/security/nss/lib/freebl/ecl/ecp_aff.c
http://github.com/zpao/v8monkey · C · 357 lines · 243 code · 20 blank · 94 comment · 48 complexity · 7c0dea250bf1d02623ed5d23e7c34032 MD5 · raw file
- /*
- * ***** BEGIN LICENSE BLOCK *****
- * 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.
- *
- * ***** END LICENSE BLOCK ***** */
- #include "ecp.h"
- #include "mplogic.h"
- #include <stdlib.h>
- /* Checks if point P(px, py) is at infinity. Uses affine coordinates. */
- mp_err
- ec_GFp_pt_is_inf_aff(const mp_int *px, const mp_int *py)
- {
- if ((mp_cmp_z(px) == 0) && (mp_cmp_z(py) == 0)) {
- return MP_YES;
- } else {
- return MP_NO;
- }
- }
- /* Sets P(px, py) to be the point at infinity. Uses affine coordinates. */
- mp_err
- ec_GFp_pt_set_inf_aff(mp_int *px, mp_int *py)
- {
- mp_zero(px);
- mp_zero(py);
- return MP_OKAY;
- }
- /* Computes R = P + Q based on IEEE P1363 A.10.1. Elliptic curve points P,
- * Q, and R can all be identical. Uses affine coordinates. Assumes input
- * is already field-encoded using field_enc, and returns output that is
- * still field-encoded. */
- mp_err
- ec_GFp_pt_add_aff(const mp_int *px, const mp_int *py, const mp_int *qx,
- const mp_int *qy, mp_int *rx, mp_int *ry,
- const ECGroup *group)
- {
- mp_err res = MP_OKAY;
- mp_int lambda, temp, tempx, tempy;
- MP_DIGITS(&lambda) = 0;
- MP_DIGITS(&temp) = 0;
- MP_DIGITS(&tempx) = 0;
- MP_DIGITS(&tempy) = 0;
- MP_CHECKOK(mp_init(&lambda));
- MP_CHECKOK(mp_init(&temp));
- MP_CHECKOK(mp_init(&tempx));
- MP_CHECKOK(mp_init(&tempy));
- /* if P = inf, then R = Q */
- if (ec_GFp_pt_is_inf_aff(px, py) == 0) {
- MP_CHECKOK(mp_copy(qx, rx));
- MP_CHECKOK(mp_copy(qy, ry));
- res = MP_OKAY;
- goto CLEANUP;
- }
- /* if Q = inf, then R = P */
- if (ec_GFp_pt_is_inf_aff(qx, qy) == 0) {
- MP_CHECKOK(mp_copy(px, rx));
- MP_CHECKOK(mp_copy(py, ry));
- res = MP_OKAY;
- goto CLEANUP;
- }
- /* if px != qx, then lambda = (py-qy) / (px-qx) */
- if (mp_cmp(px, qx) != 0) {
- MP_CHECKOK(group->meth->field_sub(py, qy, &tempy, group->meth));
- MP_CHECKOK(group->meth->field_sub(px, qx, &tempx, group->meth));
- MP_CHECKOK(group->meth->
- field_div(&tempy, &tempx, &lambda, group->meth));
- } else {
- /* if py != qy or qy = 0, then R = inf */
- if (((mp_cmp(py, qy) != 0)) || (mp_cmp_z(qy) == 0)) {
- mp_zero(rx);
- mp_zero(ry);
- res = MP_OKAY;
- goto CLEANUP;
- }
- /* lambda = (3qx^2+a) / (2qy) */
- MP_CHECKOK(group->meth->field_sqr(qx, &tempx, group->meth));
- MP_CHECKOK(mp_set_int(&temp, 3));
- if (group->meth->field_enc) {
- MP_CHECKOK(group->meth->field_enc(&temp, &temp, group->meth));
- }
- MP_CHECKOK(group->meth->
- field_mul(&tempx, &temp, &tempx, group->meth));
- MP_CHECKOK(group->meth->
- field_add(&tempx, &group->curvea, &tempx, group->meth));
- MP_CHECKOK(mp_set_int(&temp, 2));
- if (group->meth->field_enc) {
- MP_CHECKOK(group->meth->field_enc(&temp, &temp, group->meth));
- }
- MP_CHECKOK(group->meth->field_mul(qy, &temp, &tempy, group->meth));
- MP_CHECKOK(group->meth->
- field_div(&tempx, &tempy, &lambda, group->meth));
- }
- /* rx = lambda^2 - px - qx */
- MP_CHECKOK(group->meth->field_sqr(&lambda, &tempx, group->meth));
- MP_CHECKOK(group->meth->field_sub(&tempx, px, &tempx, group->meth));
- MP_CHECKOK(group->meth->field_sub(&tempx, qx, &tempx, group->meth));
- /* ry = (x1-x2) * lambda - y1 */
- MP_CHECKOK(group->meth->field_sub(qx, &tempx, &tempy, group->meth));
- MP_CHECKOK(group->meth->
- field_mul(&tempy, &lambda, &tempy, group->meth));
- MP_CHECKOK(group->meth->field_sub(&tempy, qy, &tempy, group->meth));
- MP_CHECKOK(mp_copy(&tempx, rx));
- MP_CHECKOK(mp_copy(&tempy, ry));
- CLEANUP:
- mp_clear(&lambda);
- mp_clear(&temp);
- mp_clear(&tempx);
- mp_clear(&tempy);
- return res;
- }
- /* Computes R = P - Q. Elliptic curve points P, Q, and R can all be
- * identical. Uses affine coordinates. Assumes input is already
- * field-encoded using field_enc, and returns output that is still
- * field-encoded. */
- mp_err
- ec_GFp_pt_sub_aff(const mp_int *px, const mp_int *py, const mp_int *qx,
- const mp_int *qy, mp_int *rx, mp_int *ry,
- const ECGroup *group)
- {
- mp_err res = MP_OKAY;
- mp_int nqy;
- MP_DIGITS(&nqy) = 0;
- MP_CHECKOK(mp_init(&nqy));
- /* nqy = -qy */
- MP_CHECKOK(group->meth->field_neg(qy, &nqy, group->meth));
- res = group->point_add(px, py, qx, &nqy, rx, ry, group);
- CLEANUP:
- mp_clear(&nqy);
- return res;
- }
- /* Computes R = 2P. Elliptic curve points P and R can be identical. Uses
- * affine coordinates. Assumes input is already field-encoded using
- * field_enc, and returns output that is still field-encoded. */
- mp_err
- ec_GFp_pt_dbl_aff(const mp_int *px, const mp_int *py, mp_int *rx,
- mp_int *ry, const ECGroup *group)
- {
- return ec_GFp_pt_add_aff(px, py, px, py, rx, ry, group);
- }
- /* by default, this routine is unused and thus doesn't need to be compiled */
- #ifdef ECL_ENABLE_GFP_PT_MUL_AFF
- /* Computes R = nP based on IEEE P1363 A.10.3. Elliptic curve points P and
- * R can be identical. Uses affine coordinates. Assumes input is already
- * field-encoded using field_enc, and returns output that is still
- * field-encoded. */
- mp_err
- ec_GFp_pt_mul_aff(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 k, k3, qx, qy, sx, sy;
- int b1, b3, i, l;
- MP_DIGITS(&k) = 0;
- MP_DIGITS(&k3) = 0;
- MP_DIGITS(&qx) = 0;
- MP_DIGITS(&qy) = 0;
- MP_DIGITS(&sx) = 0;
- MP_DIGITS(&sy) = 0;
- MP_CHECKOK(mp_init(&k));
- MP_CHECKOK(mp_init(&k3));
- MP_CHECKOK(mp_init(&qx));
- MP_CHECKOK(mp_init(&qy));
- MP_CHECKOK(mp_init(&sx));
- MP_CHECKOK(mp_init(&sy));
- /* if n = 0 then r = inf */
- if (mp_cmp_z(n) == 0) {
- mp_zero(rx);
- mp_zero(ry);
- res = MP_OKAY;
- goto CLEANUP;
- }
- /* Q = P, k = n */
- MP_CHECKOK(mp_copy(px, &qx));
- MP_CHECKOK(mp_copy(py, &qy));
- MP_CHECKOK(mp_copy(n, &k));
- /* if n < 0 then Q = -Q, k = -k */
- if (mp_cmp_z(n) < 0) {
- MP_CHECKOK(group->meth->field_neg(&qy, &qy, group->meth));
- MP_CHECKOK(mp_neg(&k, &k));
- }
- #ifdef ECL_DEBUG /* basic double and add method */
- l = mpl_significant_bits(&k) - 1;
- MP_CHECKOK(mp_copy(&qx, &sx));
- MP_CHECKOK(mp_copy(&qy, &sy));
- for (i = l - 1; i >= 0; i--) {
- /* S = 2S */
- MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group));
- /* if k_i = 1, then S = S + Q */
- if (mpl_get_bit(&k, i) != 0) {
- MP_CHECKOK(group->
- point_add(&sx, &sy, &qx, &qy, &sx, &sy, group));
- }
- }
- #else /* double and add/subtract method from
- * standard */
- /* k3 = 3 * k */
- MP_CHECKOK(mp_set_int(&k3, 3));
- MP_CHECKOK(mp_mul(&k, &k3, &k3));
- /* S = Q */
- MP_CHECKOK(mp_copy(&qx, &sx));
- MP_CHECKOK(mp_copy(&qy, &sy));
- /* l = index of high order bit in binary representation of 3*k */
- l = mpl_significant_bits(&k3) - 1;
- /* for i = l-1 downto 1 */
- for (i = l - 1; i >= 1; i--) {
- /* S = 2S */
- MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group));
- b3 = MP_GET_BIT(&k3, i);
- b1 = MP_GET_BIT(&k, i);
- /* if k3_i = 1 and k_i = 0, then S = S + Q */
- if ((b3 == 1) && (b1 == 0)) {
- MP_CHECKOK(group->
- point_add(&sx, &sy, &qx, &qy, &sx, &sy, group));
- /* if k3_i = 0 and k_i = 1, then S = S - Q */
- } else if ((b3 == 0) && (b1 == 1)) {
- MP_CHECKOK(group->
- point_sub(&sx, &sy, &qx, &qy, &sx, &sy, group));
- }
- }
- #endif
- /* output S */
- MP_CHECKOK(mp_copy(&sx, rx));
- MP_CHECKOK(mp_copy(&sy, ry));
- CLEANUP:
- mp_clear(&k);
- mp_clear(&k3);
- mp_clear(&qx);
- mp_clear(&qy);
- mp_clear(&sx);
- mp_clear(&sy);
- return res;
- }
- #endif
- /* Validates a point on a GFp curve. */
- mp_err
- ec_GFp_validate_point(const mp_int *px, const mp_int *py, const ECGroup *group)
- {
- mp_err res = MP_NO;
- mp_int accl, accr, tmp, pxt, pyt;
- MP_DIGITS(&accl) = 0;
- MP_DIGITS(&accr) = 0;
- MP_DIGITS(&tmp) = 0;
- MP_DIGITS(&pxt) = 0;
- MP_DIGITS(&pyt) = 0;
- MP_CHECKOK(mp_init(&accl));
- MP_CHECKOK(mp_init(&accr));
- MP_CHECKOK(mp_init(&tmp));
- MP_CHECKOK(mp_init(&pxt));
- MP_CHECKOK(mp_init(&pyt));
- /* 1: Verify that publicValue is not the point at infinity */
- if (ec_GFp_pt_is_inf_aff(px, py) == MP_YES) {
- res = MP_NO;
- goto CLEANUP;
- }
- /* 2: Verify that the coordinates of publicValue are elements
- * of the field.
- */
- if ((MP_SIGN(px) == MP_NEG) || (mp_cmp(px, &group->meth->irr) >= 0) ||
- (MP_SIGN(py) == MP_NEG) || (mp_cmp(py, &group->meth->irr) >= 0)) {
- res = MP_NO;
- goto CLEANUP;
- }
- /* 3: Verify that publicValue is on the curve. */
- if (group->meth->field_enc) {
- group->meth->field_enc(px, &pxt, group->meth);
- group->meth->field_enc(py, &pyt, group->meth);
- } else {
- mp_copy(px, &pxt);
- mp_copy(py, &pyt);
- }
- /* left-hand side: y^2 */
- MP_CHECKOK( group->meth->field_sqr(&pyt, &accl, group->meth) );
- /* right-hand side: x^3 + a*x + b */
- MP_CHECKOK( group->meth->field_sqr(&pxt, &tmp, group->meth) );
- MP_CHECKOK( group->meth->field_mul(&pxt, &tmp, &accr, group->meth) );
- MP_CHECKOK( group->meth->field_mul(&group->curvea, &pxt, &tmp, group->meth) );
- MP_CHECKOK( group->meth->field_add(&tmp, &accr, &accr, group->meth) );
- MP_CHECKOK( group->meth->field_add(&accr, &group->curveb, &accr, group->meth) );
- /* check LHS - RHS == 0 */
- MP_CHECKOK( group->meth->field_sub(&accl, &accr, &accr, group->meth) );
- if (mp_cmp_z(&accr) != 0) {
- res = MP_NO;
- goto CLEANUP;
- }
- /* 4: Verify that the order of the curve times the publicValue
- * is the point at infinity.
- */
- 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;
- }
- res = MP_YES;
- CLEANUP:
- mp_clear(&accl);
- mp_clear(&accr);
- mp_clear(&tmp);
- mp_clear(&pxt);
- mp_clear(&pyt);
- return res;
- }