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 "mplogic.h"
andre@0: #include <stdlib.h>
andre@0: 
andre@0: /* Checks if point P(px, py) is at infinity.  Uses affine coordinates. */
andre@0: mp_err
andre@0: ec_GFp_pt_is_inf_aff(const mp_int *px, const mp_int *py)
andre@0: {
andre@0: 
andre@0: 	if ((mp_cmp_z(px) == 0) && (mp_cmp_z(py) == 0)) {
andre@0: 		return MP_YES;
andre@0: 	} else {
andre@0: 		return MP_NO;
andre@0: 	}
andre@0: 
andre@0: }
andre@0: 
andre@0: /* Sets P(px, py) to be the point at infinity.  Uses affine coordinates. */
andre@0: mp_err
andre@0: ec_GFp_pt_set_inf_aff(mp_int *px, mp_int *py)
andre@0: {
andre@0: 	mp_zero(px);
andre@0: 	mp_zero(py);
andre@0: 	return MP_OKAY;
andre@0: }
andre@0: 
andre@0: /* Computes R = P + Q based on IEEE P1363 A.10.1. Elliptic curve points P, 
andre@0:  * Q, and R can all be identical. Uses affine coordinates. Assumes input
andre@0:  * is already field-encoded using field_enc, and returns output that is
andre@0:  * still field-encoded. */
andre@0: mp_err
andre@0: ec_GFp_pt_add_aff(const mp_int *px, const mp_int *py, const mp_int *qx,
andre@0: 				  const mp_int *qy, mp_int *rx, mp_int *ry,
andre@0: 				  const ECGroup *group)
andre@0: {
andre@0: 	mp_err res = MP_OKAY;
andre@0: 	mp_int lambda, temp, tempx, tempy;
andre@0: 
andre@0: 	MP_DIGITS(&lambda) = 0;
andre@0: 	MP_DIGITS(&temp) = 0;
andre@0: 	MP_DIGITS(&tempx) = 0;
andre@0: 	MP_DIGITS(&tempy) = 0;
andre@0: 	MP_CHECKOK(mp_init(&lambda));
andre@0: 	MP_CHECKOK(mp_init(&temp));
andre@0: 	MP_CHECKOK(mp_init(&tempx));
andre@0: 	MP_CHECKOK(mp_init(&tempy));
andre@0: 	/* if P = inf, then R = Q */
andre@0: 	if (ec_GFp_pt_is_inf_aff(px, py) == 0) {
andre@0: 		MP_CHECKOK(mp_copy(qx, rx));
andre@0: 		MP_CHECKOK(mp_copy(qy, ry));
andre@0: 		res = MP_OKAY;
andre@0: 		goto CLEANUP;
andre@0: 	}
andre@0: 	/* if Q = inf, then R = P */
andre@0: 	if (ec_GFp_pt_is_inf_aff(qx, qy) == 0) {
andre@0: 		MP_CHECKOK(mp_copy(px, rx));
andre@0: 		MP_CHECKOK(mp_copy(py, ry));
andre@0: 		res = MP_OKAY;
andre@0: 		goto CLEANUP;
andre@0: 	}
andre@0: 	/* if px != qx, then lambda = (py-qy) / (px-qx) */
andre@0: 	if (mp_cmp(px, qx) != 0) {
andre@0: 		MP_CHECKOK(group->meth->field_sub(py, qy, &tempy, group->meth));
andre@0: 		MP_CHECKOK(group->meth->field_sub(px, qx, &tempx, group->meth));
andre@0: 		MP_CHECKOK(group->meth->
andre@0: 				   field_div(&tempy, &tempx, &lambda, group->meth));
andre@0: 	} else {
andre@0: 		/* if py != qy or qy = 0, then R = inf */
andre@0: 		if (((mp_cmp(py, qy) != 0)) || (mp_cmp_z(qy) == 0)) {
andre@0: 			mp_zero(rx);
andre@0: 			mp_zero(ry);
andre@0: 			res = MP_OKAY;
andre@0: 			goto CLEANUP;
andre@0: 		}
andre@0: 		/* lambda = (3qx^2+a) / (2qy) */
andre@0: 		MP_CHECKOK(group->meth->field_sqr(qx, &tempx, group->meth));
andre@0: 		MP_CHECKOK(mp_set_int(&temp, 3));
andre@0: 		if (group->meth->field_enc) {
andre@0: 			MP_CHECKOK(group->meth->field_enc(&temp, &temp, group->meth));
andre@0: 		}
andre@0: 		MP_CHECKOK(group->meth->
andre@0: 				   field_mul(&tempx, &temp, &tempx, group->meth));
andre@0: 		MP_CHECKOK(group->meth->
andre@0: 				   field_add(&tempx, &group->curvea, &tempx, group->meth));
andre@0: 		MP_CHECKOK(mp_set_int(&temp, 2));
andre@0: 		if (group->meth->field_enc) {
andre@0: 			MP_CHECKOK(group->meth->field_enc(&temp, &temp, group->meth));
andre@0: 		}
andre@0: 		MP_CHECKOK(group->meth->field_mul(qy, &temp, &tempy, group->meth));
andre@0: 		MP_CHECKOK(group->meth->
andre@0: 				   field_div(&tempx, &tempy, &lambda, group->meth));
andre@0: 	}
andre@0: 	/* rx = lambda^2 - px - qx */
andre@0: 	MP_CHECKOK(group->meth->field_sqr(&lambda, &tempx, group->meth));
andre@0: 	MP_CHECKOK(group->meth->field_sub(&tempx, px, &tempx, group->meth));
andre@0: 	MP_CHECKOK(group->meth->field_sub(&tempx, qx, &tempx, group->meth));
andre@0: 	/* ry = (x1-x2) * lambda - y1 */
andre@0: 	MP_CHECKOK(group->meth->field_sub(qx, &tempx, &tempy, group->meth));
andre@0: 	MP_CHECKOK(group->meth->
andre@0: 			   field_mul(&tempy, &lambda, &tempy, group->meth));
andre@0: 	MP_CHECKOK(group->meth->field_sub(&tempy, qy, &tempy, group->meth));
andre@0: 	MP_CHECKOK(mp_copy(&tempx, rx));
andre@0: 	MP_CHECKOK(mp_copy(&tempy, ry));
andre@0: 
andre@0:   CLEANUP:
andre@0: 	mp_clear(&lambda);
andre@0: 	mp_clear(&temp);
andre@0: 	mp_clear(&tempx);
andre@0: 	mp_clear(&tempy);
andre@0: 	return res;
andre@0: }
andre@0: 
andre@0: /* Computes R = P - Q. Elliptic curve points P, Q, and R can all be
andre@0:  * identical. Uses affine coordinates. Assumes input is already
andre@0:  * field-encoded using field_enc, and returns output that is still
andre@0:  * field-encoded. */
andre@0: mp_err
andre@0: ec_GFp_pt_sub_aff(const mp_int *px, const mp_int *py, const mp_int *qx,
andre@0: 				  const mp_int *qy, mp_int *rx, mp_int *ry,
andre@0: 				  const ECGroup *group)
andre@0: {
andre@0: 	mp_err res = MP_OKAY;
andre@0: 	mp_int nqy;
andre@0: 
andre@0: 	MP_DIGITS(&nqy) = 0;
andre@0: 	MP_CHECKOK(mp_init(&nqy));
andre@0: 	/* nqy = -qy */
andre@0: 	MP_CHECKOK(group->meth->field_neg(qy, &nqy, group->meth));
andre@0: 	res = group->point_add(px, py, qx, &nqy, rx, ry, group);
andre@0:   CLEANUP:
andre@0: 	mp_clear(&nqy);
andre@0: 	return res;
andre@0: }
andre@0: 
andre@0: /* Computes R = 2P. Elliptic curve points P and R can be identical. Uses
andre@0:  * affine coordinates. Assumes input is already field-encoded using
andre@0:  * field_enc, and returns output that is still field-encoded. */
andre@0: mp_err
andre@0: ec_GFp_pt_dbl_aff(const mp_int *px, const mp_int *py, mp_int *rx,
andre@0: 				  mp_int *ry, const ECGroup *group)
andre@0: {
andre@0: 	return ec_GFp_pt_add_aff(px, py, px, py, rx, ry, group);
andre@0: }
andre@0: 
andre@0: /* by default, this routine is unused and thus doesn't need to be compiled */
andre@0: #ifdef ECL_ENABLE_GFP_PT_MUL_AFF
andre@0: /* Computes R = nP based on IEEE P1363 A.10.3. Elliptic curve points P and 
andre@0:  * R can be identical. Uses affine coordinates. Assumes input is already
andre@0:  * field-encoded using field_enc, and returns output that is still
andre@0:  * field-encoded. */
andre@0: mp_err
andre@0: ec_GFp_pt_mul_aff(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 k, k3, qx, qy, sx, sy;
andre@0: 	int b1, b3, i, l;
andre@0: 
andre@0: 	MP_DIGITS(&k) = 0;
andre@0: 	MP_DIGITS(&k3) = 0;
andre@0: 	MP_DIGITS(&qx) = 0;
andre@0: 	MP_DIGITS(&qy) = 0;
andre@0: 	MP_DIGITS(&sx) = 0;
andre@0: 	MP_DIGITS(&sy) = 0;
andre@0: 	MP_CHECKOK(mp_init(&k));
andre@0: 	MP_CHECKOK(mp_init(&k3));
andre@0: 	MP_CHECKOK(mp_init(&qx));
andre@0: 	MP_CHECKOK(mp_init(&qy));
andre@0: 	MP_CHECKOK(mp_init(&sx));
andre@0: 	MP_CHECKOK(mp_init(&sy));
andre@0: 
andre@0: 	/* if n = 0 then r = inf */
andre@0: 	if (mp_cmp_z(n) == 0) {
andre@0: 		mp_zero(rx);
andre@0: 		mp_zero(ry);
andre@0: 		res = MP_OKAY;
andre@0: 		goto CLEANUP;
andre@0: 	}
andre@0: 	/* Q = P, k = n */
andre@0: 	MP_CHECKOK(mp_copy(px, &qx));
andre@0: 	MP_CHECKOK(mp_copy(py, &qy));
andre@0: 	MP_CHECKOK(mp_copy(n, &k));
andre@0: 	/* if n < 0 then Q = -Q, k = -k */
andre@0: 	if (mp_cmp_z(n) < 0) {
andre@0: 		MP_CHECKOK(group->meth->field_neg(&qy, &qy, group->meth));
andre@0: 		MP_CHECKOK(mp_neg(&k, &k));
andre@0: 	}
andre@0: #ifdef ECL_DEBUG				/* basic double and add method */
andre@0: 	l = mpl_significant_bits(&k) - 1;
andre@0: 	MP_CHECKOK(mp_copy(&qx, &sx));
andre@0: 	MP_CHECKOK(mp_copy(&qy, &sy));
andre@0: 	for (i = l - 1; i >= 0; i--) {
andre@0: 		/* S = 2S */
andre@0: 		MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group));
andre@0: 		/* if k_i = 1, then S = S + Q */
andre@0: 		if (mpl_get_bit(&k, i) != 0) {
andre@0: 			MP_CHECKOK(group->
andre@0: 					   point_add(&sx, &sy, &qx, &qy, &sx, &sy, group));
andre@0: 		}
andre@0: 	}
andre@0: #else							/* double and add/subtract method from
andre@0: 								 * standard */
andre@0: 	/* k3 = 3 * k */
andre@0: 	MP_CHECKOK(mp_set_int(&k3, 3));
andre@0: 	MP_CHECKOK(mp_mul(&k, &k3, &k3));
andre@0: 	/* S = Q */
andre@0: 	MP_CHECKOK(mp_copy(&qx, &sx));
andre@0: 	MP_CHECKOK(mp_copy(&qy, &sy));
andre@0: 	/* l = index of high order bit in binary representation of 3*k */
andre@0: 	l = mpl_significant_bits(&k3) - 1;
andre@0: 	/* for i = l-1 downto 1 */
andre@0: 	for (i = l - 1; i >= 1; i--) {
andre@0: 		/* S = 2S */
andre@0: 		MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group));
andre@0: 		b3 = MP_GET_BIT(&k3, i);
andre@0: 		b1 = MP_GET_BIT(&k, i);
andre@0: 		/* if k3_i = 1 and k_i = 0, then S = S + Q */
andre@0: 		if ((b3 == 1) && (b1 == 0)) {
andre@0: 			MP_CHECKOK(group->
andre@0: 					   point_add(&sx, &sy, &qx, &qy, &sx, &sy, group));
andre@0: 			/* if k3_i = 0 and k_i = 1, then S = S - Q */
andre@0: 		} else if ((b3 == 0) && (b1 == 1)) {
andre@0: 			MP_CHECKOK(group->
andre@0: 					   point_sub(&sx, &sy, &qx, &qy, &sx, &sy, group));
andre@0: 		}
andre@0: 	}
andre@0: #endif
andre@0: 	/* output S */
andre@0: 	MP_CHECKOK(mp_copy(&sx, rx));
andre@0: 	MP_CHECKOK(mp_copy(&sy, ry));
andre@0: 
andre@0:   CLEANUP:
andre@0: 	mp_clear(&k);
andre@0: 	mp_clear(&k3);
andre@0: 	mp_clear(&qx);
andre@0: 	mp_clear(&qy);
andre@0: 	mp_clear(&sx);
andre@0: 	mp_clear(&sy);
andre@0: 	return res;
andre@0: }
andre@0: #endif
andre@0: 
andre@0: /* Validates a point on a GFp curve. */
andre@0: mp_err 
andre@0: ec_GFp_validate_point(const mp_int *px, const mp_int *py, const ECGroup *group)
andre@0: {
andre@0: 	mp_err res = MP_NO;
andre@0: 	mp_int accl, accr, tmp, pxt, pyt;
andre@0: 
andre@0: 	MP_DIGITS(&accl) = 0;
andre@0: 	MP_DIGITS(&accr) = 0;
andre@0: 	MP_DIGITS(&tmp) = 0;
andre@0: 	MP_DIGITS(&pxt) = 0;
andre@0: 	MP_DIGITS(&pyt) = 0;
andre@0: 	MP_CHECKOK(mp_init(&accl));
andre@0: 	MP_CHECKOK(mp_init(&accr));
andre@0: 	MP_CHECKOK(mp_init(&tmp));
andre@0: 	MP_CHECKOK(mp_init(&pxt));
andre@0: 	MP_CHECKOK(mp_init(&pyt));
andre@0: 
andre@0:     /* 1: Verify that publicValue is not the point at infinity */
andre@0: 	if (ec_GFp_pt_is_inf_aff(px, py) == MP_YES) {
andre@0: 		res = MP_NO;
andre@0: 		goto CLEANUP;
andre@0: 	}
andre@0:     /* 2: Verify that the coordinates of publicValue are elements 
andre@0:      *    of the field.
andre@0:      */
andre@0: 	if ((MP_SIGN(px) == MP_NEG) || (mp_cmp(px, &group->meth->irr) >= 0) || 
andre@0: 		(MP_SIGN(py) == MP_NEG) || (mp_cmp(py, &group->meth->irr) >= 0)) {
andre@0: 		res = MP_NO;
andre@0: 		goto CLEANUP;
andre@0: 	}
andre@0:     /* 3: Verify that publicValue is on the curve. */
andre@0: 	if (group->meth->field_enc) {
andre@0: 		group->meth->field_enc(px, &pxt, group->meth);
andre@0: 		group->meth->field_enc(py, &pyt, group->meth);
andre@0: 	} else {
andre@0: 		mp_copy(px, &pxt);
andre@0: 		mp_copy(py, &pyt);
andre@0: 	}
andre@0: 	/* left-hand side: y^2  */
andre@0: 	MP_CHECKOK( group->meth->field_sqr(&pyt, &accl, group->meth) );
andre@0: 	/* right-hand side: x^3 + a*x + b = (x^2 + a)*x + b by Horner's rule */
andre@0: 	MP_CHECKOK( group->meth->field_sqr(&pxt, &tmp, group->meth) );
andre@0: 	MP_CHECKOK( group->meth->field_add(&tmp, &group->curvea, &tmp, group->meth) );
andre@0: 	MP_CHECKOK( group->meth->field_mul(&tmp, &pxt, &accr, group->meth) );
andre@0: 	MP_CHECKOK( group->meth->field_add(&accr, &group->curveb, &accr, group->meth) );
andre@0: 	/* check LHS - RHS == 0 */
andre@0: 	MP_CHECKOK( group->meth->field_sub(&accl, &accr, &accr, group->meth) );
andre@0: 	if (mp_cmp_z(&accr) != 0) {
andre@0: 		res = MP_NO;
andre@0: 		goto CLEANUP;
andre@0: 	}
andre@0:     /* 4: Verify that the order of the curve times the publicValue
andre@0:      *    is the point at infinity.
andre@0:      */
andre@0: 	MP_CHECKOK( ECPoint_mul(group, &group->order, px, py, &pxt, &pyt) );
andre@0: 	if (ec_GFp_pt_is_inf_aff(&pxt, &pyt) != MP_YES) {
andre@0: 		res = MP_NO;
andre@0: 		goto CLEANUP;
andre@0: 	}
andre@0: 
andre@0: 	res = MP_YES;
andre@0: 
andre@0: CLEANUP:
andre@0: 	mp_clear(&accl);
andre@0: 	mp_clear(&accr);
andre@0: 	mp_clear(&tmp);
andre@0: 	mp_clear(&pxt);
andre@0: 	mp_clear(&pyt);
andre@0: 	return res;
andre@0: }