| /* |
| * Copyright (c) 2007, 2017, Oracle and/or its affiliates. All rights reserved. |
| * Use is subject to license terms. |
| * |
| * This library is free software; you can redistribute it and/or |
| * modify it under the terms of the GNU Lesser General Public |
| * License as published by the Free Software Foundation; either |
| * version 2.1 of the License, or (at your option) any later version. |
| * |
| * This library is distributed in the hope that it will be useful, |
| * but WITHOUT ANY WARRANTY; without even the implied warranty of |
| * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
| * Lesser General Public License for more details. |
| * |
| * You should have received a copy of the GNU Lesser General Public License |
| * along with this library; if not, write to the Free Software Foundation, |
| * Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. |
| * |
| * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA |
| * or visit www.oracle.com if you need additional information or have any |
| * questions. |
| */ |
| |
| /* ********************************************************************* |
| * |
| * 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 |
| * |
| * Last Modified Date from the Original Code: May 2017 |
| *********************************************************************** */ |
| |
| #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)); |
| |
| /* |
| * Additional checks for point equality and point at infinity |
| */ |
| if (mp_cmp(px, &A) == 0 && mp_cmp(py, &B) == 0) { |
| /* POINT_DOUBLE(P) */ |
| MP_CHECKOK(ec_GFp_pt_dbl_jac(px, py, pz, rx, ry, rz, group)); |
| goto CLEANUP; |
| } |
| |
| /* 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, int timing) |
| { |
| 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, timing); |
| } else if ((k2 == NULL) || (px == NULL) || (py == NULL)) { |
| return ECPoint_mul(group, k1, NULL, NULL, rx, ry, timing); |
| } |
| |
| /* 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; |
| } |
