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openssl/crypto/bn/bntest.c
Emilia Kasper d46e946d26 BN_mod_exp_mont_consttime: check for zero modulus. 
Don't dereference |d| when |top| is zero. Also test that various BIGNUM methods behave correctly on zero/even inputs.

Follow-up to b11980d79a

Reviewed-by: Rich Salz <rsalz@openssl.org>
2015-08-31 19:33:42 +02:00

2137 lines
54 KiB
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/* crypto/bn/bntest.c */
/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
* All rights reserved.
*
* This package is an SSL implementation written
* by Eric Young (eay@cryptsoft.com).
* The implementation was written so as to conform with Netscapes SSL.
*
* This library is free for commercial and non-commercial use as long as
* the following conditions are aheared to. The following conditions
* apply to all code found in this distribution, be it the RC4, RSA,
* lhash, DES, etc., code; not just the SSL code. The SSL documentation
* included with this distribution is covered by the same copyright terms
* except that the holder is Tim Hudson (tjh@cryptsoft.com).
*
* Copyright remains Eric Young's, and as such any Copyright notices in
* the code are not to be removed.
* If this package is used in a product, Eric Young should be given attribution
* as the author of the parts of the library used.
* This can be in the form of a textual message at program startup or
* in documentation (online or textual) provided with the package.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* 3. All advertising materials mentioning features or use of this software
* must display the following acknowledgement:
* "This product includes cryptographic software written by
* Eric Young (eay@cryptsoft.com)"
* The word 'cryptographic' can be left out if the rouines from the library
* being used are not cryptographic related :-).
* 4. If you include any Windows specific code (or a derivative thereof) from
* the apps directory (application code) you must include an acknowledgement:
* "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
*
* THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*
* The licence and distribution terms for any publically available version or
* derivative of this code cannot be changed. i.e. this code cannot simply be
* copied and put under another distribution licence
* [including the GNU Public Licence.]
*/
/* ====================================================================
* Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
*
* Portions of the attached software ("Contribution") are developed by
* SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
*
* The Contribution is licensed pursuant to the Eric Young open source
* license provided above.
*
* The binary polynomial arithmetic software is originally written by
* Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
*
*/
/*
* Until the key-gen callbacks are modified to use newer prototypes, we allow
* deprecated functions for openssl-internal code
*/
#ifdef OPENSSL_NO_DEPRECATED
# undef OPENSSL_NO_DEPRECATED
#endif
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "e_os.h"
#include <openssl/bio.h>
#include <openssl/bn.h>
#include <openssl/rand.h>
#include <openssl/x509.h>
#include <openssl/err.h>
const int num0 = 100; /* number of tests */
const int num1 = 50; /* additional tests for some functions */
const int num2 = 5; /* number of tests for slow functions */
int test_add(BIO *bp);
int test_sub(BIO *bp);
int test_lshift1(BIO *bp);
int test_lshift(BIO *bp, BN_CTX *ctx, BIGNUM *a_);
int test_rshift1(BIO *bp);
int test_rshift(BIO *bp, BN_CTX *ctx);
int test_div(BIO *bp, BN_CTX *ctx);
int test_div_word(BIO *bp);
int test_div_recp(BIO *bp, BN_CTX *ctx);
int test_mul(BIO *bp);
int test_sqr(BIO *bp, BN_CTX *ctx);
int test_mont(BIO *bp, BN_CTX *ctx);
int test_mod(BIO *bp, BN_CTX *ctx);
int test_mod_mul(BIO *bp, BN_CTX *ctx);
int test_mod_exp(BIO *bp, BN_CTX *ctx);
int test_mod_exp_mont_consttime(BIO *bp, BN_CTX *ctx);
int test_mod_exp_mont5(BIO *bp, BN_CTX *ctx);
int test_exp(BIO *bp, BN_CTX *ctx);
int test_gf2m_add(BIO *bp);
int test_gf2m_mod(BIO *bp);
int test_gf2m_mod_mul(BIO *bp, BN_CTX *ctx);
int test_gf2m_mod_sqr(BIO *bp, BN_CTX *ctx);
int test_gf2m_mod_inv(BIO *bp, BN_CTX *ctx);
int test_gf2m_mod_div(BIO *bp, BN_CTX *ctx);
int test_gf2m_mod_exp(BIO *bp, BN_CTX *ctx);
int test_gf2m_mod_sqrt(BIO *bp, BN_CTX *ctx);
int test_gf2m_mod_solve_quad(BIO *bp, BN_CTX *ctx);
int test_kron(BIO *bp, BN_CTX *ctx);
int test_sqrt(BIO *bp, BN_CTX *ctx);
int rand_neg(void);
static int results = 0;
static unsigned char lst[] =
"\xC6\x4F\x43\x04\x2A\xEA\xCA\x6E\x58\x36\x80\x5B\xE8\xC9"
"\x9B\x04\x5D\x48\x36\xC2\xFD\x16\xC9\x64\xF0";
static const char rnd_seed[] =
"string to make the random number generator think it has entropy";
static void message(BIO *out, char *m)
{
fprintf(stderr, "test %s\n", m);
BIO_puts(out, "print \"test ");
BIO_puts(out, m);
BIO_puts(out, "\\n\"\n");
}
int main(int argc, char *argv[])
{
BN_CTX *ctx;
BIO *out;
char *outfile = NULL;
results = 0;
RAND_seed(rnd_seed, sizeof rnd_seed); /* or BN_generate_prime may fail */
argc--;
argv++;
while (argc >= 1) {
if (strcmp(*argv, "-results") == 0)
results = 1;
else if (strcmp(*argv, "-out") == 0) {
if (--argc < 1)
break;
outfile = *(++argv);
}
argc--;
argv++;
}
ctx = BN_CTX_new();
if (ctx == NULL)
EXIT(1);
out = BIO_new(BIO_s_file());
if (out == NULL)
EXIT(1);
if (outfile == NULL) {
BIO_set_fp(out, stdout, BIO_NOCLOSE);
} else {
if (!BIO_write_filename(out, outfile)) {
perror(outfile);
EXIT(1);
}
}
if (!results)
BIO_puts(out, "obase=16\nibase=16\n");
message(out, "BN_add");
if (!test_add(out))
goto err;
(void)BIO_flush(out);
message(out, "BN_sub");
if (!test_sub(out))
goto err;
(void)BIO_flush(out);
message(out, "BN_lshift1");
if (!test_lshift1(out))
goto err;
(void)BIO_flush(out);
message(out, "BN_lshift (fixed)");
if (!test_lshift(out, ctx, BN_bin2bn(lst, sizeof(lst) - 1, NULL)))
goto err;
(void)BIO_flush(out);
message(out, "BN_lshift");
if (!test_lshift(out, ctx, NULL))
goto err;
(void)BIO_flush(out);
message(out, "BN_rshift1");
if (!test_rshift1(out))
goto err;
(void)BIO_flush(out);
message(out, "BN_rshift");
if (!test_rshift(out, ctx))
goto err;
(void)BIO_flush(out);
message(out, "BN_sqr");
if (!test_sqr(out, ctx))
goto err;
(void)BIO_flush(out);
message(out, "BN_mul");
if (!test_mul(out))
goto err;
(void)BIO_flush(out);
message(out, "BN_div");
if (!test_div(out, ctx))
goto err;
(void)BIO_flush(out);
message(out, "BN_div_word");
if (!test_div_word(out))
goto err;
(void)BIO_flush(out);
message(out, "BN_div_recp");
if (!test_div_recp(out, ctx))
goto err;
(void)BIO_flush(out);
message(out, "BN_mod");
if (!test_mod(out, ctx))
goto err;
(void)BIO_flush(out);
message(out, "BN_mod_mul");
if (!test_mod_mul(out, ctx))
goto err;
(void)BIO_flush(out);
message(out, "BN_mont");
if (!test_mont(out, ctx))
goto err;
(void)BIO_flush(out);
message(out, "BN_mod_exp");
if (!test_mod_exp(out, ctx))
goto err;
(void)BIO_flush(out);
message(out, "BN_mod_exp_mont_consttime");
if (!test_mod_exp_mont_consttime(out, ctx))
goto err;
if (!test_mod_exp_mont5(out, ctx))
goto err;
(void)BIO_flush(out);
message(out, "BN_exp");
if (!test_exp(out, ctx))
goto err;
(void)BIO_flush(out);
message(out, "BN_kronecker");
if (!test_kron(out, ctx))
goto err;
(void)BIO_flush(out);
message(out, "BN_mod_sqrt");
if (!test_sqrt(out, ctx))
goto err;
(void)BIO_flush(out);
#ifndef OPENSSL_NO_EC2M
message(out, "BN_GF2m_add");
if (!test_gf2m_add(out))
goto err;
(void)BIO_flush(out);
message(out, "BN_GF2m_mod");
if (!test_gf2m_mod(out))
goto err;
(void)BIO_flush(out);
message(out, "BN_GF2m_mod_mul");
if (!test_gf2m_mod_mul(out, ctx))
goto err;
(void)BIO_flush(out);
message(out, "BN_GF2m_mod_sqr");
if (!test_gf2m_mod_sqr(out, ctx))
goto err;
(void)BIO_flush(out);
message(out, "BN_GF2m_mod_inv");
if (!test_gf2m_mod_inv(out, ctx))
goto err;
(void)BIO_flush(out);
message(out, "BN_GF2m_mod_div");
if (!test_gf2m_mod_div(out, ctx))
goto err;
(void)BIO_flush(out);
message(out, "BN_GF2m_mod_exp");
if (!test_gf2m_mod_exp(out, ctx))
goto err;
(void)BIO_flush(out);
message(out, "BN_GF2m_mod_sqrt");
if (!test_gf2m_mod_sqrt(out, ctx))
goto err;
(void)BIO_flush(out);
message(out, "BN_GF2m_mod_solve_quad");
if (!test_gf2m_mod_solve_quad(out, ctx))
goto err;
(void)BIO_flush(out);
#endif
BN_CTX_free(ctx);
BIO_free(out);
EXIT(0);
err:
BIO_puts(out, "1\n"); /* make sure the Perl script fed by bc
* notices the failure, see test_bn in
* test/Makefile.ssl */
(void)BIO_flush(out);
ERR_load_crypto_strings();
ERR_print_errors_fp(stderr);
EXIT(1);
return (1);
}
int test_add(BIO *bp)
{
BIGNUM a, b, c;
int i;
BN_init(&a);
BN_init(&b);
BN_init(&c);
BN_bntest_rand(&a, 512, 0, 0);
for (i = 0; i < num0; i++) {
BN_bntest_rand(&b, 450 + i, 0, 0);
a.neg = rand_neg();
b.neg = rand_neg();
BN_add(&c, &a, &b);
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");
}
a.neg = !a.neg;
b.neg = !b.neg;
BN_add(&c, &c, &b);
BN_add(&c, &c, &a);
if (!BN_is_zero(&c)) {
fprintf(stderr, "Add test failed!\n");
return 0;
}
}
BN_free(&a);
BN_free(&b);
BN_free(&c);
return (1);
}
int test_sub(BIO *bp)
{
BIGNUM a, b, c;
int i;
BN_init(&a);
BN_init(&b);
BN_init(&c);
for (i = 0; i < num0 + num1; i++) {
if (i < num1) {
BN_bntest_rand(&a, 512, 0, 0);
BN_copy(&b, &a);
if (BN_set_bit(&a, i) == 0)
return (0);
BN_add_word(&b, i);
} else {
BN_bntest_rand(&b, 400 + i - num1, 0, 0);
a.neg = rand_neg();
b.neg = rand_neg();
}
BN_sub(&c, &a, &b);
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_add(&c, &c, &b);
BN_sub(&c, &c, &a);
if (!BN_is_zero(&c)) {
fprintf(stderr, "Subtract test failed!\n");
return 0;
}
}
BN_free(&a);
BN_free(&b);
BN_free(&c);
return (1);
}
int test_div(BIO *bp, BN_CTX *ctx)
{
BIGNUM a, b, c, d, e;
int i;
BN_init(&a);
BN_init(&b);
BN_init(&c);
BN_init(&d);
BN_init(&e);
BN_one(&a);
BN_zero(&b);
if (BN_div(&d, &c, &a, &b, ctx)) {
fprintf(stderr, "Division by zero succeeded!\n");
return 0;
}
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_div(&d, &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, &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, "Division test failed!\n");
return 0;
}
}
BN_free(&a);
BN_free(&b);
BN_free(&c);
BN_free(&d);
BN_free(&e);
return (1);
}
static void print_word(BIO *bp, BN_ULONG w)
{
#ifdef SIXTY_FOUR_BIT
if (sizeof(w) > sizeof(unsigned long)) {
unsigned long h = (unsigned long)(w >> 32), l = (unsigned long)(w);
if (h)
BIO_printf(bp, "%lX%08lX", h, l);
else
BIO_printf(bp, "%lX", l);
return;
}
#endif
BIO_printf(bp, BN_HEX_FMT1, w);
}
int test_div_word(BIO *bp)
{
BIGNUM a, b;
BN_ULONG r, s;
int i;
BN_init(&a);
BN_init(&b);
for (i = 0; i < num0; i++) {
do {
BN_bntest_rand(&a, 512, -1, 0);
BN_bntest_rand(&b, BN_BITS2, -1, 0);
} while (BN_is_zero(&b));
s = b.d[0];
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");
goto err;
}
/* 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();
if (mont == NULL)
return 0;
BN_zero(&n);
if (BN_MONT_CTX_set(mont, &n, ctx)) {
fprintf(stderr, "BN_MONT_CTX_set succeeded for zero modulus!\n");
return 0;
}
BN_set_word(&n, 16);
if (BN_MONT_CTX_set(mont, &n, ctx)) {
fprintf(stderr, "BN_MONT_CTX_set succeeded for even modulus!\n");
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();
BN_one(a);
BN_one(b);
BN_zero(c);
if (BN_mod_mul(e, a, b, c, ctx)) {
fprintf(stderr, "BN_mod_mul with zero modulus succeeded!\n");
return 0;
}
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_one(a);
BN_one(b);
BN_zero(c);
if (BN_mod_exp(d, a, b, c, ctx)) {
fprintf(stderr, "BN_mod_exp with zero modulus succeeded!\n");
return 0;
}
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_one(a);
BN_one(b);
BN_zero(c);
if (BN_mod_exp_mont_consttime(d, a, b, c, ctx, NULL)) {
fprintf(stderr, "BN_mod_exp_mont_consttime with zero modulus "
"succeeded\n");
return 0;
}
BN_set_word(c, 16);
if (BN_mod_exp_mont_consttime(d, a, b, c, ctx, NULL)) {
fprintf(stderr, "BN_mod_exp_mont_consttime with even modulus "
"succeeded\n");
return 0;
}
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);
}
/*
* Test constant-time modular exponentiation with 1024-bit inputs, which on
* x86_64 cause a different code branch to be taken.
*/
int test_mod_exp_mont5(BIO *bp, BN_CTX *ctx)
{
BIGNUM *a, *p, *m, *d, *e;
BN_MONT_CTX *mont;
a = BN_new();
p = BN_new();
m = BN_new();
d = BN_new();
e = BN_new();
mont = BN_MONT_CTX_new();
BN_bntest_rand(m, 1024, 0, 1); /* must be odd for montgomery */
/* Zero exponent */
BN_bntest_rand(a, 1024, 0, 0);
BN_zero(p);
if (!BN_mod_exp_mont_consttime(d, a, p, m, ctx, NULL))
return 0;
if (!BN_is_one(d)) {
fprintf(stderr, "Modular exponentiation test failed!\n");
return 0;
}
/* Zero input */
BN_bntest_rand(p, 1024, 0, 0);
BN_zero(a);
if (!BN_mod_exp_mont_consttime(d, a, p, m, ctx, NULL))
return 0;
if (!BN_is_zero(d)) {
fprintf(stderr, "Modular exponentiation test failed!\n");
return 0;
}
/*
* Craft an input whose Montgomery representation is 1, i.e., shorter
* than the modulus m, in order to test the const time precomputation
* scattering/gathering.
*/
BN_one(a);
BN_MONT_CTX_set(mont, m, ctx);
if (!BN_from_montgomery(e, a, mont, ctx))
return 0;
if (!BN_mod_exp_mont_consttime(d, e, p, m, ctx, NULL))
return 0;
if (!BN_mod_exp_simple(a, e, p, m, ctx))
return 0;
if (BN_cmp(a, d) != 0) {
fprintf(stderr, "Modular exponentiation test failed!\n");
return 0;
}
/* Finally, some regular test vectors. */
BN_bntest_rand(e, 1024, 0, 0);
if (!BN_mod_exp_mont_consttime(d, e, p, m, ctx, NULL))
return 0;
if (!BN_mod_exp_simple(a, e, p, m, ctx))
return 0;
if (BN_cmp(a, d) != 0) {
fprintf(stderr, "Modular exponentiation test failed!\n");
return 0;
}
BN_free(a);
BN_free(p);
BN_free(m);
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);
}
#ifndef OPENSSL_NO_EC2M
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;
}
#endif
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]);
}
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