mirror of
https://github.com/rn10950/RetroZilla.git
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275 lines
8.5 KiB
C
275 lines
8.5 KiB
C
/*
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* ***** BEGIN LICENSE BLOCK *****
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* Version: MPL 1.1/GPL 2.0/LGPL 2.1
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*
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* The contents of this file are subject to the Mozilla Public License Version
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* 1.1 (the "License"); you may not use this file except in compliance with
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* the License. You may obtain a copy of the License at
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* http://www.mozilla.org/MPL/
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*
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* Software distributed under the License is distributed on an "AS IS" basis,
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* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
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* for the specific language governing rights and limitations under the
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* License.
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*
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* The Original Code is the elliptic curve math library for binary polynomial field curves.
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*
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* The Initial Developer of the Original Code is
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* Sun Microsystems, Inc.
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* Portions created by the Initial Developer are Copyright (C) 2003
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* the Initial Developer. All Rights Reserved.
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*
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* Contributor(s):
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* Sheueling Chang-Shantz <sheueling.chang@sun.com>,
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* Stephen Fung <fungstep@hotmail.com>, and
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* Douglas Stebila <douglas@stebila.ca>, Sun Microsystems Laboratories.
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*
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* Alternatively, the contents of this file may be used under the terms of
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* either the GNU General Public License Version 2 or later (the "GPL"), or
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* the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
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* in which case the provisions of the GPL or the LGPL are applicable instead
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* of those above. If you wish to allow use of your version of this file only
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* under the terms of either the GPL or the LGPL, and not to allow others to
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* use your version of this file under the terms of the MPL, indicate your
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* decision by deleting the provisions above and replace them with the notice
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* and other provisions required by the GPL or the LGPL. If you do not delete
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* the provisions above, a recipient may use your version of this file under
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* the terms of any one of the MPL, the GPL or the LGPL.
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*
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* ***** END LICENSE BLOCK ***** */
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#include "ec2.h"
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#include "mplogic.h"
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#include "mp_gf2m.h"
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#include <stdlib.h>
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/* Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery
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* projective coordinates. Uses algorithm Mdouble in appendix of Lopez, J.
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* and Dahab, R. "Fast multiplication on elliptic curves over GF(2^m)
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* without precomputation". modified to not require precomputation of
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* c=b^{2^{m-1}}. */
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static mp_err
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gf2m_Mdouble(mp_int *x, mp_int *z, const ECGroup *group)
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{
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mp_err res = MP_OKAY;
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mp_int t1;
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MP_DIGITS(&t1) = 0;
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MP_CHECKOK(mp_init(&t1));
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MP_CHECKOK(group->meth->field_sqr(x, x, group->meth));
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MP_CHECKOK(group->meth->field_sqr(z, &t1, group->meth));
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MP_CHECKOK(group->meth->field_mul(x, &t1, z, group->meth));
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MP_CHECKOK(group->meth->field_sqr(x, x, group->meth));
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MP_CHECKOK(group->meth->field_sqr(&t1, &t1, group->meth));
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MP_CHECKOK(group->meth->
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field_mul(&group->curveb, &t1, &t1, group->meth));
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MP_CHECKOK(group->meth->field_add(x, &t1, x, group->meth));
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CLEANUP:
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mp_clear(&t1);
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return res;
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}
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/* Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in
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* Montgomery projective coordinates. Uses algorithm Madd in appendix of
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* Lopex, J. and Dahab, R. "Fast multiplication on elliptic curves over
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* GF(2^m) without precomputation". */
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static mp_err
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gf2m_Madd(const mp_int *x, mp_int *x1, mp_int *z1, mp_int *x2, mp_int *z2,
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const ECGroup *group)
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{
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mp_err res = MP_OKAY;
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mp_int t1, t2;
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MP_DIGITS(&t1) = 0;
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MP_DIGITS(&t2) = 0;
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MP_CHECKOK(mp_init(&t1));
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MP_CHECKOK(mp_init(&t2));
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MP_CHECKOK(mp_copy(x, &t1));
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MP_CHECKOK(group->meth->field_mul(x1, z2, x1, group->meth));
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MP_CHECKOK(group->meth->field_mul(z1, x2, z1, group->meth));
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MP_CHECKOK(group->meth->field_mul(x1, z1, &t2, group->meth));
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MP_CHECKOK(group->meth->field_add(z1, x1, z1, group->meth));
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MP_CHECKOK(group->meth->field_sqr(z1, z1, group->meth));
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MP_CHECKOK(group->meth->field_mul(z1, &t1, x1, group->meth));
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MP_CHECKOK(group->meth->field_add(x1, &t2, x1, group->meth));
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CLEANUP:
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mp_clear(&t1);
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mp_clear(&t2);
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return res;
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}
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/* Compute the x, y affine coordinates from the point (x1, z1) (x2, z2)
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* using Montgomery point multiplication algorithm Mxy() in appendix of
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* Lopex, J. and Dahab, R. "Fast multiplication on elliptic curves over
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* GF(2^m) without precomputation". Returns: 0 on error 1 if return value
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* should be the point at infinity 2 otherwise */
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static int
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gf2m_Mxy(const mp_int *x, const mp_int *y, mp_int *x1, mp_int *z1,
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mp_int *x2, mp_int *z2, const ECGroup *group)
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{
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mp_err res = MP_OKAY;
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int ret = 0;
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mp_int t3, t4, t5;
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MP_DIGITS(&t3) = 0;
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MP_DIGITS(&t4) = 0;
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MP_DIGITS(&t5) = 0;
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MP_CHECKOK(mp_init(&t3));
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MP_CHECKOK(mp_init(&t4));
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MP_CHECKOK(mp_init(&t5));
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if (mp_cmp_z(z1) == 0) {
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mp_zero(x2);
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mp_zero(z2);
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ret = 1;
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goto CLEANUP;
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}
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if (mp_cmp_z(z2) == 0) {
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MP_CHECKOK(mp_copy(x, x2));
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MP_CHECKOK(group->meth->field_add(x, y, z2, group->meth));
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ret = 2;
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goto CLEANUP;
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}
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MP_CHECKOK(mp_set_int(&t5, 1));
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if (group->meth->field_enc) {
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MP_CHECKOK(group->meth->field_enc(&t5, &t5, group->meth));
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}
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MP_CHECKOK(group->meth->field_mul(z1, z2, &t3, group->meth));
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MP_CHECKOK(group->meth->field_mul(z1, x, z1, group->meth));
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MP_CHECKOK(group->meth->field_add(z1, x1, z1, group->meth));
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MP_CHECKOK(group->meth->field_mul(z2, x, z2, group->meth));
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MP_CHECKOK(group->meth->field_mul(z2, x1, x1, group->meth));
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MP_CHECKOK(group->meth->field_add(z2, x2, z2, group->meth));
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MP_CHECKOK(group->meth->field_mul(z2, z1, z2, group->meth));
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MP_CHECKOK(group->meth->field_sqr(x, &t4, group->meth));
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MP_CHECKOK(group->meth->field_add(&t4, y, &t4, group->meth));
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MP_CHECKOK(group->meth->field_mul(&t4, &t3, &t4, group->meth));
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MP_CHECKOK(group->meth->field_add(&t4, z2, &t4, group->meth));
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MP_CHECKOK(group->meth->field_mul(&t3, x, &t3, group->meth));
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MP_CHECKOK(group->meth->field_div(&t5, &t3, &t3, group->meth));
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MP_CHECKOK(group->meth->field_mul(&t3, &t4, &t4, group->meth));
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MP_CHECKOK(group->meth->field_mul(x1, &t3, x2, group->meth));
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MP_CHECKOK(group->meth->field_add(x2, x, z2, group->meth));
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MP_CHECKOK(group->meth->field_mul(z2, &t4, z2, group->meth));
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MP_CHECKOK(group->meth->field_add(z2, y, z2, group->meth));
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ret = 2;
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CLEANUP:
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mp_clear(&t3);
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mp_clear(&t4);
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mp_clear(&t5);
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if (res == MP_OKAY) {
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return ret;
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} else {
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return 0;
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}
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}
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/* Computes R = nP based on algorithm 2P of Lopex, J. and Dahab, R. "Fast
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* multiplication on elliptic curves over GF(2^m) without
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* precomputation". Elliptic curve points P and R can be identical. Uses
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* Montgomery projective coordinates. */
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mp_err
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ec_GF2m_pt_mul_mont(const mp_int *n, const mp_int *px, const mp_int *py,
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mp_int *rx, mp_int *ry, const ECGroup *group)
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{
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mp_err res = MP_OKAY;
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mp_int x1, x2, z1, z2;
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int i, j;
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mp_digit top_bit, mask;
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MP_DIGITS(&x1) = 0;
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MP_DIGITS(&x2) = 0;
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MP_DIGITS(&z1) = 0;
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MP_DIGITS(&z2) = 0;
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MP_CHECKOK(mp_init(&x1));
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MP_CHECKOK(mp_init(&x2));
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MP_CHECKOK(mp_init(&z1));
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MP_CHECKOK(mp_init(&z2));
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/* if result should be point at infinity */
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if ((mp_cmp_z(n) == 0) || (ec_GF2m_pt_is_inf_aff(px, py) == MP_YES)) {
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MP_CHECKOK(ec_GF2m_pt_set_inf_aff(rx, ry));
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goto CLEANUP;
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}
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MP_CHECKOK(mp_copy(px, &x1)); /* x1 = px */
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MP_CHECKOK(mp_set_int(&z1, 1)); /* z1 = 1 */
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MP_CHECKOK(group->meth->field_sqr(&x1, &z2, group->meth)); /* z2 =
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* x1^2 =
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* px^2 */
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MP_CHECKOK(group->meth->field_sqr(&z2, &x2, group->meth));
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MP_CHECKOK(group->meth->field_add(&x2, &group->curveb, &x2, group->meth)); /* x2
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* =
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* px^4
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* +
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* b
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*/
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/* find top-most bit and go one past it */
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i = MP_USED(n) - 1;
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j = MP_DIGIT_BIT - 1;
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top_bit = 1;
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top_bit <<= MP_DIGIT_BIT - 1;
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mask = top_bit;
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while (!(MP_DIGITS(n)[i] & mask)) {
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mask >>= 1;
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j--;
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}
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mask >>= 1;
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j--;
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/* if top most bit was at word break, go to next word */
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if (!mask) {
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i--;
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j = MP_DIGIT_BIT - 1;
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mask = top_bit;
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}
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for (; i >= 0; i--) {
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for (; j >= 0; j--) {
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if (MP_DIGITS(n)[i] & mask) {
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MP_CHECKOK(gf2m_Madd(px, &x1, &z1, &x2, &z2, group));
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MP_CHECKOK(gf2m_Mdouble(&x2, &z2, group));
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} else {
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MP_CHECKOK(gf2m_Madd(px, &x2, &z2, &x1, &z1, group));
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MP_CHECKOK(gf2m_Mdouble(&x1, &z1, group));
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}
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mask >>= 1;
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}
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j = MP_DIGIT_BIT - 1;
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mask = top_bit;
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}
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/* convert out of "projective" coordinates */
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i = gf2m_Mxy(px, py, &x1, &z1, &x2, &z2, group);
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if (i == 0) {
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res = MP_BADARG;
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goto CLEANUP;
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} else if (i == 1) {
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MP_CHECKOK(ec_GF2m_pt_set_inf_aff(rx, ry));
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} else {
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MP_CHECKOK(mp_copy(&x2, rx));
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MP_CHECKOK(mp_copy(&z2, ry));
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}
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CLEANUP:
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mp_clear(&x1);
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mp_clear(&x2);
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mp_clear(&z1);
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mp_clear(&z2);
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return res;
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}
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