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/*
* ***** BEGIN LICENSE BLOCK *****
* 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 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>
*
* 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.
*
* ***** END LICENSE BLOCK ***** */
#include "ecp.h"
#include "mpi.h"
#include "mplogic.h"
#include "mpi-priv.h"
#include <stdlib.h>
#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);
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));
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;
}
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