jdk-sandbox: comparison jdk/src/share/native/sun/security/ec/ecp

equal deleted inserted replaced

-:c197e38bf15a
+:e549cea58864
+/* *********************************************************************
+*
+* Sun elects to have this file available under and governed by the
+* Mozilla Public License Version 1.1 ("MPL") (see
+* http://www.mozilla.org/MPL/ for full license text). For the avoidance
+* of doubt and subject to the following, Sun also elects to allow
+* licensees to use this file under the MPL, the GNU General Public
+* License version 2 only or the Lesser General Public License version
+* 2.1 only. Any references to the "GNU General Public License version 2
+* or later" or "GPL" in the following shall be construed to mean the
+* GNU General Public License version 2 only. Any references to the "GNU
+* Lesser General Public License version 2.1 or later" or "LGPL" in the
+* following shall be construed to mean the GNU Lesser General Public
+* License version 2.1 only. However, the following notice accompanied
+* the original version of this file:
+*
+* Version: MPL 1.1/GPL 2.0/LGPL 2.1
+*
+* The contents of this file are subject to the Mozilla Public License Version
+* 1.1 (the "License"); you may not use this file except in compliance with
+* the License. You may obtain a copy of the License at
+* http://www.mozilla.org/MPL/
+*
+* Software distributed under the License is distributed on an "AS IS" basis,
+* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
+* for the specific language governing rights and limitations under the
+* License.
+*
+* The Original Code is the elliptic curve math library for prime field curves.
+*
+* The Initial Developer of the Original Code is
+* Sun Microsystems, Inc.
+* Portions created by the Initial Developer are Copyright (C) 2003
+* the Initial Developer. All Rights Reserved.
+*
+* Contributor(s):
+*   Sheueling Chang-Shantz <sheueling.chang@sun.com>,
+*   Stephen Fung <fungstep@hotmail.com>, and
+*   Douglas Stebila <douglas@stebila.ca>, Sun Microsystems Laboratories.
+*   Bodo Moeller <moeller@cdc.informatik.tu-darmstadt.de>,
+*   Nils Larsch <nla@trustcenter.de>, and
+*   Lenka Fibikova <fibikova@exp-math.uni-essen.de>, the OpenSSL Project
+*
+* Alternatively, the contents of this file may be used under the terms of
+* either the GNU General Public License Version 2 or later (the "GPL"), or
+* the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
+* in which case the provisions of the GPL or the LGPL are applicable instead
+* of those above. If you wish to allow use of your version of this file only
+* under the terms of either the GPL or the LGPL, and not to allow others to
+* use your version of this file under the terms of the MPL, indicate your
+* decision by deleting the provisions above and replace them with the notice
+* and other provisions required by the GPL or the LGPL. If you do not delete
+* the provisions above, a recipient may use your version of this file under
+* the terms of any one of the MPL, the GPL or the LGPL.
+*
+*********************************************************************** */
+/*
+* Copyright 2007 Sun Microsystems, Inc.  All rights reserved.
+* Use is subject to license terms.
+*/
+#pragma ident   "%Z%%M% %I%     %E% SMI"
+#include "ecp.h"
+#include "mplogic.h"
+#ifndef _KERNEL
+#include <stdlib.h>
+#endif
+#ifdef ECL_DEBUG
+#include <assert.h>
+#endif
+/* Converts a point P(px, py) from affine coordinates to Jacobian
+* projective coordinates R(rx, ry, rz). Assumes input is already
+* field-encoded using field_enc, and returns output that is still
+* field-encoded. */
+mp_err
+ec_GFp_pt_aff2jac(const mp_int *px, const mp_int *py, mp_int *rx,
+mp_int *ry, mp_int *rz, const ECGroup *group)
+{
+mp_err res = MP_OKAY;
+if (ec_GFp_pt_is_inf_aff(px, py) == MP_YES) {
+MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, rz));
+} else {
+MP_CHECKOK(mp_copy(px, rx));
+MP_CHECKOK(mp_copy(py, ry));
+MP_CHECKOK(mp_set_int(rz, 1));
+if (group->meth->field_enc) {
+MP_CHECKOK(group->meth->field_enc(rz, rz, group->meth));
+}
+}
+CLEANUP:
+return res;
+}
+/* Converts a point P(px, py, pz) from Jacobian projective coordinates to
+* affine coordinates R(rx, ry).  P and R can share x and y coordinates.
+* Assumes input is already field-encoded using field_enc, and returns
+* output that is still field-encoded. */
+mp_err
+ec_GFp_pt_jac2aff(const mp_int *px, const mp_int *py, const mp_int *pz,
+mp_int *rx, mp_int *ry, const ECGroup *group)
+{
+mp_err res = MP_OKAY;
+mp_int z1, z2, z3;
+MP_DIGITS(&z1) = 0;
+MP_DIGITS(&z2) = 0;
+MP_DIGITS(&z3) = 0;
+MP_CHECKOK(mp_init(&z1, FLAG(px)));
+MP_CHECKOK(mp_init(&z2, FLAG(px)));
+MP_CHECKOK(mp_init(&z3, FLAG(px)));
+/* if point at infinity, then set point at infinity and exit */
+if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {
+MP_CHECKOK(ec_GFp_pt_set_inf_aff(rx, ry));
+goto CLEANUP;
+}
+/* transform (px, py, pz) into (px / pz^2, py / pz^3) */
+if (mp_cmp_d(pz, 1) == 0) {
+MP_CHECKOK(mp_copy(px, rx));
+MP_CHECKOK(mp_copy(py, ry));
+} else {
+MP_CHECKOK(group->meth->field_div(NULL, pz, &z1, group->meth));
+MP_CHECKOK(group->meth->field_sqr(&z1, &z2, group->meth));
+MP_CHECKOK(group->meth->field_mul(&z1, &z2, &z3, group->meth));
+MP_CHECKOK(group->meth->field_mul(px, &z2, rx, group->meth));
+MP_CHECKOK(group->meth->field_mul(py, &z3, ry, group->meth));
+}
+CLEANUP:
+mp_clear(&z1);
+mp_clear(&z2);
+mp_clear(&z3);
+return res;
+}
+/* Checks if point P(px, py, pz) is at infinity. Uses Jacobian
+* coordinates. */
+mp_err
+ec_GFp_pt_is_inf_jac(const mp_int *px, const mp_int *py, const mp_int *pz)
+{
+return mp_cmp_z(pz);
+}
+/* Sets P(px, py, pz) to be the point at infinity.  Uses Jacobian
+* coordinates. */
+mp_err
+ec_GFp_pt_set_inf_jac(mp_int *px, mp_int *py, mp_int *pz)
+{
+mp_zero(pz);
+return MP_OKAY;
+}
+/* Computes R = P + Q where R is (rx, ry, rz), P is (px, py, pz) and Q is
+* (qx, qy, 1).  Elliptic curve points P, Q, and R can all be identical.
+* Uses mixed Jacobian-affine coordinates. Assumes input is already
+* field-encoded using field_enc, and returns output that is still
+* field-encoded. Uses equation (2) from Brown, Hankerson, Lopez, and
+* Menezes. Software Implementation of the NIST Elliptic Curves Over Prime
+* Fields. */
+mp_err
+ec_GFp_pt_add_jac_aff(const mp_int *px, const mp_int *py, const mp_int *pz,
+const mp_int *qx, const mp_int *qy, mp_int *rx,
+mp_int *ry, mp_int *rz, const ECGroup *group)
+{
+mp_err res = MP_OKAY;
+mp_int A, B, C, D, C2, C3;
+MP_DIGITS(&A) = 0;
+MP_DIGITS(&B) = 0;
+MP_DIGITS(&C) = 0;
+MP_DIGITS(&D) = 0;
+MP_DIGITS(&C2) = 0;
+MP_DIGITS(&C3) = 0;
+MP_CHECKOK(mp_init(&A, FLAG(px)));
+MP_CHECKOK(mp_init(&B, FLAG(px)));
+MP_CHECKOK(mp_init(&C, FLAG(px)));
+MP_CHECKOK(mp_init(&D, FLAG(px)));
+MP_CHECKOK(mp_init(&C2, FLAG(px)));
+MP_CHECKOK(mp_init(&C3, FLAG(px)));
+/* If either P or Q is the point at infinity, then return the other
+* point */
+if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {
+MP_CHECKOK(ec_GFp_pt_aff2jac(qx, qy, rx, ry, rz, group));
+goto CLEANUP;
+}
+if (ec_GFp_pt_is_inf_aff(qx, qy) == MP_YES) {
+MP_CHECKOK(mp_copy(px, rx));
+MP_CHECKOK(mp_copy(py, ry));
+MP_CHECKOK(mp_copy(pz, rz));
+goto CLEANUP;
+}
+/* A = qx * pz^2, B = qy * pz^3 */
+MP_CHECKOK(group->meth->field_sqr(pz, &A, group->meth));
+MP_CHECKOK(group->meth->field_mul(&A, pz, &B, group->meth));
+MP_CHECKOK(group->meth->field_mul(&A, qx, &A, group->meth));
+MP_CHECKOK(group->meth->field_mul(&B, qy, &B, group->meth));
+/* C = A - px, D = B - py */
+MP_CHECKOK(group->meth->field_sub(&A, px, &C, group->meth));
+MP_CHECKOK(group->meth->field_sub(&B, py, &D, group->meth));
+/* C2 = C^2, C3 = C^3 */
+MP_CHECKOK(group->meth->field_sqr(&C, &C2, group->meth));
+MP_CHECKOK(group->meth->field_mul(&C, &C2, &C3, group->meth));
+/* rz = pz * C */
+MP_CHECKOK(group->meth->field_mul(pz, &C, rz, group->meth));
+/* C = px * C^2 */
+MP_CHECKOK(group->meth->field_mul(px, &C2, &C, group->meth));
+/* A = D^2 */
+MP_CHECKOK(group->meth->field_sqr(&D, &A, group->meth));
+/* rx = D^2 - (C^3 + 2 * (px * C^2)) */
+MP_CHECKOK(group->meth->field_add(&C, &C, rx, group->meth));
+MP_CHECKOK(group->meth->field_add(&C3, rx, rx, group->meth));
+MP_CHECKOK(group->meth->field_sub(&A, rx, rx, group->meth));
+/* C3 = py * C^3 */
+MP_CHECKOK(group->meth->field_mul(py, &C3, &C3, group->meth));
+/* ry = D * (px * C^2 - rx) - py * C^3 */
+MP_CHECKOK(group->meth->field_sub(&C, rx, ry, group->meth));
+MP_CHECKOK(group->meth->field_mul(&D, ry, ry, group->meth));
+MP_CHECKOK(group->meth->field_sub(ry, &C3, ry, group->meth));
+CLEANUP:
+mp_clear(&A);
+mp_clear(&B);
+mp_clear(&C);
+mp_clear(&D);
+mp_clear(&C2);
+mp_clear(&C3);
+return res;
+}
+/* Computes R = 2P.  Elliptic curve points P and R can be identical.  Uses
+* Jacobian coordinates.
+*
+* Assumes input is already field-encoded using field_enc, and returns
+* output that is still field-encoded.
+*
+* This routine implements Point Doubling in the Jacobian Projective
+* space as described in the paper "Efficient elliptic curve exponentiation
+* using mixed coordinates", by H. Cohen, A Miyaji, T. Ono.
+*/
+mp_err
+ec_GFp_pt_dbl_jac(const mp_int *px, const mp_int *py, const mp_int *pz,
+mp_int *rx, mp_int *ry, mp_int *rz, const ECGroup *group)
+{
+mp_err res = MP_OKAY;
+mp_int t0, t1, M, S;
+MP_DIGITS(&t0) = 0;
+MP_DIGITS(&t1) = 0;
+MP_DIGITS(&M) = 0;
+MP_DIGITS(&S) = 0;
+MP_CHECKOK(mp_init(&t0, FLAG(px)));
+MP_CHECKOK(mp_init(&t1, FLAG(px)));
+MP_CHECKOK(mp_init(&M, FLAG(px)));
+MP_CHECKOK(mp_init(&S, FLAG(px)));
+if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {
+MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, rz));
+goto CLEANUP;
+}
+if (mp_cmp_d(pz, 1) == 0) {
+/* M = 3 * px^2 + a */
+MP_CHECKOK(group->meth->field_sqr(px, &t0, group->meth));
+MP_CHECKOK(group->meth->field_add(&t0, &t0, &M, group->meth));
+MP_CHECKOK(group->meth->field_add(&t0, &M, &t0, group->meth));
+MP_CHECKOK(group->meth->
+field_add(&t0, &group->curvea, &M, group->meth));
+} else if (mp_cmp_int(&group->curvea, -3, FLAG(px)) == 0) {
+/* M = 3 * (px + pz^2) * (px - pz^2) */
+MP_CHECKOK(group->meth->field_sqr(pz, &M, group->meth));
+MP_CHECKOK(group->meth->field_add(px, &M, &t0, group->meth));
+MP_CHECKOK(group->meth->field_sub(px, &M, &t1, group->meth));
+MP_CHECKOK(group->meth->field_mul(&t0, &t1, &M, group->meth));
+MP_CHECKOK(group->meth->field_add(&M, &M, &t0, group->meth));
+MP_CHECKOK(group->meth->field_add(&t0, &M, &M, group->meth));
+} else {
+/* M = 3 * (px^2) + a * (pz^4) */
+MP_CHECKOK(group->meth->field_sqr(px, &t0, group->meth));
+MP_CHECKOK(group->meth->field_add(&t0, &t0, &M, group->meth));
+MP_CHECKOK(group->meth->field_add(&t0, &M, &t0, group->meth));
+MP_CHECKOK(group->meth->field_sqr(pz, &M, group->meth));
+MP_CHECKOK(group->meth->field_sqr(&M, &M, group->meth));
+MP_CHECKOK(group->meth->
+field_mul(&M, &group->curvea, &M, group->meth));
+MP_CHECKOK(group->meth->field_add(&M, &t0, &M, group->meth));
+}
+/* rz = 2 * py * pz */
+/* t0 = 4 * py^2 */
+if (mp_cmp_d(pz, 1) == 0) {
+MP_CHECKOK(group->meth->field_add(py, py, rz, group->meth));
+MP_CHECKOK(group->meth->field_sqr(rz, &t0, group->meth));
+} else {
+MP_CHECKOK(group->meth->field_add(py, py, &t0, group->meth));
+MP_CHECKOK(group->meth->field_mul(&t0, pz, rz, group->meth));
+MP_CHECKOK(group->meth->field_sqr(&t0, &t0, group->meth));
+}
+/* S = 4 * px * py^2 = px * (2 * py)^2 */
+MP_CHECKOK(group->meth->field_mul(px, &t0, &S, group->meth));
+/* rx = M^2 - 2 * S */
+MP_CHECKOK(group->meth->field_add(&S, &S, &t1, group->meth));
+MP_CHECKOK(group->meth->field_sqr(&M, rx, group->meth));
+MP_CHECKOK(group->meth->field_sub(rx, &t1, rx, group->meth));
+/* ry = M * (S - rx) - 8 * py^4 */
+MP_CHECKOK(group->meth->field_sqr(&t0, &t1, group->meth));
+if (mp_isodd(&t1)) {
+MP_CHECKOK(mp_add(&t1, &group->meth->irr, &t1));
+}
+MP_CHECKOK(mp_div_2(&t1, &t1));
+MP_CHECKOK(group->meth->field_sub(&S, rx, &S, group->meth));
+MP_CHECKOK(group->meth->field_mul(&M, &S, &M, group->meth));
+MP_CHECKOK(group->meth->field_sub(&M, &t1, ry, group->meth));
+CLEANUP:
+mp_clear(&t0);
+mp_clear(&t1);
+mp_clear(&M);
+mp_clear(&S);
+return res;
+}
+/* by default, this routine is unused and thus doesn't need to be compiled */
+#ifdef ECL_ENABLE_GFP_PT_MUL_JAC
+/* Computes R = nP where R is (rx, ry) and P is (px, py). The parameters
+* a, b and p are the elliptic curve coefficients and the prime that
+* determines the field GFp.  Elliptic curve points P and R can be
+* identical.  Uses mixed Jacobian-affine coordinates. Assumes input is
+* already field-encoded using field_enc, and returns output that is still
+* field-encoded. Uses 4-bit window method. */
+mp_err
+ec_GFp_pt_mul_jac(const mp_int *n, const mp_int *px, const mp_int *py,
+mp_int *rx, mp_int *ry, const ECGroup *group)
+{
+mp_err res = MP_OKAY;
+mp_int precomp[16][2], rz;
+int i, ni, d;
+MP_DIGITS(&rz) = 0;
+for (i = 0; i < 16; i++) {
+MP_DIGITS(&precomp[i][0]) = 0;
+MP_DIGITS(&precomp[i][1]) = 0;
+}
+ARGCHK(group != NULL, MP_BADARG);
+ARGCHK((n != NULL) && (px != NULL) && (py != NULL), MP_BADARG);
+/* initialize precomputation table */
+for (i = 0; i < 16; i++) {
+MP_CHECKOK(mp_init(&precomp[i][0]));
+MP_CHECKOK(mp_init(&precomp[i][1]));
+}
+/* fill precomputation table */
+mp_zero(&precomp[0][0]);
+mp_zero(&precomp[0][1]);
+MP_CHECKOK(mp_copy(px, &precomp[1][0]));
+MP_CHECKOK(mp_copy(py, &precomp[1][1]));
+for (i = 2; i < 16; i++) {
+MP_CHECKOK(group->
+point_add(&precomp[1][0], &precomp[1][1],
+&precomp[i - 1][0], &precomp[i - 1][1],
+&precomp[i][0], &precomp[i][1], group));
+}
+d = (mpl_significant_bits(n) + 3) / 4;
+/* R = inf */
+MP_CHECKOK(mp_init(&rz));
+MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, &rz));
+for (i = d - 1; i >= 0; i--) {
+/* compute window ni */
+ni = MP_GET_BIT(n, 4 * i + 3);
+ni <<= 1;
+ni |= MP_GET_BIT(n, 4 * i + 2);
+ni <<= 1;
+ni |= MP_GET_BIT(n, 4 * i + 1);
+ni <<= 1;
+ni |= MP_GET_BIT(n, 4 * i);
+/* R = 2^4 * R */
+MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group));
+MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group));
+MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group));
+MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group));
+/* R = R + (ni * P) */
+MP_CHECKOK(ec_GFp_pt_add_jac_aff
+(rx, ry, &rz, &precomp[ni][0], &precomp[ni][1], rx, ry,
+&rz, group));
+}
+/* convert result S to affine coordinates */
+MP_CHECKOK(ec_GFp_pt_jac2aff(rx, ry, &rz, rx, ry, group));
+CLEANUP:
+mp_clear(&rz);
+for (i = 0; i < 16; i++) {
+mp_clear(&precomp[i][0]);
+mp_clear(&precomp[i][1]);
+}
+return res;
+}
+#endif
+/* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G +
+* k2 * P(x, y), where G is the generator (base point) of the group of
+* points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL.
+* Uses mixed Jacobian-affine coordinates. Input and output values are
+* assumed to be NOT field-encoded. Uses algorithm 15 (simultaneous
+* multiple point multiplication) from Brown, Hankerson, Lopez, Menezes.
+* Software Implementation of the NIST Elliptic Curves over Prime Fields. */
+mp_err
+ec_GFp_pts_mul_jac(const mp_int *k1, const mp_int *k2, const mp_int *px,
+const mp_int *py, mp_int *rx, mp_int *ry,
+const ECGroup *group)
+{
+mp_err res = MP_OKAY;
+mp_int precomp[4][4][2];
+mp_int rz;
+const mp_int *a, *b;
+int i, j;
+int ai, bi, d;
+for (i = 0; i < 4; i++) {
+for (j = 0; j < 4; j++) {
+MP_DIGITS(&precomp[i][j][0]) = 0;
+MP_DIGITS(&precomp[i][j][1]) = 0;
+}
+}
+MP_DIGITS(&rz) = 0;
+ARGCHK(group != NULL, MP_BADARG);
+ARGCHK(!((k1 == NULL)
+&& ((k2 == NULL) || (px == NULL)
+|| (py == NULL))), MP_BADARG);
+/* if some arguments are not defined used ECPoint_mul */
+if (k1 == NULL) {
+return ECPoint_mul(group, k2, px, py, rx, ry);
+} else if ((k2 == NULL) || (px == NULL) || (py == NULL)) {
+return ECPoint_mul(group, k1, NULL, NULL, rx, ry);
+}
+/* initialize precomputation table */
+for (i = 0; i < 4; i++) {
+for (j = 0; j < 4; j++) {
+MP_CHECKOK(mp_init(&precomp[i][j][0], FLAG(k1)));
+MP_CHECKOK(mp_init(&precomp[i][j][1], FLAG(k1)));
+}
+}
+/* fill precomputation table */
+/* assign {k1, k2} = {a, b} such that len(a) >= len(b) */
+if (mpl_significant_bits(k1) < mpl_significant_bits(k2)) {
+a = k2;
+b = k1;
+if (group->meth->field_enc) {
+MP_CHECKOK(group->meth->
+field_enc(px, &precomp[1][0][0], group->meth));
+MP_CHECKOK(group->meth->
+field_enc(py, &precomp[1][0][1], group->meth));
+} else {
+MP_CHECKOK(mp_copy(px, &precomp[1][0][0]));
+MP_CHECKOK(mp_copy(py, &precomp[1][0][1]));
+}
+MP_CHECKOK(mp_copy(&group->genx, &precomp[0][1][0]));
+MP_CHECKOK(mp_copy(&group->geny, &precomp[0][1][1]));
+} else {
+a = k1;
+b = k2;
+MP_CHECKOK(mp_copy(&group->genx, &precomp[1][0][0]));
+MP_CHECKOK(mp_copy(&group->geny, &precomp[1][0][1]));
+if (group->meth->field_enc) {
+MP_CHECKOK(group->meth->
+field_enc(px, &precomp[0][1][0], group->meth));
+MP_CHECKOK(group->meth->
+field_enc(py, &precomp[0][1][1], group->meth));
+} else {
+MP_CHECKOK(mp_copy(px, &precomp[0][1][0]));
+MP_CHECKOK(mp_copy(py, &precomp[0][1][1]));
+}
+}
+/* precompute [*][0][*] */
+mp_zero(&precomp[0][0][0]);
+mp_zero(&precomp[0][0][1]);
+MP_CHECKOK(group->
+point_dbl(&precomp[1][0][0], &precomp[1][0][1],
+&precomp[2][0][0], &precomp[2][0][1], group));
+MP_CHECKOK(group->
+point_add(&precomp[1][0][0], &precomp[1][0][1],
+&precomp[2][0][0], &precomp[2][0][1],
+&precomp[3][0][0], &precomp[3][0][1], group));
+/* precompute [*][1][*] */
+for (i = 1; i < 4; i++) {
+MP_CHECKOK(group->
+point_add(&precomp[0][1][0], &precomp[0][1][1],
+&precomp[i][0][0], &precomp[i][0][1],
+&precomp[i][1][0], &precomp[i][1][1], group));
+}
+/* precompute [*][2][*] */
+MP_CHECKOK(group->
+point_dbl(&precomp[0][1][0], &precomp[0][1][1],
+&precomp[0][2][0], &precomp[0][2][1], group));
+for (i = 1; i < 4; i++) {
+MP_CHECKOK(group->
+point_add(&precomp[0][2][0], &precomp[0][2][1],
+&precomp[i][0][0], &precomp[i][0][1],
+&precomp[i][2][0], &precomp[i][2][1], group));
+}
+/* precompute [*][3][*] */
+MP_CHECKOK(group->
+point_add(&precomp[0][1][0], &precomp[0][1][1],
+&precomp[0][2][0], &precomp[0][2][1],
+&precomp[0][3][0], &precomp[0][3][1], group));
+for (i = 1; i < 4; i++) {
+MP_CHECKOK(group->
+point_add(&precomp[0][3][0], &precomp[0][3][1],
+&precomp[i][0][0], &precomp[i][0][1],
+&precomp[i][3][0], &precomp[i][3][1], group));
+}
+d = (mpl_significant_bits(a) + 1) / 2;
+/* R = inf */
+MP_CHECKOK(mp_init(&rz, FLAG(k1)));
+MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, &rz));
+for (i = d - 1; i >= 0; i--) {
+ai = MP_GET_BIT(a, 2 * i + 1);
+ai <<= 1;
+ai |= MP_GET_BIT(a, 2 * i);
+bi = MP_GET_BIT(b, 2 * i + 1);
+bi <<= 1;
+bi |= MP_GET_BIT(b, 2 * i);
+/* R = 2^2 * R */
+MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group));
+MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group));
+/* R = R + (ai * A + bi * B) */
+MP_CHECKOK(ec_GFp_pt_add_jac_aff
+(rx, ry, &rz, &precomp[ai][bi][0], &precomp[ai][bi][1],
+rx, ry, &rz, group));
+}
+MP_CHECKOK(ec_GFp_pt_jac2aff(rx, ry, &rz, rx, ry, group));
+if (group->meth->field_dec) {
+MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth));
+MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth));
+}
+CLEANUP:
+mp_clear(&rz);
+for (i = 0; i < 4; i++) {
+for (j = 0; j < 4; j++) {
+mp_clear(&precomp[i][j][0]);
+mp_clear(&precomp[i][j][1]);
+}
+}
+return res;
+}