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bntest.c
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/*
* Copyright 1995-2017 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
*/
#include "../e_os.h"
#include <assert.h>
#include <errno.h>
#include <stdio.h>
#include <string.h>
#include <ctype.h>
#include "internal/nelem.h"
#include "internal/numbers.h"
#include <openssl/bn.h>
#include <openssl/crypto.h>
#include <openssl/err.h>
#include <openssl/rand.h>
#include "testutil.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 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.
*
* To avoid this, we define a dummy variant of bn_expand2() here, and to
* avoid possible clashes with libcrypto, we rename it first, using a macro.
*/
#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"
/*
* Things in boring, not in openssl. TODO we should add them.
*/
#define HAVE_BN_PADDED 0
#define HAVE_BN_SQRT 0
typedef struct filetest_st {
const char *name;
int (*func)(STANZA *s);
} FILETEST;
typedef struct mpitest_st {
const char *base10;
const char *mpi;
size_t mpi_len;
} MPITEST;
static const int NUM0 = 100; /* number of tests */
static const int NUM1 = 50; /* additional tests for some functions */
static BN_CTX *ctx;
/*
* Polynomial coefficients used in GFM tests.
*/
#ifndef OPENSSL_NO_EC2M
static int p0[] = { 163, 7, 6, 3, 0, -1 };
static int p1[] = { 193, 15, 0, -1 };
#endif
/*
* 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;
for ( ; --i >= 0; pp++)
if (strcasecmp(pp->key, key) == 0)
return pp->value;
return NULL;
}
/*
* Parse BIGNUM, return number of bytes parsed.
*/
static int parseBN(BIGNUM **out, const char *in)
{
*out = NULL;
return BN_hex2bn(out, in);
}
static int parsedecBN(BIGNUM **out, const char *in)
{
*out = NULL;
return BN_dec2bn(out, in);
}
static BIGNUM *getBN(STANZA *s, const char *attribute)
{
const char *hex;
BIGNUM *ret = NULL;
if ((hex = findattr(s, attribute)) == NULL) {
TEST_error("%s:%d: Can't find %s", s->test_file, s->start, attribute);
return NULL;
}
if (parseBN(&ret, hex) != (int)strlen(hex)) {
TEST_error("Could not decode '%s'", hex);
return NULL;
}
return ret;
}
static int getint(STANZA *s, int *out, const char *attribute)
{
BIGNUM *ret;
BN_ULONG word;
int st = 0;
if (!TEST_ptr(ret = getBN(s, attribute))
|| !TEST_ulong_le(word = BN_get_word(ret), INT_MAX))
goto err;
*out = (int)word;
st = 1;
err:
BN_free(ret);
return st;
}
static int equalBN(const char *op, const BIGNUM *expected, const BIGNUM *actual)
{
if (BN_cmp(expected, actual) == 0)
return 1;
TEST_error("unexpected %s value", op);
TEST_BN_eq(expected, actual);
return 0;
}
/*
* 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 };
return sign[(neg++) % 8];
}
static int test_sub(void)
{
BIGNUM *a = NULL, *b = NULL, *c = NULL;
int i, st = 0;
if (!TEST_ptr(a = BN_new())
|| !TEST_ptr(b = BN_new())
|| !TEST_ptr(c = BN_new()))
goto err;
for (i = 0; i < NUM0 + NUM1; i++) {
if (i < NUM1) {
BN_bntest_rand(a, 512, 0, 0);
BN_copy(b, a);
if (!TEST_int_ne(BN_set_bit(a, i), 0))
goto err;
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);
BN_add(c, c, b);
BN_sub(c, c, a);
if (!TEST_BN_eq_zero(c))
goto err;
}
st = 1;
err:
BN_free(a);
BN_free(b);
BN_free(c);
return st;
}
static int test_div_recip(void)
{
BIGNUM *a = NULL, *b = NULL, *c = NULL, *d = NULL, *e = NULL;
BN_RECP_CTX *recp = NULL;
int st = 0, i;
if (!TEST_ptr(a = BN_new())
|| !TEST_ptr(b = BN_new())
|| !TEST_ptr(c = BN_new())
|| !TEST_ptr(d = BN_new())
|| !TEST_ptr(e = BN_new())
|| !TEST_ptr(recp = BN_RECP_CTX_new()))
goto err;
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);
BN_mul(e, d, b, ctx);
BN_add(d, e, c);
BN_sub(d, d, a);
if (!TEST_BN_eq_zero(d))
goto err;
}
st = 1;
err:
BN_free(a);
BN_free(b);
BN_free(c);
BN_free(d);
BN_free(e);
BN_RECP_CTX_free(recp);
return st;
}
static int test_mod(void)
{
BIGNUM *a = NULL, *b = NULL, *c = NULL, *d = NULL, *e = NULL;
int st = 0, i;
if (!TEST_ptr(a = BN_new())
|| !TEST_ptr(b = BN_new())
|| !TEST_ptr(c = BN_new())
|| !TEST_ptr(d = BN_new())
|| !TEST_ptr(e = BN_new()))
goto err;
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);
BN_div(d, e, a, b, ctx);
BN_sub(e, e, c);
if (!TEST_BN_eq_zero(e))
goto err;
}
st = 1;
err:
BN_free(a);
BN_free(b);
BN_free(c);
BN_free(d);
BN_free(e);
return st;
}
static const char *bn1strings[] = {
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000000000FFFFFFFF00",
"0000000000000000000000000000000000000000000000000000000000000000",
"0000000000000000000000000000000000000000000000000000000000000000",
"0000000000000000000000000000000000000000000000000000000000000000",
"0000000000000000000000000000000000000000000000000000000000000000",
"0000000000000000000000000000000000000000000000000000000000000000",
"0000000000000000000000000000000000000000000000000000000000000000",
"0000000000000000000000000000000000000000000000000000000000000000",
"00000000000000000000000000000000000000000000000000FFFFFFFFFFFFFF",
NULL
};
static const char *bn2strings[] = {
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000000000FFFFFFFF0000000000",
"0000000000000000000000000000000000000000000000000000000000000000",
"0000000000000000000000000000000000000000000000000000000000000000",
"0000000000000000000000000000000000000000000000000000000000000000",
"0000000000000000000000000000000000000000000000000000000000000000",
"0000000000000000000000000000000000000000000000000000000000000000",
"0000000000000000000000000000000000000000000000000000000000000000",
"0000000000000000000000000000000000000000000000000000000000000000",
"000000000000000000000000000000000000000000FFFFFFFFFFFFFF00000000",
NULL
};
static char *glue(const char *list[])
{
size_t len = 0;
char *p, *save;
int i;
for (i = 0; list[i] != NULL; i++)
len += strlen(list[i]);
if (!TEST_ptr(p = save = OPENSSL_malloc(len + 1)))
return NULL;
for (i = 0; list[i] != NULL; i++)
p += strlen(strcpy(p, list[i]));
return save;
}
/*
* 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(void)
{
BIGNUM *a = NULL, *p = NULL, *m = NULL, *d = NULL, *e = NULL;
BIGNUM *b = NULL, *n = NULL, *c = NULL;
BN_MONT_CTX *mont = NULL;
char *bigstring;
int st = 0;
if (!TEST_ptr(a = BN_new())
|| !TEST_ptr(p = BN_new())
|| !TEST_ptr(m = BN_new())
|| !TEST_ptr(d = BN_new())
|| !TEST_ptr(e = BN_new())
|| !TEST_ptr(b = BN_new())
|| !TEST_ptr(n = BN_new())
|| !TEST_ptr(c = BN_new())
|| !TEST_ptr(mont = BN_MONT_CTX_new()))
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 (!TEST_true(BN_mod_exp_mont_consttime(d, a, p, m, ctx, NULL)))
goto err;
if (!TEST_BN_eq_one(d))
goto err;
/* 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 (!TEST_BN_eq(c, d))
goto err;
/* Regression test for carry bug in sqr[x]8x_mont */
bigstring = glue(bn1strings);
BN_hex2bn(&n, bigstring);
OPENSSL_free(bigstring);
bigstring = glue(bn2strings);
BN_hex2bn(&a, bigstring);
OPENSSL_free(bigstring);
BN_free(b);
b = BN_dup(a);
BN_MONT_CTX_set(mont, n, ctx);
BN_mod_mul_montgomery(c, a, a, mont, ctx);
BN_mod_mul_montgomery(d, a, b, mont, ctx);
if (!TEST_BN_eq(c, d))
goto err;
/* Zero input */
BN_bntest_rand(p, 1024, 0, 0);
BN_zero(a);
if (!TEST_true(BN_mod_exp_mont_consttime(d, a, p, m, ctx, NULL))
|| !TEST_BN_eq_zero(d))
goto err;
/*
* 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 (!TEST_true(BN_from_montgomery(e, a, mont, ctx))
|| !TEST_true(BN_mod_exp_mont_consttime(d, e, p, m, ctx, NULL))
|| !TEST_true(BN_mod_exp_simple(a, e, p, m, ctx))
|| !TEST_BN_eq(a, d))
goto err;
/* Finally, some regular test vectors. */
BN_bntest_rand(e, 1024, 0, 0);
if (!TEST_true(BN_mod_exp_mont_consttime(d, e, p, m, ctx, NULL))
|| !TEST_true(BN_mod_exp_simple(a, e, p, m, ctx))
|| !TEST_BN_eq(a, d))
goto err;
st = 1;
err:
BN_MONT_CTX_free(mont);
BN_free(a);
BN_free(p);
BN_free(m);
BN_free(d);
BN_free(e);
BN_free(b);
BN_free(n);
BN_free(c);
return st;
}
#ifndef OPENSSL_NO_EC2M
static int test_gf2m_add(void)
{
BIGNUM *a = NULL, *b = NULL, *c = NULL;
int i, st = 0;
if (!TEST_ptr(a = BN_new())
|| !TEST_ptr(b = BN_new())
|| !TEST_ptr(c = BN_new()))
goto err;
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);
/* Test that two added values have the correct parity. */
if (!TEST_false((BN_is_odd(a) && BN_is_odd(c))
|| (!BN_is_odd(a) && !BN_is_odd(c))))
goto err;
BN_GF2m_add(c, c, c);
/* Test that c + c = 0. */
if (!TEST_BN_eq_zero(c))
goto err;
}
st = 1;
err:
BN_free(a);
BN_free(b);
BN_free(c);
return st;
}
static int test_gf2m_mod(void)
{
BIGNUM *a = NULL, *b[2] = {NULL,NULL}, *c = NULL, *d = NULL, *e = NULL;
int i, j, st = 0;
if (!TEST_ptr(a = BN_new())
|| !TEST_ptr(b[0] = BN_new())
|| !TEST_ptr(b[1] = BN_new())
|| !TEST_ptr(c = BN_new())
|| !TEST_ptr(d = BN_new())
|| !TEST_ptr(e = BN_new()))
goto err;
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 (!TEST_BN_eq_zero(e))
goto err;
}
}
st = 1;
err:
BN_free(a);
BN_free(b[0]);
BN_free(b[1]);
BN_free(c);
BN_free(d);
BN_free(e);
return st;
}
static int test_gf2m_mul(void)
{
BIGNUM *a, *b[2] = {NULL, NULL}, *c = NULL, *d = NULL;
BIGNUM *e = NULL, *f = NULL, *g = NULL, *h = NULL;
int i, j, st = 0;
if (!TEST_ptr(a = BN_new())
|| !TEST_ptr(b[0] = BN_new())
|| !TEST_ptr(b[1] = BN_new())
|| !TEST_ptr(c = BN_new())
|| !TEST_ptr(d = BN_new())
|| !TEST_ptr(e = BN_new())
|| !TEST_ptr(f = BN_new())
|| !TEST_ptr(g = BN_new())
|| !TEST_ptr(h = BN_new()))
goto err;
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 (!TEST_BN_eq_zero(f))
goto err;
}
}
st = 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 st;
}
static int test_gf2m_sqr(void)
{
BIGNUM *a = NULL, *b[2] = {NULL,NULL}, *c = NULL, *d = NULL;
int i, j, st = 0;
if (!TEST_ptr(a = BN_new())
|| !TEST_ptr(b[0] = BN_new())
|| !TEST_ptr(b[1] = BN_new())
|| !TEST_ptr(c = BN_new())
|| !TEST_ptr(d = BN_new()))
goto err;
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 (!TEST_BN_eq_zero(d))
goto err;
}
}
st = 1;
err:
BN_free(a);
BN_free(b[0]);
BN_free(b[1]);
BN_free(c);
BN_free(d);
return st;
}
static int test_gf2m_modinv(void)
{
BIGNUM *a = NULL, *b[2] = {NULL,NULL}, *c = NULL, *d = NULL;
int i, j, st = 0;
if (!TEST_ptr(a = BN_new())
|| !TEST_ptr(b[0] = BN_new())
|| !TEST_ptr(b[1] = BN_new())
|| !TEST_ptr(c = BN_new())
|| !TEST_ptr(d = BN_new()))
goto err;
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);
/* Test that ((1/a)*a) = 1. */
if (!TEST_BN_eq_one(d))
goto err;
}
}
st = 1;
err:
BN_free(a);
BN_free(b[0]);
BN_free(b[1]);
BN_free(c);
BN_free(d);
return st;
}
static int test_gf2m_moddiv(void)
{
BIGNUM *a = NULL, *b[2] = {NULL,NULL}, *c = NULL, *d = NULL;
BIGNUM *e = NULL, *f = NULL;
int i, j, st = 0;
if (!TEST_ptr(a = BN_new())
|| !TEST_ptr(b[0] = BN_new())
|| !TEST_ptr(b[1] = BN_new())
|| !TEST_ptr(c = BN_new())
|| !TEST_ptr(d = BN_new())
|| !TEST_ptr(e = BN_new())
|| !TEST_ptr(f = BN_new()))
goto err;
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);
/* Test that ((a/c)*c)/a = 1. */
if (!TEST_BN_eq_one(f))
goto err;
}
}
st = 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 st;
}
static int test_gf2m_modexp(void)
{
BIGNUM *a = NULL, *b[2] = {NULL,NULL}, *c = NULL, *d = NULL;
BIGNUM *e = NULL, *f = NULL;
int i, j, st = 0;
if (!TEST_ptr(a = BN_new())
|| !TEST_ptr(b[0] = BN_new())
|| !TEST_ptr(b[1] = BN_new())
|| !TEST_ptr(c = BN_new())
|| !TEST_ptr(d = BN_new())
|| !TEST_ptr(e = BN_new())
|| !TEST_ptr(f = BN_new()))
goto err;
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);
BN_GF2m_add(f, e, f);
/* Test that a^(c+d)=a^c*a^d. */
if (!TEST_BN_eq_zero(f))
goto err;
}
}
st = 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 st;
}
static int test_gf2m_modsqrt(void)
{
BIGNUM *a = NULL, *b[2] = {NULL,NULL}, *c = NULL, *d = NULL;
BIGNUM *e = NULL, *f = NULL;
int i, j, st = 0;
if (!TEST_ptr(a = BN_new())
|| !TEST_ptr(b[0] = BN_new())
|| !TEST_ptr(b[1] = BN_new())
|| !TEST_ptr(c = BN_new())
|| !TEST_ptr(d = BN_new())
|| !TEST_ptr(e = BN_new())
|| !TEST_ptr(f = BN_new()))
goto err;
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);
BN_GF2m_add(f, c, e);
/* Test that d^2 = a, where d = sqrt(a). */
if (!TEST_BN_eq_zero(f))
goto err;
}
}
st = 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 st;
}
static int test_gf2m_modsolvequad(void)
{
BIGNUM *a = NULL, *b[2] = {NULL,NULL}, *c = NULL, *d = NULL;
BIGNUM *e = NULL;
int i, j, s = 0, t, st = 0;
if (!TEST_ptr(a = BN_new())
|| !TEST_ptr(b[0] = BN_new())
|| !TEST_ptr(b[1] = BN_new())
|| !TEST_ptr(c = BN_new())
|| !TEST_ptr(d = BN_new())
|| !TEST_ptr(e = BN_new()))
goto err;
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]);
BN_GF2m_add(e, e, d);
/*
* Test that solution of quadratic c satisfies c^2 + c = a.
*/
if (!TEST_BN_eq_zero(e))
goto err;
}
}
}
if (!TEST_int_ge(s, 0)) {
TEST_info("%d tests found no roots; probably an error", NUM0);
goto err;
}
st = 1;
err:
BN_free(a);
BN_free(b[0]);
BN_free(b[1]);
BN_free(c);
BN_free(d);
BN_free(e);
return st;
}
#endif
static int test_kronecker(void)
{
BIGNUM *a = NULL, *b = NULL, *r = NULL, *t = NULL;
int i, legendre, kronecker, st = 0;
if (!TEST_ptr(a = BN_new())
|| !TEST_ptr(b = BN_new())
|| !TEST_ptr(r = BN_new())
|| !TEST_ptr(t = BN_new()))
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 (!TEST_true(BN_generate_prime_ex(b, 512, 0, NULL, NULL, NULL)))
goto err;
b->neg = rand_neg();
for (i = 0; i < NUM0; i++) {
if (!TEST_true(BN_bntest_rand(a, 512, 0, 0)))
goto err;
a->neg = rand_neg();
/* t := (|b|-1)/2 (note that b is odd) */
if (!TEST_true(BN_copy(t, b)))
goto err;
t->neg = 0;
if (!TEST_true(BN_sub_word(t, 1)))
goto err;
if (!TEST_true(BN_rshift1(t, t)))
goto err;
/* r := a^t mod b */
b->neg = 0;
if (!TEST_true(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 (!TEST_true(BN_add_word(r, 1)))
goto err;
if (!TEST_int_eq(BN_ucmp(r, b), 0)) {
TEST_info("Legendre symbol computation failed");
goto err;
}
legendre = -1;
}
if (!TEST_int_ge(kronecker = BN_kronecker(a, b, ctx), -1))
goto err;
/* we actually need BN_kronecker(a, |b|) */
if (a->neg && b->neg)
kronecker = -kronecker;
if (!TEST_int_eq(legendre, kronecker))
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 = NULL, *b = NULL, *sum = NULL, *ret = NULL;
BN_ULONG b_word;
int st = 0;
if (!TEST_ptr(a = getBN(s, "A"))
|| !TEST_ptr(b = getBN(s, "B"))
|| !TEST_ptr(sum = getBN(s, "Sum"))
|| !TEST_ptr(ret = BN_new()))
goto err;
if (!TEST_true(BN_add(ret, a, b))
|| !equalBN("A + B", sum, ret)
|| !TEST_true(BN_sub(ret, sum, a))
|| !equalBN("Sum - A", b, ret)
|| !TEST_true(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 (!TEST_true(BN_copy(ret, a))
|| !TEST_true(BN_add(ret, ret, b))
|| !equalBN("A + B (r is a)", sum, ret)
|| !TEST_true(BN_copy(ret, b))
|| !TEST_true(BN_add(ret, a, ret))
|| !equalBN("A + B (r is b)", sum, ret)
|| !TEST_true(BN_copy(ret, sum))
|| !TEST_true(BN_sub(ret, ret, a))
|| !equalBN("Sum - A (r is a)", b, ret)
|| !TEST_true(BN_copy(ret, a))
|| !TEST_true(BN_sub(ret, sum, ret))
|| !equalBN("Sum - A (r is b)", b, ret)
|| !TEST_true(BN_copy(ret, sum))
|| !TEST_true(BN_sub(ret, ret, b))
|| !equalBN("Sum - B (r is a)", a, ret)
|| !TEST_true(BN_copy(ret, b))
|| !TEST_true(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 (!TEST_true(BN_uadd(ret, a, b))
|| !equalBN("A +u B", sum, ret)
|| !TEST_true(BN_usub(ret, sum, a))
|| !equalBN("Sum -u A", b, ret)
|| !TEST_true(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 (!TEST_true(BN_copy(ret, a))
|| !TEST_true(BN_uadd(ret, ret, b))
|| !equalBN("A +u B (r is a)", sum, ret)
|| !TEST_true(BN_copy(ret, b))
|| !TEST_true(BN_uadd(ret, a, ret))
|| !equalBN("A +u B (r is b)", sum, ret)
|| !TEST_true(BN_copy(ret, sum))
|| !TEST_true(BN_usub(ret, ret, a))
|| !equalBN("Sum -u A (r is a)", b, ret)
|| !TEST_true(BN_copy(ret, a))
|| !TEST_true(BN_usub(ret, sum, ret))
|| !equalBN("Sum -u A (r is b)", b, ret)
|| !TEST_true(BN_copy(ret, sum))
|| !TEST_true(BN_usub(ret, ret, b))
|| !equalBN("Sum -u B (r is a)", a, ret)
|| !TEST_true(BN_copy(ret, b))
|| !TEST_true(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 (!TEST_true(BN_copy(ret, a))
|| !TEST_true(BN_add_word(ret, b_word))
|| !equalBN("A + B (word)", sum, ret)
|| !TEST_true(BN_copy(ret, sum))
|| !TEST_true(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 = NULL, *lshift1 = NULL, *zero = NULL, *ret = NULL;
BIGNUM *two = NULL, *remainder = NULL;