| /* ********************************************************************* |
| * |
| * Sun elects to have this file available under and governed by the |
| * Mozilla Public License Version 1.1 ("MPL") (see |
| * http://www.mozilla.org/MPL/ for full license text). For the avoidance |
| * of doubt and subject to the following, Sun also elects to allow |
| * licensees to use this file under the MPL, the GNU General Public |
| * License version 2 only or the Lesser General Public License version |
| * 2.1 only. Any references to the "GNU General Public License version 2 |
| * or later" or "GPL" in the following shall be construed to mean the |
| * GNU General Public License version 2 only. Any references to the "GNU |
| * Lesser General Public License version 2.1 or later" or "LGPL" in the |
| * following shall be construed to mean the GNU Lesser General Public |
| * License version 2.1 only. However, the following notice accompanied |
| * the original version of this file: |
| * |
| * 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): |
| * Douglas Stebila <douglas@stebila.ca> |
| * |
| * 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. |
| * |
| *********************************************************************** */ |
| /* |
| * Copyright (c) 2007, Oracle and/or its affiliates. All rights reserved. |
| * Use is subject to license terms. |
| */ |
| |
| #pragma ident "%Z%%M% %I% %E% SMI" |
| |
| #include "ecp.h" |
| #include "mpi.h" |
| #include "mplogic.h" |
| #include "mpi-priv.h" |
| #ifndef _KERNEL |
| #include <stdlib.h> |
| #endif |
| |
| /* Fast modular reduction for p384 = 2^384 - 2^128 - 2^96 + 2^32 - 1. a can be r. |
| * Uses algorithm 2.30 from Hankerson, Menezes, Vanstone. Guide to |
| * Elliptic Curve Cryptography. */ |
| mp_err |
| ec_GFp_nistp384_mod(const mp_int *a, mp_int *r, const GFMethod *meth) |
| { |
| mp_err res = MP_OKAY; |
| int a_bits = mpl_significant_bits(a); |
| int i; |
| |
| /* m1, m2 are statically-allocated mp_int of exactly the size we need */ |
| mp_int m[10]; |
| |
| #ifdef ECL_THIRTY_TWO_BIT |
| mp_digit s[10][12]; |
| for (i = 0; i < 10; i++) { |
| MP_SIGN(&m[i]) = MP_ZPOS; |
| MP_ALLOC(&m[i]) = 12; |
| MP_USED(&m[i]) = 12; |
| MP_DIGITS(&m[i]) = s[i]; |
| } |
| #else |
| mp_digit s[10][6]; |
| for (i = 0; i < 10; i++) { |
| MP_SIGN(&m[i]) = MP_ZPOS; |
| MP_ALLOC(&m[i]) = 6; |
| MP_USED(&m[i]) = 6; |
| MP_DIGITS(&m[i]) = s[i]; |
| } |
| #endif |
| |
| #ifdef ECL_THIRTY_TWO_BIT |
| /* for polynomials larger than twice the field size or polynomials |
| * not using all words, use regular reduction */ |
| if ((a_bits > 768) || (a_bits <= 736)) { |
| MP_CHECKOK(mp_mod(a, &meth->irr, r)); |
| } else { |
| for (i = 0; i < 12; i++) { |
| s[0][i] = MP_DIGIT(a, i); |
| } |
| s[1][0] = 0; |
| s[1][1] = 0; |
| s[1][2] = 0; |
| s[1][3] = 0; |
| s[1][4] = MP_DIGIT(a, 21); |
| s[1][5] = MP_DIGIT(a, 22); |
| s[1][6] = MP_DIGIT(a, 23); |
| s[1][7] = 0; |
| s[1][8] = 0; |
| s[1][9] = 0; |
| s[1][10] = 0; |
| s[1][11] = 0; |
| for (i = 0; i < 12; i++) { |
| s[2][i] = MP_DIGIT(a, i+12); |
| } |
| s[3][0] = MP_DIGIT(a, 21); |
| s[3][1] = MP_DIGIT(a, 22); |
| s[3][2] = MP_DIGIT(a, 23); |
| for (i = 3; i < 12; i++) { |
| s[3][i] = MP_DIGIT(a, i+9); |
| } |
| s[4][0] = 0; |
| s[4][1] = MP_DIGIT(a, 23); |
| s[4][2] = 0; |
| s[4][3] = MP_DIGIT(a, 20); |
| for (i = 4; i < 12; i++) { |
| s[4][i] = MP_DIGIT(a, i+8); |
| } |
| s[5][0] = 0; |
| s[5][1] = 0; |
| s[5][2] = 0; |
| s[5][3] = 0; |
| s[5][4] = MP_DIGIT(a, 20); |
| s[5][5] = MP_DIGIT(a, 21); |
| s[5][6] = MP_DIGIT(a, 22); |
| s[5][7] = MP_DIGIT(a, 23); |
| s[5][8] = 0; |
| s[5][9] = 0; |
| s[5][10] = 0; |
| s[5][11] = 0; |
| s[6][0] = MP_DIGIT(a, 20); |
| s[6][1] = 0; |
| s[6][2] = 0; |
| s[6][3] = MP_DIGIT(a, 21); |
| s[6][4] = MP_DIGIT(a, 22); |
| s[6][5] = MP_DIGIT(a, 23); |
| s[6][6] = 0; |
| s[6][7] = 0; |
| s[6][8] = 0; |
| s[6][9] = 0; |
| s[6][10] = 0; |
| s[6][11] = 0; |
| s[7][0] = MP_DIGIT(a, 23); |
| for (i = 1; i < 12; i++) { |
| s[7][i] = MP_DIGIT(a, i+11); |
| } |
| s[8][0] = 0; |
| s[8][1] = MP_DIGIT(a, 20); |
| s[8][2] = MP_DIGIT(a, 21); |
| s[8][3] = MP_DIGIT(a, 22); |
| s[8][4] = MP_DIGIT(a, 23); |
| s[8][5] = 0; |
| s[8][6] = 0; |
| s[8][7] = 0; |
| s[8][8] = 0; |
| s[8][9] = 0; |
| s[8][10] = 0; |
| s[8][11] = 0; |
| s[9][0] = 0; |
| s[9][1] = 0; |
| s[9][2] = 0; |
| s[9][3] = MP_DIGIT(a, 23); |
| s[9][4] = MP_DIGIT(a, 23); |
| s[9][5] = 0; |
| s[9][6] = 0; |
| s[9][7] = 0; |
| s[9][8] = 0; |
| s[9][9] = 0; |
| s[9][10] = 0; |
| s[9][11] = 0; |
| |
| MP_CHECKOK(mp_add(&m[0], &m[1], r)); |
| MP_CHECKOK(mp_add(r, &m[1], r)); |
| MP_CHECKOK(mp_add(r, &m[2], r)); |
| MP_CHECKOK(mp_add(r, &m[3], r)); |
| MP_CHECKOK(mp_add(r, &m[4], r)); |
| MP_CHECKOK(mp_add(r, &m[5], r)); |
| MP_CHECKOK(mp_add(r, &m[6], r)); |
| MP_CHECKOK(mp_sub(r, &m[7], r)); |
| MP_CHECKOK(mp_sub(r, &m[8], r)); |
| MP_CHECKOK(mp_submod(r, &m[9], &meth->irr, r)); |
| s_mp_clamp(r); |
| } |
| #else |
| /* for polynomials larger than twice the field size or polynomials |
| * not using all words, use regular reduction */ |
| if ((a_bits > 768) || (a_bits <= 736)) { |
| MP_CHECKOK(mp_mod(a, &meth->irr, r)); |
| } else { |
| for (i = 0; i < 6; i++) { |
| s[0][i] = MP_DIGIT(a, i); |
| } |
| s[1][0] = 0; |
| s[1][1] = 0; |
| s[1][2] = (MP_DIGIT(a, 10) >> 32) | (MP_DIGIT(a, 11) << 32); |
| s[1][3] = MP_DIGIT(a, 11) >> 32; |
| s[1][4] = 0; |
| s[1][5] = 0; |
| for (i = 0; i < 6; i++) { |
| s[2][i] = MP_DIGIT(a, i+6); |
| } |
| s[3][0] = (MP_DIGIT(a, 10) >> 32) | (MP_DIGIT(a, 11) << 32); |
| s[3][1] = (MP_DIGIT(a, 11) >> 32) | (MP_DIGIT(a, 6) << 32); |
| for (i = 2; i < 6; i++) { |
| s[3][i] = (MP_DIGIT(a, i+4) >> 32) | (MP_DIGIT(a, i+5) << 32); |
| } |
| s[4][0] = (MP_DIGIT(a, 11) >> 32) << 32; |
| s[4][1] = MP_DIGIT(a, 10) << 32; |
| for (i = 2; i < 6; i++) { |
| s[4][i] = MP_DIGIT(a, i+4); |
| } |
| s[5][0] = 0; |
| s[5][1] = 0; |
| s[5][2] = MP_DIGIT(a, 10); |
| s[5][3] = MP_DIGIT(a, 11); |
| s[5][4] = 0; |
| s[5][5] = 0; |
| s[6][0] = (MP_DIGIT(a, 10) << 32) >> 32; |
| s[6][1] = (MP_DIGIT(a, 10) >> 32) << 32; |
| s[6][2] = MP_DIGIT(a, 11); |
| s[6][3] = 0; |
| s[6][4] = 0; |
| s[6][5] = 0; |
| s[7][0] = (MP_DIGIT(a, 11) >> 32) | (MP_DIGIT(a, 6) << 32); |
| for (i = 1; i < 6; i++) { |
| s[7][i] = (MP_DIGIT(a, i+5) >> 32) | (MP_DIGIT(a, i+6) << 32); |
| } |
| s[8][0] = MP_DIGIT(a, 10) << 32; |
| s[8][1] = (MP_DIGIT(a, 10) >> 32) | (MP_DIGIT(a, 11) << 32); |
| s[8][2] = MP_DIGIT(a, 11) >> 32; |
| s[8][3] = 0; |
| s[8][4] = 0; |
| s[8][5] = 0; |
| s[9][0] = 0; |
| s[9][1] = (MP_DIGIT(a, 11) >> 32) << 32; |
| s[9][2] = MP_DIGIT(a, 11) >> 32; |
| s[9][3] = 0; |
| s[9][4] = 0; |
| s[9][5] = 0; |
| |
| MP_CHECKOK(mp_add(&m[0], &m[1], r)); |
| MP_CHECKOK(mp_add(r, &m[1], r)); |
| MP_CHECKOK(mp_add(r, &m[2], r)); |
| MP_CHECKOK(mp_add(r, &m[3], r)); |
| MP_CHECKOK(mp_add(r, &m[4], r)); |
| MP_CHECKOK(mp_add(r, &m[5], r)); |
| MP_CHECKOK(mp_add(r, &m[6], r)); |
| MP_CHECKOK(mp_sub(r, &m[7], r)); |
| MP_CHECKOK(mp_sub(r, &m[8], r)); |
| MP_CHECKOK(mp_submod(r, &m[9], &meth->irr, r)); |
| s_mp_clamp(r); |
| } |
| #endif |
| |
| CLEANUP: |
| return res; |
| } |
| |
| /* Compute the square of polynomial a, reduce modulo p384. Store the |
| * result in r. r could be a. Uses optimized modular reduction for p384. |
| */ |
| mp_err |
| ec_GFp_nistp384_sqr(const mp_int *a, mp_int *r, const GFMethod *meth) |
| { |
| mp_err res = MP_OKAY; |
| |
| MP_CHECKOK(mp_sqr(a, r)); |
| MP_CHECKOK(ec_GFp_nistp384_mod(r, r, meth)); |
| CLEANUP: |
| return res; |
| } |
| |
| /* Compute the product of two polynomials a and b, reduce modulo p384. |
| * Store the result in r. r could be a or b; a could be b. Uses |
| * optimized modular reduction for p384. */ |
| mp_err |
| ec_GFp_nistp384_mul(const mp_int *a, const mp_int *b, mp_int *r, |
| const GFMethod *meth) |
| { |
| mp_err res = MP_OKAY; |
| |
| MP_CHECKOK(mp_mul(a, b, r)); |
| MP_CHECKOK(ec_GFp_nistp384_mod(r, r, meth)); |
| CLEANUP: |
| return res; |
| } |
| |
| /* Wire in fast field arithmetic and precomputation of base point for |
| * named curves. */ |
| mp_err |
| ec_group_set_gfp384(ECGroup *group, ECCurveName name) |
| { |
| if (name == ECCurve_NIST_P384) { |
| group->meth->field_mod = &ec_GFp_nistp384_mod; |
| group->meth->field_mul = &ec_GFp_nistp384_mul; |
| group->meth->field_sqr = &ec_GFp_nistp384_sqr; |
| } |
| return MP_OKAY; |
| } |
