| /* |
| * 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 binary polynomial 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. |
| * |
| * Last Modified Date from the Original Code: May 2017 |
| *********************************************************************** */ |
| |
| #include "ec2.h" |
| #include "mplogic.h" |
| #include "mp_gf2m.h" |
| #ifndef _KERNEL |
| #include <stdlib.h> |
| #endif |
| |
| /* Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery |
| * projective coordinates. Uses algorithm Mdouble in appendix of Lopez, J. |
| * and Dahab, R. "Fast multiplication on elliptic curves over GF(2^m) |
| * without precomputation". modified to not require precomputation of |
| * c=b^{2^{m-1}}. */ |
| static mp_err |
| gf2m_Mdouble(mp_int *x, mp_int *z, const ECGroup *group, int kmflag) |
| { |
| mp_err res = MP_OKAY; |
| mp_int t1; |
| |
| MP_DIGITS(&t1) = 0; |
| MP_CHECKOK(mp_init(&t1, kmflag)); |
| |
| MP_CHECKOK(group->meth->field_sqr(x, x, group->meth)); |
| MP_CHECKOK(group->meth->field_sqr(z, &t1, group->meth)); |
| MP_CHECKOK(group->meth->field_mul(x, &t1, z, group->meth)); |
| MP_CHECKOK(group->meth->field_sqr(x, x, group->meth)); |
| MP_CHECKOK(group->meth->field_sqr(&t1, &t1, group->meth)); |
| MP_CHECKOK(group->meth-> |
| field_mul(&group->curveb, &t1, &t1, group->meth)); |
| MP_CHECKOK(group->meth->field_add(x, &t1, x, group->meth)); |
| |
| CLEANUP: |
| mp_clear(&t1); |
| return res; |
| } |
| |
| /* Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in |
| * Montgomery projective coordinates. Uses algorithm Madd in appendix of |
| * Lopex, J. and Dahab, R. "Fast multiplication on elliptic curves over |
| * GF(2^m) without precomputation". */ |
| static mp_err |
| gf2m_Madd(const mp_int *x, mp_int *x1, mp_int *z1, mp_int *x2, mp_int *z2, |
| const ECGroup *group, int kmflag) |
| { |
| mp_err res = MP_OKAY; |
| mp_int t1, t2; |
| |
| MP_DIGITS(&t1) = 0; |
| MP_DIGITS(&t2) = 0; |
| MP_CHECKOK(mp_init(&t1, kmflag)); |
| MP_CHECKOK(mp_init(&t2, kmflag)); |
| |
| MP_CHECKOK(mp_copy(x, &t1)); |
| MP_CHECKOK(group->meth->field_mul(x1, z2, x1, group->meth)); |
| MP_CHECKOK(group->meth->field_mul(z1, x2, z1, group->meth)); |
| MP_CHECKOK(group->meth->field_mul(x1, z1, &t2, group->meth)); |
| MP_CHECKOK(group->meth->field_add(z1, x1, z1, group->meth)); |
| MP_CHECKOK(group->meth->field_sqr(z1, z1, group->meth)); |
| MP_CHECKOK(group->meth->field_mul(z1, &t1, x1, group->meth)); |
| MP_CHECKOK(group->meth->field_add(x1, &t2, x1, group->meth)); |
| |
| CLEANUP: |
| mp_clear(&t1); |
| mp_clear(&t2); |
| return res; |
| } |
| |
| /* Compute the x, y affine coordinates from the point (x1, z1) (x2, z2) |
| * using Montgomery point multiplication algorithm Mxy() in appendix of |
| * Lopex, J. and Dahab, R. "Fast multiplication on elliptic curves over |
| * GF(2^m) without precomputation". Returns: 0 on error 1 if return value |
| * should be the point at infinity 2 otherwise */ |
| static int |
| gf2m_Mxy(const mp_int *x, const mp_int *y, mp_int *x1, mp_int *z1, |
| mp_int *x2, mp_int *z2, const ECGroup *group) |
| { |
| mp_err res = MP_OKAY; |
| int ret = 0; |
| mp_int t3, t4, t5; |
| |
| MP_DIGITS(&t3) = 0; |
| MP_DIGITS(&t4) = 0; |
| MP_DIGITS(&t5) = 0; |
| MP_CHECKOK(mp_init(&t3, FLAG(x2))); |
| MP_CHECKOK(mp_init(&t4, FLAG(x2))); |
| MP_CHECKOK(mp_init(&t5, FLAG(x2))); |
| |
| if (mp_cmp_z(z1) == 0) { |
| mp_zero(x2); |
| mp_zero(z2); |
| ret = 1; |
| goto CLEANUP; |
| } |
| |
| if (mp_cmp_z(z2) == 0) { |
| MP_CHECKOK(mp_copy(x, x2)); |
| MP_CHECKOK(group->meth->field_add(x, y, z2, group->meth)); |
| ret = 2; |
| goto CLEANUP; |
| } |
| |
| MP_CHECKOK(mp_set_int(&t5, 1)); |
| if (group->meth->field_enc) { |
| MP_CHECKOK(group->meth->field_enc(&t5, &t5, group->meth)); |
| } |
| |
| MP_CHECKOK(group->meth->field_mul(z1, z2, &t3, group->meth)); |
| |
| MP_CHECKOK(group->meth->field_mul(z1, x, z1, group->meth)); |
| MP_CHECKOK(group->meth->field_add(z1, x1, z1, group->meth)); |
| MP_CHECKOK(group->meth->field_mul(z2, x, z2, group->meth)); |
| MP_CHECKOK(group->meth->field_mul(z2, x1, x1, group->meth)); |
| MP_CHECKOK(group->meth->field_add(z2, x2, z2, group->meth)); |
| |
| MP_CHECKOK(group->meth->field_mul(z2, z1, z2, group->meth)); |
| MP_CHECKOK(group->meth->field_sqr(x, &t4, group->meth)); |
| MP_CHECKOK(group->meth->field_add(&t4, y, &t4, group->meth)); |
| MP_CHECKOK(group->meth->field_mul(&t4, &t3, &t4, group->meth)); |
| MP_CHECKOK(group->meth->field_add(&t4, z2, &t4, group->meth)); |
| |
| MP_CHECKOK(group->meth->field_mul(&t3, x, &t3, group->meth)); |
| MP_CHECKOK(group->meth->field_div(&t5, &t3, &t3, group->meth)); |
| MP_CHECKOK(group->meth->field_mul(&t3, &t4, &t4, group->meth)); |
| MP_CHECKOK(group->meth->field_mul(x1, &t3, x2, group->meth)); |
| MP_CHECKOK(group->meth->field_add(x2, x, z2, group->meth)); |
| |
| MP_CHECKOK(group->meth->field_mul(z2, &t4, z2, group->meth)); |
| MP_CHECKOK(group->meth->field_add(z2, y, z2, group->meth)); |
| |
| ret = 2; |
| |
| CLEANUP: |
| mp_clear(&t3); |
| mp_clear(&t4); |
| mp_clear(&t5); |
| if (res == MP_OKAY) { |
| return ret; |
| } else { |
| return 0; |
| } |
| } |
| |
| /* Computes R = nP based on algorithm 2P of Lopex, J. and Dahab, R. "Fast |
| * multiplication on elliptic curves over GF(2^m) without |
| * precomputation". Elliptic curve points P and R can be identical. Uses |
| * Montgomery projective coordinates. The timing parameter is ignored |
| * because this algorithm resists timing attacks by default. */ |
| mp_err |
| ec_GF2m_pt_mul_mont(const mp_int *n, 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 x1, x2, z1, z2; |
| int i, j; |
| mp_digit top_bit, mask; |
| |
| MP_DIGITS(&x1) = 0; |
| MP_DIGITS(&x2) = 0; |
| MP_DIGITS(&z1) = 0; |
| MP_DIGITS(&z2) = 0; |
| MP_CHECKOK(mp_init(&x1, FLAG(n))); |
| MP_CHECKOK(mp_init(&x2, FLAG(n))); |
| MP_CHECKOK(mp_init(&z1, FLAG(n))); |
| MP_CHECKOK(mp_init(&z2, FLAG(n))); |
| |
| /* if result should be point at infinity */ |
| if ((mp_cmp_z(n) == 0) || (ec_GF2m_pt_is_inf_aff(px, py) == MP_YES)) { |
| MP_CHECKOK(ec_GF2m_pt_set_inf_aff(rx, ry)); |
| goto CLEANUP; |
| } |
| |
| MP_CHECKOK(mp_copy(px, &x1)); /* x1 = px */ |
| MP_CHECKOK(mp_set_int(&z1, 1)); /* z1 = 1 */ |
| MP_CHECKOK(group->meth->field_sqr(&x1, &z2, group->meth)); /* z2 = |
| * x1^2 = |
| * px^2 */ |
| MP_CHECKOK(group->meth->field_sqr(&z2, &x2, group->meth)); |
| MP_CHECKOK(group->meth->field_add(&x2, &group->curveb, &x2, group->meth)); /* x2 |
| * = |
| * px^4 |
| * + |
| * b |
| */ |
| |
| /* find top-most bit and go one past it */ |
| i = MP_USED(n) - 1; |
| j = MP_DIGIT_BIT - 1; |
| top_bit = 1; |
| top_bit <<= MP_DIGIT_BIT - 1; |
| mask = top_bit; |
| while (!(MP_DIGITS(n)[i] & mask)) { |
| mask >>= 1; |
| j--; |
| } |
| mask >>= 1; |
| j--; |
| |
| /* if top most bit was at word break, go to next word */ |
| if (!mask) { |
| i--; |
| j = MP_DIGIT_BIT - 1; |
| mask = top_bit; |
| } |
| |
| for (; i >= 0; i--) { |
| for (; j >= 0; j--) { |
| if (MP_DIGITS(n)[i] & mask) { |
| MP_CHECKOK(gf2m_Madd(px, &x1, &z1, &x2, &z2, group, FLAG(n))); |
| MP_CHECKOK(gf2m_Mdouble(&x2, &z2, group, FLAG(n))); |
| } else { |
| MP_CHECKOK(gf2m_Madd(px, &x2, &z2, &x1, &z1, group, FLAG(n))); |
| MP_CHECKOK(gf2m_Mdouble(&x1, &z1, group, FLAG(n))); |
| } |
| mask >>= 1; |
| } |
| j = MP_DIGIT_BIT - 1; |
| mask = top_bit; |
| } |
| |
| /* convert out of "projective" coordinates */ |
| i = gf2m_Mxy(px, py, &x1, &z1, &x2, &z2, group); |
| if (i == 0) { |
| res = MP_BADARG; |
| goto CLEANUP; |
| } else if (i == 1) { |
| MP_CHECKOK(ec_GF2m_pt_set_inf_aff(rx, ry)); |
| } else { |
| MP_CHECKOK(mp_copy(&x2, rx)); |
| MP_CHECKOK(mp_copy(&z2, ry)); |
| } |
| |
| CLEANUP: |
| mp_clear(&x1); |
| mp_clear(&x2); |
| mp_clear(&z1); |
| mp_clear(&z2); |
| return res; |
| } |
