bn_nist.c
/* crypto/bn/bn_nist.c */
/*
* Written by Nils Larsch for the OpenSSL project
*/
/* ====================================================================
* Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in
* the documentation and/or other materials provided with the
* distribution.
*
* 3. All advertising materials mentioning features or use of this
* software must display the following acknowledgment:
* "This product includes software developed by the OpenSSL Project
* for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
*
* 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
* endorse or promote products derived from this software without
* prior written permission. For written permission, please contact
* openssl-core@openssl.org.
*
* 5. Products derived from this software may not be called "OpenSSL"
* nor may "OpenSSL" appear in their names without prior written
* permission of the OpenSSL Project.
*
* 6. Redistributions of any form whatsoever must retain the following
* acknowledgment:
* "This product includes software developed by the OpenSSL Project
* for use in the OpenSSL Toolkit (http://www.openssl.org/)"
*
* THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
* EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
* ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
* STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
* OF THE POSSIBILITY OF SUCH DAMAGE.
* ====================================================================
*
* This product includes cryptographic software written by Eric Young
* (eay@cryptsoft.com). This product includes software written by Tim
* Hudson (tjh@cryptsoft.com).
*
*/
#include "bn_lcl.h"
#include "cryptlib.h"
#define BN_NIST_192_TOP (192+BN_BITS2-1)/BN_BITS2
#define BN_NIST_224_TOP (224+BN_BITS2-1)/BN_BITS2
#define BN_NIST_256_TOP (256+BN_BITS2-1)/BN_BITS2
#define BN_NIST_384_TOP (384+BN_BITS2-1)/BN_BITS2
#define BN_NIST_521_TOP (521+BN_BITS2-1)/BN_BITS2
/* pre-computed tables are "carry-less" values of modulus*(i+1) */
#if BN_BITS2 == 64
static const BN_ULONG _nist_p_192[][BN_NIST_192_TOP] = {
{0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFEULL, 0xFFFFFFFFFFFFFFFFULL},
{0xFFFFFFFFFFFFFFFEULL, 0xFFFFFFFFFFFFFFFDULL, 0xFFFFFFFFFFFFFFFFULL},
{0xFFFFFFFFFFFFFFFDULL, 0xFFFFFFFFFFFFFFFCULL, 0xFFFFFFFFFFFFFFFFULL}
};
static const BN_ULONG _nist_p_192_sqr[] = {
0x0000000000000001ULL, 0x0000000000000002ULL, 0x0000000000000001ULL,
0xFFFFFFFFFFFFFFFEULL, 0xFFFFFFFFFFFFFFFDULL, 0xFFFFFFFFFFFFFFFFULL
};
static const BN_ULONG _nist_p_224[][BN_NIST_224_TOP] = {
{0x0000000000000001ULL, 0xFFFFFFFF00000000ULL,
0xFFFFFFFFFFFFFFFFULL, 0x00000000FFFFFFFFULL},
{0x0000000000000002ULL, 0xFFFFFFFE00000000ULL,
0xFFFFFFFFFFFFFFFFULL, 0x00000001FFFFFFFFULL} /* this one is
* "carry-full" */
};
static const BN_ULONG _nist_p_224_sqr[] = {
0x0000000000000001ULL, 0xFFFFFFFE00000000ULL,
0xFFFFFFFFFFFFFFFFULL, 0x0000000200000000ULL,
0x0000000000000000ULL, 0xFFFFFFFFFFFFFFFEULL,
0xFFFFFFFFFFFFFFFFULL
};
static const BN_ULONG _nist_p_256[][BN_NIST_256_TOP] = {
{0xFFFFFFFFFFFFFFFFULL, 0x00000000FFFFFFFFULL,
0x0000000000000000ULL, 0xFFFFFFFF00000001ULL},
{0xFFFFFFFFFFFFFFFEULL, 0x00000001FFFFFFFFULL,
0x0000000000000000ULL, 0xFFFFFFFE00000002ULL},
{0xFFFFFFFFFFFFFFFDULL, 0x00000002FFFFFFFFULL,
0x0000000000000000ULL, 0xFFFFFFFD00000003ULL},
{0xFFFFFFFFFFFFFFFCULL, 0x00000003FFFFFFFFULL,
0x0000000000000000ULL, 0xFFFFFFFC00000004ULL},
{0xFFFFFFFFFFFFFFFBULL, 0x00000004FFFFFFFFULL,
0x0000000000000000ULL, 0xFFFFFFFB00000005ULL},
};
static const BN_ULONG _nist_p_256_sqr[] = {
0x0000000000000001ULL, 0xFFFFFFFE00000000ULL,
0xFFFFFFFFFFFFFFFFULL, 0x00000001FFFFFFFEULL,
0x00000001FFFFFFFEULL, 0x00000001FFFFFFFEULL,
0xFFFFFFFE00000001ULL, 0xFFFFFFFE00000002ULL
};
static const BN_ULONG _nist_p_384[][BN_NIST_384_TOP] = {
{0x00000000FFFFFFFFULL, 0xFFFFFFFF00000000ULL, 0xFFFFFFFFFFFFFFFEULL,
0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL},
{0x00000001FFFFFFFEULL, 0xFFFFFFFE00000000ULL, 0xFFFFFFFFFFFFFFFDULL,
0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL},
{0x00000002FFFFFFFDULL, 0xFFFFFFFD00000000ULL, 0xFFFFFFFFFFFFFFFCULL,
0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL},
{0x00000003FFFFFFFCULL, 0xFFFFFFFC00000000ULL, 0xFFFFFFFFFFFFFFFBULL,
0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL},
{0x00000004FFFFFFFBULL, 0xFFFFFFFB00000000ULL, 0xFFFFFFFFFFFFFFFAULL,
0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL},
};
static const BN_ULONG _nist_p_384_sqr[] = {
0xFFFFFFFE00000001ULL, 0x0000000200000000ULL, 0xFFFFFFFE00000000ULL,
0x0000000200000000ULL, 0x0000000000000001ULL, 0x0000000000000000ULL,
0x00000001FFFFFFFEULL, 0xFFFFFFFE00000000ULL, 0xFFFFFFFFFFFFFFFDULL,
0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL
};
static const BN_ULONG _nist_p_521[] =
{ 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL,
0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL,
0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL,
0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL,
0x00000000000001FFULL
};
static const BN_ULONG _nist_p_521_sqr[] = {
0x0000000000000001ULL, 0x0000000000000000ULL, 0x0000000000000000ULL,
0x0000000000000000ULL, 0x0000000000000000ULL, 0x0000000000000000ULL,
0x0000000000000000ULL, 0x0000000000000000ULL, 0xFFFFFFFFFFFFFC00ULL,
0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL,
0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL,
0xFFFFFFFFFFFFFFFFULL, 0x000000000003FFFFULL
};
#elif BN_BITS2 == 32
static const BN_ULONG _nist_p_192[][BN_NIST_192_TOP] = {
{0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF},
{0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFD, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF},
{0xFFFFFFFD, 0xFFFFFFFF, 0xFFFFFFFC, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}
};
static const BN_ULONG _nist_p_192_sqr[] = {
0x00000001, 0x00000000, 0x00000002, 0x00000000, 0x00000001, 0x00000000,
0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFD, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF
};
static const BN_ULONG _nist_p_224[][BN_NIST_224_TOP] = {
{0x00000001, 0x00000000, 0x00000000, 0xFFFFFFFF,
0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF},
{0x00000002, 0x00000000, 0x00000000, 0xFFFFFFFE,
0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}
};
static const BN_ULONG _nist_p_224_sqr[] = {
0x00000001, 0x00000000, 0x00000000, 0xFFFFFFFE,
0xFFFFFFFF, 0xFFFFFFFF, 0x00000000, 0x00000002,
0x00000000, 0x00000000, 0xFFFFFFFE, 0xFFFFFFFF,
0xFFFFFFFF, 0xFFFFFFFF
};
static const BN_ULONG _nist_p_256[][BN_NIST_256_TOP] = {
{0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000000,
0x00000000, 0x00000000, 0x00000001, 0xFFFFFFFF},
{0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000001,
0x00000000, 0x00000000, 0x00000002, 0xFFFFFFFE},
{0xFFFFFFFD, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000002,
0x00000000, 0x00000000, 0x00000003, 0xFFFFFFFD},
{0xFFFFFFFC, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000003,
0x00000000, 0x00000000, 0x00000004, 0xFFFFFFFC},
{0xFFFFFFFB, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000004,
0x00000000, 0x00000000, 0x00000005, 0xFFFFFFFB},
};
static const BN_ULONG _nist_p_256_sqr[] = {
0x00000001, 0x00000000, 0x00000000, 0xFFFFFFFE,
0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFE, 0x00000001,
0xFFFFFFFE, 0x00000001, 0xFFFFFFFE, 0x00000001,
0x00000001, 0xFFFFFFFE, 0x00000002, 0xFFFFFFFE
};
static const BN_ULONG _nist_p_384[][BN_NIST_384_TOP] = {
{0xFFFFFFFF, 0x00000000, 0x00000000, 0xFFFFFFFF, 0xFFFFFFFE, 0xFFFFFFFF,
0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF},
{0xFFFFFFFE, 0x00000001, 0x00000000, 0xFFFFFFFE, 0xFFFFFFFD, 0xFFFFFFFF,
0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF},
{0xFFFFFFFD, 0x00000002, 0x00000000, 0xFFFFFFFD, 0xFFFFFFFC, 0xFFFFFFFF,
0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF},
{0xFFFFFFFC, 0x00000003, 0x00000000, 0xFFFFFFFC, 0xFFFFFFFB, 0xFFFFFFFF,
0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF},
{0xFFFFFFFB, 0x00000004, 0x00000000, 0xFFFFFFFB, 0xFFFFFFFA, 0xFFFFFFFF,
0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF},
};
static const BN_ULONG _nist_p_384_sqr[] = {
0x00000001, 0xFFFFFFFE, 0x00000000, 0x00000002, 0x00000000, 0xFFFFFFFE,
0x00000000, 0x00000002, 0x00000001, 0x00000000, 0x00000000, 0x00000000,
0xFFFFFFFE, 0x00000001, 0x00000000, 0xFFFFFFFE, 0xFFFFFFFD, 0xFFFFFFFF,
0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF
};
static const BN_ULONG _nist_p_521[] = { 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF,
0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF,
0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF,
0xFFFFFFFF, 0x000001FF
};
static const BN_ULONG _nist_p_521_sqr[] = {
0x00000001, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
0x00000000, 0x00000000, 0x00000000, 0x00000000, 0xFFFFFC00, 0xFFFFFFFF,
0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF,
0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF,
0xFFFFFFFF, 0xFFFFFFFF, 0x0003FFFF
};
#else
# error "unsupported BN_BITS2"
#endif
static const BIGNUM _bignum_nist_p_192 = {
(BN_ULONG *)_nist_p_192[0],
BN_NIST_192_TOP,
BN_NIST_192_TOP,
0,
BN_FLG_STATIC_DATA
};
static const BIGNUM _bignum_nist_p_224 = {
(BN_ULONG *)_nist_p_224[0],
BN_NIST_224_TOP,
BN_NIST_224_TOP,
0,
BN_FLG_STATIC_DATA
};
static const BIGNUM _bignum_nist_p_256 = {
(BN_ULONG *)_nist_p_256[0],
BN_NIST_256_TOP,
BN_NIST_256_TOP,
0,
BN_FLG_STATIC_DATA
};
static const BIGNUM _bignum_nist_p_384 = {
(BN_ULONG *)_nist_p_384[0],
BN_NIST_384_TOP,
BN_NIST_384_TOP,
0,
BN_FLG_STATIC_DATA
};
static const BIGNUM _bignum_nist_p_521 = {
(BN_ULONG *)_nist_p_521,
BN_NIST_521_TOP,
BN_NIST_521_TOP,
0,
BN_FLG_STATIC_DATA
};
const BIGNUM *BN_get0_nist_prime_192(void)
{
return &_bignum_nist_p_192;
}
const BIGNUM *BN_get0_nist_prime_224(void)
{
return &_bignum_nist_p_224;
}
const BIGNUM *BN_get0_nist_prime_256(void)
{
return &_bignum_nist_p_256;
}
const BIGNUM *BN_get0_nist_prime_384(void)
{
return &_bignum_nist_p_384;
}
const BIGNUM *BN_get0_nist_prime_521(void)
{
return &_bignum_nist_p_521;
}
static void nist_cp_bn_0(BN_ULONG *buf, BN_ULONG *a, int top, int max)
{
int i;
BN_ULONG *_tmp1 = (buf), *_tmp2 = (a);
#ifdef BN_DEBUG
OPENSSL_assert(top <= max);
#endif
for (i = (top); i != 0; i--)
*_tmp1++ = *_tmp2++;
for (i = (max) - (top); i != 0; i--)
*_tmp1++ = (BN_ULONG)0;
}
static void nist_cp_bn(BN_ULONG *buf, BN_ULONG *a, int top)
{
int i;
BN_ULONG *_tmp1 = (buf), *_tmp2 = (a);
for (i = (top); i != 0; i--)
*_tmp1++ = *_tmp2++;
}
#if BN_BITS2 == 64
# define bn_cp_64(to, n, from, m) (to)[n] = (m>=0)?((from)[m]):0;
# define bn_64_set_0(to, n) (to)[n] = (BN_ULONG)0;
/*
* two following macros are implemented under assumption that they
* are called in a sequence with *ascending* n, i.e. as they are...
*/
# define bn_cp_32_naked(to, n, from, m) (((n)&1)?(to[(n)/2]|=((m)&1)?(from[(m)/2]&BN_MASK2h):(from[(m)/2]<<32))\
:(to[(n)/2] =((m)&1)?(from[(m)/2]>>32):(from[(m)/2]&BN_MASK2l)))
# define bn_32_set_0(to, n) (((n)&1)?(to[(n)/2]&=BN_MASK2l):(to[(n)/2]=0));
# define bn_cp_32(to,n,from,m) ((m)>=0)?bn_cp_32_naked(to,n,from,m):bn_32_set_0(to,n)
#else
# define bn_cp_64(to, n, from, m) \
{ \
bn_cp_32(to, (n)*2, from, (m)*2); \
bn_cp_32(to, (n)*2+1, from, (m)*2+1); \
}
# define bn_64_set_0(to, n) \
{ \
bn_32_set_0(to, (n)*2); \
bn_32_set_0(to, (n)*2+1); \
}
# if BN_BITS2 == 32
# define bn_cp_32(to, n, from, m) (to)[n] = (m>=0)?((from)[m]):0;
# define bn_32_set_0(to, n) (to)[n] = (BN_ULONG)0;
# endif
#endif /* BN_BITS2 != 64 */
#define nist_set_192(to, from, a1, a2, a3) \
{ \
bn_cp_64(to, 0, from, (a3) - 3) \
bn_cp_64(to, 1, from, (a2) - 3) \
bn_cp_64(to, 2, from, (a1) - 3) \
}
int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
BN_CTX *ctx)
{
int top = a->top, i;
int carry;
register BN_ULONG *r_d, *a_d = a->d;
BN_ULONG t_d[BN_NIST_192_TOP],
buf[BN_NIST_192_TOP], c_d[BN_NIST_192_TOP], *res;
size_t mask;
static const BIGNUM _bignum_nist_p_192_sqr = {
(BN_ULONG *)_nist_p_192_sqr,
sizeof(_nist_p_192_sqr) / sizeof(_nist_p_192_sqr[0]),
sizeof(_nist_p_192_sqr) / sizeof(_nist_p_192_sqr[0]),
0, BN_FLG_STATIC_DATA
};
field = &_bignum_nist_p_192; /* just to make sure */
if (BN_is_negative(a) || BN_ucmp(a, &_bignum_nist_p_192_sqr) >= 0)
return BN_nnmod(r, a, field, ctx);
i = BN_ucmp(field, a);
if (i == 0) {
BN_zero(r);
return 1;
} else if (i > 0)
return (r == a) ? 1 : (BN_copy(r, a) != NULL);
if (r != a) {
if (!bn_wexpand(r, BN_NIST_192_TOP))
return 0;
r_d = r->d;
nist_cp_bn(r_d, a_d, BN_NIST_192_TOP);
} else
r_d = a_d;
nist_cp_bn_0(buf, a_d + BN_NIST_192_TOP, top - BN_NIST_192_TOP,
BN_NIST_192_TOP);
nist_set_192(t_d, buf, 0, 3, 3);
carry = (int)bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
nist_set_192(t_d, buf, 4, 4, 0);
carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
nist_set_192(t_d, buf, 5, 5, 5)
carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
if (carry > 0)
carry =
(int)bn_sub_words(r_d, r_d, _nist_p_192[carry - 1],
BN_NIST_192_TOP);
else
carry = 1;
/*
* we need 'if (carry==0 || result>=modulus) result-=modulus;'
* as comparison implies subtraction, we can write
* 'tmp=result-modulus; if (!carry || !borrow) result=tmp;'
* this is what happens below, but without explicit if:-) a.
*/
mask =
0 - (size_t)bn_sub_words(c_d, r_d, _nist_p_192[0], BN_NIST_192_TOP);
mask &= 0 - (size_t)carry;
res = (BN_ULONG *)(((size_t)c_d & ~mask) | ((size_t)r_d & mask));
nist_cp_bn(r_d, res, BN_NIST_192_TOP);
r->top = BN_NIST_192_TOP;
bn_correct_top(r);
return 1;
}
typedef BN_ULONG (*bn_addsub_f) (BN_ULONG *, const BN_ULONG *,
const BN_ULONG *, int);
#define nist_set_224(to, from, a1, a2, a3, a4, a5, a6, a7) \
{ \
bn_cp_32(to, 0, from, (a7) - 7) \
bn_cp_32(to, 1, from, (a6) - 7) \
bn_cp_32(to, 2, from, (a5) - 7) \
bn_cp_32(to, 3, from, (a4) - 7) \
bn_cp_32(to, 4, from, (a3) - 7) \
bn_cp_32(to, 5, from, (a2) - 7) \
bn_cp_32(to, 6, from, (a1) - 7) \
}
int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
BN_CTX *ctx)
{
int top = a->top, i;
int carry;
BN_ULONG *r_d, *a_d = a->d;
BN_ULONG t_d[BN_NIST_224_TOP],
buf[BN_NIST_224_TOP], c_d[BN_NIST_224_TOP], *res;
size_t mask;
union {
bn_addsub_f f;
size_t p;
} u;
static const BIGNUM _bignum_nist_p_224_sqr = {
(BN_ULONG *)_nist_p_224_sqr,
sizeof(_nist_p_224_sqr) / sizeof(_nist_p_224_sqr[0]),
sizeof(_nist_p_224_sqr) / sizeof(_nist_p_224_sqr[0]),
0, BN_FLG_STATIC_DATA
};
field = &_bignum_nist_p_224; /* just to make sure */
if (BN_is_negative(a) || BN_ucmp(a, &_bignum_nist_p_224_sqr) >= 0)
return BN_nnmod(r, a, field, ctx);
i = BN_ucmp(field, a);
if (i == 0) {
BN_zero(r);
return 1;
} else if (i > 0)
return (r == a) ? 1 : (BN_copy(r, a) != NULL);
if (r != a) {
if (!bn_wexpand(r, BN_NIST_224_TOP))
return 0;
r_d = r->d;
nist_cp_bn(r_d, a_d, BN_NIST_224_TOP);
} else
r_d = a_d;
#if BN_BITS2==64
/* copy upper 256 bits of 448 bit number ... */
nist_cp_bn_0(t_d, a_d + (BN_NIST_224_TOP - 1),
top - (BN_NIST_224_TOP - 1), BN_NIST_224_TOP);
/* ... and right shift by 32 to obtain upper 224 bits */
nist_set_224(buf, t_d, 14, 13, 12, 11, 10, 9, 8);
/* truncate lower part to 224 bits too */
r_d[BN_NIST_224_TOP - 1] &= BN_MASK2l;
#else
nist_cp_bn_0(buf, a_d + BN_NIST_224_TOP, top - BN_NIST_224_TOP,
BN_NIST_224_TOP);
#endif
nist_set_224(t_d, buf, 10, 9, 8, 7, 0, 0, 0);
carry = (int)bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP);
nist_set_224(t_d, buf, 0, 13, 12, 11, 0, 0, 0);
carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP);
nist_set_224(t_d, buf, 13, 12, 11, 10, 9, 8, 7);
carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP);
nist_set_224(t_d, buf, 0, 0, 0, 0, 13, 12, 11);
carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP);
#if BN_BITS2==64
carry = (int)(r_d[BN_NIST_224_TOP - 1] >> 32);
#endif
u.f = bn_sub_words;
if (carry > 0) {
carry =
(int)bn_sub_words(r_d, r_d, _nist_p_224[carry - 1],
BN_NIST_224_TOP);
#if BN_BITS2==64
carry = (int)(~(r_d[BN_NIST_224_TOP - 1] >> 32)) & 1;
#endif
} else if (carry < 0) {
/*
* it's a bit more comlicated logic in this case. if bn_add_words
* yields no carry, then result has to be adjusted by unconditionally
* *adding* the modulus. but if it does, then result has to be
* compared to the modulus and conditionally adjusted by
* *subtracting* the latter.
*/
carry =
(int)bn_add_words(r_d, r_d, _nist_p_224[-carry - 1],
BN_NIST_224_TOP);
mask = 0 - (size_t)carry;
u.p = ((size_t)bn_sub_words & mask) | ((size_t)bn_add_words & ~mask);
} else
carry = 1;
/* otherwise it's effectively same as in BN_nist_mod_192... */
mask = 0 - (size_t)(*u.f) (c_d, r_d, _nist_p_224[0], BN_NIST_224_TOP);
mask &= 0 - (size_t)carry;
res = (BN_ULONG *)(((size_t)c_d & ~mask) | ((size_t)r_d & mask));
nist_cp_bn(r_d, res, BN_NIST_224_TOP);
r->top = BN_NIST_224_TOP;
bn_correct_top(r);
return 1;
}
#define nist_set_256(to, from, a1, a2, a3, a4, a5, a6, a7, a8) \
{ \
bn_cp_32(to, 0, from, (a8) - 8) \
bn_cp_32(to, 1, from, (a7) - 8) \
bn_cp_32(to, 2, from, (a6) - 8) \
bn_cp_32(to, 3, from, (a5) - 8) \
bn_cp_32(to, 4, from, (a4) - 8) \
bn_cp_32(to, 5, from, (a3) - 8) \
bn_cp_32(to, 6, from, (a2) - 8) \
bn_cp_32(to, 7, from, (a1) - 8) \
}
int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
BN_CTX *ctx)
{
int i, top = a->top;
int carry = 0;
register BN_ULONG *a_d = a->d, *r_d;
BN_ULONG t_d[BN_NIST_256_TOP],
buf[BN_NIST_256_TOP], c_d[BN_NIST_256_TOP], *res;
size_t mask;
union {
bn_addsub_f f;
size_t p;
} u;
static const BIGNUM _bignum_nist_p_256_sqr = {
(BN_ULONG *)_nist_p_256_sqr,
sizeof(_nist_p_256_sqr) / sizeof(_nist_p_256_sqr[0]),
sizeof(_nist_p_256_sqr) / sizeof(_nist_p_256_sqr[0]),
0, BN_FLG_STATIC_DATA
};
field = &_bignum_nist_p_256; /* just to make sure */
if (BN_is_negative(a) || BN_ucmp(a, &_bignum_nist_p_256_sqr) >= 0)
return BN_nnmod(r, a, field, ctx);
i = BN_ucmp(field, a);
if (i == 0) {
BN_zero(r);
return 1;
} else if (i > 0)
return (r == a) ? 1 : (BN_copy(r, a) != NULL);
if (r != a) {
if (!bn_wexpand(r, BN_NIST_256_TOP))
return 0;
r_d = r->d;
nist_cp_bn(r_d, a_d, BN_NIST_256_TOP);
} else
r_d = a_d;
nist_cp_bn_0(buf, a_d + BN_NIST_256_TOP, top - BN_NIST_256_TOP,
BN_NIST_256_TOP);
/*
* S1
*/
nist_set_256(t_d, buf, 15, 14, 13, 12, 11, 0, 0, 0);
/*
* S2
*/
nist_set_256(c_d, buf, 0, 15, 14, 13, 12, 0, 0, 0);
carry = (int)bn_add_words(t_d, t_d, c_d, BN_NIST_256_TOP);
/* left shift */
{
register BN_ULONG *ap, t, c;
ap = t_d;
c = 0;
for (i = BN_NIST_256_TOP; i != 0; --i) {
t = *ap;
*(ap++) = ((t << 1) | c) & BN_MASK2;
c = (t & BN_TBIT) ? 1 : 0;
}
carry <<= 1;
carry |= c;
}
carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
/*
* S3
*/
nist_set_256(t_d, buf, 15, 14, 0, 0, 0, 10, 9, 8);
carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
/*
* S4
*/
nist_set_256(t_d, buf, 8, 13, 15, 14, 13, 11, 10, 9);
carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
/*
* D1
*/
nist_set_256(t_d, buf, 10, 8, 0, 0, 0, 13, 12, 11);
carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
/*
* D2
*/
nist_set_256(t_d, buf, 11, 9, 0, 0, 15, 14, 13, 12);
carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
/*
* D3
*/
nist_set_256(t_d, buf, 12, 0, 10, 9, 8, 15, 14, 13);
carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
/*
* D4
*/
nist_set_256(t_d, buf, 13, 0, 11, 10, 9, 0, 15, 14);
carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
/* see BN_nist_mod_224 for explanation */
u.f = bn_sub_words;
if (carry > 0)
carry =
(int)bn_sub_words(r_d, r_d, _nist_p_256[carry - 1],
BN_NIST_256_TOP);
else if (carry < 0) {
carry =
(int)bn_add_words(r_d, r_d, _nist_p_256[-carry - 1],
BN_NIST_256_TOP);
mask = 0 - (size_t)carry;
u.p = ((size_t)bn_sub_words & mask) | ((size_t)bn_add_words & ~mask);
} else
carry = 1;
mask = 0 - (size_t)(*u.f) (c_d, r_d, _nist_p_256[0], BN_NIST_256_TOP);
mask &= 0 - (size_t)carry;
res = (BN_ULONG *)(((size_t)c_d & ~mask) | ((size_t)r_d & mask));
nist_cp_bn(r_d, res, BN_NIST_256_TOP);
r->top = BN_NIST_256_TOP;
bn_correct_top(r);
return 1;
}
#define nist_set_384(to,from,a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12) \
{ \
bn_cp_32(to, 0, from, (a12) - 12) \
bn_cp_32(to, 1, from, (a11) - 12) \
bn_cp_32(to, 2, from, (a10) - 12) \
bn_cp_32(to, 3, from, (a9) - 12) \
bn_cp_32(to, 4, from, (a8) - 12) \
bn_cp_32(to, 5, from, (a7) - 12) \
bn_cp_32(to, 6, from, (a6) - 12) \
bn_cp_32(to, 7, from, (a5) - 12) \
bn_cp_32(to, 8, from, (a4) - 12) \
bn_cp_32(to, 9, from, (a3) - 12) \
bn_cp_32(to, 10, from, (a2) - 12) \
bn_cp_32(to, 11, from, (a1) - 12) \
}
int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
BN_CTX *ctx)
{
int i, top = a->top;
int carry = 0;
register BN_ULONG *r_d, *a_d = a->d;
BN_ULONG t_d[BN_NIST_384_TOP],
buf[BN_NIST_384_TOP], c_d[BN_NIST_384_TOP], *res;
size_t mask;
union {
bn_addsub_f f;
size_t p;
} u;
static const BIGNUM _bignum_nist_p_384_sqr = {
(BN_ULONG *)_nist_p_384_sqr,
sizeof(_nist_p_384_sqr) / sizeof(_nist_p_384_sqr[0]),
sizeof(_nist_p_384_sqr) / sizeof(_nist_p_384_sqr[0]),
0, BN_FLG_STATIC_DATA
};
field = &_bignum_nist_p_384; /* just to make sure */
if (BN_is_negative(a) || BN_ucmp(a, &_bignum_nist_p_384_sqr) >= 0)
return BN_nnmod(r, a, field, ctx);
i = BN_ucmp(field, a);
if (i == 0) {
BN_zero(r);
return 1;
} else if (i > 0)
return (r == a) ? 1 : (BN_copy(r, a) != NULL);
if (r != a) {
if (!bn_wexpand(r, BN_NIST_384_TOP))
return 0;
r_d = r->d;
nist_cp_bn(r_d, a_d, BN_NIST_384_TOP);
} else
r_d = a_d;
nist_cp_bn_0(buf, a_d + BN_NIST_384_TOP, top - BN_NIST_384_TOP,
BN_NIST_384_TOP);
/*
* S1
*/
nist_set_256(t_d, buf, 0, 0, 0, 0, 0, 23 - 4, 22 - 4, 21 - 4);
/* left shift */
{
register BN_ULONG *ap, t, c;
ap = t_d;
c = 0;
for (i = 3; i != 0; --i) {
t = *ap;
*(ap++) = ((t << 1) | c) & BN_MASK2;
c = (t & BN_TBIT) ? 1 : 0;
}
*ap = c;
}
carry = (int)bn_add_words(r_d + (128 / BN_BITS2), r_d + (128 / BN_BITS2),
t_d, BN_NIST_256_TOP);
/*
* S2
*/
carry += (int)bn_add_words(r_d, r_d, buf, BN_NIST_384_TOP);
/*
* S3
*/
nist_set_384(t_d, buf, 20, 19, 18, 17, 16, 15, 14, 13, 12, 23, 22, 21);
carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
/*
* S4
*/
nist_set_384(t_d, buf, 19, 18, 17, 16, 15, 14, 13, 12, 20, 0, 23, 0);
carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
/*
* S5
*/
nist_set_384(t_d, buf, 0, 0, 0, 0, 23, 22, 21, 20, 0, 0, 0, 0);
carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
/*
* S6
*/
nist_set_384(t_d, buf, 0, 0, 0, 0, 0, 0, 23, 22, 21, 0, 0, 20);
carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
/*
* D1
*/
nist_set_384(t_d, buf, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 23);
carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
/*
* D2
*/
nist_set_384(t_d, buf, 0, 0, 0, 0, 0, 0, 0, 23, 22, 21, 20, 0);
carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
/*
* D3
*/
nist_set_384(t_d, buf, 0, 0, 0, 0, 0, 0, 0, 23, 23, 0, 0, 0);
carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
/* see BN_nist_mod_224 for explanation */
u.f = bn_sub_words;
if (carry > 0)
carry =
(int)bn_sub_words(r_d, r_d, _nist_p_384[carry - 1],
BN_NIST_384_TOP);
else if (carry < 0) {
carry =
(int)bn_add_words(r_d, r_d, _nist_p_384[-carry - 1],
BN_NIST_384_TOP);
mask = 0 - (size_t)carry;
u.p = ((size_t)bn_sub_words & mask) | ((size_t)bn_add_words & ~mask);
} else
carry = 1;
mask = 0 - (size_t)(*u.f) (c_d, r_d, _nist_p_384[0], BN_NIST_384_TOP);
mask &= 0 - (size_t)carry;
res = (BN_ULONG *)(((size_t)c_d & ~mask) | ((size_t)r_d & mask));
nist_cp_bn(r_d, res, BN_NIST_384_TOP);
r->top = BN_NIST_384_TOP;
bn_correct_top(r);
return 1;
}
#define BN_NIST_521_RSHIFT (521%BN_BITS2)
#define BN_NIST_521_LSHIFT (BN_BITS2-BN_NIST_521_RSHIFT)
#define BN_NIST_521_TOP_MASK ((BN_ULONG)BN_MASK2>>BN_NIST_521_LSHIFT)
int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
BN_CTX *ctx)
{
int top = a->top, i;
BN_ULONG *r_d, *a_d = a->d, t_d[BN_NIST_521_TOP], val, tmp, *res;
size_t mask;
static const BIGNUM _bignum_nist_p_521_sqr = {
(BN_ULONG *)_nist_p_521_sqr,
sizeof(_nist_p_521_sqr) / sizeof(_nist_p_521_sqr[0]),
sizeof(_nist_p_521_sqr) / sizeof(_nist_p_521_sqr[0]),
0, BN_FLG_STATIC_DATA
};
field = &_bignum_nist_p_521; /* just to make sure */
if (BN_is_negative(a) || BN_ucmp(a, &_bignum_nist_p_521_sqr) >= 0)
return BN_nnmod(r, a, field, ctx);
i = BN_ucmp(field, a);
if (i == 0) {
BN_zero(r);
return 1;
} else if (i > 0)
return (r == a) ? 1 : (BN_copy(r, a) != NULL);
if (r != a) {
if (!bn_wexpand(r, BN_NIST_521_TOP))
return 0;
r_d = r->d;
nist_cp_bn(r_d, a_d, BN_NIST_521_TOP);
} else
r_d = a_d;
/* upper 521 bits, copy ... */
nist_cp_bn_0(t_d, a_d + (BN_NIST_521_TOP - 1),
top - (BN_NIST_521_TOP - 1), BN_NIST_521_TOP);
/* ... and right shift */
for (val = t_d[0], i = 0; i < BN_NIST_521_TOP - 1; i++) {
tmp = val >> BN_NIST_521_RSHIFT;
val = t_d[i + 1];
t_d[i] = (tmp | val << BN_NIST_521_LSHIFT) & BN_MASK2;
}
t_d[i] = val >> BN_NIST_521_RSHIFT;
/* lower 521 bits */
r_d[i] &= BN_NIST_521_TOP_MASK;
bn_add_words(r_d, r_d, t_d, BN_NIST_521_TOP);
mask = 0 - (size_t)bn_sub_words(t_d, r_d, _nist_p_521, BN_NIST_521_TOP);
res = (BN_ULONG *)(((size_t)t_d & ~mask) | ((size_t)r_d & mask));
nist_cp_bn(r_d, res, BN_NIST_521_TOP);
r->top = BN_NIST_521_TOP;
bn_correct_top(r);
return 1;
}
