2017-04-19 07:56:45 +00:00
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/* This Source Code Form is subject to the terms of the Mozilla Public
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* License, v. 2.0. If a copy of the MPL was not distributed with this
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* file, You can obtain one at http://mozilla.org/MPL/2.0/. */
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#include "ecp.h"
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#include "mplogic.h"
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#include <stdlib.h>
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/* Checks if point P(px, py) is at infinity. Uses affine coordinates. */
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mp_err
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ec_GFp_pt_is_inf_aff(const mp_int *px, const mp_int *py)
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{
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2020-01-24 01:47:36 +00:00
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if ((mp_cmp_z(px) == 0) && (mp_cmp_z(py) == 0)) {
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return MP_YES;
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} else {
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return MP_NO;
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}
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2017-04-19 07:56:45 +00:00
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}
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/* Sets P(px, py) to be the point at infinity. Uses affine coordinates. */
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mp_err
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ec_GFp_pt_set_inf_aff(mp_int *px, mp_int *py)
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{
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2020-01-24 01:47:36 +00:00
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mp_zero(px);
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mp_zero(py);
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return MP_OKAY;
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2017-04-19 07:56:45 +00:00
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}
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2020-01-24 01:47:36 +00:00
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/* Computes R = P + Q based on IEEE P1363 A.10.1. Elliptic curve points P,
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2017-04-19 07:56:45 +00:00
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* Q, and R can all be identical. Uses affine coordinates. Assumes input
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* is already field-encoded using field_enc, and returns output that is
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* still field-encoded. */
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mp_err
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ec_GFp_pt_add_aff(const mp_int *px, const mp_int *py, const mp_int *qx,
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2020-01-24 01:47:36 +00:00
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const mp_int *qy, mp_int *rx, mp_int *ry,
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const ECGroup *group)
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2017-04-19 07:56:45 +00:00
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{
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2020-01-24 01:47:36 +00:00
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mp_err res = MP_OKAY;
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mp_int lambda, temp, tempx, tempy;
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2017-04-19 07:56:45 +00:00
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2020-01-24 01:47:36 +00:00
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MP_DIGITS(&lambda) = 0;
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MP_DIGITS(&temp) = 0;
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MP_DIGITS(&tempx) = 0;
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MP_DIGITS(&tempy) = 0;
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MP_CHECKOK(mp_init(&lambda));
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MP_CHECKOK(mp_init(&temp));
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MP_CHECKOK(mp_init(&tempx));
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MP_CHECKOK(mp_init(&tempy));
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/* if P = inf, then R = Q */
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if (ec_GFp_pt_is_inf_aff(px, py) == 0) {
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MP_CHECKOK(mp_copy(qx, rx));
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MP_CHECKOK(mp_copy(qy, ry));
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res = MP_OKAY;
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goto CLEANUP;
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}
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/* if Q = inf, then R = P */
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if (ec_GFp_pt_is_inf_aff(qx, qy) == 0) {
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MP_CHECKOK(mp_copy(px, rx));
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MP_CHECKOK(mp_copy(py, ry));
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res = MP_OKAY;
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goto CLEANUP;
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}
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/* if px != qx, then lambda = (py-qy) / (px-qx) */
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if (mp_cmp(px, qx) != 0) {
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MP_CHECKOK(group->meth->field_sub(py, qy, &tempy, group->meth));
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MP_CHECKOK(group->meth->field_sub(px, qx, &tempx, group->meth));
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MP_CHECKOK(group->meth->field_div(&tempy, &tempx, &lambda, group->meth));
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} else {
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/* if py != qy or qy = 0, then R = inf */
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if (((mp_cmp(py, qy) != 0)) || (mp_cmp_z(qy) == 0)) {
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mp_zero(rx);
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mp_zero(ry);
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res = MP_OKAY;
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goto CLEANUP;
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}
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/* lambda = (3qx^2+a) / (2qy) */
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MP_CHECKOK(group->meth->field_sqr(qx, &tempx, group->meth));
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MP_CHECKOK(mp_set_int(&temp, 3));
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if (group->meth->field_enc) {
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MP_CHECKOK(group->meth->field_enc(&temp, &temp, group->meth));
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}
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MP_CHECKOK(group->meth->field_mul(&tempx, &temp, &tempx, group->meth));
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MP_CHECKOK(group->meth->field_add(&tempx, &group->curvea, &tempx, group->meth));
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MP_CHECKOK(mp_set_int(&temp, 2));
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if (group->meth->field_enc) {
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MP_CHECKOK(group->meth->field_enc(&temp, &temp, group->meth));
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}
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MP_CHECKOK(group->meth->field_mul(qy, &temp, &tempy, group->meth));
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MP_CHECKOK(group->meth->field_div(&tempx, &tempy, &lambda, group->meth));
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}
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/* rx = lambda^2 - px - qx */
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MP_CHECKOK(group->meth->field_sqr(&lambda, &tempx, group->meth));
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MP_CHECKOK(group->meth->field_sub(&tempx, px, &tempx, group->meth));
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MP_CHECKOK(group->meth->field_sub(&tempx, qx, &tempx, group->meth));
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/* ry = (x1-x2) * lambda - y1 */
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MP_CHECKOK(group->meth->field_sub(qx, &tempx, &tempy, group->meth));
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MP_CHECKOK(group->meth->field_mul(&tempy, &lambda, &tempy, group->meth));
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MP_CHECKOK(group->meth->field_sub(&tempy, qy, &tempy, group->meth));
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MP_CHECKOK(mp_copy(&tempx, rx));
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MP_CHECKOK(mp_copy(&tempy, ry));
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2017-04-19 07:56:45 +00:00
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2020-01-24 01:47:36 +00:00
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CLEANUP:
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mp_clear(&lambda);
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mp_clear(&temp);
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mp_clear(&tempx);
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mp_clear(&tempy);
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return res;
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2017-04-19 07:56:45 +00:00
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}
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/* Computes R = P - Q. Elliptic curve points P, Q, and R can all be
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* identical. Uses affine coordinates. Assumes input is already
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* 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_sub_aff(const mp_int *px, const mp_int *py, const mp_int *qx,
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2020-01-24 01:47:36 +00:00
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const mp_int *qy, mp_int *rx, mp_int *ry,
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const ECGroup *group)
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2017-04-19 07:56:45 +00:00
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{
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2020-01-24 01:47:36 +00:00
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mp_err res = MP_OKAY;
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mp_int nqy;
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2017-04-19 07:56:45 +00:00
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2020-01-24 01:47:36 +00:00
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MP_DIGITS(&nqy) = 0;
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MP_CHECKOK(mp_init(&nqy));
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/* nqy = -qy */
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MP_CHECKOK(group->meth->field_neg(qy, &nqy, group->meth));
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res = group->point_add(px, py, qx, &nqy, rx, ry, group);
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CLEANUP:
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mp_clear(&nqy);
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return res;
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2017-04-19 07:56:45 +00:00
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}
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/* Computes R = 2P. Elliptic curve points P and R can be identical. Uses
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* affine coordinates. Assumes input is already field-encoded using
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* field_enc, and returns output that is still field-encoded. */
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mp_err
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ec_GFp_pt_dbl_aff(const mp_int *px, const mp_int *py, mp_int *rx,
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2020-01-24 01:47:36 +00:00
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mp_int *ry, const ECGroup *group)
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2017-04-19 07:56:45 +00:00
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{
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2020-01-24 01:47:36 +00:00
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return ec_GFp_pt_add_aff(px, py, px, py, rx, ry, group);
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2017-04-19 07:56:45 +00:00
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}
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/* by default, this routine is unused and thus doesn't need to be compiled */
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#ifdef ECL_ENABLE_GFP_PT_MUL_AFF
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2020-01-24 01:47:36 +00:00
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/* Computes R = nP based on IEEE P1363 A.10.3. Elliptic curve points P and
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2017-04-19 07:56:45 +00:00
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* R can be identical. Uses affine coordinates. Assumes input is already
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* 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_mul_aff(const mp_int *n, const mp_int *px, const mp_int *py,
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2020-01-24 01:47:36 +00:00
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mp_int *rx, mp_int *ry, const ECGroup *group)
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2017-04-19 07:56:45 +00:00
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{
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2020-01-24 01:47:36 +00:00
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mp_err res = MP_OKAY;
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mp_int k, k3, qx, qy, sx, sy;
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int b1, b3, i, l;
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2017-04-19 07:56:45 +00:00
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2020-01-24 01:47:36 +00:00
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MP_DIGITS(&k) = 0;
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MP_DIGITS(&k3) = 0;
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MP_DIGITS(&qx) = 0;
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MP_DIGITS(&qy) = 0;
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MP_DIGITS(&sx) = 0;
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MP_DIGITS(&sy) = 0;
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MP_CHECKOK(mp_init(&k));
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MP_CHECKOK(mp_init(&k3));
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MP_CHECKOK(mp_init(&qx));
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MP_CHECKOK(mp_init(&qy));
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MP_CHECKOK(mp_init(&sx));
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MP_CHECKOK(mp_init(&sy));
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2017-04-19 07:56:45 +00:00
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2020-01-24 01:47:36 +00:00
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/* if n = 0 then r = inf */
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if (mp_cmp_z(n) == 0) {
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mp_zero(rx);
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mp_zero(ry);
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res = MP_OKAY;
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goto CLEANUP;
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}
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/* Q = P, k = n */
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MP_CHECKOK(mp_copy(px, &qx));
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MP_CHECKOK(mp_copy(py, &qy));
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MP_CHECKOK(mp_copy(n, &k));
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/* if n < 0 then Q = -Q, k = -k */
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if (mp_cmp_z(n) < 0) {
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MP_CHECKOK(group->meth->field_neg(&qy, &qy, group->meth));
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MP_CHECKOK(mp_neg(&k, &k));
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}
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#ifdef ECL_DEBUG /* basic double and add method */
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l = mpl_significant_bits(&k) - 1;
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MP_CHECKOK(mp_copy(&qx, &sx));
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MP_CHECKOK(mp_copy(&qy, &sy));
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for (i = l - 1; i >= 0; i--) {
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/* S = 2S */
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MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group));
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/* if k_i = 1, then S = S + Q */
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if (mpl_get_bit(&k, i) != 0) {
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MP_CHECKOK(group->point_add(&sx, &sy, &qx, &qy, &sx, &sy, group));
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}
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}
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#else /* double and add/subtract method from \
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* standard */
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/* k3 = 3 * k */
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MP_CHECKOK(mp_set_int(&k3, 3));
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MP_CHECKOK(mp_mul(&k, &k3, &k3));
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/* S = Q */
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MP_CHECKOK(mp_copy(&qx, &sx));
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MP_CHECKOK(mp_copy(&qy, &sy));
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/* l = index of high order bit in binary representation of 3*k */
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l = mpl_significant_bits(&k3) - 1;
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/* for i = l-1 downto 1 */
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for (i = l - 1; i >= 1; i--) {
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/* S = 2S */
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MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group));
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b3 = MP_GET_BIT(&k3, i);
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b1 = MP_GET_BIT(&k, i);
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/* if k3_i = 1 and k_i = 0, then S = S + Q */
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if ((b3 == 1) && (b1 == 0)) {
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MP_CHECKOK(group->point_add(&sx, &sy, &qx, &qy, &sx, &sy, group));
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/* if k3_i = 0 and k_i = 1, then S = S - Q */
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} else if ((b3 == 0) && (b1 == 1)) {
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MP_CHECKOK(group->point_sub(&sx, &sy, &qx, &qy, &sx, &sy, group));
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}
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}
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2017-04-19 07:56:45 +00:00
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#endif
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2020-01-24 01:47:36 +00:00
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/* output S */
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MP_CHECKOK(mp_copy(&sx, rx));
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MP_CHECKOK(mp_copy(&sy, ry));
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2017-04-19 07:56:45 +00:00
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2020-01-24 01:47:36 +00:00
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CLEANUP:
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mp_clear(&k);
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mp_clear(&k3);
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mp_clear(&qx);
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mp_clear(&qy);
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mp_clear(&sx);
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mp_clear(&sy);
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return res;
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2017-04-19 07:56:45 +00:00
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}
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#endif
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/* Validates a point on a GFp curve. */
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2020-01-24 01:47:36 +00:00
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mp_err
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2017-04-19 07:56:45 +00:00
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ec_GFp_validate_point(const mp_int *px, const mp_int *py, const ECGroup *group)
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{
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2020-01-24 01:47:36 +00:00
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mp_err res = MP_NO;
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mp_int accl, accr, tmp, pxt, pyt;
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2017-04-19 07:56:45 +00:00
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2020-01-24 01:47:36 +00:00
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MP_DIGITS(&accl) = 0;
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MP_DIGITS(&accr) = 0;
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MP_DIGITS(&tmp) = 0;
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MP_DIGITS(&pxt) = 0;
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MP_DIGITS(&pyt) = 0;
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MP_CHECKOK(mp_init(&accl));
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MP_CHECKOK(mp_init(&accr));
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MP_CHECKOK(mp_init(&tmp));
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MP_CHECKOK(mp_init(&pxt));
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MP_CHECKOK(mp_init(&pyt));
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2017-04-19 07:56:45 +00:00
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/* 1: Verify that publicValue is not the point at infinity */
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2020-01-24 01:47:36 +00:00
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if (ec_GFp_pt_is_inf_aff(px, py) == MP_YES) {
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res = MP_NO;
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goto CLEANUP;
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}
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/* 2: Verify that the coordinates of publicValue are elements
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2017-04-19 07:56:45 +00:00
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* of the field.
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*/
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2020-01-24 01:47:36 +00:00
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if ((MP_SIGN(px) == MP_NEG) || (mp_cmp(px, &group->meth->irr) >= 0) ||
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(MP_SIGN(py) == MP_NEG) || (mp_cmp(py, &group->meth->irr) >= 0)) {
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res = MP_NO;
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goto CLEANUP;
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}
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2017-04-19 07:56:45 +00:00
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/* 3: Verify that publicValue is on the curve. */
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2020-01-24 01:47:36 +00:00
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if (group->meth->field_enc) {
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group->meth->field_enc(px, &pxt, group->meth);
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group->meth->field_enc(py, &pyt, group->meth);
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} else {
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MP_CHECKOK(mp_copy(px, &pxt));
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MP_CHECKOK(mp_copy(py, &pyt));
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}
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/* left-hand side: y^2 */
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MP_CHECKOK(group->meth->field_sqr(&pyt, &accl, group->meth));
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/* right-hand side: x^3 + a*x + b = (x^2 + a)*x + b by Horner's rule */
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MP_CHECKOK(group->meth->field_sqr(&pxt, &tmp, group->meth));
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MP_CHECKOK(group->meth->field_add(&tmp, &group->curvea, &tmp, group->meth));
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MP_CHECKOK(group->meth->field_mul(&tmp, &pxt, &accr, group->meth));
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MP_CHECKOK(group->meth->field_add(&accr, &group->curveb, &accr, group->meth));
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/* check LHS - RHS == 0 */
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|
MP_CHECKOK(group->meth->field_sub(&accl, &accr, &accr, group->meth));
|
|
|
|
if (mp_cmp_z(&accr) != 0) {
|
|
|
|
res = MP_NO;
|
|
|
|
goto CLEANUP;
|
|
|
|
}
|
2017-04-19 07:56:45 +00:00
|
|
|
/* 4: Verify that the order of the curve times the publicValue
|
|
|
|
* is the point at infinity.
|
|
|
|
*/
|
2020-01-24 01:47:36 +00:00
|
|
|
MP_CHECKOK(ECPoint_mul(group, &group->order, px, py, &pxt, &pyt));
|
|
|
|
if (ec_GFp_pt_is_inf_aff(&pxt, &pyt) != MP_YES) {
|
|
|
|
res = MP_NO;
|
|
|
|
goto CLEANUP;
|
|
|
|
}
|
2017-04-19 07:56:45 +00:00
|
|
|
|
2020-01-24 01:47:36 +00:00
|
|
|
res = MP_YES;
|
2017-04-19 07:56:45 +00:00
|
|
|
|
|
|
|
CLEANUP:
|
2020-01-24 01:47:36 +00:00
|
|
|
mp_clear(&accl);
|
|
|
|
mp_clear(&accr);
|
|
|
|
mp_clear(&tmp);
|
|
|
|
mp_clear(&pxt);
|
|
|
|
mp_clear(&pyt);
|
|
|
|
return res;
|
2017-04-19 07:56:45 +00:00
|
|
|
}
|