
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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))
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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))
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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))
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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))
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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))
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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))
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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))
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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))
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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))
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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))
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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))
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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))
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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))
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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))
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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))
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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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EXIT(0);
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err:
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BIO_puts(out, "1\n"); /* make sure the Perl script fed by bc
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* notices the failure, see test_bn in
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* 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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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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if (!results) {
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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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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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if (i < num1) {
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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)
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return (0);
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BN_add_word(&b, i);
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} else {
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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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if (!results) {
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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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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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if (i < num1) {
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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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} 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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if (!results) {
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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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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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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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unsigned long h = (unsigned long)(w >> 32), l = (unsigned long)(w);
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if (h)
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BIO_printf(bp, "%lX%08lX", h, l);
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else
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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, "%lX", 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++) {
|
|
do {
|
|
BN_bntest_rand(&a, 512, -1, 0);
|
|
BN_bntest_rand(&b, BN_BITS2, -1, 0);
|
|
s = b.d[0];
|
|
} while (!s);
|
|
|
|
BN_copy(&b, &a);
|
|
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, ret = 0;
|
|
|
|
a = BN_new();
|
|
c = BN_new();
|
|
d = BN_new();
|
|
e = BN_new();
|
|
if (a == NULL || c == NULL || d == NULL || e == NULL) {
|
|
goto err;
|
|
}
|
|
|
|
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");
|
|
goto err;
|
|
}
|
|
}
|
|
|
|
/* Regression test for a BN_sqr overflow bug. */
|
|
BN_hex2bn(&a,
|
|
"80000000000000008000000000000001"
|
|
"FFFFFFFFFFFFFFFE0000000000000000");
|
|
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_mul(d, a, a, ctx);
|
|
if (BN_cmp(c, d)) {
|
|
fprintf(stderr, "Square test failed: BN_sqr and BN_mul produce "
|
|
"different results!\n");
|
|
#ifdef OPENSSL_FIPS
|
|
/*
|
|
* This test fails if we are linked to the FIPS module. Unfortunately
|
|
* that can't be fixed so we print out the error but continue anyway.
|
|
*/
|
|
fprintf(stderr, " FIPS build: ignoring.\n");
|
|
#else
|
|
goto err;
|
|
#endif
|
|
}
|
|
|
|
/* Regression test for a BN_sqr overflow bug. */
|
|
BN_hex2bn(&a,
|
|
"80000000000000000000000080000001"
|
|
"FFFFFFFE000000000000000000000000");
|
|
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_mul(d, a, a, ctx);
|
|
if (BN_cmp(c, d)) {
|
|
fprintf(stderr, "Square test failed: BN_sqr and BN_mul produce "
|
|
"different results!\n");
|
|
goto err;
|
|
}
|
|
ret = 1;
|
|
err:
|
|
if (a != NULL)
|
|
BN_free(a);
|
|
if (c != NULL)
|
|
BN_free(c);
|
|
if (d != NULL)
|
|
BN_free(d);
|
|
if (e != NULL)
|
|
BN_free(e);
|
|
return ret;
|
|
}
|
|
|
|
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();
|
|
|
|
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;
|
|
unsigned int p0[] = { 163, 7, 6, 3, 0 };
|
|
unsigned int p1[] = { 193, 15, 0 };
|
|
|
|
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;
|
|
unsigned int p0[] = { 163, 7, 6, 3, 0 };
|
|
unsigned int p1[] = { 193, 15, 0 };
|
|
|
|
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;
|
|
unsigned int p0[] = { 163, 7, 6, 3, 0 };
|
|
unsigned int p1[] = { 193, 15, 0 };
|
|
|
|
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;
|
|
unsigned int p0[] = { 163, 7, 6, 3, 0 };
|
|
unsigned int p1[] = { 193, 15, 0 };
|
|
|
|
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;
|
|
unsigned int p0[] = { 163, 7, 6, 3, 0 };
|
|
unsigned int p1[] = { 193, 15, 0 };
|
|
|
|
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;
|
|
unsigned int p0[] = { 163, 7, 6, 3, 0 };
|
|
unsigned int p1[] = { 193, 15, 0 };
|
|
|
|
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;
|
|
unsigned int p0[] = { 163, 7, 6, 3, 0 };
|
|
unsigned int p1[] = { 193, 15, 0 };
|
|
|
|
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;
|
|
unsigned int p0[] = { 163, 7, 6, 3, 0 };
|
|
unsigned int p1[] = { 193, 15, 0 };
|
|
|
|
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]);
|
|
}
|