1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
|
/* 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/. */
#ifndef __ecp_h_
#define __ecp_h_
#include "ecl-priv.h"
/* Checks if point P(px, py) is at infinity. Uses affine coordinates. */
mp_err ec_GFp_pt_is_inf_aff(const mp_int *px, const mp_int *py);
/* Sets P(px, py) to be the point at infinity. Uses affine coordinates. */
mp_err ec_GFp_pt_set_inf_aff(mp_int *px, mp_int *py);
/* Computes R = P + Q where R is (rx, ry), P is (px, py) and Q is (qx,
* qy). Uses affine coordinates. */
mp_err ec_GFp_pt_add_aff(const mp_int *px, const mp_int *py,
const mp_int *qx, const mp_int *qy, mp_int *rx,
mp_int *ry, const ECGroup *group);
/* Computes R = P - Q. Uses affine coordinates. */
mp_err ec_GFp_pt_sub_aff(const mp_int *px, const mp_int *py,
const mp_int *qx, const mp_int *qy, mp_int *rx,
mp_int *ry, const ECGroup *group);
/* Computes R = 2P. Uses affine coordinates. */
mp_err ec_GFp_pt_dbl_aff(const mp_int *px, const mp_int *py, mp_int *rx,
mp_int *ry, const ECGroup *group);
/* Validates a point on a GFp curve. */
mp_err ec_GFp_validate_point(const mp_int *px, const mp_int *py, const ECGroup *group);
#ifdef ECL_ENABLE_GFP_PT_MUL_AFF
/* Computes R = nP where R is (rx, ry) and P is (px, py). The parameters
* a, b and p are the elliptic curve coefficients and the prime that
* determines the field GFp. Uses affine coordinates. */
mp_err ec_GFp_pt_mul_aff(const mp_int *n, const mp_int *px,
const mp_int *py, mp_int *rx, mp_int *ry,
const ECGroup *group);
#endif
/* Converts a point P(px, py) from affine coordinates to Jacobian
* projective coordinates R(rx, ry, rz). */
mp_err ec_GFp_pt_aff2jac(const mp_int *px, const mp_int *py, mp_int *rx,
mp_int *ry, mp_int *rz, const ECGroup *group);
/* Converts a point P(px, py, pz) from Jacobian projective coordinates to
* affine coordinates R(rx, ry). */
mp_err ec_GFp_pt_jac2aff(const mp_int *px, const mp_int *py,
const mp_int *pz, mp_int *rx, mp_int *ry,
const ECGroup *group);
/* Checks if point P(px, py, pz) is at infinity. Uses Jacobian
* coordinates. */
mp_err ec_GFp_pt_is_inf_jac(const mp_int *px, const mp_int *py,
const mp_int *pz);
/* Sets P(px, py, pz) to be the point at infinity. Uses Jacobian
* coordinates. */
mp_err ec_GFp_pt_set_inf_jac(mp_int *px, mp_int *py, mp_int *pz);
/* Computes R = P + Q where R is (rx, ry, rz), P is (px, py, pz) and Q is
* (qx, qy, qz). Uses Jacobian coordinates. */
mp_err ec_GFp_pt_add_jac_aff(const mp_int *px, const mp_int *py,
const mp_int *pz, const mp_int *qx,
const mp_int *qy, mp_int *rx, mp_int *ry,
mp_int *rz, const ECGroup *group);
/* Computes R = 2P. Uses Jacobian coordinates. */
mp_err ec_GFp_pt_dbl_jac(const mp_int *px, const mp_int *py,
const mp_int *pz, mp_int *rx, mp_int *ry,
mp_int *rz, const ECGroup *group);
#ifdef ECL_ENABLE_GFP_PT_MUL_JAC
/* Computes R = nP where R is (rx, ry) and P is (px, py). The parameters
* a, b and p are the elliptic curve coefficients and the prime that
* determines the field GFp. Uses Jacobian coordinates. */
mp_err ec_GFp_pt_mul_jac(const mp_int *n, const mp_int *px,
const mp_int *py, mp_int *rx, mp_int *ry,
const ECGroup *group);
#endif
/* Computes R(x, y) = k1 * G + k2 * P(x, y), where G is the generator
* (base point) of the group of points on the elliptic curve. Allows k1 =
* NULL or { k2, P } = NULL. Implemented using mixed Jacobian-affine
* coordinates. Input and output values are assumed to be NOT
* field-encoded and are in affine form. */
mp_err
ec_GFp_pts_mul_jac(const mp_int *k1, const mp_int *k2, const mp_int *px,
const mp_int *py, mp_int *rx, mp_int *ry,
const ECGroup *group);
/* 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);
#endif /* __ecp_h_ */
|
