*

 *

 *

 *

 * 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;

}