| /* |
| * Copyright (c) 2007, 2011, 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. |
| * |
| * 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 |
| * |
| *********************************************************************** */ |
| |
| /* 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; |
| } |
| } |
