329 строки
8.4 KiB
C
329 строки
8.4 KiB
C
/* mpi-pow.c - MPI functions
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* Copyright (C) 1994, 1996, 1998, 2000 Free Software Foundation, Inc.
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*
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* This file is part of GnuPG.
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*
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* GnuPG is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 2 of the License, or
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* (at your option) any later version.
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*
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* GnuPG 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 General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
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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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* The GNU MP Library itself is published under the LGPL;
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* however I decided to publish this code under the plain GPL.
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*/
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#include <linux/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 ^ EXP mod MOD
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*/
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int mpi_powm(MPI res, MPI base, MPI exp, MPI mod)
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{
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mpi_ptr_t mp_marker = NULL, bp_marker = NULL, ep_marker = NULL;
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mpi_ptr_t xp_marker = NULL;
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mpi_ptr_t tspace = NULL;
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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 esign, msign, bsign, rsign;
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mpi_size_t size;
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int mod_shift_cnt;
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int negative_result;
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int assign_rp = 0;
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mpi_size_t tsize = 0; /* to avoid compiler warning */
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/* fixme: we should check that the warning is void */
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int rc = -ENOMEM;
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esize = exp->nlimbs;
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msize = mod->nlimbs;
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size = 2 * msize;
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esign = exp->sign;
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msign = mod->sign;
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rp = res->d;
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ep = exp->d;
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if (!msize)
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return -EINVAL;
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if (!esize) {
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/* Exponent is zero, result is 1 mod MOD, i.e., 1 or 0
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* depending on if MOD equals 1. */
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res->nlimbs = (msize == 1 && mod->d[0] == 1) ? 0 : 1;
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if (res->nlimbs) {
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if (mpi_resize(res, 1) < 0)
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goto enomem;
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rp = res->d;
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rp[0] = 1;
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}
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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 required by
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* mpn_divrem. This will make the intermediate values in the calculation
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* slightly larger, but the correct result is obtained after a final
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* reduction using the original MOD value. */
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mp = mp_marker = mpi_alloc_limb_space(msize);
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if (!mp)
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goto enomem;
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mod_shift_cnt = count_leading_zeros(mod->d[msize - 1]);
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if (mod_shift_cnt)
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mpihelp_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) { /* 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 = bp_marker = mpi_alloc_limb_space(bsize + 1);
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if (!bp)
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goto enomem;
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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 remainder,
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* at BP + MSIZE. */
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mpihelp_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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} else
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bp = base->d;
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if (!bsize) {
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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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if (res->alloced < size) {
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/* We have to allocate more space for RES. If any of the input
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* parameters are identical to RES, defer deallocation of the old
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* space. */
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if (rp == ep || rp == mp || rp == bp) {
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rp = mpi_alloc_limb_space(size);
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if (!rp)
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goto enomem;
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assign_rp = 1;
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} else {
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if (mpi_resize(res, size) < 0)
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goto enomem;
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rp = res->d;
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}
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} else { /* Make BASE, EXP and MOD not overlap with RES. */
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if (rp == bp) {
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/* RES and BASE are identical. Allocate temp. space for BASE. */
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BUG_ON(bp_marker);
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bp = bp_marker = mpi_alloc_limb_space(bsize);
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if (!bp)
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goto enomem;
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MPN_COPY(bp, rp, bsize);
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}
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if (rp == ep) {
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/* RES and EXP are identical. Allocate temp. space for EXP. */
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ep = ep_marker = mpi_alloc_limb_space(esize);
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if (!ep)
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goto enomem;
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MPN_COPY(ep, rp, esize);
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}
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if (rp == mp) {
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/* RES and MOD are identical. Allocate temporary space for MOD. */
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BUG_ON(mp_marker);
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mp = mp_marker = mpi_alloc_limb_space(msize);
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if (!mp)
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goto enomem;
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MPN_COPY(mp, rp, msize);
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}
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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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{
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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 = xp_marker = mpi_alloc_limb_space(2 * (msize + 1));
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if (!xp)
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goto enomem;
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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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c = count_leading_zeros(e);
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e = (e << c) << 1; /* shift the exp 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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*
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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 necessary
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* with the overlap restrictions of mpihelp_divmod. With 50% probability
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* the result after this loop will be in the area originally pointed
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* by RP (==RES->d), and with 50% probability in the area originally
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* pointed to by XP.
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*/
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for (;;) {
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while (c) {
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mpi_ptr_t tp;
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mpi_size_t xsize;
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/*if (mpihelp_mul_n(xp, rp, rp, rsize) < 0) goto enomem */
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if (rsize < KARATSUBA_THRESHOLD)
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mpih_sqr_n_basecase(xp, rp, rsize);
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else {
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if (!tspace) {
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tsize = 2 * rsize;
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tspace =
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mpi_alloc_limb_space(tsize);
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if (!tspace)
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goto enomem;
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} else if (tsize < (2 * rsize)) {
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mpi_free_limb_space(tspace);
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tsize = 2 * rsize;
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tspace =
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mpi_alloc_limb_space(tsize);
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if (!tspace)
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goto enomem;
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}
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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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mpihelp_divrem(xp + msize, 0, xp, xsize,
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mp, msize);
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xsize = msize;
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}
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tp = rp;
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rp = xp;
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xp = tp;
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rsize = xsize;
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if ((mpi_limb_signed_t) e < 0) {
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/*mpihelp_mul( xp, rp, rsize, bp, bsize ); */
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if (bsize < KARATSUBA_THRESHOLD) {
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mpi_limb_t tmp;
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if (mpihelp_mul
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(xp, rp, rsize, bp, bsize,
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&tmp) < 0)
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goto enomem;
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} else {
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if (mpihelp_mul_karatsuba_case
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(xp, rp, rsize, bp, bsize,
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&karactx) < 0)
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goto enomem;
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}
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xsize = rsize + bsize;
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if (xsize > msize) {
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mpihelp_divrem(xp + msize, 0,
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xp, xsize, mp,
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msize);
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xsize = msize;
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}
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tp = rp;
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rp = xp;
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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 MOD_SHIFT_CNT
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* steps. Adjust the result by reducing it with the original MOD.
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*
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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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*/
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if (mod_shift_cnt) {
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carry_limb =
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mpihelp_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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rp[rsize] = carry_limb;
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rsize++;
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}
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} else {
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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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mpihelp_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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mpihelp_rshift(rp, rp, rsize, mod_shift_cnt);
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MPN_NORMALIZE(rp, rsize);
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mpihelp_release_karatsuba_ctx(&karactx);
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}
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if (negative_result && rsize) {
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if (mod_shift_cnt)
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mpihelp_rshift(mp, mp, msize, mod_shift_cnt);
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mpihelp_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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res->nlimbs = rsize;
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res->sign = rsign;
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leave:
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rc = 0;
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enomem:
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if (assign_rp)
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mpi_assign_limb_space(res, rp, size);
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if (mp_marker)
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mpi_free_limb_space(mp_marker);
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if (bp_marker)
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mpi_free_limb_space(bp_marker);
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if (ep_marker)
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mpi_free_limb_space(ep_marker);
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if (xp_marker)
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mpi_free_limb_space(xp_marker);
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if (tspace)
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mpi_free_limb_space(tspace);
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return rc;
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}
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EXPORT_SYMBOL_GPL(mpi_powm);
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