| /* ********************************************************************* |
| * |
| * 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 |
| |
| #define ECP521_DIGITS ECL_CURVE_DIGITS(521) |
| |
| /* Fast modular reduction for p521 = 2^521 - 1. a can be r. Uses |
| * algorithm 2.31 from Hankerson, Menezes, Vanstone. Guide to |
| * Elliptic Curve Cryptography. */ |
| mp_err |
| ec_GFp_nistp521_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 m1; |
| |
| mp_digit s1[ECP521_DIGITS] = { 0 }; |
| |
| MP_SIGN(&m1) = MP_ZPOS; |
| MP_ALLOC(&m1) = ECP521_DIGITS; |
| MP_USED(&m1) = ECP521_DIGITS; |
| MP_DIGITS(&m1) = s1; |
| |
| if (a_bits < 521) { |
| if (a==r) return MP_OKAY; |
| return mp_copy(a, r); |
| } |
| /* for polynomials larger than twice the field size or polynomials |
| * not using all words, use regular reduction */ |
| if (a_bits > (521*2)) { |
| MP_CHECKOK(mp_mod(a, &meth->irr, r)); |
| } else { |
| #define FIRST_DIGIT (ECP521_DIGITS-1) |
| for (i = FIRST_DIGIT; i < MP_USED(a)-1; i++) { |
| s1[i-FIRST_DIGIT] = (MP_DIGIT(a, i) >> 9) |
| | (MP_DIGIT(a, 1+i) << (MP_DIGIT_BIT-9)); |
| } |
| s1[i-FIRST_DIGIT] = MP_DIGIT(a, i) >> 9; |
| |
| if ( a != r ) { |
| MP_CHECKOK(s_mp_pad(r,ECP521_DIGITS)); |
| for (i = 0; i < ECP521_DIGITS; i++) { |
| MP_DIGIT(r,i) = MP_DIGIT(a, i); |
| } |
| } |
| MP_USED(r) = ECP521_DIGITS; |
| MP_DIGIT(r,FIRST_DIGIT) &= 0x1FF; |
| |
| MP_CHECKOK(s_mp_add(r, &m1)); |
| if (MP_DIGIT(r, FIRST_DIGIT) & 0x200) { |
| MP_CHECKOK(s_mp_add_d(r,1)); |
| MP_DIGIT(r,FIRST_DIGIT) &= 0x1FF; |
| } |
| s_mp_clamp(r); |
| } |
| |
| CLEANUP: |
| return res; |
| } |
| |
| /* Compute the square of polynomial a, reduce modulo p521. Store the |
| * result in r. r could be a. Uses optimized modular reduction for p521. |
| */ |
| mp_err |
| ec_GFp_nistp521_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_nistp521_mod(r, r, meth)); |
| CLEANUP: |
| return res; |
| } |
| |
| /* Compute the product of two polynomials a and b, reduce modulo p521. |
| * Store the result in r. r could be a or b; a could be b. Uses |
| * optimized modular reduction for p521. */ |
| mp_err |
| ec_GFp_nistp521_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_nistp521_mod(r, r, meth)); |
| CLEANUP: |
| return res; |
| } |
| |
| /* Divides two field elements. If a is NULL, then returns the inverse of |
| * b. */ |
| mp_err |
| ec_GFp_nistp521_div(const mp_int *a, const mp_int *b, mp_int *r, |
| const GFMethod *meth) |
| { |
| mp_err res = MP_OKAY; |
| mp_int t; |
| |
| /* If a is NULL, then return the inverse of b, otherwise return a/b. */ |
| if (a == NULL) { |
| return mp_invmod(b, &meth->irr, r); |
| } else { |
| /* MPI doesn't support divmod, so we implement it using invmod and |
| * mulmod. */ |
| MP_CHECKOK(mp_init(&t, FLAG(b))); |
| MP_CHECKOK(mp_invmod(b, &meth->irr, &t)); |
| MP_CHECKOK(mp_mul(a, &t, r)); |
| MP_CHECKOK(ec_GFp_nistp521_mod(r, r, meth)); |
| CLEANUP: |
| mp_clear(&t); |
| return res; |
| } |
| } |
| |
| /* Wire in fast field arithmetic and precomputation of base point for |
| * named curves. */ |
| mp_err |
| ec_group_set_gfp521(ECGroup *group, ECCurveName name) |
| { |
| if (name == ECCurve_NIST_P521) { |
| group->meth->field_mod = &ec_GFp_nistp521_mod; |
| group->meth->field_mul = &ec_GFp_nistp521_mul; |
| group->meth->field_sqr = &ec_GFp_nistp521_sqr; |
| group->meth->field_div = &ec_GFp_nistp521_div; |
| } |
| return MP_OKAY; |
| } |
