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``````/* This Source Code Form is subject to the terms of the Mozilla Public
`````` * License, v. 2.0. If a copy of the MPL was not distributed with this
`````` * file, You can obtain one at http://mozilla.org/MPL/2.0/. */
``````
``````#include "ecp.h"
``````#include "mpi.h"
``````#include "mplogic.h"
``````#include "mpi-priv.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. */
``````static 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;
``````		} else if (s_mp_cmp(r, &meth->irr) == 0) {
``````			mp_zero(r);
``````		}
``````		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.
`````` */
``````static 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. */
``````static 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. */
``````static 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;
``````}
``````