| /* |
| * 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 |
| |
| /* 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, FLAG(px))); |
| MP_CHECKOK(mp_init(&temp, FLAG(px))); |
| MP_CHECKOK(mp_init(&tempx, FLAG(px))); |
| MP_CHECKOK(mp_init(&tempy, FLAG(px))); |
| /* 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, FLAG(px))); |
| /* 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, FLAG(px))); |
| MP_CHECKOK(mp_init(&accr, FLAG(px))); |
| MP_CHECKOK(mp_init(&tmp, FLAG(px))); |
| MP_CHECKOK(mp_init(&pxt, FLAG(px))); |
| MP_CHECKOK(mp_init(&pyt, FLAG(px))); |
| |
| /* 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. |
| */ |
| /* timing mitigation is not supported */ |
| MP_CHECKOK( ECPoint_mul(group, &group->order, px, py, &pxt, &pyt, /*timing*/ 0) ); |
| 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; |
| } |
