crypto/ecc/ecp_521.c

f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers/*
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * ***** BEGIN LICENSE BLOCK *****
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * Version: MPL 1.1/GPL 2.0/LGPL 2.1
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers *
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * The contents of this file are subject to the Mozilla Public License Version
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * 1.1 (the "License"); you may not use this file except in compliance with
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * the License. You may obtain a copy of the License at
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * http://www.mozilla.org/MPL/
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers *
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * Software distributed under the License is distributed on an "AS IS" basis,
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * for the specific language governing rights and limitations under the
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * License.
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers *
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * The Original Code is the elliptic curve math library for prime field curves.
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers *
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * The Initial Developer of the Original Code is
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * Sun Microsystems, Inc.
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * Portions created by the Initial Developer are Copyright (C) 2003
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * the Initial Developer. All Rights Reserved.
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers *
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * Contributor(s):
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers *   Douglas Stebila <douglas@stebila.ca>
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers *
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * Alternatively, the contents of this file may be used under the terms of
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * either the GNU General Public License Version 2 or later (the "GPL"), or
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * in which case the provisions of the GPL or the LGPL are applicable instead
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * of those above. If you wish to allow use of your version of this file only
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * under the terms of either the GPL or the LGPL, and not to allow others to
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * use your version of this file under the terms of the MPL, indicate your
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * decision by deleting the provisions above and replace them with the notice
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * and other provisions required by the GPL or the LGPL. If you do not delete
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * the provisions above, a recipient may use your version of this file under
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * the terms of any one of the MPL, the GPL or the LGPL.
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers *
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * ***** END LICENSE BLOCK ***** */
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers/*
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * Copyright 2007 Sun Microsystems, Inc.  All rights reserved.
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * Use is subject to license terms.
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers *
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * Sun elects to use this software under the MPL license.
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers */
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers#pragma ident   "%Z%%M% %I% %E% SMI"
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers#include "ecp.h"
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers#include "mpi.h"
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers#include "mplogic.h"
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers#include "mpi-priv.h"
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers#ifndef _KERNEL
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers#include <stdlib.h>
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers#endif
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers#define ECP521_DIGITS ECL_CURVE_DIGITS(521)
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers/* Fast modular reduction for p521 = 2^521 - 1.  a can be r. Uses
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * algorithm 2.31 from Hankerson, Menezes, Vanstone. Guide to
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * Elliptic Curve Cryptography. */
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowersmp_err
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowersec_GFp_nistp521_mod(const mp_int *a, mp_int *r, const GFMethod *meth)
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers{
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    mp_err res = MP_OKAY;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    int a_bits = mpl_significant_bits(a);
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    int i;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    /* m1, m2 are statically-allocated mp_int of exactly the size we need */
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    mp_int m1;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    mp_digit s1[ECP521_DIGITS] = { 0 };
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    MP_SIGN(&m1) = MP_ZPOS;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    MP_ALLOC(&m1) = ECP521_DIGITS;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    MP_USED(&m1) = ECP521_DIGITS;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    MP_DIGITS(&m1) = s1;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    if (a_bits < 521) {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        if (a==r) return MP_OKAY;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        return mp_copy(a, r);
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    }
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    /* for polynomials larger than twice the field size or polynomials
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers     * not using all words, use regular reduction */
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    if (a_bits > (521*2)) {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        MP_CHECKOK(mp_mod(a, &meth->irr, r));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    } else {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers#define FIRST_DIGIT (ECP521_DIGITS-1)
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        for (i = FIRST_DIGIT; i < MP_USED(a)-1; i++) {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers            s1[i-FIRST_DIGIT] = (MP_DIGIT(a, i) >> 9)
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers                | (MP_DIGIT(a, 1+i) << (MP_DIGIT_BIT-9));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        }
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        s1[i-FIRST_DIGIT] = MP_DIGIT(a, i) >> 9;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        if ( a != r ) {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers            MP_CHECKOK(s_mp_pad(r,ECP521_DIGITS));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers            for (i = 0; i < ECP521_DIGITS; i++) {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers                MP_DIGIT(r,i) = MP_DIGIT(a, i);
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers            }
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        }
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        MP_USED(r) = ECP521_DIGITS;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        MP_DIGIT(r,FIRST_DIGIT) &=  0x1FF;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        MP_CHECKOK(s_mp_add(r, &m1));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        if (MP_DIGIT(r, FIRST_DIGIT) & 0x200) {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers            MP_CHECKOK(s_mp_add_d(r,1));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers            MP_DIGIT(r,FIRST_DIGIT) &=  0x1FF;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        }
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        s_mp_clamp(r);
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    }
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers  CLEANUP:
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    return res;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers}
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers/* Compute the square of polynomial a, reduce modulo p521. Store the
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * result in r.  r could be a.  Uses optimized modular reduction for p521.
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers */
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowersmp_err
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowersec_GFp_nistp521_sqr(const mp_int *a, mp_int *r, const GFMethod *meth)
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers{
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    mp_err res = MP_OKAY;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    MP_CHECKOK(mp_sqr(a, r));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    MP_CHECKOK(ec_GFp_nistp521_mod(r, r, meth));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers  CLEANUP:
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    return res;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers}
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers/* Compute the product of two polynomials a and b, reduce modulo p521.
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * Store the result in r.  r could be a or b; a could be b.  Uses
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * optimized modular reduction for p521. */
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowersmp_err
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowersec_GFp_nistp521_mul(const mp_int *a, const mp_int *b, mp_int *r,
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers                    const GFMethod *meth)
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers{
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    mp_err res = MP_OKAY;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    MP_CHECKOK(mp_mul(a, b, r));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    MP_CHECKOK(ec_GFp_nistp521_mod(r, r, meth));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers  CLEANUP:
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    return res;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers}
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers/* Divides two field elements. If a is NULL, then returns the inverse of
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * b. */
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowersmp_err
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowersec_GFp_nistp521_div(const mp_int *a, const mp_int *b, mp_int *r,
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers           const GFMethod *meth)
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers{
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    mp_err res = MP_OKAY;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    mp_int t;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    /* If a is NULL, then return the inverse of b, otherwise return a/b. */
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    if (a == NULL) {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        return mp_invmod(b, &meth->irr, r);
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    } else {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        /* MPI doesn't support divmod, so we implement it using invmod and
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers         * mulmod. */
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        MP_CHECKOK(mp_init(&t, FLAG(b)));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        MP_CHECKOK(mp_invmod(b, &meth->irr, &t));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        MP_CHECKOK(mp_mul(a, &t, r));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        MP_CHECKOK(ec_GFp_nistp521_mod(r, r, meth));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers      CLEANUP:
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        mp_clear(&t);
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        return res;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    }
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers}
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers/* Wire in fast field arithmetic and precomputation of base point for
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * named curves. */
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowersmp_err
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowersec_group_set_gfp521(ECGroup *group, ECCurveName name)
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers{
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    if (name == ECCurve_NIST_P521) {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        group->meth->field_mod = &ec_GFp_nistp521_mod;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        group->meth->field_mul = &ec_GFp_nistp521_mul;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        group->meth->field_sqr = &ec_GFp_nistp521_sqr;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        group->meth->field_div = &ec_GFp_nistp521_div;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    }
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    return MP_OKAY;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers}