325 lines
9.4 KiB
C
325 lines
9.4 KiB
C
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/* mpi-pow.c - MPI functions for exponentiation
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* Copyright (C) 1994, 1996, 1998, 2000, 2002
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* 2003 Free Software Foundation, Inc.
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*
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* This file is part of Libgcrypt.
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*
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* Libgcrypt is free software; you can redistribute it and/or modify
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* it under the terms of the GNU Lesser General Public License as
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* published by the Free Software Foundation; either version 2.1 of
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* the License, or (at your option) any later version.
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*
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* Libgcrypt is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU Lesser General Public License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public
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* License along with this program; if not, see <http://www.gnu.org/licenses/>.
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*
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* Note: This code is heavily based on the GNU MP Library.
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* Actually it's the same code with only minor changes in the
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* way the data is stored; this is to support the abstraction
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* of an optional secure memory allocation which may be used
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* to avoid revealing of sensitive data due to paging etc.
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*/
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#include <config.h>
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#include <stdio.h>
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#include <stdlib.h>
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#include <string.h>
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#include "mpi-internal.h"
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#include "longlong.h"
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/****************
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* RES = BASE ^ EXPO mod MOD
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*/
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void
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gcry_mpi_powm (gcry_mpi_t res,
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gcry_mpi_t base, gcry_mpi_t expo, gcry_mpi_t mod)
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{
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/* Pointer to the limbs of the arguments, their size and signs. */
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mpi_ptr_t rp, ep, mp, bp;
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mpi_size_t esize, msize, bsize, rsize;
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int msign, bsign, rsign;
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/* Flags telling the secure allocation status of the arguments. */
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int esec, msec, bsec;
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/* Size of the result including space for temporary values. */
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mpi_size_t size;
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/* Helper. */
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int mod_shift_cnt;
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int negative_result;
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mpi_ptr_t mp_marker = NULL;
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mpi_ptr_t bp_marker = NULL;
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mpi_ptr_t ep_marker = NULL;
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mpi_ptr_t xp_marker = NULL;
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unsigned int mp_nlimbs = 0;
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unsigned int bp_nlimbs = 0;
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unsigned int ep_nlimbs = 0;
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unsigned int xp_nlimbs = 0;
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mpi_ptr_t tspace = NULL;
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mpi_size_t tsize = 0;
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esize = expo->nlimbs;
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msize = mod->nlimbs;
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size = 2 * msize;
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msign = mod->sign;
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esec = mpi_is_secure(expo);
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msec = mpi_is_secure(mod);
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bsec = mpi_is_secure(base);
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rp = res->d;
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ep = expo->d;
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if (!msize)
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msize = 1 / msize; /* Provoke a signal. */
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if (!esize)
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{
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/* Exponent is zero, result is 1 mod MOD, i.e., 1 or 0 depending
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on if MOD equals 1. */
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rp[0] = 1;
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res->nlimbs = (msize == 1 && mod->d[0] == 1) ? 0 : 1;
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res->sign = 0;
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goto leave;
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}
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/* Normalize MOD (i.e. make its most significant bit set) as
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required by mpn_divrem. This will make the intermediate values
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in the calculation slightly larger, but the correct result is
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obtained after a final reduction using the original MOD value. */
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mp_nlimbs = msec? msize:0;
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mp = mp_marker = mpi_alloc_limb_space(msize, msec);
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count_leading_zeros (mod_shift_cnt, mod->d[msize-1]);
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if (mod_shift_cnt)
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_gcry_mpih_lshift (mp, mod->d, msize, mod_shift_cnt);
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else
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MPN_COPY( mp, mod->d, msize );
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bsize = base->nlimbs;
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bsign = base->sign;
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if (bsize > msize)
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{
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/* The base is larger than the module. Reduce it.
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Allocate (BSIZE + 1) with space for remainder and quotient.
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(The quotient is (bsize - msize + 1) limbs.) */
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bp_nlimbs = bsec ? (bsize + 1):0;
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bp = bp_marker = mpi_alloc_limb_space( bsize + 1, bsec );
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MPN_COPY ( bp, base->d, bsize );
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/* We don't care about the quotient, store it above the
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* remainder, at BP + MSIZE. */
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_gcry_mpih_divrem( bp + msize, 0, bp, bsize, mp, msize );
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bsize = msize;
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/* Canonicalize the base, since we are going to multiply with it
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quite a few times. */
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MPN_NORMALIZE( bp, bsize );
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}
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else
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bp = base->d;
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if (!bsize)
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{
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res->nlimbs = 0;
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res->sign = 0;
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goto leave;
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}
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/* Make BASE, EXPO and MOD not overlap with RES. */
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if ( rp == bp )
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{
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/* RES and BASE are identical. Allocate temp. space for BASE. */
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gcry_assert (!bp_marker);
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bp_nlimbs = bsec? bsize:0;
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bp = bp_marker = mpi_alloc_limb_space( bsize, bsec );
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MPN_COPY(bp, rp, bsize);
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}
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if ( rp == ep )
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{
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/* RES and EXPO are identical. Allocate temp. space for EXPO. */
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ep_nlimbs = esec? esize:0;
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ep = ep_marker = mpi_alloc_limb_space( esize, esec );
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MPN_COPY(ep, rp, esize);
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}
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if ( rp == mp )
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{
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/* RES and MOD are identical. Allocate temporary space for MOD.*/
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gcry_assert (!mp_marker);
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mp_nlimbs = msec?msize:0;
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mp = mp_marker = mpi_alloc_limb_space( msize, msec );
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MPN_COPY(mp, rp, msize);
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}
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/* Copy base to the result. */
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if (res->alloced < size)
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{
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mpi_resize (res, size);
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rp = res->d;
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}
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MPN_COPY ( rp, bp, bsize );
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rsize = bsize;
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rsign = bsign;
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/* Main processing. */
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{
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mpi_size_t i;
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mpi_ptr_t xp;
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int c;
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mpi_limb_t e;
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mpi_limb_t carry_limb;
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struct karatsuba_ctx karactx;
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xp_nlimbs = msec? (2 * (msize + 1)):0;
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xp = xp_marker = mpi_alloc_limb_space( 2 * (msize + 1), msec );
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memset( &karactx, 0, sizeof karactx );
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negative_result = (ep[0] & 1) && base->sign;
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i = esize - 1;
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e = ep[i];
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count_leading_zeros (c, e);
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e = (e << c) << 1; /* Shift the expo bits to the left, lose msb. */
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c = BITS_PER_MPI_LIMB - 1 - c;
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/* Main loop.
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Make the result be pointed to alternately by XP and RP. This
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helps us avoid block copying, which would otherwise be
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necessary with the overlap restrictions of
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_gcry_mpih_divmod. With 50% probability the result after this
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loop will be in the area originally pointed by RP (==RES->d),
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and with 50% probability in the area originally pointed to by XP. */
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for (;;)
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{
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while (c)
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{
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mpi_ptr_t tp;
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mpi_size_t xsize;
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/*mpih_mul_n(xp, rp, rp, rsize);*/
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if ( rsize < KARATSUBA_THRESHOLD )
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_gcry_mpih_sqr_n_basecase( xp, rp, rsize );
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else
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{
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if ( !tspace )
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{
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tsize = 2 * rsize;
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tspace = mpi_alloc_limb_space( tsize, 0 );
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}
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else if ( tsize < (2*rsize) )
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{
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_gcry_mpi_free_limb_space (tspace, 0);
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tsize = 2 * rsize;
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tspace = mpi_alloc_limb_space (tsize, 0 );
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}
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_gcry_mpih_sqr_n (xp, rp, rsize, tspace);
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}
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xsize = 2 * rsize;
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if ( xsize > msize )
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{
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_gcry_mpih_divrem(xp + msize, 0, xp, xsize, mp, msize);
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xsize = msize;
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}
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tp = rp; rp = xp; xp = tp;
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rsize = xsize;
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if ( (mpi_limb_signed_t)e < 0 )
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{
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/*mpih_mul( xp, rp, rsize, bp, bsize );*/
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if( bsize < KARATSUBA_THRESHOLD )
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_gcry_mpih_mul ( xp, rp, rsize, bp, bsize );
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else
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_gcry_mpih_mul_karatsuba_case (xp, rp, rsize, bp, bsize,
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&karactx);
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xsize = rsize + bsize;
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if ( xsize > msize )
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{
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_gcry_mpih_divrem(xp + msize, 0, xp, xsize, mp, msize);
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xsize = msize;
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}
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tp = rp; rp = xp; xp = tp;
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rsize = xsize;
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}
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e <<= 1;
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c--;
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}
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i--;
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if ( i < 0 )
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break;
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e = ep[i];
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c = BITS_PER_MPI_LIMB;
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}
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/* We shifted MOD, the modulo reduction argument, left
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MOD_SHIFT_CNT steps. Adjust the result by reducing it with the
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original MOD.
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Also make sure the result is put in RES->d (where it already
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might be, see above). */
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if ( mod_shift_cnt )
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{
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carry_limb = _gcry_mpih_lshift( res->d, rp, rsize, mod_shift_cnt);
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rp = res->d;
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if ( carry_limb )
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{
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rp[rsize] = carry_limb;
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rsize++;
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}
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}
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else if (res->d != rp)
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{
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MPN_COPY (res->d, rp, rsize);
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rp = res->d;
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}
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if ( rsize >= msize )
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{
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_gcry_mpih_divrem(rp + msize, 0, rp, rsize, mp, msize);
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rsize = msize;
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}
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/* Remove any leading zero words from the result. */
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if ( mod_shift_cnt )
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_gcry_mpih_rshift( rp, rp, rsize, mod_shift_cnt);
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MPN_NORMALIZE (rp, rsize);
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_gcry_mpih_release_karatsuba_ctx (&karactx );
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}
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/* Fixup for negative results. */
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if ( negative_result && rsize )
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{
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if ( mod_shift_cnt )
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_gcry_mpih_rshift( mp, mp, msize, mod_shift_cnt);
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_gcry_mpih_sub( rp, mp, msize, rp, rsize);
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rsize = msize;
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rsign = msign;
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MPN_NORMALIZE(rp, rsize);
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}
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gcry_assert (res->d == rp);
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res->nlimbs = rsize;
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res->sign = rsign;
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leave:
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if (mp_marker)
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_gcry_mpi_free_limb_space( mp_marker, mp_nlimbs );
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if (bp_marker)
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_gcry_mpi_free_limb_space( bp_marker, bp_nlimbs );
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if (ep_marker)
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_gcry_mpi_free_limb_space( ep_marker, ep_nlimbs );
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if (xp_marker)
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_gcry_mpi_free_limb_space( xp_marker, xp_nlimbs );
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if (tspace)
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_gcry_mpi_free_limb_space( tspace, 0 );
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}
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