/*
* Copyright (c) 2007, 2011, Oracle and/or its affiliates. All rights reserved.
* Use is subject to license terms.
*
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* This library is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this library; if not, write to the Free Software Foundation,
* Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/* *********************************************************************
*
* The Original Code is the Netscape security libraries.
*
* The Initial Developer of the Original Code is
* Netscape Communications Corporation.
* Portions created by the Initial Developer are Copyright (C) 2000
* the Initial Developer. All Rights Reserved.
*
* Contributor(s):
* Sheueling Chang Shantz <sheueling.chang@sun.com>,
* Stephen Fung <stephen.fung@sun.com>, and
* Douglas Stebila <douglas@stebila.ca> of Sun Laboratories.
*
*********************************************************************** */
/* This file implements moduluar exponentiation using Montgomery's
* method for modular reduction. This file implements the method
* described as "Improvement 1" in the paper "A Cryptogrpahic Library for
* the Motorola DSP56000" by Stephen R. Dusse' and Burton S. Kaliski Jr.
* published in "Advances in Cryptology: Proceedings of EUROCRYPT '90"
* "Lecture Notes in Computer Science" volume 473, 1991, pg 230-244,
* published by Springer Verlag.
*/
#define MP_USING_CACHE_SAFE_MOD_EXP 1
#ifndef _KERNEL
#include <string.h>
#include <stddef.h> /* ptrdiff_t */
#endif
#include "mpi-priv.h"
#include "mplogic.h"
#include "mpprime.h"
#ifdef MP_USING_MONT_MULF
#include "montmulf.h"
#endif
/* if MP_CHAR_STORE_SLOW is defined, we */
/* need to know endianness of this platform. */
#ifdef MP_CHAR_STORE_SLOW
#if !defined(MP_IS_BIG_ENDIAN) && !defined(MP_IS_LITTLE_ENDIAN)
#error "You must define MP_IS_BIG_ENDIAN or MP_IS_LITTLE_ENDIAN\n" \
" if you define MP_CHAR_STORE_SLOW."
#endif
#endif
#ifndef STATIC
#define STATIC
#endif
#define MAX_ODD_INTS 32 /* 2 ** (WINDOW_BITS - 1) */
#ifndef _KERNEL
#if defined(_WIN32_WCE)
#define ABORT res = MP_UNDEF; goto CLEANUP
#else
#define ABORT abort()
#endif
#else
#define ABORT res = MP_UNDEF; goto CLEANUP
#endif /* _KERNEL */
/* computes T = REDC(T), 2^b == R */
mp_err s_mp_redc(mp_int *T, mp_mont_modulus *mmm)
{
mp_err res;
mp_size i;
i = MP_USED(T) + MP_USED(&mmm->N) + 2;
MP_CHECKOK( s_mp_pad(T, i) );
for (i = 0; i < MP_USED(&mmm->N); ++i ) {
mp_digit m_i = MP_DIGIT(T, i) * mmm->n0prime;
/* T += N * m_i * (MP_RADIX ** i); */
MP_CHECKOK( s_mp_mul_d_add_offset(&mmm->N, m_i, T, i) );
}
s_mp_clamp(T);
/* T /= R */
s_mp_div_2d(T, mmm->b);
if ((res = s_mp_cmp(T, &mmm->N)) >= 0) {
/* T = T - N */
MP_CHECKOK( s_mp_sub(T, &mmm->N) );
#ifdef DEBUG
if ((res = mp_cmp(T, &mmm->N)) >= 0) {
res = MP_UNDEF;
goto CLEANUP;
}
#endif
}
res = MP_OKAY;
CLEANUP:
return res;
}
#if !defined(MP_ASSEMBLY_MUL_MONT) && !defined(MP_MONT_USE_MP_MUL)
mp_err s_mp_mul_mont(const mp_int *a, const mp_int *b, mp_int *c,
mp_mont_modulus *mmm)
{
mp_digit *pb;
mp_digit m_i;
mp_err res;
mp_size ib;
mp_size useda, usedb;
ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
if (MP_USED(a) < MP_USED(b)) {
const mp_int *xch = b; /* switch a and b, to do fewer outer loops */
b = a;
a = xch;
}
MP_USED(c) = 1; MP_DIGIT(c, 0) = 0;
ib = MP_USED(a) + MP_MAX(MP_USED(b), MP_USED(&mmm->N)) + 2;
if((res = s_mp_pad(c, ib)) != MP_OKAY)
goto CLEANUP;
useda = MP_USED(a);
pb = MP_DIGITS(b);
s_mpv_mul_d(MP_DIGITS(a), useda, *pb++, MP_DIGITS(c));
s_mp_setz(MP_DIGITS(c) + useda + 1, ib - (useda + 1));
m_i = MP_DIGIT(c, 0) * mmm->n0prime;
s_mp_mul_d_add_offset(&mmm->N, m_i, c, 0);
/* Outer loop: Digits of b */
usedb = MP_USED(b);
for (ib = 1; ib < usedb; ib++) {
mp_digit b_i = *pb++;
/* Inner product: Digits of a */
if (b_i)
s_mpv_mul_d_add_prop(MP_DIGITS(a), useda, b_i, MP_DIGITS(c) + ib);
m_i = MP_DIGIT(c, ib) * mmm->n0prime;
s_mp_mul_d_add_offset(&mmm->N, m_i, c, ib);
}
if (usedb < MP_USED(&mmm->N)) {
for (usedb = MP_USED(&mmm->N); ib < usedb; ++ib ) {
m_i = MP_DIGIT(c, ib) * mmm->n0prime;
s_mp_mul_d_add_offset(&mmm->N, m_i, c, ib);
}
}
s_mp_clamp(c);
s_mp_div_2d(c, mmm->b);
if (s_mp_cmp(c, &mmm->N) >= 0) {
MP_CHECKOK( s_mp_sub(c, &mmm->N) );
}
res = MP_OKAY;
CLEANUP:
return res;
}
#endif