/* 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;
PTR_SIZE_INT 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-(PTR_SIZE_INT)bn_sub_words(c_d,r_d,_nist_p_192[0],BN_NIST_192_TOP);
mask &= 0-(PTR_SIZE_INT)carry;
res = (BN_ULONG *)
(((PTR_SIZE_INT)c_d&~mask) | ((PTR_SIZE_INT)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;
PTR_SIZE_INT mask;
union { bn_addsub_f f; PTR_SIZE_INT 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-(PTR_SIZE_INT)carry;
u.p = ((PTR_SIZE_INT)bn_sub_words&mask) |
((PTR_SIZE_INT)bn_add_words&~mask);
}
else
carry = 1;
/* otherwise it's effectively same as in BN_nist_mod_192... */
mask = 0-(PTR_SIZE_INT)(*u.f)(c_d,r_d,_nist_p_224[0],BN_NIST_224_TOP);
mask &= 0-(PTR_SIZE_INT)carry;
res = (BN_ULONG *)(((PTR_SIZE_INT)c_d&~mask) |
((PTR_SIZE_INT)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;
PTR_SIZE_INT mask;
union { bn_addsub_f f; PTR_SIZE_INT 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-(PTR_SIZE_INT)carry;
u.p = ((PTR_SIZE_INT)bn_sub_words&mask) |
((PTR_SIZE_INT)bn_add_words&~mask);
}
else
carry = 1;
mask = 0-(PTR_SIZE_INT)(*u.f)(c_d,r_d,_nist_p_256[0],BN_NIST_256_TOP);
mask &= 0-(PTR_SIZE_INT)carry;
res = (BN_ULONG *)(((PTR_SIZE_INT)c_d&~mask) |
((PTR_SIZE_INT)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;
PTR_SIZE_INT mask;
union { bn_addsub_f f; PTR_SIZE_INT 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-(PTR_SIZE_INT)carry;
u.p = ((PTR_SIZE_INT)bn_sub_words&mask) |
((PTR_SIZE_INT)bn_add_words&~mask);
}
else
carry = 1;
mask = 0-(PTR_SIZE_INT)(*u.f)(c_d,r_d,_nist_p_384[0],BN_NIST_384_TOP);
mask &= 0-(PTR_SIZE_INT)carry;
res = (BN_ULONG *)(((PTR_SIZE_INT)c_d&~mask) |
((PTR_SIZE_INT)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;
PTR_SIZE_INT 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-(PTR_SIZE_INT)bn_sub_words(t_d,r_d,_nist_p_521,BN_NIST_521_TOP);
res = (BN_ULONG *)(((PTR_SIZE_INT)t_d&~mask) |
((PTR_SIZE_INT)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;
}