1 /* 2 * ***** BEGIN LICENSE BLOCK ***** 3 * Version: MPL 1.1/GPL 2.0/LGPL 2.1 4 * 5 * The contents of this file are subject to the Mozilla Public License Version 6 * 1.1 (the "License"); you may not use this file except in compliance with 7 * the License. You may obtain a copy of the License at 8 * http://www.mozilla.org/MPL/ 9 * 10 * Software distributed under the License is distributed on an "AS IS" basis, 11 * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License 12 * for the specific language governing rights and limitations under the 13 * License. 14 * 15 * The Original Code is the elliptic curve math library for prime field curves. 16 * 17 * The Initial Developer of the Original Code is 18 * Sun Microsystems, Inc. 19 * Portions created by the Initial Developer are Copyright (C) 2003 20 * the Initial Developer. All Rights Reserved. 21 * 22 * Contributor(s): 23 * Douglas Stebila <douglas@stebila.ca>, Sun Microsystems Laboratories 24 * 25 * Alternatively, the contents of this file may be used under the terms of 26 * either the GNU General Public License Version 2 or later (the "GPL"), or 27 * the GNU Lesser General Public License Version 2.1 or later (the "LGPL"), 28 * in which case the provisions of the GPL or the LGPL are applicable instead 29 * of those above. If you wish to allow use of your version of this file only 30 * under the terms of either the GPL or the LGPL, and not to allow others to 31 * use your version of this file under the terms of the MPL, indicate your 32 * decision by deleting the provisions above and replace them with the notice 33 * and other provisions required by the GPL or the LGPL. If you do not delete 34 * the provisions above, a recipient may use your version of this file under 35 * the terms of any one of the MPL, the GPL or the LGPL. 36 * 37 * ***** END LICENSE BLOCK ***** */ 38 /* 39 * Copyright 2007 Sun Microsystems, Inc. All rights reserved. 40 * Use is subject to license terms. 41 * 42 * Sun elects to use this software under the MPL license. 43 */ 44 45 #ifndef _ECP_H 46 #define _ECP_H 47 48 #pragma ident "%Z%%M% %I% %E% SMI" 49 50 #include "ecl-priv.h" 51 52 /* Checks if point P(px, py) is at infinity. Uses affine coordinates. */ 53 mp_err ec_GFp_pt_is_inf_aff(const mp_int *px, const mp_int *py); 54 55 /* Sets P(px, py) to be the point at infinity. Uses affine coordinates. */ 56 mp_err ec_GFp_pt_set_inf_aff(mp_int *px, mp_int *py); 57 58 /* Computes R = P + Q where R is (rx, ry), P is (px, py) and Q is (qx, 59 * qy). Uses affine coordinates. */ 60 mp_err ec_GFp_pt_add_aff(const mp_int *px, const mp_int *py, 61 const mp_int *qx, const mp_int *qy, mp_int *rx, 62 mp_int *ry, const ECGroup *group); 63 64 /* Computes R = P - Q. Uses affine coordinates. */ 65 mp_err ec_GFp_pt_sub_aff(const mp_int *px, const mp_int *py, 66 const mp_int *qx, const mp_int *qy, mp_int *rx, 67 mp_int *ry, const ECGroup *group); 68 69 /* Computes R = 2P. Uses affine coordinates. */ 70 mp_err ec_GFp_pt_dbl_aff(const mp_int *px, const mp_int *py, mp_int *rx, 71 mp_int *ry, const ECGroup *group); 72 73 /* Validates a point on a GFp curve. */ 74 mp_err ec_GFp_validate_point(const mp_int *px, const mp_int *py, const ECGroup *group); 75 76 #ifdef ECL_ENABLE_GFP_PT_MUL_AFF 77 /* Computes R = nP where R is (rx, ry) and P is (px, py). The parameters 78 * a, b and p are the elliptic curve coefficients and the prime that 79 * determines the field GFp. Uses affine coordinates. */ 80 mp_err ec_GFp_pt_mul_aff(const mp_int *n, const mp_int *px, 81 const mp_int *py, mp_int *rx, mp_int *ry, 82 const ECGroup *group); 83 #endif 84 85 /* Converts a point P(px, py) from affine coordinates to Jacobian 86 * projective coordinates R(rx, ry, rz). */ 87 mp_err ec_GFp_pt_aff2jac(const mp_int *px, const mp_int *py, mp_int *rx, 88 mp_int *ry, mp_int *rz, const ECGroup *group); 89 90 /* Converts a point P(px, py, pz) from Jacobian projective coordinates to 91 * affine coordinates R(rx, ry). */ 92 mp_err ec_GFp_pt_jac2aff(const mp_int *px, const mp_int *py, 93 const mp_int *pz, mp_int *rx, mp_int *ry, 94 const ECGroup *group); 95 96 /* Checks if point P(px, py, pz) is at infinity. Uses Jacobian 97 * coordinates. */ 98 mp_err ec_GFp_pt_is_inf_jac(const mp_int *px, const mp_int *py, 99 const mp_int *pz); 100 101 /* Sets P(px, py, pz) to be the point at infinity. Uses Jacobian 102 * coordinates. */ 103 mp_err ec_GFp_pt_set_inf_jac(mp_int *px, mp_int *py, mp_int *pz); 104 105 /* Computes R = P + Q where R is (rx, ry, rz), P is (px, py, pz) and Q is 106 * (qx, qy, qz). Uses Jacobian coordinates. */ 107 mp_err ec_GFp_pt_add_jac_aff(const mp_int *px, const mp_int *py, 108 const mp_int *pz, const mp_int *qx, 109 const mp_int *qy, mp_int *rx, mp_int *ry, 110 mp_int *rz, const ECGroup *group); 111 112 /* Computes R = 2P. Uses Jacobian coordinates. */ 113 mp_err ec_GFp_pt_dbl_jac(const mp_int *px, const mp_int *py, 114 const mp_int *pz, mp_int *rx, mp_int *ry, 115 mp_int *rz, const ECGroup *group); 116 117 #ifdef ECL_ENABLE_GFP_PT_MUL_JAC 118 /* Computes R = nP where R is (rx, ry) and P is (px, py). The parameters 119 * a, b and p are the elliptic curve coefficients and the prime that 120 * determines the field GFp. Uses Jacobian coordinates. */ 121 mp_err ec_GFp_pt_mul_jac(const mp_int *n, const mp_int *px, 122 const mp_int *py, mp_int *rx, mp_int *ry, 123 const ECGroup *group); 124 #endif 125 126 /* Computes R(x, y) = k1 * G + k2 * P(x, y), where G is the generator 127 * (base point) of the group of points on the elliptic curve. Allows k1 = 128 * NULL or { k2, P } = NULL. Implemented using mixed Jacobian-affine 129 * coordinates. Input and output values are assumed to be NOT 130 * field-encoded and are in affine form. */ 131 mp_err 132 ec_GFp_pts_mul_jac(const mp_int *k1, const mp_int *k2, const mp_int *px, 133 const mp_int *py, mp_int *rx, mp_int *ry, 134 const ECGroup *group); 135 136 /* Computes R = nP where R is (rx, ry) and P is the base point. Elliptic 137 * curve points P and R can be identical. Uses mixed Modified-Jacobian 138 * co-ordinates for doubling and Chudnovsky Jacobian coordinates for 139 * additions. Assumes input is already field-encoded using field_enc, and 140 * returns output that is still field-encoded. Uses 5-bit window NAF 141 * method (algorithm 11) for scalar-point multiplication from Brown, 142 * Hankerson, Lopez, Menezes. Software Implementation of the NIST Elliptic 143 * Curves Over Prime Fields. */ 144 mp_err 145 ec_GFp_pt_mul_jm_wNAF(const mp_int *n, const mp_int *px, const mp_int *py, 146 mp_int *rx, mp_int *ry, const ECGroup *group); 147 148 #endif /* _ECP_H */ 149