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提交 8d1ebff4 编写于 作者: R Rich Salz
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Make bntest be (mostly) file-based. 

Test suite used from boring, written by David Benjamin.
Test driver converted from C++ to C.
Added a Perl program to check the testsuite file.
Extensive review feedback incorporated (thanks folks).
Reviewed-by: NEmilia Käsper <emilia@openssl.org>
Reviewed-by: NRichard Levitte <levitte@openssl.org>
上级 b3618f44
隐藏空白更改
内联 并排
Showing with 12360 addition and 1754 deletion
test/bntest.c
浏览文件 @ 8d1ebff4
......@@ -6,37 +6,25 @@
* in the file LICENSE in the source distribution or at
* https://www.openssl.org/source/license.html
*/
/* ====================================================================
* 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.
*
*/
#include <assert.h>
#include <errno.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <ctype.h>
#include "e_os.h"
#include <openssl/bio.h>
#include <internal/numbers.h>
#include <openssl/bn.h>
#include <openssl/rand.h>
#include <openssl/x509.h>
#include <openssl/crypto.h>
#include <openssl/err.h>
#include <openssl/rand.h>
#include "testutil.h"
#include "test_main_custom.h"
/*
* In bn_lcl.h, bn_expand() is defined as a static ossl_inline function.
* This is fine in itself, it will end up as an unused static function in
* the worst case. However, it referenses bn_expand2(), which is a private
* the worst case. However, it references bn_expand2(), which is a private
* function in libcrypto and therefore unavailable on some systems. This
* may result in a linker error because of unresolved symbols.
*
......@@ -46,335 +34,148 @@
#define bn_expand2 dummy_bn_expand2
BIGNUM *bn_expand2(BIGNUM *b, int words);
BIGNUM *bn_expand2(BIGNUM *b, int words) { return NULL; }
#include "../crypto/bn/bn_lcl.h"
static const int num0 = 100; /* number of tests */
static const int num1 = 50; /* additional tests for some functions */
static 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 test_small_prime(BIO *bp, BN_CTX *ctx);
int test_bn2dec(BIO *bp);
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;
CRYPTO_set_mem_debug(1);
CRYPTO_mem_ctrl(CRYPTO_MEM_CHECK_ON);
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 | BIO_FP_TEXT);
} else {
if (!BIO_write_filename(out, outfile)) {
perror(outfile);
EXIT(1);
}
}
#ifdef OPENSSL_SYS_VMS
{
BIO *tmpbio = BIO_new(BIO_f_linebuffer());
out = BIO_push(tmpbio, out);
}
#endif
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);
#define MAXPAIRS 20
message(out, "BN_div_word");
if (!test_div_word(out))
goto err;
(void)BIO_flush(out);
/*
* Things in boring, not in openssl. TODO we should add them.
*/
#define HAVE_BN_PADDED 0
#define HAVE_BN_SQRT 0
message(out, "BN_div_recp");
if (!test_div_recp(out, ctx))
goto err;
(void)BIO_flush(out);
typedef struct pair_st {
char *key;
char *value;
} PAIR;
message(out, "BN_mod");
if (!test_mod(out, ctx))
goto err;
(void)BIO_flush(out);
typedef struct stanza_st {
int start;
int numpairs;
PAIR pairs[MAXPAIRS];
} STANZA;
message(out, "BN_mod_mul");
if (!test_mod_mul(out, ctx))
goto err;
(void)BIO_flush(out);
typedef struct filetest_st {
const char *name;
int (*func)(STANZA *s);
} FILETEST;
message(out, "BN_mont");
if (!test_mont(out, ctx))
goto err;
(void)BIO_flush(out);
typedef struct mpitest_st {
const char *base10;
const char *mpi;
size_t mpi_len;
} MPITEST;
message(out, "BN_mod_exp");
if (!test_mod_exp(out, ctx))
goto err;
(void)BIO_flush(out);
static const int NUM0 = 100; /* number of tests */
static const int NUM1 = 50; /* additional tests for some functions */
static FILE *fp;
static BN_CTX *ctx;
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);
/*
* Look for |key| in the stanza and return it or NULL if not found.
*/
static const char *findattr(STANZA *s, const char *key)
{
int i = s->numpairs;
PAIR *pp = s->pairs;
message(out, "BN_kronecker");
if (!test_kron(out, ctx))
goto err;
(void)BIO_flush(out);
for ( ; --i >= 0; pp++)
if (strcasecmp(pp->key, key) == 0)
return pp->value;
return NULL;
}
message(out, "BN_mod_sqrt");
if (!test_sqrt(out, ctx))
goto err;
(void)BIO_flush(out);
/*
* Parse BIGNUM, return number of bytes parsed.
*/
static int parseBN(BIGNUM **out, const char *in)
{
*out = NULL;
return BN_hex2bn(out, in);
}
message(out, "Small prime generation");
if (!test_small_prime(out, ctx))
goto err;
(void)BIO_flush(out);
static int parsedecBN(BIGNUM **out, const char *in)
{
*out = NULL;
return BN_dec2bn(out, in);
}
message(out, "BN_bn2dec");
if (!test_bn2dec(out))
goto err;
(void)BIO_flush(out);
static BIGNUM *getBN(STANZA *s, const char *attribute)
{
const char *hex;
BIGNUM *ret = NULL;
#ifndef OPENSSL_NO_EC2M
message(out, "BN_GF2m_add");
if (!test_gf2m_add(out))
goto err;
(void)BIO_flush(out);
if ((hex = findattr(s, attribute)) == NULL) {
fprintf(stderr, "Can't find %s in test at line %d\n",
attribute, s->start);
return NULL;
}
message(out, "BN_GF2m_mod");
if (!test_gf2m_mod(out))
goto err;
(void)BIO_flush(out);
if (parseBN(&ret, hex) != (int)strlen(hex)) {
fprintf(stderr, "Could not decode '%s'.\n", hex);
return NULL;
}
return ret;
}
message(out, "BN_GF2m_mod_mul");
if (!test_gf2m_mod_mul(out, ctx))
goto err;
(void)BIO_flush(out);
static int getint(STANZA *s, int *out, const char *attribute)
{
BIGNUM *ret = getBN(s, attribute);
BN_ULONG word;
int st = 0;
message(out, "BN_GF2m_mod_sqr");
if (!test_gf2m_mod_sqr(out, ctx))
if (ret == NULL)
goto err;
(void)BIO_flush(out);
message(out, "BN_GF2m_mod_inv");
if (!test_gf2m_mod_inv(out, ctx))
if ((word = BN_get_word(ret)) > INT_MAX)
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);
*out = (int)word;
st = 1;
err:
BN_free(ret);
return st;
}
message(out, "BN_GF2m_mod_exp");
if (!test_gf2m_mod_exp(out, ctx))
goto err;
(void)BIO_flush(out);
static int equalBN(const char *op, const BIGNUM *expected, const BIGNUM *actual)
{
char *exstr = NULL;
char *actstr = NULL;
message(out, "BN_GF2m_mod_sqrt");
if (!test_gf2m_mod_sqrt(out, ctx))
goto err;
(void)BIO_flush(out);
if (BN_cmp(expected, actual) == 0)
return 1;
message(out, "BN_GF2m_mod_solve_quad");
if (!test_gf2m_mod_solve_quad(out, ctx))
exstr = BN_bn2hex(expected);
actstr = BN_bn2hex(actual);
if (exstr == NULL || actstr == NULL)
goto err;
(void)BIO_flush(out);
#endif
BN_CTX_free(ctx);
BIO_free(out);
ERR_print_errors_fp(stderr);
#ifndef OPENSSL_NO_CRYPTO_MDEBUG
if (CRYPTO_mem_leaks_fp(stderr) <= 0)
EXIT(1);
#endif
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);
BN_CTX_free(ctx);
BIO_free(out);
fprintf(stderr, "Got %s =\n", op);
fprintf(stderr, "\t%s\n", actstr);
fprintf(stderr, "wanted:\n");
fprintf(stderr, "\t%s\n", exstr);
ERR_print_errors_fp(stderr);
EXIT(1);
err:
OPENSSL_free(exstr);
OPENSSL_free(actstr);
return 0;
}
int test_add(BIO *bp)
{
BIGNUM *a, *b, *c;
int i;
a = BN_new();
b = BN_new();
c = BN_new();
/*
* Return a "random" flag for if a BN should be negated.
*/
static int rand_neg(void)
{
static unsigned int neg = 0;
static int sign[8] = { 0, 0, 0, 1, 1, 0, 1, 1 };
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);
return sign[(neg++) % 8];
}
int test_sub(BIO *bp)
static int test_sub()
{
BIGNUM *a, *b, *c;
int i;
......@@ -383,188 +184,34 @@ int test_sub(BIO *bp)
b = BN_new();
c = BN_new();
for (i = 0; i < num0 + num1; i++) {
if (i < num1) {
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);
return 0;
BN_add_word(b, i);
} else {
BN_bntest_rand(b, 400 + i - num1, 0, 0);
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;
a = BN_new();
b = BN_new();
c = BN_new();
d = BN_new();
e = BN_new();
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");
printf("Subtract 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)
{
int i = sizeof(w) * 8;
char *fmt = NULL;
unsigned char byte;
do {
i -= 8;
byte = (unsigned char)(w >> i);
if (fmt == NULL)
fmt = byte ? "%X" : NULL;
else
fmt = "%02X";
if (fmt != NULL)
BIO_printf(bp, fmt, byte);
} while (i);
/* If we haven't printed anything, at least print a zero! */
if (fmt == NULL)
BIO_printf(bp, "0");
return 1;
}
int test_div_word(BIO *bp)
{
BIGNUM *a, *b;
BN_ULONG r, rmod, s;
int i;
a = BN_new();
b = BN_new();
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);
rmod = BN_mod_word(b, s);
r = BN_div_word(b, s);
if (rmod != r) {
fprintf(stderr, "Mod (word) test failed!\n");
return 0;
}
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)
static int test_div_recip()
{
BIGNUM *a, *b, *c, *d, *e;
BN_RECP_CTX *recp;
......@@ -577,47 +224,28 @@ int test_div_recp(BIO *bp, BN_CTX *ctx)
d = BN_new();
e = BN_new();
for (i = 0; i < num0 + num1; i++) {
if (i < num1) {
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);
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");
printf("Reciprocal division test failed!\n");
printf("a=");
BN_print_fp(stdout, a);
printf("\nb=");
BN_print_fp(stdout, b);
printf("\n");
return 0;
}
}
......@@ -627,18 +255,14 @@ int test_div_recp(BIO *bp, BN_CTX *ctx)
BN_free(d);
BN_free(e);
BN_RECP_CTX_free(recp);
return (1);
return 1;
}
int test_mul(BIO *bp)
static int test_mod()
{
BIGNUM *a, *b, *c, *d, *e;
int i;
BN_CTX *ctx;
ctx = BN_CTX_new();
if (ctx == NULL)
EXIT(1);
a = BN_new();
b = BN_new();
......@@ -646,29 +270,16 @@ int test_mul(BIO *bp)
d = BN_new();
e = BN_new();
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);
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_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");
BN_mod(c, a, b, ctx);
BN_div(d, e, a, b, ctx);
BN_sub(e, e, c);
if (!BN_is_zero(e)) {
printf("Modulo test failed!\n");
return 0;
}
}
......@@ -677,747 +288,288 @@ int test_mul(BIO *bp)
BN_free(c);
BN_free(d);
BN_free(e);
BN_CTX_free(ctx);
return (1);
return 1;
}
int test_sqr(BIO *bp, BN_CTX *ctx)
/*
* Test constant-time modular exponentiation with 1024-bit inputs, which on
* x86_64 cause a different code branch to be taken.
*/
static int test_modexp_mont5()
{
BIGNUM *a, *c, *d, *e;
int i, ret = 0;
BIGNUM *a, *p, *m, *d, *e, *b, *n, *c;
BN_MONT_CTX *mont;
a = BN_new();
c = BN_new();
p = BN_new();
m = BN_new();
d = BN_new();
e = BN_new();
if (a == NULL || c == NULL || d == NULL || e == NULL) {
goto err;
}
b = BN_new();
n = BN_new();
c = BN_new();
mont = BN_MONT_CTX_new();
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;
}
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)) {
printf("Modular exponentiation test failed!\n");
return 0;
}
/* Regression test for a BN_sqr overflow bug. */
/* Regression test for carry bug in mulx4x_mont */
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);
"7878787878787878787878787878787878787878787878787878787878787878"
"7878787878787878787878787878787878787878787878787878787878787878"
"7878787878787878787878787878787878787878787878787878787878787878"
"7878787878787878787878787878787878787878787878787878787878787878");
BN_hex2bn(&b,
"095D72C08C097BA488C5E439C655A192EAFB6380073D8C2664668EDDB4060744"
"E16E57FB4EDB9AE10A0CEFCDC28A894F689A128379DB279D48A2E20849D68593"
"9B7803BCF46CEBF5C533FB0DD35B080593DE5472E3FE5DB951B8BFF9B4CB8F03"
"9CC638A5EE8CDD703719F8000E6A9F63BEED5F2FCD52FF293EA05A251BB4AB81");
BN_hex2bn(&n,
"D78AF684E71DB0C39CFF4E64FB9DB567132CB9C50CC98009FEB820B26F2DED9B"
"91B9B5E2B83AE0AE4EB4E0523CA726BFBE969B89FD754F674CE99118C3F2D1C5"
"D81FDC7C54E02B60262B241D53C040E99E45826ECA37A804668E690E1AFC1CA4"
"2C9A15D84D4954425F0B7642FC0BD9D7B24E2618D2DCC9B729D944BADACFDDAF");
BN_MONT_CTX_set(mont, n, ctx);
BN_mod_mul_montgomery(c, a, b, mont, ctx);
BN_mod_mul_montgomery(d, b, a, mont, ctx);
if (BN_cmp(c, d)) {
fprintf(stderr, "Square test failed: BN_sqr and BN_mul produce "
"different results!\n");
goto err;
fprintf(stderr, "Montgomery multiplication test failed:"
" a*b != b*a.\n");
return 0;
}
/* 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:
BN_free(a);
BN_free(c);
BN_free(d);
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;
a = BN_new();
b = BN_new();
c = BN_new();
d = BN_new();
A = BN_new();
B = BN_new();
n = BN_new();
mont = BN_MONT_CTX_new();
if (mont == NULL)
/* 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;
BN_zero(n);
if (BN_MONT_CTX_set(mont, n, ctx)) {
fprintf(stderr, "BN_MONT_CTX_set succeeded for zero modulus!\n");
if (!BN_is_zero(d)) {
fprintf(stderr, "Modular exponentiation test failed!\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");
/*
* 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) {
printf("Modular exponentiation test failed!\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) {
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;
}
}
/* Regression test for carry bug in mulx4x_mont */
BN_hex2bn(&a,
"7878787878787878787878787878787878787878787878787878787878787878"
"7878787878787878787878787878787878787878787878787878787878787878"
"7878787878787878787878787878787878787878787878787878787878787878"
"7878787878787878787878787878787878787878787878787878787878787878");
BN_hex2bn(&b,
"095D72C08C097BA488C5E439C655A192EAFB6380073D8C2664668EDDB4060744"
"E16E57FB4EDB9AE10A0CEFCDC28A894F689A128379DB279D48A2E20849D68593"
"9B7803BCF46CEBF5C533FB0DD35B080593DE5472E3FE5DB951B8BFF9B4CB8F03"
"9CC638A5EE8CDD703719F8000E6A9F63BEED5F2FCD52FF293EA05A251BB4AB81");
BN_hex2bn(&n,
"D78AF684E71DB0C39CFF4E64FB9DB567132CB9C50CC98009FEB820B26F2DED9B"
"91B9B5E2B83AE0AE4EB4E0523CA726BFBE969B89FD754F674CE99118C3F2D1C5"
"D81FDC7C54E02B60262B241D53C040E99E45826ECA37A804668E690E1AFC1CA4"
"2C9A15D84D4954425F0B7642FC0BD9D7B24E2618D2DCC9B729D944BADACFDDAF");
BN_MONT_CTX_set(mont, n, ctx);
BN_mod_mul_montgomery(c, a, b, mont, ctx);
BN_mod_mul_montgomery(d, b, a, mont, ctx);
if (BN_cmp(c, d)) {
fprintf(stderr, "Montgomery multiplication test failed:"
" a*b != b*a.\n");
/* 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) {
printf("Modular exponentiation test failed!\n");
return 0;
}
BN_MONT_CTX_free(mont);
BN_free(a);
BN_free(b);
BN_free(c);
BN_free(p);
BN_free(m);
BN_free(d);
BN_free(A);
BN_free(B);
BN_free(e);
BN_free(b);
BN_free(n);
return (1);
BN_free(c);
return 1;
}
int test_mod(BIO *bp, BN_CTX *ctx)
#ifndef OPENSSL_NO_EC2M
static int test_gf2m_add()
{
BIGNUM *a, *b, *c, *d, *e;
int i;
BIGNUM *a, *b, *c;
int i, st = 0;
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);
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_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_GF2m_add(c, a, b);
/* 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))) {
printf("GF(2^m) addition test (a) failed!\n");
goto err;
}
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_GF2m_add(c, c, c);
/* Test that c + c = 0. */
if (!BN_is_zero(c)) {
printf("GF(2^m) addition test (b) failed!\n");
goto err;
}
}
st = 1;
err:
BN_free(a);
BN_free(b);
BN_free(c);
BN_free(d);
BN_free(e);
return (1);
return st;
}
int test_mod_mul(BIO *bp, BN_CTX *ctx)
static int test_gf2m_mod()
{
BIGNUM *a, *b, *c, *d, *e;
int i, j;
static int p0[] = { 163, 7, 6, 3, 0, -1 };
static int p1[] = { 193, 15, 0, -1 };
BIGNUM *a, *b[2], *c, *d, *e;
int i, j, st = 0;
a = BN_new();
b = BN_new();
b[0] = BN_new();
b[1] = 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;
BN_GF2m_arr2poly(p0, b[0]);
BN_GF2m_arr2poly(p1, b[1]);
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;
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]);
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)) {
printf("GF(2^m) modulo test failed!\n");
goto err;
}
}
}
st = 1;
err:
BN_free(a);
BN_free(b);
BN_free(b[0]);
BN_free(b[1]);
BN_free(c);
BN_free(d);
BN_free(e);
return (1);
return st;
}
int test_mod_exp(BIO *bp, BN_CTX *ctx)
static int test_gf2m_mul()
{
BIGNUM *a, *b, *c, *d, *e;
int i;
BIGNUM *a, *b[2], *c, *d, *e, *f, *g, *h;
int i, j, st = 0;
int p0[] = { 163, 7, 6, 3, 0, -1 };
int p1[] = { 193, 15, 0, -1 };
a = BN_new();
b = 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_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);
BN_GF2m_arr2poly(p0, b[0]);
BN_GF2m_arr2poly(p1, b[1]);
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, " - ");
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);
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)) {
printf("GF(2^m) modular multiplication test failed!\n");
goto err;
}
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;
}
}
/* Regression test for carry propagation bug in sqr8x_reduction */
BN_hex2bn(&a, "050505050505");
BN_hex2bn(&b, "02");
BN_hex2bn(&c,
"4141414141414141414141274141414141414141414141414141414141414141"
"4141414141414141414141414141414141414141414141414141414141414141"
"4141414141414141414141800000000000000000000000000000000000000000"
"0000000000000000000000000000000000000000000000000000000000000000"
"0000000000000000000000000000000000000000000000000000000000000000"
"0000000000000000000000000000000000000000000000000000000001");
BN_mod_exp(d, a, b, c, ctx);
BN_mul(e, a, a, ctx);
if (BN_cmp(d, e)) {
fprintf(stderr, "BN_mod_exp and BN_mul produce different results!\n");
return 0;
}
st = 1;
err:
BN_free(a);
BN_free(b);
BN_free(b[0]);
BN_free(b[1]);
BN_free(c);
BN_free(d);
BN_free(e);
return (1);
BN_free(f);
BN_free(g);
BN_free(h);
return st;
}
int test_mod_exp_mont_consttime(BIO *bp, BN_CTX *ctx)
static int test_gf2m_sqr()
{
BIGNUM *a, *b, *c, *d, *e;
int i;
BIGNUM *a, *b[2], *c, *d;
int i, j, st = 0;
int p0[] = { 163, 7, 6, 3, 0, -1 };
int p1[] = { 193, 15, 0, -1 };
a = BN_new();
b = BN_new();
b[0] = BN_new();
b[1] = 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);
BN_GF2m_arr2poly(p0, b[0]);
BN_GF2m_arr2poly(p1, b[1]);
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, " - ");
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);
BN_GF2m_add(d, c, d);
/* Test that a*a = a^2. */
if (!BN_is_zero(d)) {
printf("GF(2^m) modular squaring test failed!\n");
goto err;
}
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;
}
}
st = 1;
err:
BN_free(a);
BN_free(b);
BN_free(b[0]);
BN_free(b[1]);
BN_free(c);
BN_free(d);
BN_free(e);
return (1);
return st;
}
/*
* 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)
static int test_gf2m_modinv()
{
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_MONT_CTX_free(mont);
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;
a = BN_new();
b = BN_new();
c = BN_new();
for (i = 0; i < num0; i++) {
BN_rand(a, 512, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ANY);
BN_copy(b, BN_value_one());
a->neg = rand_neg();
b->neg = rand_neg();
BN_GF2m_add(c, a, b);
/* 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]);
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);
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);
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 };
BIGNUM *a, *b[2], *c, *d;
int i, j, st = 0;
int p0[] = { 163, 7, 6, 3, 0, -1 };
int p1[] = { 193, 15, 0, -1 };
a = BN_new();
b[0] = BN_new();
......@@ -1428,32 +580,32 @@ int test_gf2m_mod_inv(BIO *bp, BN_CTX *ctx)
BN_GF2m_arr2poly(p0, b[0]);
BN_GF2m_arr2poly(p1, b[1]);
for (i = 0; i < num0; i++) {
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);
/* Test that ((1/a)*a) = 1. */
if (!BN_is_one(d)) {
fprintf(stderr, "GF(2^m) modular inversion test failed!\n");
printf("GF(2^m) modular inversion test failed!\n");
goto err;
}
}
}
ret = 1;
st = 1;
err:
BN_free(a);
BN_free(b[0]);
BN_free(b[1]);
BN_free(c);
BN_free(d);
return ret;
return st;
}
int test_gf2m_mod_div(BIO *bp, BN_CTX *ctx)
static int test_gf2m_moddiv()
{
BIGNUM *a, *b[2], *c, *d, *e, *f;
int i, j, ret = 0;
int i, j, st = 0;
int p0[] = { 163, 7, 6, 3, 0, -1 };
int p1[] = { 193, 15, 0, -1 };
......@@ -1468,7 +620,7 @@ int test_gf2m_mod_div(BIO *bp, BN_CTX *ctx)
BN_GF2m_arr2poly(p0, b[0]);
BN_GF2m_arr2poly(p1, b[1]);
for (i = 0; i < num0; i++) {
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++) {
......@@ -1477,12 +629,12 @@ int test_gf2m_mod_div(BIO *bp, BN_CTX *ctx)
BN_GF2m_mod_div(f, a, e, b[j], ctx);
/* Test that ((a/c)*c)/a = 1. */
if (!BN_is_one(f)) {
fprintf(stderr, "GF(2^m) modular division test failed!\n");
printf("GF(2^m) modular division test failed!\n");
goto err;
}
}
}
ret = 1;
st = 1;
err:
BN_free(a);
BN_free(b[0]);
......@@ -1491,13 +643,13 @@ int test_gf2m_mod_div(BIO *bp, BN_CTX *ctx)
BN_free(d);
BN_free(e);
BN_free(f);
return ret;
return st;
}
int test_gf2m_mod_exp(BIO *bp, BN_CTX *ctx)
static int test_gf2m_modexp()
{
BIGNUM *a, *b[2], *c, *d, *e, *f;
int i, j, ret = 0;
int i, j, st = 0;
int p0[] = { 163, 7, 6, 3, 0, -1 };
int p1[] = { 193, 15, 0, -1 };
......@@ -1512,7 +664,7 @@ int test_gf2m_mod_exp(BIO *bp, BN_CTX *ctx)
BN_GF2m_arr2poly(p0, b[0]);
BN_GF2m_arr2poly(p1, b[1]);
for (i = 0; i < num0; i++) {
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);
......@@ -1525,13 +677,12 @@ int test_gf2m_mod_exp(BIO *bp, BN_CTX *ctx)
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");
printf("GF(2^m) modular exponentiation test failed!\n");
goto err;
}
}
}
ret = 1;
st = 1;
err:
BN_free(a);
BN_free(b[0]);
......@@ -1540,13 +691,13 @@ int test_gf2m_mod_exp(BIO *bp, BN_CTX *ctx)
BN_free(d);
BN_free(e);
BN_free(f);
return ret;
return st;
}
int test_gf2m_mod_sqrt(BIO *bp, BN_CTX *ctx)
static int test_gf2m_modsqrt()
{
BIGNUM *a, *b[2], *c, *d, *e, *f;
int i, j, ret = 0;
int i, j, st = 0;
int p0[] = { 163, 7, 6, 3, 0, -1 };
int p1[] = { 193, 15, 0, -1 };
......@@ -1561,7 +712,7 @@ int test_gf2m_mod_sqrt(BIO *bp, BN_CTX *ctx)
BN_GF2m_arr2poly(p0, b[0]);
BN_GF2m_arr2poly(p1, b[1]);
for (i = 0; i < num0; i++) {
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]);
......@@ -1570,12 +721,12 @@ int test_gf2m_mod_sqrt(BIO *bp, BN_CTX *ctx)
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");
printf("GF(2^m) modular square root test failed!\n");
goto err;
}
}
}
ret = 1;
st = 1;
err:
BN_free(a);
BN_free(b[0]);
......@@ -1584,13 +735,13 @@ int test_gf2m_mod_sqrt(BIO *bp, BN_CTX *ctx)
BN_free(d);
BN_free(e);
BN_free(f);
return ret;
return st;
}
int test_gf2m_mod_solve_quad(BIO *bp, BN_CTX *ctx)
static int test_gf2m_modsolvequad()
{
BIGNUM *a, *b[2], *c, *d, *e;
int i, j, s = 0, t, ret = 0;
int i, j, s = 0, t, st = 0;
int p0[] = { 163, 7, 6, 3, 0, -1 };
int p1[] = { 193, 15, 0, -1 };
......@@ -1604,7 +755,7 @@ int test_gf2m_mod_solve_quad(BIO *bp, BN_CTX *ctx)
BN_GF2m_arr2poly(p0, b[0]);
BN_GF2m_arr2poly(p1, b[1]);
for (i = 0; i < num0; i++) {
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);
......@@ -1618,8 +769,7 @@ int test_gf2m_mod_solve_quad(BIO *bp, BN_CTX *ctx)
* 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");
printf("GF(2^m) modular solve quadratic test failed!\n");
goto err;
}
......@@ -1627,14 +777,12 @@ int test_gf2m_mod_solve_quad(BIO *bp, BN_CTX *ctx)
}
}
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");
printf("All %i tests of GF(2^m) modular solve quadratic resulted in no roots;\n",
NUM0);
printf("this is very unlikely and probably indicates an error.\n");
goto err;
}
ret = 1;
st = 1;
err:
BN_free(a);
BN_free(b[0]);
......@@ -1642,453 +790,1392 @@ int test_gf2m_mod_solve_quad(BIO *bp, BN_CTX *ctx)
BN_free(c);
BN_free(d);
BN_free(e);
return ret;
return st;
}
#endif
static int genprime_cb(int p, int n, BN_GENCB *arg)
static int test_kronecker()
{
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;
BIGNUM *a, *b, *r, *t;
int i;
int legendre, kronecker;
int st = 0;
a = BN_new();
b = BN_new();
r = BN_new();
t = BN_new();
if (a == NULL || b == NULL || r == NULL || t == NULL)
goto err;
/*
* 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, NULL))
goto err;
b->neg = rand_neg();
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)) {
printf("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) {
printf("legendre != kronecker; a = ");
BN_print_fp(stdout, a);
printf(", b = ");
BN_print_fp(stdout, b);
printf("\n");
goto err;
}
}
st = 1;
err:
BN_free(a);
BN_free(b);
BN_free(r);
BN_free(t);
return st;
}
static int file_sum(STANZA *s)
{
BIGNUM *a = getBN(s, "A");
BIGNUM *b = getBN(s, "B");
BIGNUM *sum = getBN(s, "Sum");
BIGNUM *ret = BN_new();
BN_ULONG b_word;
int st = 0;
if (a == NULL || b == NULL || sum == NULL || ret == NULL)
goto err;
if (!BN_add(ret, a, b)
|| !equalBN("A + B", sum, ret)
|| !BN_sub(ret, sum, a)
|| !equalBN("Sum - A", b, ret)
|| !BN_sub(ret, sum, b)
|| !equalBN("Sum - B", a, ret))
goto err;
/*
* Test that the functions work when |r| and |a| point to the same BIGNUM,
* or when |r| and |b| point to the same BIGNUM.
* TODO: Test where all of |r|, |a|, and |b| point to the same BIGNUM.
*/
if (!BN_copy(ret, a)
|| !BN_add(ret, ret, b)
|| !equalBN("A + B (r is a)", sum, ret)
|| !BN_copy(ret, b)
|| !BN_add(ret, a, ret)
|| !equalBN("A + B (r is b)", sum, ret)
|| !BN_copy(ret, sum)
|| !BN_sub(ret, ret, a)
|| !equalBN("Sum - A (r is a)", b, ret)
|| !BN_copy(ret, a)
|| !BN_sub(ret, sum, ret)
|| !equalBN("Sum - A (r is b)", b, ret)
|| !BN_copy(ret, sum)
|| !BN_sub(ret, ret, b)
|| !equalBN("Sum - B (r is a)", a, ret)
|| !BN_copy(ret, b)
|| !BN_sub(ret, sum, ret)
|| !equalBN("Sum - B (r is b)", a, ret))
goto err;
/*
* Test BN_uadd() and BN_usub() with the prerequisites they are
* documented as having. Note that these functions are frequently used
* when the prerequisites don't hold. In those cases, they are supposed
* to work as if the prerequisite hold, but we don't test that yet.
* TODO: test that.
*/
if (!BN_is_negative(a) && !BN_is_negative(b) && BN_cmp(a, b) >= 0) {
if (!BN_uadd(ret, a, b)
|| !equalBN("A +u B", sum, ret)
|| !BN_usub(ret, sum, a)
|| !equalBN("Sum -u A", b, ret)
|| !BN_usub(ret, sum, b)
|| !equalBN("Sum -u B", a, ret))
goto err;
/*
* Test that the functions work when |r| and |a| point to the same
* BIGNUM, or when |r| and |b| point to the same BIGNUM.
* TODO: Test where all of |r|, |a|, and |b| point to the same BIGNUM.
*/
if (!BN_copy(ret, a)
|| !BN_uadd(ret, ret, b)
|| !equalBN("A +u B (r is a)", sum, ret)
|| !BN_copy(ret, b)
|| !BN_uadd(ret, a, ret)
|| !equalBN("A +u B (r is b)", sum, ret)
|| !BN_copy(ret, sum)
|| !BN_usub(ret, ret, a)
|| !equalBN("Sum -u A (r is a)", b, ret)
|| !BN_copy(ret, a)
|| !BN_usub(ret, sum, ret)
|| !equalBN("Sum -u A (r is b)", b, ret)
|| !BN_copy(ret, sum)
|| !BN_usub(ret, ret, b)
|| !equalBN("Sum -u B (r is a)", a, ret)
|| !BN_copy(ret, b)
|| !BN_usub(ret, sum, ret)
|| !equalBN("Sum -u B (r is b)", a, ret))
goto err;
}
/*
* Test with BN_add_word() and BN_sub_word() if |b| is small enough.
*/
b_word = BN_get_word(b);
if (!BN_is_negative(b) && b_word != (BN_ULONG)-1) {
if (!BN_copy(ret, a)
|| !BN_add_word(ret, b_word)
|| !equalBN("A + B (word)", sum, ret)
|| !BN_copy(ret, sum)
|| !BN_sub_word(ret, b_word)
|| !equalBN("Sum - B (word)", a, ret))
goto err;
}
st = 1;
err:
BN_free(a);
BN_free(b);
BN_free(sum);
BN_free(ret);
return st;
}
static int file_lshift1(STANZA *s)
{
BIGNUM *a = getBN(s, "A");
BIGNUM *lshift1 = getBN(s, "LShift1");
BIGNUM *zero = BN_new();
BIGNUM *ret = BN_new();
BIGNUM *two = BN_new();
BIGNUM *remainder = BN_new();
int st = 0;
if (a == NULL || lshift1 == NULL || zero == NULL
|| ret == NULL || two == NULL || remainder == NULL)
goto err;
BN_zero(zero);
if (!BN_set_word(two, 2)
|| !BN_add(ret, a, a)
|| !equalBN("A + A", lshift1, ret)
|| !BN_mul(ret, a, two, ctx)
|| !equalBN("A * 2", lshift1, ret)
|| !BN_div(ret, remainder, lshift1, two, ctx)
|| !equalBN("LShift1 / 2", a, ret)
|| !equalBN("LShift1 % 2", zero, remainder)
|| !BN_lshift1(ret, a)
|| !equalBN("A << 1", lshift1, ret)
|| !BN_rshift1(ret, lshift1)
|| !equalBN("LShift >> 1", a, ret)
|| !BN_rshift1(ret, lshift1)
|| !equalBN("LShift >> 1", a, ret))
goto err;
/* Set the LSB to 1 and test rshift1 again. */
if (!BN_set_bit(lshift1, 0)
|| !BN_div(ret, NULL /* rem */ , lshift1, two, ctx)
|| !equalBN("(LShift1 | 1) / 2", a, ret)
|| !BN_rshift1(ret, lshift1)
|| !equalBN("(LShift | 1) >> 1", a, ret))
goto err;
st = 1;
err:
BN_free(a);
BN_free(lshift1);
BN_free(zero);
BN_free(ret);
BN_free(two);
BN_free(remainder);
return st;
}
static int file_lshift(STANZA *s)
{
BIGNUM *a = getBN(s, "A");
BIGNUM *lshift = getBN(s, "LShift");
BIGNUM *ret = BN_new();
int n = 0;
int st = 0;
if (a == NULL || lshift == NULL || ret == NULL || !getint(s, &n, "N"))
goto err;
if (!BN_lshift(ret, a, n)
|| !equalBN("A << N", lshift, ret)
|| !BN_rshift(ret, lshift, n)
|| !equalBN("A >> N", a, ret))
goto err;
st = 1;
err:
BN_free(a);
BN_free(lshift);
BN_free(ret);
return st;
}
static int file_rshift(STANZA *s)
{
BIGNUM *a = getBN(s, "A");
BIGNUM *rshift = getBN(s, "RShift");
BIGNUM *ret = BN_new();
int n = 0;
int st = 0;
if (a == NULL || rshift == NULL || ret == NULL || !getint(s, &n, "N"))
goto err;
if (!BN_rshift(ret, a, n)
|| !equalBN("A >> N", rshift, ret))
goto err;
st = 1;
err:
BN_free(a);
BN_free(rshift);
BN_free(ret);
return st;
}
static int file_square(STANZA *s)
{
BIGNUM *a = getBN(s, "A");
BIGNUM *square = getBN(s, "Square");
BIGNUM *zero = BN_new();
BIGNUM *ret = BN_new();
BIGNUM *remainder = BN_new();
BIGNUM *tmp = NULL;
int st = 0;
if (a == NULL || square == NULL || zero == NULL || ret == NULL
|| remainder == NULL)
goto err;
BN_zero(zero);
if (!BN_sqr(ret, a, ctx)
|| !equalBN("A^2", square, ret)
|| !BN_mul(ret, a, a, ctx)
|| !equalBN("A * A", square, ret)
|| !BN_div(ret, remainder, square, a, ctx)
|| !equalBN("Square / A", a, ret)
|| !equalBN("Square % A", zero, remainder))
goto err;
#if HAVE_BN_SQRT
BN_set_negative(a, 0);
if (!BN_sqrt(ret, square, ctx)
|| !equalBN("sqrt(Square)", a, ret))
goto err;
/* BN_sqrt should fail on non-squares and negative numbers. */
if (!BN_is_zero(square)) {
tmp = BN_new();
if (tmp == NULL || !BN_copy(tmp, square))
goto err;
BN_set_negative(tmp, 1);
if (BN_sqrt(ret, tmp, ctx)) {
fprintf(stderr, "BN_sqrt succeeded on a negative number");
goto err;
}
ERR_clear_error();
BN_set_negative(tmp, 0);
if (BN_add(tmp, tmp, BN_value_one()))
goto err;
if (BN_sqrt(ret, tmp, ctx)) {
fprintf(stderr, "BN_sqrt succeeded on a non-square");
goto err;
}
ERR_clear_error();
}
#endif
st = 1;
err:
BN_free(a);
BN_free(square);
BN_free(zero);
BN_free(ret);
BN_free(remainder);
BN_free(tmp);
return st;
}
static int file_product(STANZA *s)
{
BIGNUM *a = getBN(s, "A");
BIGNUM *b = getBN(s, "B");
BIGNUM *product = getBN(s, "Product");
BIGNUM *ret = BN_new();
BIGNUM *remainder = BN_new();
BIGNUM *zero = BN_new();
int st = 0;
if (a == NULL || b == NULL || product == NULL || ret == NULL
|| remainder == NULL || zero == NULL)
goto err;
BN_zero(zero);
if (!BN_mul(ret, a, b, ctx)
|| !equalBN("A * B", product, ret)
|| !BN_div(ret, remainder, product, a, ctx)
|| !equalBN("Product / A", b, ret)
|| !equalBN("Product % A", zero, remainder)
|| !BN_div(ret, remainder, product, b, ctx)
|| !equalBN("Product / B", a, ret)
|| !equalBN("Product % B", zero, remainder))
goto err;
st = 1;
err:
BN_free(a);
BN_free(b);
BN_free(product);
BN_free(ret);
BN_free(remainder);
BN_free(zero);
return st;
}
static int file_quotient(STANZA *s)
{
BIGNUM *a = getBN(s, "A");
BIGNUM *b = getBN(s, "B");
BIGNUM *quotient = getBN(s, "Quotient");
BIGNUM *remainder = getBN(s, "Remainder");
BIGNUM *ret = BN_new();
BIGNUM *ret2 = BN_new();
BIGNUM *nnmod = BN_new();
BN_ULONG b_word, ret_word;
int st = 0;
if (a == NULL || b == NULL || quotient == NULL || remainder == NULL
|| ret == NULL || ret2 == NULL || nnmod == NULL)
goto err;
if (!BN_div(ret, ret2, a, b, ctx)
|| !equalBN("A / B", quotient, ret)
|| !equalBN("A % B", remainder, ret2)
|| !BN_mul(ret, quotient, b, ctx)
|| !BN_add(ret, ret, remainder)
|| !equalBN("Quotient * B + Remainder", a, ret))
goto err;
/*
* Test with BN_mod_word() and BN_div_word() if the divisor is
* small enough.
*/
b_word = BN_get_word(b);
if (!BN_is_negative(b) && b_word != (BN_ULONG)-1) {
BN_ULONG remainder_word = BN_get_word(remainder);
assert(remainder_word != (BN_ULONG)-1);
if (!BN_copy(ret, a))
goto err;
ret_word = BN_div_word(ret, b_word);
if (ret_word != remainder_word) {
#ifdef BN_DEC_FMT1
fprintf(stderr,
"Got A %% B (word) = " BN_DEC_FMT1 ", wanted " BN_DEC_FMT1 "\n",
ret_word, remainder_word);
#else
fprintf(stderr, "Got A %% B (word) mismatch\n");
#endif
goto err;
}
if (!equalBN ("A / B (word)", quotient, ret))
goto err;
ret_word = BN_mod_word(a, b_word);
if (ret_word != remainder_word) {
#ifdef BN_DEC_FMT1
fprintf(stderr,
"Got A %% B (word) = " BN_DEC_FMT1 ", wanted " BN_DEC_FMT1 "\n",
ret_word, remainder_word);
#else
fprintf(stderr, "Got A %% B (word) mismatch\n");
#endif
goto err;
}
}
/* Test BN_nnmod. */
if (!BN_is_negative(b)) {
if (!BN_copy(nnmod, remainder)
|| (BN_is_negative(nnmod) && !BN_add(nnmod, nnmod, b))
|| !BN_nnmod(ret, a, b, ctx)
|| !equalBN("A % B (non-negative)", nnmod, ret))
goto err;
}
st = 1;
err:
BN_free(a);
BN_free(b);
BN_free(quotient);
BN_free(remainder);
BN_free(ret);
BN_free(ret2);
BN_free(nnmod);
return st;
}
static int file_modmul(STANZA *s)
{
BIGNUM *a = getBN(s, "A");
BIGNUM *b = getBN(s, "B");
BIGNUM *m = getBN(s, "M");
BIGNUM *mod_mul = getBN(s, "ModMul");
BIGNUM *ret = BN_new();
int st = 0;
if (a == NULL || b == NULL || m == NULL || mod_mul == NULL || ret == NULL)
goto err;
if (!BN_mod_mul(ret, a, b, m, ctx)
|| !equalBN("A * B (mod M)", mod_mul, ret))
goto err;
if (BN_is_odd(m)) {
/* Reduce |a| and |b| and test the Montgomery version. */
BN_MONT_CTX *mont = BN_MONT_CTX_new();
BIGNUM *a_tmp = BN_new();
BIGNUM *b_tmp = BN_new();
if (mont == NULL || a_tmp == NULL || b_tmp == NULL
|| !BN_MONT_CTX_set(mont, m, ctx)
|| !BN_nnmod(a_tmp, a, m, ctx)
|| !BN_nnmod(b_tmp, b, m, ctx)
|| !BN_to_montgomery(a_tmp, a_tmp, mont, ctx)
|| !BN_to_montgomery(b_tmp, b_tmp, mont, ctx)
|| !BN_mod_mul_montgomery(ret, a_tmp, b_tmp, mont, ctx)
|| !BN_from_montgomery(ret, ret, mont, ctx)
|| !equalBN("A * B (mod M) (mont)", mod_mul, ret)) {
st = 0;
} else {
st = 1;
}
BN_MONT_CTX_free(mont);
BN_free(a_tmp);
BN_free(b_tmp);
if (st == 0)
goto err;
}
st = 1;
err:
BN_free(a);
BN_free(b);
BN_free(m);
BN_free(mod_mul);
BN_free(ret);
return st;
}
static int file_modexp(STANZA *s)
{
BIGNUM *a = getBN(s, "A");
BIGNUM *e = getBN(s, "E");
BIGNUM *m = getBN(s, "M");
BIGNUM *mod_exp = getBN(s, "ModExp");
BIGNUM *ret = BN_new();
BIGNUM *b = NULL, *c = NULL, *d = BN_new();
int st = 0;
if (a == NULL || e == NULL || m == NULL || mod_exp == NULL || ret == NULL)
goto err;
if (!BN_mod_exp(ret, a, e, m, ctx)
|| !equalBN("A ^ E (mod M)", mod_exp, ret))
goto err;
if (BN_is_odd(m)) {
if (!BN_mod_exp_mont(ret, a, e, m, ctx, NULL)
|| !equalBN("A ^ E (mod M) (mont)", mod_exp, ret)
|| !BN_mod_exp_mont_consttime(ret, a, e, m, ctx, NULL)
|| !equalBN("A ^ E (mod M) (mont const", mod_exp, ret))
goto err;
}
/* Regression test for carry propagation bug in sqr8x_reduction */
BN_hex2bn(&a, "050505050505");
BN_hex2bn(&b, "02");
BN_hex2bn(&c,
"4141414141414141414141274141414141414141414141414141414141414141"
"4141414141414141414141414141414141414141414141414141414141414141"
"4141414141414141414141800000000000000000000000000000000000000000"
"0000000000000000000000000000000000000000000000000000000000000000"
"0000000000000000000000000000000000000000000000000000000000000000"
"0000000000000000000000000000000000000000000000000000000001");
BN_mod_exp(d, a, b, c, ctx);
BN_mul(e, a, a, ctx);
if (BN_cmp(d, e)) {
fprintf(stderr, "BN_mod_exp and BN_mul produce different results!\n");
goto err;
}
st = 1;
err:
BN_free(a);
BN_free(b);
BN_free(c);
BN_free(d);
BN_free(e);
BN_free(m);
BN_free(mod_exp);
BN_free(ret);
return st;
}
static int file_exp(STANZA *s)
{
BIGNUM *a = getBN(s, "A");
BIGNUM *e = getBN(s, "E");
BIGNUM *exp = getBN(s, "Exp");
BIGNUM *ret = BN_new();
int st = 0;
if (a == NULL || e == NULL || exp == NULL || ret == NULL)
goto err;
if (!BN_exp(ret, a, e, ctx)
|| !equalBN("A ^ E", exp, ret))
goto err;
st = 1;
err:
BN_free(a);
BN_free(e);
BN_free(exp);
BN_free(ret);
return st;
}
static int file_modsqrt(STANZA *s)
{
BIGNUM *a = getBN(s, "A");
BIGNUM *p = getBN(s, "P");
BIGNUM *mod_sqrt = getBN(s, "ModSqrt");
BIGNUM *ret = BN_new();
BIGNUM *ret2 = BN_new();
int st = 0;
if (a == NULL || p == NULL || mod_sqrt == NULL
|| ret == NULL || ret2 == NULL)
goto err;
/* There are two possible answers. */
if (!BN_mod_sqrt(ret, a, p, ctx) || !BN_sub(ret2, p, ret))
goto err;
if (BN_cmp(ret2, mod_sqrt) != 0
&& !equalBN("sqrt(A) (mod P)", mod_sqrt, ret))
goto err;
st = 1;
err:
BN_free(a);
BN_free(p);
BN_free(mod_sqrt);
BN_free(ret);
BN_free(ret2);
return st;
}
static int test_bn2padded()
{
#if HAVE_BN_PADDED
uint8_t zeros[256], out[256], reference[128];
BIGNUM *n = BN_new();
int st = 0;
/* Test edge case at 0. */
if (n == NULL)
goto err;
if (!BN_bn2bin_padded(NULL, 0, n)) {
fprintf(stderr,
"BN_bn2bin_padded failed to encode 0 in an empty buffer.\n");
goto err;
}
memset(out, -1, sizeof(out));
if (!BN_bn2bin_padded(out, sizeof(out), n)) {
fprintf(stderr,
"BN_bn2bin_padded failed to encode 0 in a non-empty buffer.\n");
goto err;
}
memset(zeros, 0, sizeof(zeros));
if (memcmp(zeros, out, sizeof(out))) {
fprintf(stderr, "BN_bn2bin_padded did not zero buffer.\n");
goto err;
}
/* Test a random numbers at various byte lengths. */
for (size_t bytes = 128 - 7; bytes <= 128; bytes++) {
#define TOP_BIT_ON 0
#define BOTTOM_BIT_NOTOUCH 0
if (!BN_rand(n, bytes * 8, TOP_BIT_ON, BOTTOM_BIT_NOTOUCH)) {
ERR_print_errors_fp(stderr);
goto err;
}
if (BN_num_bytes(n) != bytes
|| BN_bn2bin(n, reference) != bytes) {
fprintf(stderr, "Bad result from BN_rand; bytes.\n");
goto err;
}
/* Empty buffer should fail. */
if (BN_bn2bin_padded(NULL, 0, n)) {
fprintf(stderr,
"BN_bn2bin_padded incorrectly succeeded on empty buffer.\n");
goto err;
}
/* One byte short should fail. */
if (BN_bn2bin_padded(out, bytes - 1, n)) {
fprintf(stderr,
"BN_bn2bin_padded incorrectly succeeded on short.\n");
goto err;
}
/* Exactly right size should encode. */
if (!BN_bn2bin_padded(out, bytes, n)
|| memcmp(out, reference, bytes) != 0) {
fprintf(stderr,
"BN_bn2bin_padded gave a bad result.\n");
goto err;
}
/* Pad up one byte extra. */
if (!BN_bn2bin_padded(out, bytes + 1, n)
|| memcmp(out + 1, reference, bytes)
|| memcmp(out, zeros, 1)) {
fprintf(stderr,
"BN_bn2bin_padded gave a bad result.\n");
goto err;
}
/* Pad up to 256. */
if (!BN_bn2bin_padded(out, sizeof(out), n)
|| memcmp(out + sizeof(out) - bytes, reference, bytes)
|| memcmp(out, zeros, sizeof(out) - bytes)) {
fprintf(stderr,
"BN_bn2bin_padded gave a bad result.\n");
goto err;
}
}
st = 1;
err:
BN_free(n);
return st;
#else
return ctx != NULL;
#endif
}
static int test_dec2bn()
{
BIGNUM *bn = NULL;
int st = 0;
int ret = parsedecBN(&bn, "0");
if (ret != 1 || !BN_is_zero(bn) || BN_is_negative(bn)) {
fprintf(stderr, "BN_dec2bn(0) gave a bad result.\n");
goto err;
}
BN_free(bn);
ret = parsedecBN(&bn, "256");
if (ret != 3 || !BN_is_word(bn, 256) || BN_is_negative(bn)) {
fprintf(stderr, "BN_dec2bn(256) gave a bad result.\n");
goto err;
}
BN_free(bn);
ret = parsedecBN(&bn, "-42");
if (ret != 3 || !BN_abs_is_word(bn, 42) || !BN_is_negative(bn)) {
fprintf(stderr, "BN_dec2bn(42) gave a bad result.\n");
goto err;
}
BN_free(bn);
ret = parsedecBN(&bn, "-0");
if (ret != 2 || !BN_is_zero(bn) || BN_is_negative(bn)) {
fprintf(stderr, "BN_dec2bn(-0) gave a bad result.\n");
goto err;
}
BN_free(bn);
ret = parsedecBN(&bn, "42trailing garbage is ignored");
if (ret != 2 || !BN_abs_is_word(bn, 42)
|| BN_is_negative(bn)) {
fprintf(stderr, "BN_dec2bn(42trailing...) gave a bad result.\n");
goto err;
}
st = 1;
err:
BN_free(bn);
return st;
}
static int test_hex2bn()
{
BIGNUM *bn = NULL;
int ret, st = 0;
ret = parseBN(&bn, "0");
if (ret != 1 || !BN_is_zero(bn) || BN_is_negative(bn)) {
fprintf(stderr, "BN_hex2bn(0) gave a bad result.\n");
goto err;
}
BN_free(bn);
ret = parseBN(&bn, "256");
if (ret != 3 || !BN_is_word(bn, 0x256) || BN_is_negative(bn)) {
fprintf(stderr, "BN_hex2bn(256) gave a bad result.\n");
goto err;
}
BN_free(bn);
ret = parseBN(&bn, "-42");
if (ret != 3 || !BN_abs_is_word(bn, 0x42) || !BN_is_negative(bn)) {
fprintf(stderr, "BN_hex2bn(-42) gave a bad result.\n");
goto err;
}
BN_free(bn);
ret = parseBN(&bn, "-0");
if (ret != 2 || !BN_is_zero(bn) || BN_is_negative(bn)) {
fprintf(stderr, "BN_hex2bn(-0) gave a bad result.\n");
goto err;
}
BN_free(bn);
ret = parseBN(&bn, "abctrailing garbage is ignored");
if (ret != 3 || !BN_is_word(bn, 0xabc) || BN_is_negative(bn)) {
fprintf(stderr, "BN_hex2bn(abctrail...) gave a bad result.\n");
goto err;
}
st = 1;
err:
BN_free(bn);
return st;
}
static int test_asc2bn()
{
BIGNUM *bn = BN_new();
int st = 0;
if (!BN_asc2bn(&bn, "0") || !BN_is_zero(bn) || BN_is_negative(bn)) {
fprintf(stderr, "BN_asc2bn(0) gave a bad result.\n");
goto err;
}
if (!BN_asc2bn(&bn, "256") || !BN_is_word(bn, 256) || BN_is_negative(bn)) {
fprintf(stderr, "BN_asc2bn(256) gave a bad result.\n");
goto err;
}
if (!BN_asc2bn(&bn, "-42")
|| !BN_abs_is_word(bn, 42) || !BN_is_negative(bn)) {
fprintf(stderr, "BN_asc2bn(-42) gave a bad result.\n");
goto err;
}
if (!BN_asc2bn(&bn, "0x1234")
|| !BN_is_word(bn, 0x1234) || BN_is_negative(bn)) {
fprintf(stderr, "BN_asc2bn(0x1234) gave a bad result.\n");
goto err;
}
if (!BN_asc2bn(&bn, "0X1234")
|| !BN_is_word(bn, 0x1234) || BN_is_negative(bn)) {
fprintf(stderr, "BN_asc2bn(0X1234) gave a bad result.\n");
goto err;
}
if (!BN_asc2bn(&bn, "-0xabcd")
|| !BN_abs_is_word(bn, 0xabcd) || !BN_is_negative(bn)) {
fprintf(stderr, "BN_asc2bn(-0xabcd) gave a bad result.\n");
goto err;
}
if (!BN_asc2bn(&bn, "-0") || !BN_is_zero(bn) || BN_is_negative(bn)) {
fprintf(stderr, "BN_asc2bn(-0) gave a bad result.\n");
goto err;
}
if (!BN_asc2bn(&bn, "123trailing garbage is ignored")
|| !BN_is_word(bn, 123) || BN_is_negative(bn)) {
fprintf(stderr, "BN_asc2bn(123trail...) gave a bad result.\n");
goto err;
}
st = 1;
err:
BN_free(bn);
return st;
}
static const MPITEST kMPITests[] = {
{"0", "\x00\x00\x00\x00", 4},
{"1", "\x00\x00\x00\x01\x01", 5},
{"-1", "\x00\x00\x00\x01\x81", 5},
{"128", "\x00\x00\x00\x02\x00\x80", 6},
{"256", "\x00\x00\x00\x02\x01\x00", 6},
{"-256", "\x00\x00\x00\x02\x81\x00", 6},
};
static int test_mpi()
{
uint8_t scratch[8];
int i = (int)sizeof(kMPITests) / sizeof(kMPITests[0]);
const MPITEST *test = kMPITests;
size_t mpi_len, mpi_len2;
BIGNUM *bn = BN_new();
BIGNUM *bn2 = NULL;
int st = 0;
for ( ; --i >= 0; test++) {
if (!BN_asc2bn(&bn, test->base10)) {
fprintf(stderr, "Can't convert %s\n", test->base10);
goto err;
}
mpi_len = BN_bn2mpi(bn, NULL);
if (mpi_len > sizeof (scratch)) {
fprintf(stderr,
"MPI test #%u: MPI size is too large to test.\n",
(unsigned)i);
goto err;
}
mpi_len2 = BN_bn2mpi(bn, scratch);
if (mpi_len != mpi_len2) {
fprintf(stderr, "MPI test #%u: length changes.\n",
(unsigned)i);
goto err;
}
if (mpi_len != test->mpi_len
|| memcmp(test->mpi, scratch, mpi_len) != 0) {
fprintf(stderr, "MPI test #%u failed:\n", (unsigned)i);
goto err;
}
bn2 = BN_mpi2bn(scratch, mpi_len, NULL);
if (bn2 == NULL) {
fprintf(stderr, "MPI test #%u: failed to parse\n",
(unsigned)i);
goto err;
}
if (BN_cmp(bn, bn2) != 0) {
fprintf(stderr, "MPI test #%u: wrong result\n",
(unsigned)i);
BN_free(bn2);
goto err;
}
BN_free(bn2);
}
st = 1;
err:
BN_free(bn);
return st;
}
int test_kron(BIO *bp, BN_CTX *ctx)
static int test_rand()
{
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;
BIGNUM *bn = BN_new();
int st = 0;
BN_GENCB_set(&cb, genprime_cb, NULL);
if (bn == NULL)
return 0;
/*
* 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.)
* Test BN_rand for degenerate cases with |top| and |bottom| parameters.
*/
if (BN_rand(bn, 0, 0 /* top */ , 0 /* bottom */ )) {
fprintf(stderr, "BN_rand1 gave a bad result.\n");
goto err;
}
if (BN_rand(bn, 0, 1 /* top */ , 1 /* bottom */ )) {
fprintf(stderr, "BN_rand2 gave a bad result.\n");
goto err;
}
if (!BN_generate_prime_ex(b, 512, 0, NULL, NULL, &cb))
if (!BN_rand(bn, 1, 0 /* top */ , 0 /* bottom */ ) || !BN_is_word(bn, 1)) {
fprintf(stderr, "BN_rand3 gave a bad result.\n");
goto err;
b->neg = rand_neg();
putc('\n', stderr);
}
if (BN_rand(bn, 1, 1 /* top */ , 0 /* bottom */ )) {
fprintf(stderr, "BN_rand4 gave a bad result.\n");
goto err;
}
if (!BN_rand(bn, 1, -1 /* top */ , 1 /* bottom */ ) || !BN_is_word(bn, 1)) {
fprintf(stderr, "BN_rand5 gave a bad result.\n");
goto err;
}
for (i = 0; i < num0; i++) {
if (!BN_bntest_rand(a, 512, 0, 0))
goto err;
a->neg = rand_neg();
if (!BN_rand(bn, 2, 1 /* top */ , 0 /* bottom */ ) || !BN_is_word(bn, 3)) {
fprintf(stderr, "BN_rand6 gave a bad result.\n");
goto err;
}
/* t := (|b|-1)/2 (note that b is odd) */
if (!BN_copy(t, b))
st = 1;
err:
BN_free(bn);
return st;
}
static int test_negzero()
{
BIGNUM *a = BN_new();
BIGNUM *b = BN_new();
BIGNUM *c = BN_new();
BIGNUM *d = BN_new();
BIGNUM *numerator = NULL, *denominator = NULL;
int consttime, st = 0;
if (a == NULL || b == NULL || c == NULL || d == NULL)
goto err;
/* Test that BN_mul never gives negative zero. */
if (!BN_set_word(a, 1))
goto err;
BN_set_negative(a, 1);
BN_zero(b);
if (!BN_mul(c, a, b, ctx))
goto err;
if (!BN_is_zero(c) || BN_is_negative(c)) {
fprintf(stderr, "Multiplication test failed!\n");
goto err;
}
for (consttime = 0; consttime < 2; consttime++) {
numerator = BN_new();
denominator = BN_new();
if (numerator == NULL || denominator == NULL)
goto err;
t->neg = 0;
if (!BN_sub_word(t, 1))
if (consttime) {
BN_set_flags(numerator, BN_FLG_CONSTTIME);
BN_set_flags(denominator, BN_FLG_CONSTTIME);
}
/* Test that BN_div never gives negative zero in the quotient. */
if (!BN_set_word(numerator, 1) || !BN_set_word(denominator, 2))
goto err;
if (!BN_rshift1(t, t))
BN_set_negative(numerator, 1);
if (!BN_div(a, b, numerator, denominator, ctx))
goto err;
/* r := a^t mod b */
b->neg = 0;
if (!BN_mod_exp_recp(r, a, t, b, ctx))
if (!BN_is_zero(a) || BN_is_negative(a)) {
fprintf(stderr, "Incorrect quotient (consttime = %d).\n",
consttime);
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)
/* Test that BN_div never gives negative zero in the remainder. */
if (!BN_set_word(denominator, 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");
if (!BN_div(a, b, numerator, denominator, ctx))
goto err;
if (!BN_is_zero(b) || BN_is_negative(b)) {
fprintf(stderr, "Incorrect remainder (consttime = %d).\n",
consttime);
goto err;
}
BN_free(numerator);
BN_free(denominator);
numerator = denominator = NULL;
}
putc('.', stderr);
fflush(stderr);
/* Test that BN_set_negative will not produce a negative zero. */
BN_zero(a);
BN_set_negative(a, 1);
if (BN_is_negative(a)) {
fprintf(stderr, "BN_set_negative produced a negative zero.\n");
goto err;
}
putc('\n', stderr);
fflush(stderr);
ret = 1;
err:
st = 1;
err:
BN_free(a);
BN_free(b);
BN_free(r);
BN_free(t);
return ret;
BN_free(c);
BN_free(d);
BN_free(numerator);
BN_free(denominator);
return st;
}
int test_sqrt(BIO *bp, BN_CTX *ctx)
static int test_badmod()
{
BN_GENCB cb;
BIGNUM *a, *p, *r;
int i, j;
int ret = 0;
BIGNUM *a = BN_new();
BIGNUM *b = BN_new();
BIGNUM *zero = BN_new();
BN_MONT_CTX *mont = BN_MONT_CTX_new();
int st = 0;
a = BN_new();
p = BN_new();
r = BN_new();
if (a == NULL || p == NULL || r == NULL)
if (a == NULL || b == NULL || zero == NULL || mont == NULL)
goto err;
BN_zero(zero);
BN_GENCB_set(&cb, genprime_cb, NULL);
if (BN_div(a, b, BN_value_one(), zero, ctx)) {
fprintf(stderr, "Division by zero succeeded!\n");
goto err;
}
ERR_clear_error();
for (i = 0; i < 16; i++) {
if (i < 8) {
unsigned primes[8] = { 2, 3, 5, 7, 11, 13, 17, 19 };
if (BN_mod_mul(a, BN_value_one(), BN_value_one(), zero, ctx)) {
fprintf(stderr, "BN_mod_mul with zero modulus succeeded!\n");
goto err;
}
ERR_clear_error();
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_mod_exp(a, BN_value_one(), BN_value_one(), zero, ctx)) {
fprintf(stderr, "BN_mod_exp with zero modulus succeeded!\n");
goto err;
}
ERR_clear_error();
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_exp_mont(a, BN_value_one(), BN_value_one(), zero, ctx, NULL)) {
fprintf(stderr, "BN_mod_exp_mont with zero modulus succeeded!\n");
goto err;
}
ERR_clear_error();
if (!BN_mod_sqrt(r, a, p, ctx))
goto err;
if (!BN_mod_sqr(r, r, p, ctx))
goto err;
if (BN_mod_exp_mont_consttime(a, BN_value_one(), BN_value_one(),
zero, ctx, NULL)) {
fprintf(stderr,
"BN_mod_exp_mont_consttime with zero modulus succeeded!\n");
goto err;
}
ERR_clear_error();
if (!BN_nnmod(a, a, p, ctx))
goto err;
if (BN_MONT_CTX_set(mont, zero, ctx)) {
fprintf(stderr, "BN_MONT_CTX_set succeeded for zero modulus!\n");
goto err;
}
ERR_clear_error();
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;
}
/* Some operations also may not be used with an even modulus. */
if (!BN_set_word(b, 16))
goto err;
putc('.', stderr);
fflush(stderr);
}
if (BN_MONT_CTX_set(mont, b, ctx)) {
fprintf(stderr,
"BN_MONT_CTX_set succeeded for even modulus!\n");
goto err;
}
ERR_clear_error();
putc('\n', stderr);
fflush(stderr);
if (BN_mod_exp_mont(a, BN_value_one(), BN_value_one(), b, ctx, NULL)) {
fprintf(stderr,
"BN_mod_exp_mont with even modulus succeeded!\n");
goto err;
}
ret = 1;
err:
ERR_clear_error();
if (BN_mod_exp_mont_consttime(a, BN_value_one(), BN_value_one(),
b, ctx, NULL)) {
fprintf(stderr,
"BN_mod_exp_mont_consttime with even modulus succeeded!\n");
goto err;
}
ERR_clear_error();
st = 1;
err:
BN_free(a);
BN_free(p);
BN_free(r);
return ret;
BN_free(b);
BN_free(zero);
BN_MONT_CTX_free(mont);
return st;
}
int test_small_prime(BIO *bp, BN_CTX *ctx)
static int test_expmodzero()
{
static const int bits = 10;
int ret = 0;
BIGNUM *r;
BIGNUM *zero = BN_new();
BIGNUM *a = BN_new();
BIGNUM *r = BN_new();
int st = 0;
r = BN_new();
if (!BN_generate_prime_ex(r, bits, 0, NULL, NULL, NULL))
if (zero == NULL || a == NULL || r == NULL || !BN_rand(a, 1024, 0, 0))
goto err;
if (BN_num_bits(r) != bits) {
BIO_printf(bp, "Expected %d bit prime, got %d bit number\n", bits,
BN_num_bits(r));
BN_zero(zero);
if (!BN_mod_exp(r, a, zero, BN_value_one(), NULL)
|| !BN_is_zero(r)
|| !BN_mod_exp_mont(r, a, zero, BN_value_one(), NULL, NULL)
|| !BN_is_zero(r)
|| !BN_mod_exp_mont_consttime(r, a, zero, BN_value_one(), NULL, NULL)
|| !BN_is_zero(r)
|| !BN_mod_exp_mont_word(r, 42, zero, BN_value_one(), NULL, NULL)
|| !BN_is_zero(r))
goto err;
}
ret = 1;
err:
BN_clear_free(r);
return ret;
st = 1;
err:
BN_free(zero);
BN_free(a);
BN_free(r);
return st;
}
int test_bn2dec(BIO *bp)
static int test_smallprime()
{
static const char *bn2dec_tests[] = {
"0",
"1",
"-1",
"100",
"-100",
"123456789012345678901234567890",
"-123456789012345678901234567890",
"123456789012345678901234567890123456789012345678901234567890",
"-123456789012345678901234567890123456789012345678901234567890",
};
int ret = 0;
size_t i;
BIGNUM *bn = NULL;
char *dec = NULL;
static const int kBits = 10;
BIGNUM *r = BN_new();
int st = 0;
for (i = 0; i < OSSL_NELEM(bn2dec_tests); i++) {
if (!BN_dec2bn(&bn, bn2dec_tests[i]))
goto err;
if (r == NULL
|| !BN_generate_prime_ex(r, (int)kBits, 0, NULL, NULL, NULL))
goto err;
if (BN_num_bits(r) != kBits) {
fprintf(stderr, "Expected %u bit prime, got %u bit number\n",
kBits, BN_num_bits(r));
goto err;
}
dec = BN_bn2dec(bn);
if (dec == NULL) {
fprintf(stderr, "BN_bn2dec failed on %s.\n", bn2dec_tests[i]);
goto err;
}
st = 1;
err:
BN_free(r);
return st;
}
if (strcmp(dec, bn2dec_tests[i]) != 0) {
fprintf(stderr, "BN_bn2dec gave %s, wanted %s.\n", dec,
bn2dec_tests[i]);
goto err;
}
OPENSSL_free(dec);
dec = NULL;
}
/* Delete leading and trailing spaces from a string */
static char *strip_spaces(char *p)
{
char *q;
ret = 1;
/* Skip over leading spaces */
while (*p && isspace(*p))
p++;
if (!*p)
return NULL;
err:
BN_free(bn);
OPENSSL_free(dec);
return ret;
for (q = p + strlen(p) - 1; q != p && isspace(*q); )
*q-- = '\0';
return *p ? p : NULL;
}
int test_lshift(BIO *bp, BN_CTX *ctx, BIGNUM *a_)
/*
* Read next test stanza; return 1 if found, 0 on EOF or error.
*/
static int readstanza(STANZA *s, int *linesread)
{
BIGNUM *a, *b, *c, *d;
int i;
PAIR *pp = s->pairs;
char *p, *equals, *key, *value;
char buff[1024];
while (fgets(buff, sizeof(buff), fp) != NULL) {
(*linesread)++;
if ((p = strchr(buff, '\n')) == NULL) {
fprintf(stderr, "Line %d too long.\n", s->start);
return 0;
}
*p = '\0';
b = BN_new();
c = BN_new();
d = BN_new();
BN_one(c);
/* Blank line marks end of tests. */
if (buff[0] == '\0')
break;
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");
/* Lines starting with a pound sign are ignored. */
if (buff[0] == '#')
continue;
if ((equals = strchr(buff, '=')) == NULL) {
fprintf(stderr, "Line %d missing equals.\n", s->start);
return 0;
}
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");
*equals++ = '\0';
key = strip_spaces(buff);
value = strip_spaces(equals);
if (key == NULL || value == NULL) {
fprintf(stderr, "Line %d missing field.\n", s->start);
return 0;
}
s->numpairs++;
if (s->numpairs >= MAXPAIRS) {
fprintf(stderr, "Line %d too many lines\n", s->start);
return 0;
}
pp->key = OPENSSL_strdup(key);
pp->value = OPENSSL_strdup(value);
pp++;
}
BN_free(a);
BN_free(b);
BN_free(c);
BN_free(d);
return (1);
/* If we read anything, return ok. */
return 1;
}
int test_lshift1(BIO *bp)
static void clearstanza(STANZA *s)
{
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;
}
PAIR *pp = s->pairs;
int i = s->numpairs;
int start = s->start;
BN_copy(a, b);
for ( ; --i >= 0; pp++) {
OPENSSL_free(pp->key);
OPENSSL_free(pp->value);
}
BN_free(a);
BN_free(b);
BN_free(c);
return (1);
memset(s, 0, sizeof(*s));
s->start = start;
}
int test_rshift(BIO *bp, BN_CTX *ctx)
static int file_test_run(STANZA *s)
{
BIGNUM *a, *b, *c, *d, *e;
int i;
static const FILETEST filetests[] = {
{"Sum", file_sum},
{"LShift1", file_lshift1},
{"LShift", file_lshift},
{"RShift", file_rshift},
{"Square", file_square},
{"Product", file_product},
{"Quotient", file_quotient},
{"ModMul", file_modmul},
{"ModExp", file_modexp},
{"Exp", file_exp},
{"ModSqrt", file_modsqrt},
};
int numtests = OSSL_NELEM(filetests);
const FILETEST *tp = filetests;
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;
}
for ( ; --numtests >= 0; tp++) {
if (findattr(s, tp->name) != NULL)
return tp->func(s);
}
BN_free(a);
BN_free(b);
BN_free(c);
BN_free(d);
BN_free(e);
return (1);
fprintf(stderr, "Unknown test at %d\n", s->start);
return 0;
}
int test_rshift1(BIO *bp)
static int file_tests()
{
BIGNUM *a, *b, *c;
int i;
a = BN_new();
b = BN_new();
c = BN_new();
STANZA s;
int linesread = 0, result = 0;
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;
/* Read test file. */
memset(&s, 0, sizeof(s));
while (!feof(fp) && readstanza(&s, &linesread)) {
if (s.numpairs == 0)
continue;
if (!file_test_run(&s)) {
if (result == 0)
fprintf(stderr, "Test at %d failed\n", s.start);
goto err;
}
BN_copy(a, b);
clearstanza(&s);
s.start = linesread;
}
BN_free(a);
BN_free(b);
BN_free(c);
return (1);
result = 1;
err:
return result;
}
int rand_neg(void)
int test_main(int argc, char *argv[])
{
static unsigned int neg = 0;
static int sign[8] = { 0, 0, 0, 1, 1, 0, 1, 1 };
static const char rnd_seed[] =
"If not seeded, BN_generate_prime might fail";
int result = 0;
if (argc != 2) {
fprintf(stderr, "%s TEST_FILE\n", argv[0]);
return 1;
}
ADD_TEST(test_sub);
ADD_TEST(test_div_recip);
ADD_TEST(test_mod);
ADD_TEST(test_modexp_mont5);
ADD_TEST(test_kronecker);
ADD_TEST(test_rand);
ADD_TEST(test_bn2padded);
ADD_TEST(test_dec2bn);
ADD_TEST(test_hex2bn);
ADD_TEST(test_asc2bn);
ADD_TEST(test_mpi);
ADD_TEST(test_negzero);
ADD_TEST(test_badmod);
ADD_TEST(test_expmodzero);
ADD_TEST(test_smallprime);
#ifndef OPENSSL_NO_EC2M
ADD_TEST(test_gf2m_add);
ADD_TEST(test_gf2m_mod);
ADD_TEST(test_gf2m_mul);
ADD_TEST(test_gf2m_sqr);
ADD_TEST(test_gf2m_modinv);
ADD_TEST(test_gf2m_moddiv);
ADD_TEST(test_gf2m_modexp);
ADD_TEST(test_gf2m_modsqrt);
ADD_TEST(test_gf2m_modsolvequad);
#endif
ADD_TEST(file_tests);
return (sign[(neg++) % 8]);
RAND_seed(rnd_seed, sizeof rnd_seed);
ctx = BN_CTX_new();
TEST_check(ctx != NULL);
fp = fopen(argv[1], "r");
TEST_check(fp != NULL);
result = run_tests(argv[0]);
fclose(fp);
BN_CTX_free(ctx);
return result;
}
test/bntests.pl 0 → 100755
浏览文件 @ 8d1ebff4
#! /usr/bin/env perl
# Copyright 2008-2016 The OpenSSL Project Authors. All Rights Reserved.
#
# Licensed under the OpenSSL license (the "License"). You may not use
# this file except in compliance with the License. You can obtain a copy
# in the file LICENSE in the source distribution or at
# https://www.openssl.org/source/license.html
# Run the tests specified in bntests.txt, as a check against OpenSSL.
use strict;
use warnings;
use Math::BigInt;
my $EXPECTED_FAILURES = 0;
my $failures = 0;
sub bn
{
my $x = shift;
my ($sign, $hex) = ($x =~ /^([+\-]?)(.*)$/);
$hex = '0x' . $hex if $hex !~ /^0x/;
return Math::BigInt->from_hex($sign.$hex);
}
sub evaluate
{
my $lineno = shift;
my %s = @_;
if ( defined $s{'Sum'} ) {
# Sum = A + B
my $sum = bn($s{'Sum'});
my $a = bn($s{'A'});
my $b = bn($s{'B'});
return if $sum == $a + $b;
} elsif ( defined $s{'LShift1'} ) {
# LShift1 = A * 2
my $lshift1 = bn($s{'LShift1'});
my $a = bn($s{'A'});
return if $lshift1 == $a->bmul(2);
} elsif ( defined $s{'LShift'} ) {
# LShift = A * 2**N
my $lshift = bn($s{'LShift'});
my $a = bn($s{'A'});
my $n = bn($s{'N'});
return if $lshift == $a->blsft($n);
} elsif ( defined $s{'RShift'} ) {
# RShift = A / 2**N
my $rshift = bn($s{'RShift'});
my $a = bn($s{'A'});
my $n = bn($s{'N'});
return if $rshift == $a->brsft($n);
} elsif ( defined $s{'Square'} ) {
# Square = A * A
my $square = bn($s{'Square'});
my $a = bn($s{'A'});
return if $square == $a->bmul($a);
} elsif ( defined $s{'Product'} ) {
# Product = A * B
my $product = bn($s{'Product'});
my $a = bn($s{'A'});
my $b = bn($s{'B'});
return if $product == $a->bmul($b);
} elsif ( defined $s{'Quotient'} ) {
# Quotient = A / B
# Remainder = A - B * Quotient
my $quotient = bn($s{'Quotient'});
my $remainder = bn($s{'Remainder'});
my $a = bn($s{'A'});
my $b = bn($s{'B'});
# First the remainder test.
$b->bmul($quotient);
my $rempassed = $remainder == $a->bsub($b) ? 1 : 0;
# Math::BigInt->bdiv() is documented to do floored division,
# i.e. 1 / -4 = -1, while OpenSSL BN_div does truncated
# division, i.e. 1 / -4 = 0. We need to make the operation
# work like OpenSSL's BN_div to be able to verify.
$a = bn($s{'A'});
$b = bn($s{'B'});
my $neg = $a->is_neg() ? !$b->is_neg() : $b->is_neg();
$a->babs();
$b->babs();
$a->bdiv($b);
$a->bneg() if $neg;
return if $rempassed && $quotient == $a;
} elsif ( defined $s{'ModMul'} ) {
# ModMul = (A * B) mod M
my $modmul = bn($s{'ModMul'});
my $a = bn($s{'A'});
my $b = bn($s{'B'});
my $m = bn($s{'M'});
$a->bmul($b);
return if $modmul == $a->bmod($m);
} elsif ( defined $s{'ModExp'} ) {
# ModExp = (A ** E) mod M
my $modexp = bn($s{'ModExp'});
my $a = bn($s{'A'});
my $e = bn($s{'E'});
my $m = bn($s{'M'});
return if $modexp == $a->bmodpow($e, $m);
} elsif ( defined $s{'Exp'} ) {
my $exp = bn($s{'Exp'});
my $a = bn($s{'A'});
my $e = bn($s{'E'});
return if $exp == $a ** $e;
} elsif ( defined $s{'ModSqrt'} ) {
# (ModSqrt * ModSqrt) mod P = A mod P
my $modsqrt = bn($s{'ModSqrt'});
my $a = bn($s{'A'});
my $p = bn($s{'P'});
$modsqrt->bmul($modsqrt);
$modsqrt->bmod($p);
$a->bmod($p);
return if $modsqrt == $a;
} else {
print "# Unknown test: ";
}
$failures++;
print "# #$failures Test (before line $lineno) failed\n";
foreach ( keys %s ) {
print "$_ = $s{$_}\n";
}
print "\n";
}
my $infile = shift || 'bntests.txt';
die "No such file, $infile" unless -f $infile;
open my $IN, $infile || die "Can't read $infile, $!\n";
my %stanza = ();
my $l = 0;
while ( <$IN> ) {
$l++;
s|\R$||;
next if /^#/;
if ( /^$/ ) {
if ( keys %stanza ) {
evaluate($l, %stanza);
%stanza = ();
}
next;
}
# Parse 'key = value'
if ( ! /\s*([^\s]*)\s*=\s*(.*)\s*/ ) {
print "Skipping $_\n";
next;
}
$stanza{$1} = $2;
};
evaluate($l, %stanza) if keys %stanza;
die "Got $failures, expected $EXPECTED_FAILURES"
if $infile eq 'bntests.txt' and $failures != $EXPECTED_FAILURES;
close($IN)
test/bntests.txt 0 → 100644
浏览文件 @ 8d1ebff4
因为 它太大了无法显示 source diff 。你可以改为 查看blob。
test/build.info
浏览文件 @ 8d1ebff4
......@@ -35,7 +35,7 @@ IF[{- !$disabled{tests} -}]
INCLUDE[sanitytest]=../include
DEPEND[sanitytest]=../libcrypto
SOURCE[bntest]=bntest.c
SOURCE[bntest]=bntest.c testutil.c test_main_custom.c
INCLUDE[bntest]=.. ../crypto/include ../include
DEPEND[bntest]=../libcrypto
......
test/recipes/10-test_bn.t
浏览文件 @ 8d1ebff4
......@@ -16,69 +16,7 @@ use OpenSSL::Test qw/:DEFAULT srctop_file/;
setup("test_bn");
plan tests => 3;
plan tests => 1;
require_ok(srctop_file("test","recipes","bc.pl"));
my $testresults = "tmp.bntest";
my $init = ok(run(test(["bntest"], stdout => $testresults)), 'initialize');
SKIP: {
skip "Initializing failed, skipping", 1 if !$init;
subtest 'Checking the bn results' => sub {
my @lines = ();
if (open DATA, $testresults) {
@lines = <DATA>;
close DATA;
}
map { s/\R//; } @lines; # chomp(@lines);
plan tests => scalar grep(/^print /, @lines);
my $l = "";
while (scalar @lines) {
$l = shift @lines;
last if $l =~ /^print /;
}
while (1) {
$l =~ s/^print "//;
$l =~ s/\\n"//;
my $t = $l;
my @operations = ();
$l = undef;
while (scalar @lines) {
$l = shift @lines;
last if $l =~ /^print /;
push @operations, $l;
$l = undef;
}
ok(check_operations(@operations), "verify $t");
last unless $l;
}
};
}
unlink $testresults;
sub check_operations {
my $failcount = 0;
foreach my $line (@_) {
my $result = calc(split /\s+/, $line);
if ($result ne "0" && $result ne "0x0") {
$failcount++;
print STDERR "Failed! $line => $result\n";
}
}
return $failcount == 0;
}
ok(run(test(["bntest", srctop_file("test", "bntests.txt")])),
"running bntest bntests.txt");
test/recipes/bc.pl 已删除 100644 → 0
浏览文件 @ b3618f44
#! /usr/bin/env perl
# Copyright 2015-2016 The OpenSSL Project Authors. All Rights Reserved.
#
# Licensed under the OpenSSL license (the "License"). You may not use
# this file except in compliance with the License. You can obtain a copy
# in the file LICENSE in the source distribution or at
# https://www.openssl.org/source/license.html
use strict;
use warnings;
use Math::BigInt;
sub calc {
@_ = __adder(@_);
if (scalar @_ != 1) { return "NaN"; }
return shift;
}
sub __canonhex {
my ($sign, $hex) = (shift =~ /^([+\-]?)(.*)$/);
$hex = "0x".$hex if $hex !~ /^0x/;
return $sign.$hex;
}
sub __adder {
@_ = __multiplier(@_);
while (scalar @_ > 1 && $_[1] =~ /^[\+\-]$/) {
my $operand1 = Math::BigInt->from_hex(__canonhex(shift));
my $operator = shift;
@_ = __multiplier(@_);
my $operand2 = Math::BigInt->from_hex(__canonhex(shift));
if ($operator eq "+") {
$operand1->badd($operand2);
} elsif ($operator eq "-") {
$operand1->bsub($operand2);
} else {
die "SOMETHING WENT AWFULLY WRONG";
}
unshift @_, $operand1->as_hex();
}
return @_;
}
sub __multiplier {
@_ = __power(@_);
while (scalar @_ > 1 && $_[1] =~ /^[\*\/%]$/) {
my $operand1 = Math::BigInt->from_hex(__canonhex(shift));
my $operator = shift;
@_ = __power(@_);
my $operand2 = Math::BigInt->from_hex(__canonhex(shift));
if ($operator eq "*") {
$operand1->bmul($operand2);
} elsif ($operator eq "/") {
# Math::BigInt->bdiv() is documented to do floored division,
# i.e. 1 / -4 = -1, while bc and OpenSSL BN_div do truncated
# division, i.e. 1 / -4 = 0. We need to make the operation
# work like OpenSSL's BN_div to be able to verify.
my $neg = ($operand1->is_neg()
? !$operand2->is_neg() : $operand2->is_neg());
$operand1->babs();
$operand2->babs();
$operand1->bdiv($operand2);
if ($neg) { $operand1->bneg(); }
} elsif ($operator eq "%") {
# Here's a bit of a quirk...
# With OpenSSL's BN, as well as bc, the result of -10 % 3 is -1
# while Math::BigInt, the result is 2.
# The latter is mathematically more correct, but...
my $o1isneg = $operand1->is_neg();
$operand1->babs();
# Math::BigInt does something different with a negative modulus,
# while OpenSSL's BN and bc treat it like a positive number...
$operand2->babs();
$operand1->bmod($operand2);
if ($o1isneg) { $operand1->bneg(); }
} else {
die "SOMETHING WENT AWFULLY WRONG";
}
unshift @_, $operand1->as_hex();
}
return @_;
}
sub __power {
@_ = __paren(@_);
while (scalar @_ > 1 && $_[1] eq "^") {
my $operand1 = Math::BigInt->from_hex(__canonhex(shift));
shift;
@_ = __paren(@_);
my $operand2 = Math::BigInt->from_hex(__canonhex(shift));
$operand1->bpow($operand2);
unshift @_, $operand1->as_hex();
}
return @_;
}
# returns array ( $result, @remaining )
sub __paren {
if (scalar @_ > 0 && $_[0] eq "(") {
shift;
my @result = __adder(@_);
if (scalar @_ == 0 || $_[0] ne ")") {
return ("NaN");
}
shift;
return @result;
}
return @_;
}
1;
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