andre@0: /* This Source Code Form is subject to the terms of the Mozilla Public
andre@0:  * License, v. 2.0. If a copy of the MPL was not distributed with this
andre@0:  * file, You can obtain one at http://mozilla.org/MPL/2.0/. */
andre@0: 
andre@0: /* Uses Montgomery reduction for field arithmetic.  See mpi/mpmontg.c for
andre@0:  * code implementation. */
andre@0: 
andre@0: #include "mpi.h"
andre@0: #include "mplogic.h"
andre@0: #include "mpi-priv.h"
andre@0: #include "ecl-priv.h"
andre@0: #include "ecp.h"
andre@0: #include <stdlib.h>
andre@0: #include <stdio.h>
andre@0: 
andre@0: /* Construct a generic GFMethod for arithmetic over prime fields with
andre@0:  * irreducible irr. */
andre@0: GFMethod *
andre@0: GFMethod_consGFp_mont(const mp_int *irr)
andre@0: {
andre@0: 	mp_err res = MP_OKAY;
andre@0: 	GFMethod *meth = NULL;
andre@0: 	mp_mont_modulus *mmm;
andre@0: 
andre@0: 	meth = GFMethod_consGFp(irr);
andre@0: 	if (meth == NULL)
andre@0: 		return NULL;
andre@0: 
andre@0: 	mmm = (mp_mont_modulus *) malloc(sizeof(mp_mont_modulus));
andre@0: 	if (mmm == NULL) {
andre@0: 		res = MP_MEM;
andre@0: 		goto CLEANUP;
andre@0: 	}
andre@0: 
andre@0: 	meth->field_mul = &ec_GFp_mul_mont;
andre@0: 	meth->field_sqr = &ec_GFp_sqr_mont;
andre@0: 	meth->field_div = &ec_GFp_div_mont;
andre@0: 	meth->field_enc = &ec_GFp_enc_mont;
andre@0: 	meth->field_dec = &ec_GFp_dec_mont;
andre@0: 	meth->extra1 = mmm;
andre@0: 	meth->extra2 = NULL;
andre@0: 	meth->extra_free = &ec_GFp_extra_free_mont;
andre@0: 
andre@0: 	mmm->N = meth->irr;
andre@0: 	mmm->n0prime = 0 - s_mp_invmod_radix(MP_DIGIT(&meth->irr, 0));
andre@0: 
andre@0:   CLEANUP:
andre@0: 	if (res != MP_OKAY) {
andre@0: 		GFMethod_free(meth);
andre@0: 		return NULL;
andre@0: 	}
andre@0: 	return meth;
andre@0: }
andre@0: 
andre@0: /* Wrapper functions for generic prime field arithmetic. */
andre@0: 
andre@0: /* Field multiplication using Montgomery reduction. */
andre@0: mp_err
andre@0: ec_GFp_mul_mont(const mp_int *a, const mp_int *b, mp_int *r,
andre@0: 				const GFMethod *meth)
andre@0: {
andre@0: 	mp_err res = MP_OKAY;
andre@0: 
andre@0: #ifdef MP_MONT_USE_MP_MUL
andre@0: 	/* if MP_MONT_USE_MP_MUL is defined, then the function s_mp_mul_mont
andre@0: 	 * is not implemented and we have to use mp_mul and s_mp_redc directly 
andre@0: 	 */
andre@0: 	MP_CHECKOK(mp_mul(a, b, r));
andre@0: 	MP_CHECKOK(s_mp_redc(r, (mp_mont_modulus *) meth->extra1));
andre@0: #else
andre@0: 	mp_int s;
andre@0: 
andre@0: 	MP_DIGITS(&s) = 0;
andre@0: 	/* s_mp_mul_mont doesn't allow source and destination to be the same */
andre@0: 	if ((a == r) || (b == r)) {
andre@0: 		MP_CHECKOK(mp_init(&s));
andre@0: 		MP_CHECKOK(s_mp_mul_mont
andre@0: 				   (a, b, &s, (mp_mont_modulus *) meth->extra1));
andre@0: 		MP_CHECKOK(mp_copy(&s, r));
andre@0: 		mp_clear(&s);
andre@0: 	} else {
andre@0: 		return s_mp_mul_mont(a, b, r, (mp_mont_modulus *) meth->extra1);
andre@0: 	}
andre@0: #endif
andre@0:   CLEANUP:
andre@0: 	return res;
andre@0: }
andre@0: 
andre@0: /* Field squaring using Montgomery reduction. */
andre@0: mp_err
andre@0: ec_GFp_sqr_mont(const mp_int *a, mp_int *r, const GFMethod *meth)
andre@0: {
andre@0: 	return ec_GFp_mul_mont(a, a, r, meth);
andre@0: }
andre@0: 
andre@0: /* Field division using Montgomery reduction. */
andre@0: mp_err
andre@0: ec_GFp_div_mont(const mp_int *a, const mp_int *b, mp_int *r,
andre@0: 				const GFMethod *meth)
andre@0: {
andre@0: 	mp_err res = MP_OKAY;
andre@0: 
andre@0: 	/* if A=aZ represents a encoded in montgomery coordinates with Z and # 
andre@0: 	 * and \ respectively represent multiplication and division in
andre@0: 	 * montgomery coordinates, then A\B = (a/b)Z = (A/B)Z and Binv =
andre@0: 	 * (1/b)Z = (1/B)(Z^2) where B # Binv = Z */
andre@0: 	MP_CHECKOK(ec_GFp_div(a, b, r, meth));
andre@0: 	MP_CHECKOK(ec_GFp_enc_mont(r, r, meth));
andre@0: 	if (a == NULL) {
andre@0: 		MP_CHECKOK(ec_GFp_enc_mont(r, r, meth));
andre@0: 	}
andre@0:   CLEANUP:
andre@0: 	return res;
andre@0: }
andre@0: 
andre@0: /* Encode a field element in Montgomery form. See s_mp_to_mont in
andre@0:  * mpi/mpmontg.c */
andre@0: mp_err
andre@0: ec_GFp_enc_mont(const mp_int *a, mp_int *r, const GFMethod *meth)
andre@0: {
andre@0: 	mp_mont_modulus *mmm;
andre@0: 	mp_err res = MP_OKAY;
andre@0: 
andre@0: 	mmm = (mp_mont_modulus *) meth->extra1;
andre@0: 	MP_CHECKOK(mp_copy(a, r));
andre@0: 	MP_CHECKOK(s_mp_lshd(r, MP_USED(&mmm->N)));
andre@0: 	MP_CHECKOK(mp_mod(r, &mmm->N, r));
andre@0:   CLEANUP:
andre@0: 	return res;
andre@0: }
andre@0: 
andre@0: /* Decode a field element from Montgomery form. */
andre@0: mp_err
andre@0: ec_GFp_dec_mont(const mp_int *a, mp_int *r, const GFMethod *meth)
andre@0: {
andre@0: 	mp_err res = MP_OKAY;
andre@0: 
andre@0: 	if (a != r) {
andre@0: 		MP_CHECKOK(mp_copy(a, r));
andre@0: 	}
andre@0: 	MP_CHECKOK(s_mp_redc(r, (mp_mont_modulus *) meth->extra1));
andre@0:   CLEANUP:
andre@0: 	return res;
andre@0: }
andre@0: 
andre@0: /* Free the memory allocated to the extra fields of Montgomery GFMethod
andre@0:  * object. */
andre@0: void
andre@0: ec_GFp_extra_free_mont(GFMethod *meth)
andre@0: {
andre@0: 	if (meth->extra1 != NULL) {
andre@0: 		free(meth->extra1);
andre@0: 		meth->extra1 = NULL;
andre@0: 	}
andre@0: }