ec/impl/ecp_521.c

/*
 * 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 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>
 *
 *********************************************************************** */

#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);
        unsigned 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;
}