| /* ********************************************************************* |
| * |
| * 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. |
| * |
| * 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>, Sun Microsystems Laboratories |
| * |
| * 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" |
| |
| /* Uses Montgomery reduction for field arithmetic. See mpi/mpmontg.c for |
| * code implementation. */ |
| |
| #include "mpi.h" |
| #include "mplogic.h" |
| #include "mpi-priv.h" |
| #include "ecl-priv.h" |
| #include "ecp.h" |
| #ifndef _KERNEL |
| #include <stdlib.h> |
| #include <stdio.h> |
| #endif |
| |
| /* Construct a generic GFMethod for arithmetic over prime fields with |
| * irreducible irr. */ |
| GFMethod * |
| GFMethod_consGFp_mont(const mp_int *irr) |
| { |
| mp_err res = MP_OKAY; |
| int i; |
| GFMethod *meth = NULL; |
| mp_mont_modulus *mmm; |
| |
| meth = GFMethod_consGFp(irr); |
| if (meth == NULL) |
| return NULL; |
| |
| #ifdef _KERNEL |
| mmm = (mp_mont_modulus *) kmem_alloc(sizeof(mp_mont_modulus), |
| FLAG(irr)); |
| #else |
| mmm = (mp_mont_modulus *) malloc(sizeof(mp_mont_modulus)); |
| #endif |
| if (mmm == NULL) { |
| res = MP_MEM; |
| goto CLEANUP; |
| } |
| |
| meth->field_mul = &ec_GFp_mul_mont; |
| meth->field_sqr = &ec_GFp_sqr_mont; |
| meth->field_div = &ec_GFp_div_mont; |
| meth->field_enc = &ec_GFp_enc_mont; |
| meth->field_dec = &ec_GFp_dec_mont; |
| meth->extra1 = mmm; |
| meth->extra2 = NULL; |
| meth->extra_free = &ec_GFp_extra_free_mont; |
| |
| mmm->N = meth->irr; |
| i = mpl_significant_bits(&meth->irr); |
| i += MP_DIGIT_BIT - 1; |
| mmm->b = i - i % MP_DIGIT_BIT; |
| mmm->n0prime = 0 - s_mp_invmod_radix(MP_DIGIT(&meth->irr, 0)); |
| |
| CLEANUP: |
| if (res != MP_OKAY) { |
| GFMethod_free(meth); |
| return NULL; |
| } |
| return meth; |
| } |
| |
| /* Wrapper functions for generic prime field arithmetic. */ |
| |
| /* Field multiplication using Montgomery reduction. */ |
| mp_err |
| ec_GFp_mul_mont(const mp_int *a, const mp_int *b, mp_int *r, |
| const GFMethod *meth) |
| { |
| mp_err res = MP_OKAY; |
| |
| #ifdef MP_MONT_USE_MP_MUL |
| /* if MP_MONT_USE_MP_MUL is defined, then the function s_mp_mul_mont |
| * is not implemented and we have to use mp_mul and s_mp_redc directly |
| */ |
| MP_CHECKOK(mp_mul(a, b, r)); |
| MP_CHECKOK(s_mp_redc(r, (mp_mont_modulus *) meth->extra1)); |
| #else |
| mp_int s; |
| |
| MP_DIGITS(&s) = 0; |
| /* s_mp_mul_mont doesn't allow source and destination to be the same */ |
| if ((a == r) || (b == r)) { |
| MP_CHECKOK(mp_init(&s, FLAG(a))); |
| MP_CHECKOK(s_mp_mul_mont |
| (a, b, &s, (mp_mont_modulus *) meth->extra1)); |
| MP_CHECKOK(mp_copy(&s, r)); |
| mp_clear(&s); |
| } else { |
| return s_mp_mul_mont(a, b, r, (mp_mont_modulus *) meth->extra1); |
| } |
| #endif |
| CLEANUP: |
| return res; |
| } |
| |
| /* Field squaring using Montgomery reduction. */ |
| mp_err |
| ec_GFp_sqr_mont(const mp_int *a, mp_int *r, const GFMethod *meth) |
| { |
| return ec_GFp_mul_mont(a, a, r, meth); |
| } |
| |
| /* Field division using Montgomery reduction. */ |
| mp_err |
| ec_GFp_div_mont(const mp_int *a, const mp_int *b, mp_int *r, |
| const GFMethod *meth) |
| { |
| mp_err res = MP_OKAY; |
| |
| /* if A=aZ represents a encoded in montgomery coordinates with Z and # |
| * and \ respectively represent multiplication and division in |
| * montgomery coordinates, then A\B = (a/b)Z = (A/B)Z and Binv = |
| * (1/b)Z = (1/B)(Z^2) where B # Binv = Z */ |
| MP_CHECKOK(ec_GFp_div(a, b, r, meth)); |
| MP_CHECKOK(ec_GFp_enc_mont(r, r, meth)); |
| if (a == NULL) { |
| MP_CHECKOK(ec_GFp_enc_mont(r, r, meth)); |
| } |
| CLEANUP: |
| return res; |
| } |
| |
| /* Encode a field element in Montgomery form. See s_mp_to_mont in |
| * mpi/mpmontg.c */ |
| mp_err |
| ec_GFp_enc_mont(const mp_int *a, mp_int *r, const GFMethod *meth) |
| { |
| mp_mont_modulus *mmm; |
| mp_err res = MP_OKAY; |
| |
| mmm = (mp_mont_modulus *) meth->extra1; |
| MP_CHECKOK(mpl_lsh(a, r, mmm->b)); |
| MP_CHECKOK(mp_mod(r, &mmm->N, r)); |
| CLEANUP: |
| return res; |
| } |
| |
| /* Decode a field element from Montgomery form. */ |
| mp_err |
| ec_GFp_dec_mont(const mp_int *a, mp_int *r, const GFMethod *meth) |
| { |
| mp_err res = MP_OKAY; |
| |
| if (a != r) { |
| MP_CHECKOK(mp_copy(a, r)); |
| } |
| MP_CHECKOK(s_mp_redc(r, (mp_mont_modulus *) meth->extra1)); |
| CLEANUP: |
| return res; |
| } |
| |
| /* Free the memory allocated to the extra fields of Montgomery GFMethod |
| * object. */ |
| void |
| ec_GFp_extra_free_mont(GFMethod *meth) |
| { |
| if (meth->extra1 != NULL) { |
| #ifdef _KERNEL |
| kmem_free(meth->extra1, sizeof(mp_mont_modulus)); |
| #else |
| free(meth->extra1); |
| #endif |
| meth->extra1 = NULL; |
| } |
| } |
