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bntest.c
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/*
* Copyright 1995-2019 The OpenSSL Project Authors. All Rights Reserved.
*
* Licensed under the Apache License 2.0 (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 <assert.h>
#include <errno.h>
#include <stdio.h>
#include <string.h>
#include <ctype.h>
#include <openssl/bn.h>
#include <openssl/crypto.h>
#include <openssl/err.h>
#include <openssl/rand.h>
#include "internal/nelem.h"
#include "internal/numbers.h"
#include "testutil.h"
#ifdef OPENSSL_SYS_WINDOWS
# define strcasecmp _stricmp
#endif
/*
* 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 from sparse hex-strings, return |BN_hex2bn| result.
*/
static int parse_bigBN(BIGNUM **out, const char *bn_strings[])
{
char *bigstring = glue_strings(bn_strings, NULL);
int ret = BN_hex2bn(out, bigstring);
OPENSSL_free(bigstring);
return ret;
}
/*
* 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_swap(void)
{
BIGNUM *a = NULL, *b = NULL, *c = NULL, *d = NULL;
int top, cond, st = 0;
if (!TEST_ptr(a = BN_new())
|| !TEST_ptr(b = BN_new())
|| !TEST_ptr(c = BN_new())
|| !TEST_ptr(d = BN_new()))
goto err;
if (!(TEST_true(BN_bntest_rand(a, 1024, 1, 0))
&& TEST_true(BN_bntest_rand(b, 1024, 1, 0))
&& TEST_ptr(BN_copy(c, a))
&& TEST_ptr(BN_copy(d, b))))
goto err;
top = BN_num_bits(a) / BN_BITS2;
/* regular swap */
BN_swap(a, b);
if (!equalBN("swap", a, d)
|| !equalBN("swap", b, c))
goto err;
/* conditional swap: true */
cond = 1;
BN_consttime_swap(cond, a, b, top);
if (!equalBN("cswap true", a, c)
|| !equalBN("cswap true", b, d))
goto err;
/* conditional swap: false */
cond = 0;
BN_consttime_swap(cond, a, b, top);
if (!equalBN("cswap false", a, c)
|| !equalBN("cswap false", b, d))
goto err;
/* same tests but checking flag swap */
BN_set_flags(a, BN_FLG_CONSTTIME);
BN_swap(a, b);
if (!equalBN("swap, flags", a, d)
|| !equalBN("swap, flags", b, c)
|| !TEST_true(BN_get_flags(b, BN_FLG_CONSTTIME))
|| !TEST_false(BN_get_flags(a, BN_FLG_CONSTTIME)))
goto err;
cond = 1;
BN_consttime_swap(cond, a, b, top);
if (!equalBN("cswap true, flags", a, c)
|| !equalBN("cswap true, flags", b, d)
|| !TEST_true(BN_get_flags(a, BN_FLG_CONSTTIME))
|| !TEST_false(BN_get_flags(b, BN_FLG_CONSTTIME)))
goto err;
cond = 0;
BN_consttime_swap(cond, a, b, top);
if (!equalBN("cswap false, flags", a, c)
|| !equalBN("cswap false, flags", b, d)
|| !TEST_true(BN_get_flags(a, BN_FLG_CONSTTIME))
|| !TEST_false(BN_get_flags(b, BN_FLG_CONSTTIME)))
goto err;
st = 1;
err:
BN_free(a);
BN_free(b);
BN_free(c);
BN_free(d);
return st;
}
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) {
if (!(TEST_true(BN_bntest_rand(a, 512, 0, 0)))
&& TEST_ptr(BN_copy(b, a))
&& TEST_int_ne(BN_set_bit(a, i), 0)
&& TEST_true(BN_add_word(b, i)))
goto err;
} else {
if (!TEST_true(BN_bntest_rand(b, 400 + i - NUM1, 0, 0)))
goto err;
BN_set_negative(a, rand_neg());
BN_set_negative(b, rand_neg());
}
if (!(TEST_true(BN_sub(c, a, b))
&& TEST_true(BN_add(c, c, b))
&& TEST_true(BN_sub(c, c, a))
&& 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) {
if (!(TEST_true(BN_bntest_rand(a, 400, 0, 0))
&& TEST_ptr(BN_copy(b, a))
&& TEST_true(BN_lshift(a, a, i))
&& TEST_true(BN_add_word(a, i))))
goto err;
} else {
if (!(TEST_true(BN_bntest_rand(b, 50 + 3 * (i - NUM1), 0, 0))))
goto err;
}
BN_set_negative(a, rand_neg());
BN_set_negative(b, rand_neg());
if (!(TEST_true(BN_RECP_CTX_set(recp, b, ctx))
&& TEST_true(BN_div_recp(d, c, a, recp, ctx))
&& TEST_true(BN_mul(e, d, b, ctx))
&& TEST_true(BN_add(d, e, c))
&& TEST_true(BN_sub(d, d, a))
&& 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;
if (!(TEST_true(BN_bntest_rand(a, 1024, 0, 0))))
goto err;
for (i = 0; i < NUM0; i++) {
if (!(TEST_true(BN_bntest_rand(b, 450 + i * 10, 0, 0))))
goto err;
BN_set_negative(a, rand_neg());
BN_set_negative(b, rand_neg());
if (!(TEST_true(BN_mod(c, a, b, ctx))
&& TEST_true(BN_div(d, e, a, b, ctx))
&& TEST_true(BN_sub(e, e, c))
&& 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
};
/*
* 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;
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;
/* must be odd for montgomery */
if (!(TEST_true(BN_bntest_rand(m, 1024, 0, 1))
/* Zero exponent */
&& TEST_true(BN_bntest_rand(a, 1024, 0, 0))))
goto err;
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 */
if (!(TEST_true(BN_hex2bn(&a,
"7878787878787878787878787878787878787878787878787878787878787878"
"7878787878787878787878787878787878787878787878787878787878787878"
"7878787878787878787878787878787878787878787878787878787878787878"
"7878787878787878787878787878787878787878787878787878787878787878"))
&& TEST_true(BN_hex2bn(&b,
"095D72C08C097BA488C5E439C655A192EAFB6380073D8C2664668EDDB4060744"
"E16E57FB4EDB9AE10A0CEFCDC28A894F689A128379DB279D48A2E20849D68593"
"9B7803BCF46CEBF5C533FB0DD35B080593DE5472E3FE5DB951B8BFF9B4CB8F03"
"9CC638A5EE8CDD703719F8000E6A9F63BEED5F2FCD52FF293EA05A251BB4AB81"))
&& TEST_true(BN_hex2bn(&n,
"D78AF684E71DB0C39CFF4E64FB9DB567132CB9C50CC98009FEB820B26F2DED9B"
"91B9B5E2B83AE0AE4EB4E0523CA726BFBE969B89FD754F674CE99118C3F2D1C5"
"D81FDC7C54E02B60262B241D53C040E99E45826ECA37A804668E690E1AFC1CA4"
"2C9A15D84D4954425F0B7642FC0BD9D7B24E2618D2DCC9B729D944BADACFDDAF"))))
goto err;
if (!(TEST_true(BN_MONT_CTX_set(mont, n, ctx))
&& TEST_true(BN_mod_mul_montgomery(c, a, b, mont, ctx))
&& TEST_true(BN_mod_mul_montgomery(d, b, a, mont, ctx))
&& TEST_BN_eq(c, d)))
goto err;
/* Regression test for carry bug in sqr[x]8x_mont */
if (!(TEST_true(parse_bigBN(&n, bn1strings))
&& TEST_true(parse_bigBN(&a, bn2strings))))
goto err;
BN_free(b);
if (!(TEST_ptr(b = BN_dup(a))
&& TEST_true(BN_MONT_CTX_set(mont, n, ctx))
&& TEST_true(BN_mod_mul_montgomery(c, a, a, mont, ctx))
&& TEST_true(BN_mod_mul_montgomery(d, a, b, mont, ctx))
&& TEST_BN_eq(c, d)))
goto err;
/* Regression test for carry bug in bn_sqrx8x_internal */
{
static const char *ahex[] = {
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF8FFEADBCFC4DAE7FFF908E92820306B",
"9544D954000000006C0000000000000000000000000000000000000000000000",
"00000000000000000000FF030202FFFFF8FFEBDBCFC4DAE7FFF908E92820306B",
"9544D954000000006C000000FF0302030000000000FFFFFFFFFFFFFFFFFFFFFF",
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF01FC00FF02FFFFFFFF",
"00FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00FCFD",
"FCFFFFFFFFFF000000000000000000FF0302030000000000FFFFFFFFFFFFFFFF",
"FF00FCFDFDFF030202FF00000000FFFFFFFFFFFFFFFFFF00FCFDFCFFFFFFFFFF",
NULL
};
static const char *nhex[] = {
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF8F8F8F8000000",
"00000010000000006C0000000000000000000000000000000000000000000000",
"00000000000000000000000000000000000000FFFFFFFFFFFFF8F8F8F8000000",
"00000010000000006C000000000000000000000000FFFFFFFFFFFFFFFFFFFFFF",
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
"00FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
"FFFFFFFFFFFF000000000000000000000000000000000000FFFFFFFFFFFFFFFF",
"FFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
NULL
};
if (!(TEST_true(parse_bigBN(&a, ahex))
&& TEST_true(parse_bigBN(&n, nhex))))
goto err;
}
BN_free(b);
if (!(TEST_ptr(b = BN_dup(a))
&& TEST_true(BN_MONT_CTX_set(mont, n, ctx))))
goto err;
if (!TEST_true(BN_mod_mul_montgomery(c, a, a, mont, ctx))
|| !TEST_true(BN_mod_mul_montgomery(d, a, b, mont, ctx))
|| !TEST_BN_eq(c, d))
goto err;
/* Regression test for bug in BN_from_montgomery_word */
if (!(TEST_true(BN_hex2bn(&a,
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"))
&& TEST_true(BN_hex2bn(&n,
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"))
&& TEST_true(BN_MONT_CTX_set(mont, n, ctx))
&& TEST_false(BN_mod_mul_montgomery(d, a, a, mont, ctx))))
goto err;
/* Regression test for bug in rsaz_1024_mul_avx2 */
if (!(TEST_true(BN_hex2bn(&a,
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF2020202020DF"))
&& TEST_true(BN_hex2bn(&b,
"2020202020202020202020202020202020202020202020202020202020202020"
"2020202020202020202020202020202020202020202020202020202020202020"
"20202020202020FF202020202020202020202020202020202020202020202020"
"2020202020202020202020202020202020202020202020202020202020202020"))
&& TEST_true(BN_hex2bn(&n,
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF2020202020FF"))
&& TEST_true(BN_MONT_CTX_set(mont, n, ctx))
&& TEST_true(BN_mod_exp_mont_consttime(c, a, b, n, ctx, mont))
&& TEST_true(BN_mod_exp_mont(d, a, b, n, ctx, mont))
&& TEST_BN_eq(c, d)))
goto err;
/*
* rsaz_1024_mul_avx2 expects fully-reduced inputs.
* BN_mod_exp_mont_consttime should reduce the input first.
*/
if (!(TEST_true(BN_hex2bn(&a,
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF2020202020DF"))
&& TEST_true(BN_hex2bn(&b,
"1FA53F26F8811C58BE0357897AA5E165693230BC9DF5F01DFA6A2D59229EC69D"
"9DE6A89C36E3B6957B22D6FAAD5A3C73AE587B710DBE92E83D3A9A3339A085CB"
"B58F508CA4F837924BB52CC1698B7FDC2FD74362456A595A5B58E38E38E38E38"
"E38E38E38E38E38E38E38E38E38E38E38E38E38E38E38E38E38E38E38E38E38E"))
&& TEST_true(BN_hex2bn(&n,
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF2020202020DF"))
&& TEST_true(BN_MONT_CTX_set(mont, n, ctx))
&& TEST_true(BN_mod_exp_mont_consttime(c, a, b, n, ctx, mont))))
goto err;
BN_zero(d);
if (!TEST_BN_eq(c, d))
goto err;
/* Zero input */
if (!TEST_true(BN_bntest_rand(p, 1024, 0, 0)))
goto err;
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.
*/
if (!(TEST_true(BN_one(a))
&& TEST_true(BN_MONT_CTX_set(mont, m, ctx))))
goto err;
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. */
if (!(TEST_true(BN_bntest_rand(e, 1024, 0, 0))
&& 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++) {
if (!(TEST_true(BN_rand(a, 512, 0, 0))
&& TEST_ptr(BN_copy(b, BN_value_one()))))
goto err;
BN_set_negative(a, rand_neg());
BN_set_negative(b, rand_neg());
if (!(TEST_true(BN_GF2m_add(c, a, b))
/* Test that two added values have the correct parity. */
&& TEST_false((BN_is_odd(a) && BN_is_odd(c))
|| (!BN_is_odd(a) && !BN_is_odd(c)))))
goto err;
if (!(TEST_true(BN_GF2m_add(c, c, c))
/* Test that c + c = 0. */
&& 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;
if (!(TEST_true(BN_GF2m_arr2poly(p0, b[0]))
&& TEST_true(BN_GF2m_arr2poly(p1, b[1]))))
goto err;
for (i = 0; i < NUM0; i++) {
if (!TEST_true(BN_bntest_rand(a, 1024, 0, 0)))
goto err;
for (j = 0; j < 2; j++) {
if (!(TEST_true(BN_GF2m_mod(c, a, b[j]))
&& TEST_true(BN_GF2m_add(d, a, c))
&& TEST_true(BN_GF2m_mod(e, d, b[j]))
/* Test that a + (a mod p) mod p == 0. */
&& 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;
if (!(TEST_true(BN_GF2m_arr2poly(p0, b[0]))
&& TEST_true(BN_GF2m_arr2poly(p1, b[1]))))
goto err;
for (i = 0; i < NUM0; i++) {
if (!(TEST_true(BN_bntest_rand(a, 1024, 0, 0))
&& TEST_true(BN_bntest_rand(c, 1024, 0, 0))
&& TEST_true(BN_bntest_rand(d, 1024, 0, 0))))
goto err;
for (j = 0; j < 2; j++) {
if (!(TEST_true(BN_GF2m_mod_mul(e, a, c, b[j], ctx))
&& TEST_true(BN_GF2m_add(f, a, d))
&& TEST_true(BN_GF2m_mod_mul(g, f, c, b[j], ctx))
&& TEST_true(BN_GF2m_mod_mul(h, d, c, b[j], ctx))
&& TEST_true(BN_GF2m_add(f, e, g))
&& TEST_true(BN_GF2m_add(f, f, h))
/* Test that (a+d)*c = a*c + d*c. */
&& 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;
if (!(TEST_true(BN_GF2m_arr2poly(p0, b[0]))
&& TEST_true(BN_GF2m_arr2poly(p1, b[1]))))
goto err;
for (i = 0; i < NUM0; i++) {
if (!TEST_true(BN_bntest_rand(a, 1024, 0, 0)))
goto err;
for (j = 0; j < 2; j++) {
if (!(TEST_true(BN_GF2m_mod_sqr(c, a, b[j], ctx))
&& TEST_true(BN_copy(d, a))
&& TEST_true(BN_GF2m_mod_mul(d, a, d, b[j], ctx))
&& TEST_true(BN_GF2m_add(d, c, d))
/* Test that a*a = a^2. */
&& 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;
if (!(TEST_true(BN_GF2m_arr2poly(p0, b[0]))
&& TEST_true(BN_GF2m_arr2poly(p1, b[1]))))
goto err;
for (i = 0; i < NUM0; i++) {
if (!TEST_true(BN_bntest_rand(a, 512, 0, 0)))
goto err;
for (j = 0; j < 2; j++) {
if (!(TEST_true(BN_GF2m_mod_inv(c, a, b[j], ctx))
&& TEST_true(BN_GF2m_mod_mul(d, a, c, b[j], ctx))
/* Test that ((1/a)*a) = 1. */
&& 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;
if (!(TEST_true(BN_GF2m_arr2poly(p0, b[0]))
&& TEST_true(BN_GF2m_arr2poly(p1, b[1]))))
goto err;
for (i = 0; i < NUM0; i++) {
if (!(TEST_true(BN_bntest_rand(a, 512, 0, 0))
&& TEST_true(BN_bntest_rand(c, 512, 0, 0))))
goto err;
for (j = 0; j < 2; j++) {
if (!(TEST_true(BN_GF2m_mod_div(d, a, c, b[j], ctx))
&& TEST_true(BN_GF2m_mod_mul(e, d, c, b[j], ctx))
&& TEST_true(BN_GF2m_mod_div(f, a, e, b[j], ctx))
/* Test that ((a/c)*c)/a = 1. */
&& 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;
if (!(TEST_true(BN_GF2m_arr2poly(p0, b[0]))
&& TEST_true(BN_GF2m_arr2poly(p1, b[1]))))
goto err;
for (i = 0; i < NUM0; i++) {
if (!(TEST_true(BN_bntest_rand(a, 512, 0, 0))
&& TEST_true(BN_bntest_rand(c, 512, 0, 0))
&& TEST_true(BN_bntest_rand(d, 512, 0, 0))))
goto err;
for (j = 0; j < 2; j++) {
if (!(TEST_true(BN_GF2m_mod_exp(e, a, c, b[j], ctx))
&& TEST_true(BN_GF2m_mod_exp(f, a, d, b[j], ctx))
&& TEST_true(BN_GF2m_mod_mul(e, e, f, b[j], ctx))
&& TEST_true(BN_add(f, c, d))
&& TEST_true(BN_GF2m_mod_exp(f, a, f, b[j], ctx))
&& TEST_true(BN_GF2m_add(f, e, f))
/* Test that a^(c+d)=a^c*a^d. */
&& 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;
if (!(TEST_true(BN_GF2m_arr2poly(p0, b[0]))
&& TEST_true(BN_GF2m_arr2poly(p1, b[1]))))
goto err;
for (i = 0; i < NUM0; i++) {
if (!TEST_true(BN_bntest_rand(a, 512, 0, 0)))
goto err;
for (j = 0; j < 2; j++) {
if (!(TEST_true(BN_GF2m_mod(c, a, b[j]))
&& TEST_true(BN_GF2m_mod_sqrt(d, a, b[j], ctx))
&& TEST_true(BN_GF2m_mod_sqr(e, d, b[j], ctx))
&& TEST_true(BN_GF2m_add(f, c, e))
/* Test that d^2 = a, where d = sqrt(a). */
&& 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;
if (!(TEST_true(BN_GF2m_arr2poly(p0, b[0]))
&& TEST_true(BN_GF2m_arr2poly(p1, b[1]))))
goto err;
for (i = 0; i < NUM0; i++) {
if (!TEST_true(BN_bntest_rand(a, 512, 0, 0)))
goto err;
for (j = 0; j < 2; j++) {
t = BN_GF2m_mod_solve_quad(c, a, b[j], ctx);
if (t) {
s++;
if (!(TEST_true(BN_GF2m_mod_sqr(d, c, b[j], ctx))
&& TEST_true(BN_GF2m_add(d, c, d))
&& TEST_true(BN_GF2m_mod(e, a, b[j]))
&& TEST_true(BN_GF2m_add(e, e, d))
/*
* Test that solution of quadratic c
* satisfies c^2 + c = a.
*/
&& 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)
{