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 "ecl-priv.h"
andre@0: #include "mplogic.h"
andre@0: #include <stdlib.h>
andre@0: 
andre@0: #define MAX_SCRATCH 6
andre@0: 
andre@0: /* Computes R = 2P.  Elliptic curve points P and R can be identical.  Uses 
andre@0:  * Modified Jacobian coordinates.
andre@0:  *
andre@0:  * Assumes input is already field-encoded using field_enc, and returns 
andre@0:  * output that is still field-encoded.
andre@0:  *
andre@0:  */
andre@0: mp_err
andre@0: ec_GFp_pt_dbl_jm(const mp_int *px, const mp_int *py, const mp_int *pz,
andre@0: 				 const mp_int *paz4, mp_int *rx, mp_int *ry, mp_int *rz,
andre@0: 				 mp_int *raz4, mp_int scratch[], const ECGroup *group)
andre@0: {
andre@0: 	mp_err res = MP_OKAY;
andre@0: 	mp_int *t0, *t1, *M, *S;
andre@0: 
andre@0: 	t0 = &scratch[0];
andre@0: 	t1 = &scratch[1];
andre@0: 	M = &scratch[2];
andre@0: 	S = &scratch[3];
andre@0: 
andre@0: #if MAX_SCRATCH < 4
andre@0: #error "Scratch array defined too small "
andre@0: #endif
andre@0: 
andre@0: 	/* Check for point at infinity */
andre@0: 	if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {
andre@0: 		/* Set r = pt at infinity by setting rz = 0 */
andre@0: 
andre@0: 		MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, rz));
andre@0: 		goto CLEANUP;
andre@0: 	}
andre@0: 
andre@0: 	/* M = 3 (px^2) + a*(pz^4) */
andre@0: 	MP_CHECKOK(group->meth->field_sqr(px, t0, group->meth));
andre@0: 	MP_CHECKOK(group->meth->field_add(t0, t0, M, group->meth));
andre@0: 	MP_CHECKOK(group->meth->field_add(t0, M, t0, group->meth));
andre@0: 	MP_CHECKOK(group->meth->field_add(t0, paz4, M, group->meth));
andre@0: 
andre@0: 	/* rz = 2 * py * pz */
andre@0: 	MP_CHECKOK(group->meth->field_mul(py, pz, S, group->meth));
andre@0: 	MP_CHECKOK(group->meth->field_add(S, S, rz, group->meth));
andre@0: 
andre@0: 	/* t0 = 2y^2 , t1 = 8y^4 */
andre@0: 	MP_CHECKOK(group->meth->field_sqr(py, t0, group->meth));
andre@0: 	MP_CHECKOK(group->meth->field_add(t0, t0, t0, group->meth));
andre@0: 	MP_CHECKOK(group->meth->field_sqr(t0, t1, group->meth));
andre@0: 	MP_CHECKOK(group->meth->field_add(t1, t1, t1, group->meth));
andre@0: 
andre@0: 	/* S = 4 * px * py^2 = 2 * px * t0 */
andre@0: 	MP_CHECKOK(group->meth->field_mul(px, t0, S, group->meth));
andre@0: 	MP_CHECKOK(group->meth->field_add(S, S, S, group->meth));
andre@0: 
andre@0: 
andre@0: 	/* rx = M^2 - 2S */
andre@0: 	MP_CHECKOK(group->meth->field_sqr(M, rx, group->meth));
andre@0: 	MP_CHECKOK(group->meth->field_sub(rx, S, rx, group->meth));
andre@0: 	MP_CHECKOK(group->meth->field_sub(rx, S, rx, group->meth));
andre@0: 
andre@0: 	/* ry = M * (S - rx) - t1 */
andre@0: 	MP_CHECKOK(group->meth->field_sub(S, rx, S, group->meth));
andre@0: 	MP_CHECKOK(group->meth->field_mul(S, M, ry, group->meth));
andre@0: 	MP_CHECKOK(group->meth->field_sub(ry, t1, ry, group->meth));
andre@0: 
andre@0: 	/* ra*z^4 = 2*t1*(apz4) */
andre@0: 	MP_CHECKOK(group->meth->field_mul(paz4, t1, raz4, group->meth));
andre@0: 	MP_CHECKOK(group->meth->field_add(raz4, raz4, raz4, group->meth));
andre@0: 
andre@0: 
andre@0:   CLEANUP:
andre@0: 	return res;
andre@0: }
andre@0: 
andre@0: /* Computes R = P + Q where R is (rx, ry, rz), P is (px, py, pz) and Q is
andre@0:  * (qx, qy, 1).  Elliptic curve points P, Q, and R can all be identical.
andre@0:  * Uses mixed Modified_Jacobian-affine coordinates. Assumes input is
andre@0:  * already field-encoded using field_enc, and returns output that is still
andre@0:  * field-encoded. */
andre@0: mp_err
andre@0: ec_GFp_pt_add_jm_aff(const mp_int *px, const mp_int *py, const mp_int *pz,
andre@0: 					 const mp_int *paz4, const mp_int *qx,
andre@0: 					 const mp_int *qy, mp_int *rx, mp_int *ry, mp_int *rz,
andre@0: 					 mp_int *raz4, mp_int scratch[], const ECGroup *group)
andre@0: {
andre@0: 	mp_err res = MP_OKAY;
andre@0: 	mp_int *A, *B, *C, *D, *C2, *C3;
andre@0: 
andre@0: 	A = &scratch[0];
andre@0: 	B = &scratch[1];
andre@0: 	C = &scratch[2];
andre@0: 	D = &scratch[3];
andre@0: 	C2 = &scratch[4];
andre@0: 	C3 = &scratch[5];
andre@0: 
andre@0: #if MAX_SCRATCH < 6
andre@0: #error "Scratch array defined too small "
andre@0: #endif
andre@0: 
andre@0: 	/* If either P or Q is the point at infinity, then return the other
andre@0: 	 * point */
andre@0: 	if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {
andre@0: 		MP_CHECKOK(ec_GFp_pt_aff2jac(qx, qy, rx, ry, rz, group));
andre@0: 		MP_CHECKOK(group->meth->field_sqr(rz, raz4, group->meth));
andre@0: 		MP_CHECKOK(group->meth->field_sqr(raz4, raz4, group->meth));
andre@0: 		MP_CHECKOK(group->meth->
andre@0: 				   field_mul(raz4, &group->curvea, raz4, group->meth));
andre@0: 		goto CLEANUP;
andre@0: 	}
andre@0: 	if (ec_GFp_pt_is_inf_aff(qx, qy) == MP_YES) {
andre@0: 		MP_CHECKOK(mp_copy(px, rx));
andre@0: 		MP_CHECKOK(mp_copy(py, ry));
andre@0: 		MP_CHECKOK(mp_copy(pz, rz));
andre@0: 		MP_CHECKOK(mp_copy(paz4, raz4));
andre@0: 		goto CLEANUP;
andre@0: 	}
andre@0: 
andre@0: 	/* A = qx * pz^2, B = qy * pz^3 */
andre@0: 	MP_CHECKOK(group->meth->field_sqr(pz, A, group->meth));
andre@0: 	MP_CHECKOK(group->meth->field_mul(A, pz, B, group->meth));
andre@0: 	MP_CHECKOK(group->meth->field_mul(A, qx, A, group->meth));
andre@0: 	MP_CHECKOK(group->meth->field_mul(B, qy, B, group->meth));
andre@0: 
andre@0: 	/* C = A - px, D = B - py */
andre@0: 	MP_CHECKOK(group->meth->field_sub(A, px, C, group->meth));
andre@0: 	MP_CHECKOK(group->meth->field_sub(B, py, D, group->meth));
andre@0: 
andre@0: 	/* C2 = C^2, C3 = C^3 */
andre@0: 	MP_CHECKOK(group->meth->field_sqr(C, C2, group->meth));
andre@0: 	MP_CHECKOK(group->meth->field_mul(C, C2, C3, group->meth));
andre@0: 
andre@0: 	/* rz = pz * C */
andre@0: 	MP_CHECKOK(group->meth->field_mul(pz, C, rz, group->meth));
andre@0: 
andre@0: 	/* C = px * C^2 */
andre@0: 	MP_CHECKOK(group->meth->field_mul(px, C2, C, group->meth));
andre@0: 	/* A = D^2 */
andre@0: 	MP_CHECKOK(group->meth->field_sqr(D, A, group->meth));
andre@0: 
andre@0: 	/* rx = D^2 - (C^3 + 2 * (px * C^2)) */
andre@0: 	MP_CHECKOK(group->meth->field_add(C, C, rx, group->meth));
andre@0: 	MP_CHECKOK(group->meth->field_add(C3, rx, rx, group->meth));
andre@0: 	MP_CHECKOK(group->meth->field_sub(A, rx, rx, group->meth));
andre@0: 
andre@0: 	/* C3 = py * C^3 */
andre@0: 	MP_CHECKOK(group->meth->field_mul(py, C3, C3, group->meth));
andre@0: 
andre@0: 	/* ry = D * (px * C^2 - rx) - py * C^3 */
andre@0: 	MP_CHECKOK(group->meth->field_sub(C, rx, ry, group->meth));
andre@0: 	MP_CHECKOK(group->meth->field_mul(D, ry, ry, group->meth));
andre@0: 	MP_CHECKOK(group->meth->field_sub(ry, C3, ry, group->meth));
andre@0: 
andre@0: 	/* raz4 = a * rz^4 */
andre@0: 	MP_CHECKOK(group->meth->field_sqr(rz, raz4, group->meth));
andre@0: 	MP_CHECKOK(group->meth->field_sqr(raz4, raz4, group->meth));
andre@0: 	MP_CHECKOK(group->meth->
andre@0: 			   field_mul(raz4, &group->curvea, raz4, group->meth));
andre@0: CLEANUP:
andre@0: 	return res;
andre@0: }
andre@0: 
andre@0: /* Computes R = nP where R is (rx, ry) and P is the base point. Elliptic
andre@0:  * curve points P and R can be identical. Uses mixed Modified-Jacobian
andre@0:  * co-ordinates for doubling and Chudnovsky Jacobian coordinates for
andre@0:  * additions. Assumes input is already field-encoded using field_enc, and
andre@0:  * returns output that is still field-encoded. Uses 5-bit window NAF
andre@0:  * method (algorithm 11) for scalar-point multiplication from Brown,
andre@0:  * Hankerson, Lopez, Menezes. Software Implementation of the NIST Elliptic 
andre@0:  * Curves Over Prime Fields. */
andre@0: mp_err
andre@0: ec_GFp_pt_mul_jm_wNAF(const mp_int *n, const mp_int *px, const mp_int *py,
andre@0: 					  mp_int *rx, mp_int *ry, const ECGroup *group)
andre@0: {
andre@0: 	mp_err res = MP_OKAY;
andre@0: 	mp_int precomp[16][2], rz, tpx, tpy;
andre@0: 	mp_int raz4;
andre@0: 	mp_int scratch[MAX_SCRATCH];
andre@0: 	signed char *naf = NULL;
andre@0: 	int i, orderBitSize;
andre@0: 
andre@0: 	MP_DIGITS(&rz) = 0;
andre@0: 	MP_DIGITS(&raz4) = 0;
andre@0: 	MP_DIGITS(&tpx) = 0;
andre@0: 	MP_DIGITS(&tpy) = 0;
andre@0: 	for (i = 0; i < 16; i++) {
andre@0: 		MP_DIGITS(&precomp[i][0]) = 0;
andre@0: 		MP_DIGITS(&precomp[i][1]) = 0;
andre@0: 	}
andre@0: 	for (i = 0; i < MAX_SCRATCH; i++) {
andre@0: 		MP_DIGITS(&scratch[i]) = 0;
andre@0: 	}
andre@0: 
andre@0: 	ARGCHK(group != NULL, MP_BADARG);
andre@0: 	ARGCHK((n != NULL) && (px != NULL) && (py != NULL), MP_BADARG);
andre@0: 
andre@0: 	/* initialize precomputation table */
andre@0: 	MP_CHECKOK(mp_init(&tpx));
andre@0: 	MP_CHECKOK(mp_init(&tpy));;
andre@0: 	MP_CHECKOK(mp_init(&rz));
andre@0: 	MP_CHECKOK(mp_init(&raz4));
andre@0: 
andre@0: 	for (i = 0; i < 16; i++) {
andre@0: 		MP_CHECKOK(mp_init(&precomp[i][0]));
andre@0: 		MP_CHECKOK(mp_init(&precomp[i][1]));
andre@0: 	}
andre@0: 	for (i = 0; i < MAX_SCRATCH; i++) {
andre@0: 		MP_CHECKOK(mp_init(&scratch[i]));
andre@0: 	}
andre@0: 
andre@0: 	/* Set out[8] = P */
andre@0: 	MP_CHECKOK(mp_copy(px, &precomp[8][0]));
andre@0: 	MP_CHECKOK(mp_copy(py, &precomp[8][1]));
andre@0: 
andre@0: 	/* Set (tpx, tpy) = 2P */
andre@0: 	MP_CHECKOK(group->
andre@0: 			   point_dbl(&precomp[8][0], &precomp[8][1], &tpx, &tpy,
andre@0: 						 group));
andre@0: 
andre@0: 	/* Set 3P, 5P, ..., 15P */
andre@0: 	for (i = 8; i < 15; i++) {
andre@0: 		MP_CHECKOK(group->
andre@0: 				   point_add(&precomp[i][0], &precomp[i][1], &tpx, &tpy,
andre@0: 							 &precomp[i + 1][0], &precomp[i + 1][1],
andre@0: 							 group));
andre@0: 	}
andre@0: 
andre@0: 	/* Set -15P, -13P, ..., -P */
andre@0: 	for (i = 0; i < 8; i++) {
andre@0: 		MP_CHECKOK(mp_copy(&precomp[15 - i][0], &precomp[i][0]));
andre@0: 		MP_CHECKOK(group->meth->
andre@0: 				   field_neg(&precomp[15 - i][1], &precomp[i][1],
andre@0: 							 group->meth));
andre@0: 	}
andre@0: 
andre@0: 	/* R = inf */
andre@0: 	MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, &rz));
andre@0: 
andre@0: 	orderBitSize = mpl_significant_bits(&group->order);
andre@0: 
andre@0: 	/* Allocate memory for NAF */
andre@0: 	naf = (signed char *) malloc(sizeof(signed char) * (orderBitSize + 1));
andre@0: 	if (naf == NULL) {
andre@0: 		res = MP_MEM;
andre@0: 		goto CLEANUP;
andre@0: 	}
andre@0: 
andre@0: 	/* Compute 5NAF */
andre@0: 	ec_compute_wNAF(naf, orderBitSize, n, 5);
andre@0: 
andre@0: 	/* wNAF method */
andre@0: 	for (i = orderBitSize; i >= 0; i--) {
andre@0: 		/* R = 2R */
andre@0: 		ec_GFp_pt_dbl_jm(rx, ry, &rz, &raz4, rx, ry, &rz, 
andre@0: 					     &raz4, scratch, group);
andre@0: 		if (naf[i] != 0) {
andre@0: 			ec_GFp_pt_add_jm_aff(rx, ry, &rz, &raz4,
andre@0: 								 &precomp[(naf[i] + 15) / 2][0],
andre@0: 								 &precomp[(naf[i] + 15) / 2][1], rx, ry,
andre@0: 								 &rz, &raz4, scratch, group);
andre@0: 		}
andre@0: 	}
andre@0: 
andre@0: 	/* convert result S to affine coordinates */
andre@0: 	MP_CHECKOK(ec_GFp_pt_jac2aff(rx, ry, &rz, rx, ry, group));
andre@0: 
andre@0:   CLEANUP:
andre@0: 	for (i = 0; i < MAX_SCRATCH; i++) {
andre@0: 		mp_clear(&scratch[i]);
andre@0: 	}
andre@0: 	for (i = 0; i < 16; i++) {
andre@0: 		mp_clear(&precomp[i][0]);
andre@0: 		mp_clear(&precomp[i][1]);
andre@0: 	}
andre@0: 	mp_clear(&tpx);
andre@0: 	mp_clear(&tpy);
andre@0: 	mp_clear(&rz);
andre@0: 	mp_clear(&raz4);
andre@0: 	free(naf);
andre@0: 	return res;
andre@0: }