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+/* mpi-pow.c - MPI functions
+ * Copyright (C) 1994, 1996, 1998, 2000 Free Software Foundation, Inc.
+ *
+ * This file is part of GnuPG.
+ *
+ * GnuPG is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * GnuPG 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 General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301,
+ * USA.
+ *
+ * Note: This code is heavily based on the GNU MP Library.
+ * Actually it's the same code with only minor changes in the
+ * way the data is stored; this is to support the abstraction
+ * of an optional secure memory allocation which may be used
+ * to avoid revealing of sensitive data due to paging etc.
+ * The GNU MP Library itself is published under the LGPL;
+ * however I decided to publish this code under the plain GPL.
+ */
+
+#include <config.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include "mpi-internal.h"
+#include "longlong.h"
+#include <assert.h>
+
+
+/****************
+ * RES = BASE ^ EXP mod MOD
+ */
+void
+mpi_powm( MPI res, MPI base, MPI exponent, MPI mod)
+{
+ mpi_ptr_t rp, ep, mp, bp;
+ mpi_size_t esize, msize, bsize, rsize;
+ int esign, msign, bsign, rsign;
+ int esec, msec, bsec, rsec;
+ mpi_size_t size;
+ int mod_shift_cnt;
+ int negative_result;
+ mpi_ptr_t mp_marker=NULL, bp_marker=NULL, ep_marker=NULL;
+ mpi_ptr_t xp_marker=NULL;
+ int assign_rp=0;
+ mpi_ptr_t tspace = NULL;
+ mpi_size_t tsize=0; /* to avoid compiler warning */
+ /* fixme: we should check that the warning is void*/
+
+ esize = exponent->nlimbs;
+ msize = mod->nlimbs;
+ size = 2 * msize;
+ esign = exponent->sign;
+ msign = mod->sign;
+
+ esec = mpi_is_secure(exponent);
+ msec = mpi_is_secure(mod);
+ bsec = mpi_is_secure(base);
+ rsec = mpi_is_secure(res);
+
+ rp = res->d;
+ ep = exponent->d;
+
+ if( !msize )
+ msize = 1 / msize; /* provoke a signal */
+
+ if( !esize ) {
+ /* Exponent is zero, result is 1 mod MOD, i.e., 1 or 0
+ * depending on if MOD equals 1. */
+ rp[0] = 1;
+ res->nlimbs = (msize == 1 && mod->d[0] == 1) ? 0 : 1;
+ res->sign = 0;
+ goto leave;
+ }
+
+ /* Normalize MOD (i.e. make its most significant bit set) as required by
+ * mpn_divrem. This will make the intermediate values in the calculation
+ * slightly larger, but the correct result is obtained after a final
+ * reduction using the original MOD value. */
+ mp = mp_marker = mpi_alloc_limb_space(msize, msec);
+ count_leading_zeros( mod_shift_cnt, mod->d[msize-1] );
+ if( mod_shift_cnt )
+ mpihelp_lshift( mp, mod->d, msize, mod_shift_cnt );
+ else
+ MPN_COPY( mp, mod->d, msize );
+
+ bsize = base->nlimbs;
+ bsign = base->sign;
+ if( bsize > msize ) { /* The base is larger than the module. Reduce it. */
+ /* Allocate (BSIZE + 1) with space for remainder and quotient.
+ * (The quotient is (bsize - msize + 1) limbs.) */
+ bp = bp_marker = mpi_alloc_limb_space( bsize + 1, bsec );
+ MPN_COPY( bp, base->d, bsize );
+ /* We don't care about the quotient, store it above the remainder,
+ * at BP + MSIZE. */
+ mpihelp_divrem( bp + msize, 0, bp, bsize, mp, msize );
+ bsize = msize;
+ /* Canonicalize the base, since we are going to multiply with it
+ * quite a few times. */
+ MPN_NORMALIZE( bp, bsize );
+ }
+ else
+ bp = base->d;
+
+ if( !bsize ) {
+ res->nlimbs = 0;
+ res->sign = 0;
+ goto leave;
+ }
+
+ if( res->alloced < size ) {
+ /* We have to allocate more space for RES. If any of the input
+ * parameters are identical to RES, defer deallocation of the old
+ * space. */
+ if( rp == ep || rp == mp || rp == bp ) {
+ rp = mpi_alloc_limb_space( size, rsec );
+ assign_rp = 1;
+ }
+ else {
+ mpi_resize( res, size );
+ rp = res->d;
+ }
+ }
+ else { /* Make BASE, EXPONENT and MOD not overlap with RES. */
+ if( rp == bp ) {
+ /* RES and BASE are identical. Allocate temp. space for BASE. */
+ assert( !bp_marker );
+ bp = bp_marker = mpi_alloc_limb_space( bsize, bsec );
+ MPN_COPY(bp, rp, bsize);
+ }
+ if( rp == ep ) {
+ /* RES and EXPONENT are identical.
+ Allocate temp. space for EXPONENT. */
+ ep = ep_marker = mpi_alloc_limb_space( esize, esec );
+ MPN_COPY(ep, rp, esize);
+ }
+ if( rp == mp ) {
+ /* RES and MOD are identical. Allocate temporary space for MOD.*/
+ assert( !mp_marker );
+ mp = mp_marker = mpi_alloc_limb_space( msize, msec );
+ MPN_COPY(mp, rp, msize);
+ }
+ }
+
+ MPN_COPY( rp, bp, bsize );
+ rsize = bsize;
+ rsign = bsign;
+
+ {
+ mpi_size_t i;
+ mpi_ptr_t xp = xp_marker = mpi_alloc_limb_space( 2 * (msize + 1), msec );
+ int c;
+ mpi_limb_t e;
+ mpi_limb_t carry_limb;
+ struct karatsuba_ctx karactx;
+
+ memset( &karactx, 0, sizeof karactx );
+ negative_result = (ep[0] & 1) && base->sign;
+
+ i = esize - 1;
+ e = ep[i];
+ count_leading_zeros (c, e);
+ e = (e << c) << 1; /* shift the exp bits to the left, lose msb */
+ c = BITS_PER_MPI_LIMB - 1 - c;
+
+ /* Main loop.
+ *
+ * Make the result be pointed to alternately by XP and RP. This
+ * helps us avoid block copying, which would otherwise be necessary
+ * with the overlap restrictions of mpihelp_divmod. With 50% probability
+ * the result after this loop will be in the area originally pointed
+ * by RP (==RES->d), and with 50% probability in the area originally
+ * pointed to by XP.
+ */
+
+ for(;;) {
+ while( c ) {
+ mpi_ptr_t tp;
+ mpi_size_t xsize;
+
+ /*mpihelp_mul_n(xp, rp, rp, rsize);*/
+ if( rsize < KARATSUBA_THRESHOLD )
+ mpih_sqr_n_basecase( xp, rp, rsize );
+ else {
+ if( !tspace ) {
+ tsize = 2 * rsize;
+ tspace = mpi_alloc_limb_space( tsize, 0 );
+ }
+ else if( tsize < (2*rsize) ) {
+ mpi_free_limb_space( tspace );
+ tsize = 2 * rsize;
+ tspace = mpi_alloc_limb_space( tsize, 0 );
+ }
+ mpih_sqr_n( xp, rp, rsize, tspace );
+ }
+
+ xsize = 2 * rsize;
+ if( xsize > msize ) {
+ mpihelp_divrem(xp + msize, 0, xp, xsize, mp, msize);
+ xsize = msize;
+ }
+
+ tp = rp; rp = xp; xp = tp;
+ rsize = xsize;
+
+ if( (mpi_limb_signed_t)e < 0 ) {
+ /*mpihelp_mul( xp, rp, rsize, bp, bsize );*/
+ if( bsize < KARATSUBA_THRESHOLD ) {
+ mpihelp_mul( xp, rp, rsize, bp, bsize );
+ }
+ else {
+ mpihelp_mul_karatsuba_case(
+ xp, rp, rsize, bp, bsize, &karactx );
+ }
+
+ xsize = rsize + bsize;
+ if( xsize > msize ) {
+ mpihelp_divrem(xp + msize, 0, xp, xsize, mp, msize);
+ xsize = msize;
+ }
+
+ tp = rp; rp = xp; xp = tp;
+ rsize = xsize;
+ }
+ e <<= 1;
+ c--;
+ }
+
+ i--;
+ if( i < 0 )
+ break;
+ e = ep[i];
+ c = BITS_PER_MPI_LIMB;
+ }
+
+ /* We shifted MOD, the modulo reduction argument, left MOD_SHIFT_CNT
+ * steps. Adjust the result by reducing it with the original MOD.
+ *
+ * Also make sure the result is put in RES->d (where it already
+ * might be, see above).
+ */
+ if( mod_shift_cnt ) {
+ carry_limb = mpihelp_lshift( res->d, rp, rsize, mod_shift_cnt);
+ rp = res->d;
+ if( carry_limb ) {
+ rp[rsize] = carry_limb;
+ rsize++;
+ }
+ }
+ else {
+ MPN_COPY( res->d, rp, rsize);
+ rp = res->d;
+ }
+
+ if( rsize >= msize ) {
+ mpihelp_divrem(rp + msize, 0, rp, rsize, mp, msize);
+ rsize = msize;
+ }
+
+ /* Remove any leading zero words from the result. */
+ if( mod_shift_cnt )
+ mpihelp_rshift( rp, rp, rsize, mod_shift_cnt);
+ MPN_NORMALIZE (rp, rsize);
+
+ mpihelp_release_karatsuba_ctx( &karactx );
+ }
+
+ if( negative_result && rsize ) {
+ if( mod_shift_cnt )
+ mpihelp_rshift( mp, mp, msize, mod_shift_cnt);
+ mpihelp_sub( rp, mp, msize, rp, rsize);
+ rsize = msize;
+ rsign = msign;
+ MPN_NORMALIZE(rp, rsize);
+ }
+ res->nlimbs = rsize;
+ res->sign = rsign;
+
+ leave:
+ if( assign_rp ) mpi_assign_limb_space( res, rp, size );
+ if( mp_marker ) mpi_free_limb_space( mp_marker );
+ if( bp_marker ) mpi_free_limb_space( bp_marker );
+ if( ep_marker ) mpi_free_limb_space( ep_marker );
+ if( xp_marker ) mpi_free_limb_space( xp_marker );
+ if( tspace ) mpi_free_limb_space( tspace );
+}
+
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