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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 "ecl-priv.h"

 #include "mplogic.h"

 #include <stdlib.h>

 #define MAX_SCRATCH 6

 /* Computes R = 2P.  Elliptic curve points P and R can be identical.  Uses 

  * Modified Jacobian coordinates.

  *

  * Assumes input is already field-encoded using field_enc, and returns 

  * output that is still field-encoded.

  *

  */

 mp_err

 ec_GFp_pt_dbl_jm(const mp_int *px, const mp_int *py, const mp_int *pz,

 				 const mp_int *paz4, mp_int *rx, mp_int *ry, mp_int *rz,

 				 mp_int *raz4, mp_int scratch[], const ECGroup *group)

 {

 	mp_err res = MP_OKAY;

 	mp_int *t0, *t1, *M, *S;

 	t0 = &scratch[0];

 	t1 = &scratch[1];

 	M = &scratch[2];

 	S = &scratch[3];

 #if MAX_SCRATCH < 4

 #error "Scratch array defined too small "

 #endif

 	/* Check for point at infinity */

 	if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {

 		/* Set r = pt at infinity by setting rz = 0 */

 		MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, rz));

 		goto CLEANUP;

 	}

 	/* M = 3 (px^2) + a*(pz^4) */

 	MP_CHECKOK(group->meth->field_sqr(px, t0, group->meth));

 	MP_CHECKOK(group->meth->field_add(t0, t0, M, group->meth));

 	MP_CHECKOK(group->meth->field_add(t0, M, t0, group->meth));

 	MP_CHECKOK(group->meth->field_add(t0, paz4, M, group->meth));

 	/* rz = 2 * py * pz */

 	MP_CHECKOK(group->meth->field_mul(py, pz, S, group->meth));

 	MP_CHECKOK(group->meth->field_add(S, S, rz, group->meth));

 	/* t0 = 2y^2 , t1 = 8y^4 */

 	MP_CHECKOK(group->meth->field_sqr(py, t0, group->meth));

 	MP_CHECKOK(group->meth->field_add(t0, t0, t0, group->meth));

 	MP_CHECKOK(group->meth->field_sqr(t0, t1, group->meth));

 	MP_CHECKOK(group->meth->field_add(t1, t1, t1, group->meth));

 	/* S = 4 * px * py^2 = 2 * px * t0 */

 	MP_CHECKOK(group->meth->field_mul(px, t0, S, group->meth));

 	MP_CHECKOK(group->meth->field_add(S, S, S, group->meth));

 	/* rx = M^2 - 2S */

 	MP_CHECKOK(group->meth->field_sqr(M, rx, group->meth));

 	MP_CHECKOK(group->meth->field_sub(rx, S, rx, group->meth));

 	MP_CHECKOK(group->meth->field_sub(rx, S, rx, group->meth));

 	/* ry = M * (S - rx) - t1 */

 	MP_CHECKOK(group->meth->field_sub(S, rx, S, group->meth));

 	MP_CHECKOK(group->meth->field_mul(S, M, ry, group->meth));

 	MP_CHECKOK(group->meth->field_sub(ry, t1, ry, group->meth));

 	/* ra*z^4 = 2*t1*(apz4) */

 	MP_CHECKOK(group->meth->field_mul(paz4, t1, raz4, group->meth));

 	MP_CHECKOK(group->meth->field_add(raz4, raz4, raz4, group->meth));

   CLEANUP:

 	return res;

 }

 /* Computes R = P + Q where R is (rx, ry, rz), P is (px, py, pz) and Q is

  * (qx, qy, 1).  Elliptic curve points P, Q, and R can all be identical.

  * Uses mixed Modified_Jacobian-affine coordinates. Assumes input is

  * already field-encoded using field_enc, and returns output that is still

  * field-encoded. */

 mp_err

 ec_GFp_pt_add_jm_aff(const mp_int *px, const mp_int *py, const mp_int *pz,

 					 const mp_int *paz4, const mp_int *qx,

 					 const mp_int *qy, mp_int *rx, mp_int *ry, mp_int *rz,

 					 mp_int *raz4, mp_int scratch[], const ECGroup *group)

 {

 	mp_err res = MP_OKAY;

 	mp_int *A, *B, *C, *D, *C2, *C3;

 	A = &scratch[0];

 	B = &scratch[1];

 	C = &scratch[2];

 	D = &scratch[3];

 	C2 = &scratch[4];

 	C3 = &scratch[5];

 #if MAX_SCRATCH < 6

 #error "Scratch array defined too small "

 #endif

 	/* If either P or Q is the point at infinity, then return the other

 	 * point */

 	if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {

 		MP_CHECKOK(ec_GFp_pt_aff2jac(qx, qy, rx, ry, rz, group));

 		MP_CHECKOK(group->meth->field_sqr(rz, raz4, group->meth));

 		MP_CHECKOK(group->meth->field_sqr(raz4, raz4, group->meth));

 		MP_CHECKOK(group->meth->

 				   field_mul(raz4, &group->curvea, raz4, group->meth));

 		goto CLEANUP;

 	}

 	if (ec_GFp_pt_is_inf_aff(qx, qy) == MP_YES) {

 		MP_CHECKOK(mp_copy(px, rx));

 		MP_CHECKOK(mp_copy(py, ry));

 		MP_CHECKOK(mp_copy(pz, rz));

 		MP_CHECKOK(mp_copy(paz4, raz4));

 		goto CLEANUP;

 	}

 	/* A = qx * pz^2, B = qy * pz^3 */

 	MP_CHECKOK(group->meth->field_sqr(pz, A, group->meth));

 	MP_CHECKOK(group->meth->field_mul(A, pz, B, group->meth));

 	MP_CHECKOK(group->meth->field_mul(A, qx, A, group->meth));

 	MP_CHECKOK(group->meth->field_mul(B, qy, B, group->meth));

 	/* C = A - px, D = B - py */

 	MP_CHECKOK(group->meth->field_sub(A, px, C, group->meth));

 	MP_CHECKOK(group->meth->field_sub(B, py, D, group->meth));

 	/* C2 = C^2, C3 = C^3 */

 	MP_CHECKOK(group->meth->field_sqr(C, C2, group->meth));

 	MP_CHECKOK(group->meth->field_mul(C, C2, C3, group->meth));

 	/* rz = pz * C */

 	MP_CHECKOK(group->meth->field_mul(pz, C, rz, group->meth));

 	/* C = px * C^2 */

 	MP_CHECKOK(group->meth->field_mul(px, C2, C, group->meth));

 	/* A = D^2 */

 	MP_CHECKOK(group->meth->field_sqr(D, A, group->meth));

 	/* rx = D^2 - (C^3 + 2 * (px * C^2)) */

 	MP_CHECKOK(group->meth->field_add(C, C, rx, group->meth));

 	MP_CHECKOK(group->meth->field_add(C3, rx, rx, group->meth));

 	MP_CHECKOK(group->meth->field_sub(A, rx, rx, group->meth));

 	/* C3 = py * C^3 */

 	MP_CHECKOK(group->meth->field_mul(py, C3, C3, group->meth));

 	/* ry = D * (px * C^2 - rx) - py * C^3 */

 	MP_CHECKOK(group->meth->field_sub(C, rx, ry, group->meth));

 	MP_CHECKOK(group->meth->field_mul(D, ry, ry, group->meth));

 	MP_CHECKOK(group->meth->field_sub(ry, C3, ry, group->meth));

 	/* raz4 = a * rz^4 */

 	MP_CHECKOK(group->meth->field_sqr(rz, raz4, group->meth));

 	MP_CHECKOK(group->meth->field_sqr(raz4, raz4, group->meth));

 	MP_CHECKOK(group->meth->

 			   field_mul(raz4, &group->curvea, raz4, group->meth));

 CLEANUP:

 	return res;

 }

 /* Computes R = nP where R is (rx, ry) and P is the base point. Elliptic

  * curve points P and R can be identical. Uses mixed Modified-Jacobian

  * co-ordinates for doubling and Chudnovsky Jacobian coordinates for

  * additions. Assumes input is already field-encoded using field_enc, and

  * returns output that is still field-encoded. Uses 5-bit window NAF

  * method (algorithm 11) for scalar-point multiplication from Brown,

  * Hankerson, Lopez, Menezes. Software Implementation of the NIST Elliptic 

  * Curves Over Prime Fields. */

 mp_err

 ec_GFp_pt_mul_jm_wNAF(const mp_int *n, const mp_int *px, const mp_int *py,

 					  mp_int *rx, mp_int *ry, const ECGroup *group)

 {

 	mp_err res = MP_OKAY;

 	mp_int precomp[16][2], rz, tpx, tpy;

 	mp_int raz4;

 	mp_int scratch[MAX_SCRATCH];

 	signed char *naf = NULL;

 	int i, orderBitSize;

 	MP_DIGITS(&rz) = 0;

 	MP_DIGITS(&raz4) = 0;

 	MP_DIGITS(&tpx) = 0;

 	MP_DIGITS(&tpy) = 0;

 	for (i = 0; i < 16; i++) {

 		MP_DIGITS(&precomp[i][0]) = 0;

 		MP_DIGITS(&precomp[i][1]) = 0;

 	}

 	for (i = 0; i < MAX_SCRATCH; i++) {

 		MP_DIGITS(&scratch[i]) = 0;

 	}

 	ARGCHK(group != NULL, MP_BADARG);

 	ARGCHK((n != NULL) && (px != NULL) && (py != NULL), MP_BADARG);

 	/* initialize precomputation table */

 	MP_CHECKOK(mp_init(&tpx));

 	MP_CHECKOK(mp_init(&tpy));;

 	MP_CHECKOK(mp_init(&rz));

 	MP_CHECKOK(mp_init(&raz4));

 	for (i = 0; i < 16; i++) {

 		MP_CHECKOK(mp_init(&precomp[i][0]));

 		MP_CHECKOK(mp_init(&precomp[i][1]));

 	}

 	for (i = 0; i < MAX_SCRATCH; i++) {

 		MP_CHECKOK(mp_init(&scratch[i]));

 	}

 	/* Set out[8] = P */

 	MP_CHECKOK(mp_copy(px, &precomp[8][0]));

 	MP_CHECKOK(mp_copy(py, &precomp[8][1]));

 	/* Set (tpx, tpy) = 2P */

 	MP_CHECKOK(group->

 			   point_dbl(&precomp[8][0], &precomp[8][1], &tpx, &tpy,

 						 group));

 	/* Set 3P, 5P, ..., 15P */

 	for (i = 8; i < 15; i++) {

 		MP_CHECKOK(group->

 				   point_add(&precomp[i][0], &precomp[i][1], &tpx, &tpy,

 							 &precomp[i + 1][0], &precomp[i + 1][1],

 							 group));

 	}

 	/* Set -15P, -13P, ..., -P */

 	for (i = 0; i < 8; i++) {

 		MP_CHECKOK(mp_copy(&precomp[15 - i][0], &precomp[i][0]));

 		MP_CHECKOK(group->meth->

 				   field_neg(&precomp[15 - i][1], &precomp[i][1],

 							 group->meth));

 	}

 	/* R = inf */

 	MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, &rz));

 	orderBitSize = mpl_significant_bits(&group->order);

 	/* Allocate memory for NAF */

 	naf = (signed char *) malloc(sizeof(signed char) * (orderBitSize + 1));

 	if (naf == NULL) {

 		res = MP_MEM;

 		goto CLEANUP;

 	}

 	/* Compute 5NAF */

 	ec_compute_wNAF(naf, orderBitSize, n, 5);

 	/* wNAF method */

 	for (i = orderBitSize; i >= 0; i--) {

 		/* R = 2R */

 		ec_GFp_pt_dbl_jm(rx, ry, &rz, &raz4, rx, ry, &rz, 

 					     &raz4, scratch, group);

 		if (naf[i] != 0) {

 			ec_GFp_pt_add_jm_aff(rx, ry, &rz, &raz4,

 								 &precomp[(naf[i] + 15) / 2][0],

 								 &precomp[(naf[i] + 15) / 2][1], rx, ry,

 								 &rz, &raz4, scratch, group);

 		}

 	}

 	/* convert result S to affine coordinates */

 	MP_CHECKOK(ec_GFp_pt_jac2aff(rx, ry, &rz, rx, ry, group));

   CLEANUP:

 	for (i = 0; i < MAX_SCRATCH; i++) {

 		mp_clear(&scratch[i]);

 	}

 	for (i = 0; i < 16; i++) {

 		mp_clear(&precomp[i][0]);

 		mp_clear(&precomp[i][1]);

 	}

 	mp_clear(&tpx);

 	mp_clear(&tpy);

 	mp_clear(&rz);

 	mp_clear(&raz4);

 	free(naf);

 	return res;

 }