1 /* *********************************************************************
2 *
3 * Sun elects to have this file available under and governed by the
4 * Mozilla Public License Version 1.1 ("MPL") (see
5 * http://www.mozilla.org/MPL/ for full license text). For the avoidance
6 * of doubt and subject to the following, Sun also elects to allow
7 * licensees to use this file under the MPL, the GNU General Public
8 * License version 2 only or the Lesser General Public License version
9 * 2.1 only. Any references to the "GNU General Public License version 2
10 * or later" or "GPL" in the following shall be construed to mean the
11 * GNU General Public License version 2 only. Any references to the "GNU
12 * Lesser General Public License version 2.1 or later" or "LGPL" in the
13 * following shall be construed to mean the GNU Lesser General Public
14 * License version 2.1 only. However, the following notice accompanied
15 * the original version of this file:
16 *
17 * Version: MPL 1.1/GPL 2.0/LGPL 2.1
18 *
19 * The contents of this file are subject to the Mozilla Public License Version
20 * 1.1 (the "License"); you may not use this file except in compliance with
21 * the License. You may obtain a copy of the License at
22 * http://www.mozilla.org/MPL/
23 *
24 * Software distributed under the License is distributed on an "AS IS" basis,
25 * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
26 * for the specific language governing rights and limitations under the
27 * License.
28 *
29 * The Original Code is the elliptic curve math library for prime field curves.
30 *
31 * The Initial Developer of the Original Code is
32 * Sun Microsystems, Inc.
33 * Portions created by the Initial Developer are Copyright (C) 2003
34 * the Initial Developer. All Rights Reserved.
35 *
36 * Contributor(s):
37 * Douglas Stebila <douglas@stebila.ca>, Sun Microsystems Laboratories
38 *
39 * Alternatively, the contents of this file may be used under the terms of
40 * either the GNU General Public License Version 2 or later (the "GPL"), or
41 * the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
42 * in which case the provisions of the GPL or the LGPL are applicable instead
43 * of those above. If you wish to allow use of your version of this file only
44 * under the terms of either the GPL or the LGPL, and not to allow others to
45 * use your version of this file under the terms of the MPL, indicate your
46 * decision by deleting the provisions above and replace them with the notice
47 * and other provisions required by the GPL or the LGPL. If you do not delete
48 * the provisions above, a recipient may use your version of this file under
49 * the terms of any one of the MPL, the GPL or the LGPL.
50 *
51 *********************************************************************** */
52 /*
53 * Copyright (c) 2007, Oracle and/or its affiliates. All rights reserved.
54 * Use is subject to license terms.
55 */
56
57 #ifndef _ECP_H
58 #define _ECP_H
59
60 #include "ecl-priv.h"
61
62 /* Checks if point P(px, py) is at infinity. Uses affine coordinates. */
63 mp_err ec_GFp_pt_is_inf_aff(const mp_int *px, const mp_int *py);
64
65 /* Sets P(px, py) to be the point at infinity. Uses affine coordinates. */
66 mp_err ec_GFp_pt_set_inf_aff(mp_int *px, mp_int *py);
67
68 /* Computes R = P + Q where R is (rx, ry), P is (px, py) and Q is (qx,
69 * qy). Uses affine coordinates. */
70 mp_err ec_GFp_pt_add_aff(const mp_int *px, const mp_int *py,
71 const mp_int *qx, const mp_int *qy, mp_int *rx,
72 mp_int *ry, const ECGroup *group);
73
74 /* Computes R = P - Q. Uses affine coordinates. */
75 mp_err ec_GFp_pt_sub_aff(const mp_int *px, const mp_int *py,
76 const mp_int *qx, const mp_int *qy, mp_int *rx,
77 mp_int *ry, const ECGroup *group);
78
79 /* Computes R = 2P. Uses affine coordinates. */
80 mp_err ec_GFp_pt_dbl_aff(const mp_int *px, const mp_int *py, mp_int *rx,
81 mp_int *ry, const ECGroup *group);
82
83 /* Validates a point on a GFp curve. */
84 mp_err ec_GFp_validate_point(const mp_int *px, const mp_int *py, const ECGroup *group);
85
86 #ifdef ECL_ENABLE_GFP_PT_MUL_AFF
87 /* Computes R = nP where R is (rx, ry) and P is (px, py). The parameters
88 * a, b and p are the elliptic curve coefficients and the prime that
89 * determines the field GFp. Uses affine coordinates. */
90 mp_err ec_GFp_pt_mul_aff(const mp_int *n, const mp_int *px,
91 const mp_int *py, mp_int *rx, mp_int *ry,
92 const ECGroup *group);
93 #endif
94
95 /* Converts a point P(px, py) from affine coordinates to Jacobian
96 * projective coordinates R(rx, ry, rz). */
97 mp_err ec_GFp_pt_aff2jac(const mp_int *px, const mp_int *py, mp_int *rx,
98 mp_int *ry, mp_int *rz, const ECGroup *group);
99
100 /* Converts a point P(px, py, pz) from Jacobian projective coordinates to
101 * affine coordinates R(rx, ry). */
102 mp_err ec_GFp_pt_jac2aff(const mp_int *px, const mp_int *py,
103 const mp_int *pz, mp_int *rx, mp_int *ry,
104 const ECGroup *group);
105
106 /* Checks if point P(px, py, pz) is at infinity. Uses Jacobian
107 * coordinates. */
108 mp_err ec_GFp_pt_is_inf_jac(const mp_int *px, const mp_int *py,
109 const mp_int *pz);
110
111 /* Sets P(px, py, pz) to be the point at infinity. Uses Jacobian
112 * coordinates. */
113 mp_err ec_GFp_pt_set_inf_jac(mp_int *px, mp_int *py, mp_int *pz);
114
115 /* Computes R = P + Q where R is (rx, ry, rz), P is (px, py, pz) and Q is
116 * (qx, qy, qz). Uses Jacobian coordinates. */
117 mp_err ec_GFp_pt_add_jac_aff(const mp_int *px, const mp_int *py,
118 const mp_int *pz, const mp_int *qx,
119 const mp_int *qy, mp_int *rx, mp_int *ry,
120 mp_int *rz, const ECGroup *group);
121
122 /* Computes R = 2P. Uses Jacobian coordinates. */
123 mp_err ec_GFp_pt_dbl_jac(const mp_int *px, const mp_int *py,
124 const mp_int *pz, mp_int *rx, mp_int *ry,
125 mp_int *rz, const ECGroup *group);
126
127 #ifdef ECL_ENABLE_GFP_PT_MUL_JAC
128 /* Computes R = nP where R is (rx, ry) and P is (px, py). The parameters
129 * a, b and p are the elliptic curve coefficients and the prime that
130 * determines the field GFp. Uses Jacobian coordinates. */
131 mp_err ec_GFp_pt_mul_jac(const mp_int *n, const mp_int *px,
132 const mp_int *py, mp_int *rx, mp_int *ry,
133 const ECGroup *group);
134 #endif
135
136 /* Computes R(x, y) = k1 * G + k2 * P(x, y), where G is the generator
137 * (base point) of the group of points on the elliptic curve. Allows k1 =
138 * NULL or { k2, P } = NULL. Implemented using mixed Jacobian-affine
139 * coordinates. Input and output values are assumed to be NOT
140 * field-encoded and are in affine form. */
141 mp_err
142 ec_GFp_pts_mul_jac(const mp_int *k1, const mp_int *k2, const mp_int *px,
143 const mp_int *py, mp_int *rx, mp_int *ry,
144 const ECGroup *group);
145
146 /* Computes R = nP where R is (rx, ry) and P is the base point. Elliptic
147 * curve points P and R can be identical. Uses mixed Modified-Jacobian
148 * co-ordinates for doubling and Chudnovsky Jacobian coordinates for
149 * additions. Assumes input is already field-encoded using field_enc, and
150 * returns output that is still field-encoded. Uses 5-bit window NAF
151 * method (algorithm 11) for scalar-point multiplication from Brown,
152 * Hankerson, Lopez, Menezes. Software Implementation of the NIST Elliptic
153 * Curves Over Prime Fields. */
154 mp_err
155 ec_GFp_pt_mul_jm_wNAF(const mp_int *n, const mp_int *px, const mp_int *py,
156 mp_int *rx, mp_int *ry, const ECGroup *group);
157
158 #endif /* _ECP_H */