1 /* mpi-pow.c - MPI functions
2 * Copyright (C) 1994, 1996, 1998, 2000 Free Software Foundation, Inc.
4 * This file is part of GnuPG.
6 * GnuPG is free software; you can redistribute it and/or modify
7 * it under the terms of the GNU General Public License as published by
8 * the Free Software Foundation; either version 2 of the License, or
9 * (at your option) any later version.
11 * GnuPG is distributed in the hope that it will be useful,
12 * but WITHOUT ANY WARRANTY; without even the implied warranty of
13 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14 * GNU General Public License for more details.
16 * You should have received a copy of the GNU General Public License
17 * along with this program; if not, write to the Free Software
18 * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
20 * Note: This code is heavily based on the GNU MP Library.
21 * Actually it's the same code with only minor changes in the
22 * way the data is stored; this is to support the abstraction
23 * of an optional secure memory allocation which may be used
24 * to avoid revealing of sensitive data due to paging etc.
25 * The GNU MP Library itself is published under the LGPL;
26 * however I decided to publish this code under the plain GPL.
29 #include <linux/string.h>
30 #include "mpi-internal.h"
35 * RES = BASE ^ EXP mod MOD
38 mpi_powm( MPI res, MPI base, MPI exp, MPI mod)
40 mpi_ptr_t mp_marker=NULL, bp_marker=NULL, ep_marker=NULL;
41 mpi_ptr_t xp_marker=NULL;
42 mpi_ptr_t tspace = NULL;
43 mpi_ptr_t rp, ep, mp, bp;
44 mpi_size_t esize, msize, bsize, rsize;
45 int esign, msign, bsign, rsign;
50 mpi_size_t tsize=0; /* to avoid compiler warning */
51 /* fixme: we should check that the warning is void*/
64 msize = 1 / msize; /* provoke a signal */
67 /* Exponent is zero, result is 1 mod MOD, i.e., 1 or 0
68 * depending on if MOD equals 1. */
70 res->nlimbs = (msize == 1 && mod->d[0] == 1) ? 0 : 1;
75 /* Normalize MOD (i.e. make its most significant bit set) as required by
76 * mpn_divrem. This will make the intermediate values in the calculation
77 * slightly larger, but the correct result is obtained after a final
78 * reduction using the original MOD value. */
79 mp = mp_marker = mpi_alloc_limb_space(msize);
82 count_leading_zeros( mod_shift_cnt, mod->d[msize-1] );
84 mpihelp_lshift( mp, mod->d, msize, mod_shift_cnt );
86 MPN_COPY( mp, mod->d, msize );
90 if( bsize > msize ) { /* The base is larger than the module. Reduce it. */
91 /* Allocate (BSIZE + 1) with space for remainder and quotient.
92 * (The quotient is (bsize - msize + 1) limbs.) */
93 bp = bp_marker = mpi_alloc_limb_space( bsize + 1);
96 MPN_COPY( bp, base->d, bsize );
97 /* We don't care about the quotient, store it above the remainder,
99 mpihelp_divrem( bp + msize, 0, bp, bsize, mp, msize );
101 /* Canonicalize the base, since we are going to multiply with it
102 * quite a few times. */
103 MPN_NORMALIZE( bp, bsize );
114 if( res->alloced < size ) {
115 /* We have to allocate more space for RES. If any of the input
116 * parameters are identical to RES, defer deallocation of the old
118 if( rp == ep || rp == mp || rp == bp ) {
119 rp = mpi_alloc_limb_space(size);
125 if (mpi_resize( res, size ) < 0)
130 else { /* Make BASE, EXP and MOD not overlap with RES. */
132 /* RES and BASE are identical. Allocate temp. space for BASE. */
134 bp = bp_marker = mpi_alloc_limb_space(bsize);
137 MPN_COPY(bp, rp, bsize);
140 /* RES and EXP are identical. Allocate temp. space for EXP. */
141 ep = ep_marker = mpi_alloc_limb_space(esize);
144 MPN_COPY(ep, rp, esize);
147 /* RES and MOD are identical. Allocate temporary space for MOD.*/
149 mp = mp_marker = mpi_alloc_limb_space(msize);
152 MPN_COPY(mp, rp, msize);
156 MPN_COPY( rp, bp, bsize );
165 mpi_limb_t carry_limb;
166 struct karatsuba_ctx karactx;
168 xp = xp_marker = mpi_alloc_limb_space(2 * (msize + 1));
172 memset( &karactx, 0, sizeof karactx );
173 negative_result = (ep[0] & 1) && base->sign;
177 count_leading_zeros (c, e);
178 e = (e << c) << 1; /* shift the exp bits to the left, lose msb */
179 c = BITS_PER_MPI_LIMB - 1 - c;
183 * Make the result be pointed to alternately by XP and RP. This
184 * helps us avoid block copying, which would otherwise be necessary
185 * with the overlap restrictions of mpihelp_divmod. With 50% probability
186 * the result after this loop will be in the area originally pointed
187 * by RP (==RES->d), and with 50% probability in the area originally
196 /*if (mpihelp_mul_n(xp, rp, rp, rsize) < 0) goto enomem */
197 if( rsize < KARATSUBA_THRESHOLD )
198 mpih_sqr_n_basecase( xp, rp, rsize );
202 tspace = mpi_alloc_limb_space(tsize);
206 else if( tsize < (2*rsize) ) {
207 mpi_free_limb_space( tspace );
209 tspace = mpi_alloc_limb_space(tsize);
213 mpih_sqr_n( xp, rp, rsize, tspace );
217 if( xsize > msize ) {
218 mpihelp_divrem(xp + msize, 0, xp, xsize, mp, msize);
222 tp = rp; rp = xp; xp = tp;
225 if( (mpi_limb_signed_t)e < 0 ) {
226 /*mpihelp_mul( xp, rp, rsize, bp, bsize );*/
227 if( bsize < KARATSUBA_THRESHOLD ) {
229 if (mpihelp_mul( xp, rp, rsize, bp, bsize, &tmp ) < 0)
233 if (mpihelp_mul_karatsuba_case(
234 xp, rp, rsize, bp, bsize, &karactx ) < 0)
238 xsize = rsize + bsize;
239 if( xsize > msize ) {
240 mpihelp_divrem(xp + msize, 0, xp, xsize, mp, msize);
244 tp = rp; rp = xp; xp = tp;
255 c = BITS_PER_MPI_LIMB;
258 /* We shifted MOD, the modulo reduction argument, left MOD_SHIFT_CNT
259 * steps. Adjust the result by reducing it with the original MOD.
261 * Also make sure the result is put in RES->d (where it already
262 * might be, see above).
264 if( mod_shift_cnt ) {
265 carry_limb = mpihelp_lshift( res->d, rp, rsize, mod_shift_cnt);
268 rp[rsize] = carry_limb;
273 MPN_COPY( res->d, rp, rsize);
277 if( rsize >= msize ) {
278 mpihelp_divrem(rp + msize, 0, rp, rsize, mp, msize);
282 /* Remove any leading zero words from the result. */
284 mpihelp_rshift( rp, rp, rsize, mod_shift_cnt);
285 MPN_NORMALIZE (rp, rsize);
287 mpihelp_release_karatsuba_ctx( &karactx );
290 if( negative_result && rsize ) {
292 mpihelp_rshift( mp, mp, msize, mod_shift_cnt);
293 mpihelp_sub( rp, mp, msize, rp, rsize);
296 MPN_NORMALIZE(rp, rsize);
304 if( assign_rp ) mpi_assign_limb_space( res, rp, size );
305 if( mp_marker ) mpi_free_limb_space( mp_marker );
306 if( bp_marker ) mpi_free_limb_space( bp_marker );
307 if( ep_marker ) mpi_free_limb_space( ep_marker );
308 if( xp_marker ) mpi_free_limb_space( xp_marker );
309 if( tspace ) mpi_free_limb_space( tspace );