зеркало из https://github.com/mozilla/pjs.git
324 строки
10 KiB
C
324 строки
10 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 prime 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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* Stephen Fung <fungstep@hotmail.com>, 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 "ecp.h"
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#include "ecl-priv.h"
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#include "mplogic.h"
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#include <stdlib.h>
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#define MAX_SCRATCH 6
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/* Computes R = 2P. Elliptic curve points P and R can be identical. Uses
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* Modified Jacobian coordinates.
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*
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* Assumes input is already field-encoded using field_enc, and returns
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* output that is still field-encoded.
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*
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*/
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mp_err
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ec_GFp_pt_dbl_jm(const mp_int *px, const mp_int *py, const mp_int *pz,
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const mp_int *paz4, mp_int *rx, mp_int *ry, mp_int *rz,
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mp_int *raz4, mp_int scratch[], const ECGroup *group)
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{
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mp_err res = MP_OKAY;
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mp_int *t0, *t1, *M, *S;
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t0 = &scratch[0];
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t1 = &scratch[1];
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M = &scratch[2];
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S = &scratch[3];
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#if MAX_SCRATCH < 4
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#error "Scratch array defined too small "
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#endif
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/* Check for point at infinity */
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if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {
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/* Set r = pt at infinity by setting rz = 0 */
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MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, rz));
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goto CLEANUP;
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}
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/* M = 3 (px^2) + a*(pz^4) */
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MP_CHECKOK(group->meth->field_sqr(px, t0, group->meth));
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MP_CHECKOK(group->meth->field_add(t0, t0, M, group->meth));
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MP_CHECKOK(group->meth->field_add(t0, M, t0, group->meth));
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MP_CHECKOK(group->meth->field_add(t0, paz4, M, group->meth));
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/* rz = 2 * py * pz */
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MP_CHECKOK(group->meth->field_mul(py, pz, S, group->meth));
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MP_CHECKOK(group->meth->field_add(S, S, rz, group->meth));
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/* t0 = 2y^2 , t1 = 8y^4 */
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MP_CHECKOK(group->meth->field_sqr(py, t0, group->meth));
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MP_CHECKOK(group->meth->field_add(t0, t0, t0, group->meth));
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MP_CHECKOK(group->meth->field_sqr(t0, t1, group->meth));
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MP_CHECKOK(group->meth->field_add(t1, t1, t1, group->meth));
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/* S = 4 * px * py^2 = 2 * px * t0 */
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MP_CHECKOK(group->meth->field_mul(px, t0, S, group->meth));
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MP_CHECKOK(group->meth->field_add(S, S, S, group->meth));
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/* rx = M^2 - 2S */
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MP_CHECKOK(group->meth->field_sqr(M, rx, group->meth));
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MP_CHECKOK(group->meth->field_sub(rx, S, rx, group->meth));
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MP_CHECKOK(group->meth->field_sub(rx, S, rx, group->meth));
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/* ry = M * (S - rx) - t1 */
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MP_CHECKOK(group->meth->field_sub(S, rx, S, group->meth));
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MP_CHECKOK(group->meth->field_mul(S, M, ry, group->meth));
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MP_CHECKOK(group->meth->field_sub(ry, t1, ry, group->meth));
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/* ra*z^4 = 2*t1*(apz4) */
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MP_CHECKOK(group->meth->field_mul(paz4, t1, raz4, group->meth));
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MP_CHECKOK(group->meth->field_add(raz4, raz4, raz4, group->meth));
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CLEANUP:
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return res;
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}
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/* Computes R = P + Q where R is (rx, ry, rz), P is (px, py, pz) and Q is
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* (qx, qy, 1). Elliptic curve points P, Q, and R can all be identical.
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* Uses mixed Modified_Jacobian-affine coordinates. Assumes input is
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* already field-encoded using field_enc, and returns output that is still
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* field-encoded. */
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mp_err
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ec_GFp_pt_add_jm_aff(const mp_int *px, const mp_int *py, const mp_int *pz,
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const mp_int *paz4, const mp_int *qx,
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const mp_int *qy, mp_int *rx, mp_int *ry, mp_int *rz,
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mp_int *raz4, mp_int scratch[], const ECGroup *group)
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{
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mp_err res = MP_OKAY;
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mp_int *A, *B, *C, *D, *C2, *C3;
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A = &scratch[0];
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B = &scratch[1];
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C = &scratch[2];
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D = &scratch[3];
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C2 = &scratch[4];
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C3 = &scratch[5];
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#if MAX_SCRATCH < 6
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#error "Scratch array defined too small "
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#endif
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/* If either P or Q is the point at infinity, then return the other
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* point */
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if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {
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MP_CHECKOK(ec_GFp_pt_aff2jac(qx, qy, rx, ry, rz, group));
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MP_CHECKOK(group->meth->field_sqr(rz, raz4, group->meth));
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MP_CHECKOK(group->meth->field_sqr(raz4, raz4, group->meth));
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MP_CHECKOK(group->meth->
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field_mul(raz4, &group->curvea, raz4, group->meth));
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goto CLEANUP;
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}
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if (ec_GFp_pt_is_inf_aff(qx, qy) == MP_YES) {
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MP_CHECKOK(mp_copy(px, rx));
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MP_CHECKOK(mp_copy(py, ry));
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MP_CHECKOK(mp_copy(pz, rz));
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MP_CHECKOK(mp_copy(paz4, raz4));
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goto CLEANUP;
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}
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/* A = qx * pz^2, B = qy * pz^3 */
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MP_CHECKOK(group->meth->field_sqr(pz, A, group->meth));
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MP_CHECKOK(group->meth->field_mul(A, pz, B, group->meth));
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MP_CHECKOK(group->meth->field_mul(A, qx, A, group->meth));
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MP_CHECKOK(group->meth->field_mul(B, qy, B, group->meth));
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/* C = A - px, D = B - py */
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MP_CHECKOK(group->meth->field_sub(A, px, C, group->meth));
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MP_CHECKOK(group->meth->field_sub(B, py, D, group->meth));
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/* C2 = C^2, C3 = C^3 */
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MP_CHECKOK(group->meth->field_sqr(C, C2, group->meth));
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MP_CHECKOK(group->meth->field_mul(C, C2, C3, group->meth));
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/* rz = pz * C */
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MP_CHECKOK(group->meth->field_mul(pz, C, rz, group->meth));
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/* C = px * C^2 */
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MP_CHECKOK(group->meth->field_mul(px, C2, C, group->meth));
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/* A = D^2 */
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MP_CHECKOK(group->meth->field_sqr(D, A, group->meth));
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/* rx = D^2 - (C^3 + 2 * (px * C^2)) */
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MP_CHECKOK(group->meth->field_add(C, C, rx, group->meth));
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MP_CHECKOK(group->meth->field_add(C3, rx, rx, group->meth));
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MP_CHECKOK(group->meth->field_sub(A, rx, rx, group->meth));
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/* C3 = py * C^3 */
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MP_CHECKOK(group->meth->field_mul(py, C3, C3, group->meth));
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/* ry = D * (px * C^2 - rx) - py * C^3 */
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MP_CHECKOK(group->meth->field_sub(C, rx, ry, group->meth));
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MP_CHECKOK(group->meth->field_mul(D, ry, ry, group->meth));
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MP_CHECKOK(group->meth->field_sub(ry, C3, ry, group->meth));
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/* raz4 = a * rz^4 */
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MP_CHECKOK(group->meth->field_sqr(rz, raz4, group->meth));
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MP_CHECKOK(group->meth->field_sqr(raz4, raz4, group->meth));
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MP_CHECKOK(group->meth->
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field_mul(raz4, &group->curvea, raz4, group->meth));
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CLEANUP:
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return res;
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}
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/* Computes R = nP where R is (rx, ry) and P is the base point. Elliptic
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* curve points P and R can be identical. Uses mixed Modified-Jacobian
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* co-ordinates for doubling and Chudnovsky Jacobian coordinates for
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* additions. Assumes input is already field-encoded using field_enc, and
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* returns output that is still field-encoded. Uses 5-bit window NAF
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* method (algorithm 11) for scalar-point multiplication from Brown,
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* Hankerson, Lopez, Menezes. Software Implementation of the NIST Elliptic
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* Curves Over Prime Fields. */
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mp_err
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ec_GFp_pt_mul_jm_wNAF(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 precomp[16][2], rz, tpx, tpy;
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mp_int raz4;
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mp_int scratch[MAX_SCRATCH];
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signed char *naf = NULL;
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int i, orderBitSize;
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MP_DIGITS(&rz) = 0;
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MP_DIGITS(&raz4) = 0;
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MP_DIGITS(&tpx) = 0;
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MP_DIGITS(&tpy) = 0;
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for (i = 0; i < 16; i++) {
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MP_DIGITS(&precomp[i][0]) = 0;
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MP_DIGITS(&precomp[i][1]) = 0;
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}
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for (i = 0; i < MAX_SCRATCH; i++) {
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MP_DIGITS(&scratch[i]) = 0;
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}
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ARGCHK(group != NULL, MP_BADARG);
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ARGCHK((n != NULL) && (px != NULL) && (py != NULL), MP_BADARG);
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/* initialize precomputation table */
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MP_CHECKOK(mp_init(&tpx));
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MP_CHECKOK(mp_init(&tpy));;
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MP_CHECKOK(mp_init(&rz));
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MP_CHECKOK(mp_init(&raz4));
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for (i = 0; i < 16; i++) {
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MP_CHECKOK(mp_init(&precomp[i][0]));
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MP_CHECKOK(mp_init(&precomp[i][1]));
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}
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for (i = 0; i < MAX_SCRATCH; i++) {
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MP_CHECKOK(mp_init(&scratch[i]));
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}
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/* Set out[8] = P */
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MP_CHECKOK(mp_copy(px, &precomp[8][0]));
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MP_CHECKOK(mp_copy(py, &precomp[8][1]));
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/* Set (tpx, tpy) = 2P */
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MP_CHECKOK(group->
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point_dbl(&precomp[8][0], &precomp[8][1], &tpx, &tpy,
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group));
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/* Set 3P, 5P, ..., 15P */
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for (i = 8; i < 15; i++) {
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MP_CHECKOK(group->
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point_add(&precomp[i][0], &precomp[i][1], &tpx, &tpy,
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&precomp[i + 1][0], &precomp[i + 1][1],
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group));
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}
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/* Set -15P, -13P, ..., -P */
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for (i = 0; i < 8; i++) {
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MP_CHECKOK(mp_copy(&precomp[15 - i][0], &precomp[i][0]));
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MP_CHECKOK(group->meth->
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field_neg(&precomp[15 - i][1], &precomp[i][1],
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group->meth));
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}
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/* R = inf */
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MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, &rz));
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orderBitSize = mpl_significant_bits(&group->order);
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/* Allocate memory for NAF */
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naf = (signed char *) malloc(sizeof(signed char) * (orderBitSize + 1));
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if (naf == NULL) {
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res = MP_MEM;
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goto CLEANUP;
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}
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/* Compute 5NAF */
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ec_compute_wNAF(naf, orderBitSize, n, 5);
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/* wNAF method */
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for (i = orderBitSize; i >= 0; i--) {
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/* R = 2R */
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ec_GFp_pt_dbl_jm(rx, ry, &rz, &raz4, rx, ry, &rz,
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&raz4, scratch, group);
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if (naf[i] != 0) {
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ec_GFp_pt_add_jm_aff(rx, ry, &rz, &raz4,
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&precomp[(naf[i] + 15) / 2][0],
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&precomp[(naf[i] + 15) / 2][1], rx, ry,
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&rz, &raz4, scratch, group);
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}
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}
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/* convert result S to affine coordinates */
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MP_CHECKOK(ec_GFp_pt_jac2aff(rx, ry, &rz, rx, ry, group));
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CLEANUP:
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for (i = 0; i < MAX_SCRATCH; i++) {
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mp_clear(&scratch[i]);
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}
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for (i = 0; i < 16; i++) {
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mp_clear(&precomp[i][0]);
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mp_clear(&precomp[i][1]);
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}
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mp_clear(&tpx);
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mp_clear(&tpy);
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mp_clear(&rz);
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mp_clear(&raz4);
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free(naf);
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return res;
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}
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