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: #include "ecp.h"
andre@0: #include "mpi.h"
andre@0: #include "mplogic.h"
andre@0: #include "mpi-priv.h"
andre@0: 
andre@0: #define ECP521_DIGITS ECL_CURVE_DIGITS(521)
andre@0: 
andre@0: /* Fast modular reduction for p521 = 2^521 - 1.  a can be r. Uses
andre@0:  * algorithm 2.31 from Hankerson, Menezes, Vanstone. Guide to 
andre@0:  * Elliptic Curve Cryptography. */
andre@0: static mp_err
andre@0: ec_GFp_nistp521_mod(const mp_int *a, mp_int *r, const GFMethod *meth)
andre@0: {
andre@0: 	mp_err res = MP_OKAY;
andre@0: 	int a_bits = mpl_significant_bits(a);
andre@0: 	int i;
andre@0: 
andre@0: 	/* m1, m2 are statically-allocated mp_int of exactly the size we need */
andre@0: 	mp_int m1;
andre@0: 
andre@0: 	mp_digit s1[ECP521_DIGITS] = { 0 };
andre@0: 
andre@0: 	MP_SIGN(&m1) = MP_ZPOS;
andre@0: 	MP_ALLOC(&m1) = ECP521_DIGITS;
andre@0: 	MP_USED(&m1) = ECP521_DIGITS;
andre@0: 	MP_DIGITS(&m1) = s1;
andre@0: 
andre@0: 	if (a_bits < 521) {
andre@0: 		if (a==r) return MP_OKAY;
andre@0: 		return mp_copy(a, r);
andre@0: 	}
andre@0: 	/* for polynomials larger than twice the field size or polynomials 
andre@0: 	 * not using all words, use regular reduction */
andre@0: 	if (a_bits > (521*2)) {
andre@0: 		MP_CHECKOK(mp_mod(a, &meth->irr, r));
andre@0: 	} else {
andre@0: #define FIRST_DIGIT (ECP521_DIGITS-1)
andre@0: 		for (i = FIRST_DIGIT; i < MP_USED(a)-1; i++) {
andre@0: 			s1[i-FIRST_DIGIT] = (MP_DIGIT(a, i) >> 9) 
andre@0: 				| (MP_DIGIT(a, 1+i) << (MP_DIGIT_BIT-9));
andre@0: 		}
andre@0: 		s1[i-FIRST_DIGIT] = MP_DIGIT(a, i) >> 9;
andre@0: 
andre@0: 		if ( a != r ) {
andre@0: 			MP_CHECKOK(s_mp_pad(r,ECP521_DIGITS));
andre@0: 			for (i = 0; i < ECP521_DIGITS; i++) {
andre@0: 				MP_DIGIT(r,i) = MP_DIGIT(a, i);
andre@0: 			}
andre@0: 		}
andre@0: 		MP_USED(r) = ECP521_DIGITS;
andre@0: 		MP_DIGIT(r,FIRST_DIGIT) &=  0x1FF;
andre@0: 
andre@0: 		MP_CHECKOK(s_mp_add(r, &m1));
andre@0: 		if (MP_DIGIT(r, FIRST_DIGIT) & 0x200) {
andre@0: 			MP_CHECKOK(s_mp_add_d(r,1));
andre@0: 			MP_DIGIT(r,FIRST_DIGIT) &=  0x1FF;
andre@0: 		} else if (s_mp_cmp(r, &meth->irr) == 0) {
andre@0: 			mp_zero(r);
andre@0: 		}
andre@0: 		s_mp_clamp(r);
andre@0: 	}
andre@0: 
andre@0:   CLEANUP:
andre@0: 	return res;
andre@0: }
andre@0: 
andre@0: /* Compute the square of polynomial a, reduce modulo p521. Store the
andre@0:  * result in r.  r could be a.  Uses optimized modular reduction for p521. 
andre@0:  */
andre@0: static mp_err
andre@0: ec_GFp_nistp521_sqr(const mp_int *a, mp_int *r, const GFMethod *meth)
andre@0: {
andre@0: 	mp_err res = MP_OKAY;
andre@0: 
andre@0: 	MP_CHECKOK(mp_sqr(a, r));
andre@0: 	MP_CHECKOK(ec_GFp_nistp521_mod(r, r, meth));
andre@0:   CLEANUP:
andre@0: 	return res;
andre@0: }
andre@0: 
andre@0: /* Compute the product of two polynomials a and b, reduce modulo p521.
andre@0:  * Store the result in r.  r could be a or b; a could be b.  Uses
andre@0:  * optimized modular reduction for p521. */
andre@0: static mp_err
andre@0: ec_GFp_nistp521_mul(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: 	MP_CHECKOK(mp_mul(a, b, r));
andre@0: 	MP_CHECKOK(ec_GFp_nistp521_mod(r, r, meth));
andre@0:   CLEANUP:
andre@0: 	return res;
andre@0: }
andre@0: 
andre@0: /* Divides two field elements. If a is NULL, then returns the inverse of
andre@0:  * b. */
andre@0: static mp_err
andre@0: ec_GFp_nistp521_div(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: 	mp_int t;
andre@0: 
andre@0: 	/* If a is NULL, then return the inverse of b, otherwise return a/b. */
andre@0: 	if (a == NULL) {
andre@0: 		return mp_invmod(b, &meth->irr, r);
andre@0: 	} else {
andre@0: 		/* MPI doesn't support divmod, so we implement it using invmod and 
andre@0: 		 * mulmod. */
andre@0: 		MP_CHECKOK(mp_init(&t));
andre@0: 		MP_CHECKOK(mp_invmod(b, &meth->irr, &t));
andre@0: 		MP_CHECKOK(mp_mul(a, &t, r));
andre@0: 		MP_CHECKOK(ec_GFp_nistp521_mod(r, r, meth));
andre@0: 	  CLEANUP:
andre@0: 		mp_clear(&t);
andre@0: 		return res;
andre@0: 	}
andre@0: }
andre@0: 
andre@0: /* Wire in fast field arithmetic and precomputation of base point for
andre@0:  * named curves. */
andre@0: mp_err
andre@0: ec_group_set_gfp521(ECGroup *group, ECCurveName name)
andre@0: {
andre@0: 	if (name == ECCurve_NIST_P521) {
andre@0: 		group->meth->field_mod = &ec_GFp_nistp521_mod;
andre@0: 		group->meth->field_mul = &ec_GFp_nistp521_mul;
andre@0: 		group->meth->field_sqr = &ec_GFp_nistp521_sqr;
andre@0: 		group->meth->field_div = &ec_GFp_nistp521_div;
andre@0: 	}
andre@0: 	return MP_OKAY;
andre@0: }