-
Notifications
You must be signed in to change notification settings - Fork 0
/
ECC_GF28.cc
179 lines (163 loc) · 7.04 KB
/
ECC_GF28.cc
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
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
//
// Copyright 2018, Jeremy Cooper
// All rights reserved.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions
// are met:
//
// 1. Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
//
// 2. Redistributions in binary form must reproduce the above copyright
// notice, this list of conditions and the following disclaimer in the
// documentation and/or other materials provided with the distribution.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
// FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
// COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
// INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
// BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
// LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
// CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
// LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
// ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
// POSSIBILITY OF SUCH DAMAGE.
//
#include "ECC_GF28.h"
//
// The reduction polynomial for this field in binary representation.
//
// The real polynomial is understood to be:
//
// g(x) = x^8 + x^4 + x^3 + x^2 + 1
//
// but we represent it here as g(2) with the 2^8 power removed.
//
static const uint8_t kReductionPoly = 0x1d;
//
// The field primitive generator.
//
// g(x) = x
//
// Here it is g(2)
//
static const uint8_t kAlpha = 2;
//
// The fully generated field sequence, taken from successive powers of alpha.
//
static const uint8_t kPowAlpha[255] = {
0x01,0x02,0x04,0x08,0x10,0x20,0x40,0x80,0x1d,0x3a,0x74,0xe8,0xcd,0x87,0x13,
0x26,0x4c,0x98,0x2d,0x5a,0xb4,0x75,0xea,0xc9,0x8f,0x03,0x06,0x0c,0x18,0x30,
0x60,0xc0,0x9d,0x27,0x4e,0x9c,0x25,0x4a,0x94,0x35,0x6a,0xd4,0xb5,0x77,0xee,
0xc1,0x9f,0x23,0x46,0x8c,0x05,0x0a,0x14,0x28,0x50,0xa0,0x5d,0xba,0x69,0xd2,
0xb9,0x6f,0xde,0xa1,0x5f,0xbe,0x61,0xc2,0x99,0x2f,0x5e,0xbc,0x65,0xca,0x89,
0x0f,0x1e,0x3c,0x78,0xf0,0xfd,0xe7,0xd3,0xbb,0x6b,0xd6,0xb1,0x7f,0xfe,0xe1,
0xdf,0xa3,0x5b,0xb6,0x71,0xe2,0xd9,0xaf,0x43,0x86,0x11,0x22,0x44,0x88,0x0d,
0x1a,0x34,0x68,0xd0,0xbd,0x67,0xce,0x81,0x1f,0x3e,0x7c,0xf8,0xed,0xc7,0x93,
0x3b,0x76,0xec,0xc5,0x97,0x33,0x66,0xcc,0x85,0x17,0x2e,0x5c,0xb8,0x6d,0xda,
0xa9,0x4f,0x9e,0x21,0x42,0x84,0x15,0x2a,0x54,0xa8,0x4d,0x9a,0x29,0x52,0xa4,
0x55,0xaa,0x49,0x92,0x39,0x72,0xe4,0xd5,0xb7,0x73,0xe6,0xd1,0xbf,0x63,0xc6,
0x91,0x3f,0x7e,0xfc,0xe5,0xd7,0xb3,0x7b,0xf6,0xf1,0xff,0xe3,0xdb,0xab,0x4b,
0x96,0x31,0x62,0xc4,0x95,0x37,0x6e,0xdc,0xa5,0x57,0xae,0x41,0x82,0x19,0x32,
0x64,0xc8,0x8d,0x07,0x0e,0x1c,0x38,0x70,0xe0,0xdd,0xa7,0x53,0xa6,0x51,0xa2,
0x59,0xb2,0x79,0xf2,0xf9,0xef,0xc3,0x9b,0x2b,0x56,0xac,0x45,0x8a,0x09,0x12,
0x24,0x48,0x90,0x3d,0x7a,0xf4,0xf5,0xf7,0xf3,0xfb,0xeb,0xcb,0x8b,0x0b,0x16,
0x2c,0x58,0xb0,0x7d,0xfa,0xe9,0xcf,0x83,0x1b,0x36,0x6c,0xd8,0xad,0x47,0x8e,
};
//
// This is a table of discrete logarithms in base alpha, the field primitive,
// for each field element. (The entry for the zero field element is present,
// but it of course has no valid value as log(0) is undefined).
//
static const uint8_t kLogAlpha[256] = {
0x00,0x00,0x01,0x19,0x02,0x32,0x1a,0xc6,0x03,0xdf,0x33,0xee,0x1b,0x68,0xc7,
0x4b,0x04,0x64,0xe0,0x0e,0x34,0x8d,0xef,0x81,0x1c,0xc1,0x69,0xf8,0xc8,0x08,
0x4c,0x71,0x05,0x8a,0x65,0x2f,0xe1,0x24,0x0f,0x21,0x35,0x93,0x8e,0xda,0xf0,
0x12,0x82,0x45,0x1d,0xb5,0xc2,0x7d,0x6a,0x27,0xf9,0xb9,0xc9,0x9a,0x09,0x78,
0x4d,0xe4,0x72,0xa6,0x06,0xbf,0x8b,0x62,0x66,0xdd,0x30,0xfd,0xe2,0x98,0x25,
0xb3,0x10,0x91,0x22,0x88,0x36,0xd0,0x94,0xce,0x8f,0x96,0xdb,0xbd,0xf1,0xd2,
0x13,0x5c,0x83,0x38,0x46,0x40,0x1e,0x42,0xb6,0xa3,0xc3,0x48,0x7e,0x6e,0x6b,
0x3a,0x28,0x54,0xfa,0x85,0xba,0x3d,0xca,0x5e,0x9b,0x9f,0x0a,0x15,0x79,0x2b,
0x4e,0xd4,0xe5,0xac,0x73,0xf3,0xa7,0x57,0x07,0x70,0xc0,0xf7,0x8c,0x80,0x63,
0x0d,0x67,0x4a,0xde,0xed,0x31,0xc5,0xfe,0x18,0xe3,0xa5,0x99,0x77,0x26,0xb8,
0xb4,0x7c,0x11,0x44,0x92,0xd9,0x23,0x20,0x89,0x2e,0x37,0x3f,0xd1,0x5b,0x95,
0xbc,0xcf,0xcd,0x90,0x87,0x97,0xb2,0xdc,0xfc,0xbe,0x61,0xf2,0x56,0xd3,0xab,
0x14,0x2a,0x5d,0x9e,0x84,0x3c,0x39,0x53,0x47,0x6d,0x41,0xa2,0x1f,0x2d,0x43,
0xd8,0xb7,0x7b,0xa4,0x76,0xc4,0x17,0x49,0xec,0x7f,0x0c,0x6f,0xf6,0x6c,0xa1,
0x3b,0x52,0x29,0x9d,0x55,0xaa,0xfb,0x60,0x86,0xb1,0xbb,0xcc,0x3e,0x5a,0xcb,
0x59,0x5f,0xb0,0x9c,0xa9,0xa0,0x51,0x0b,0xf5,0x16,0xeb,0x7a,0x75,0x2c,0xd7,
0x4f,0xae,0xd5,0xe9,0xe6,0xe7,0xad,0xe8,0x74,0xd6,0xf4,0xea,0xa8,0x50,0x58,
0xaf
};
//
// This is a table of the inverse of every field element. The zero element
// has no valid inverse, but it is part of the table to make lookups
// easier.
//
static const uint8_t kInverse[256] = {
0x00,0x01,0x8e,0xf4,0x47,0xa7,0x7a,0xba,0xad,0x9d,0xdd,0x98,0x3d,0xaa,0x5d,
0x96,0xd8,0x72,0xc0,0x58,0xe0,0x3e,0x4c,0x66,0x90,0xde,0x55,0x80,0xa0,0x83,
0x4b,0x2a,0x6c,0xed,0x39,0x51,0x60,0x56,0x2c,0x8a,0x70,0xd0,0x1f,0x4a,0x26,
0x8b,0x33,0x6e,0x48,0x89,0x6f,0x2e,0xa4,0xc3,0x40,0x5e,0x50,0x22,0xcf,0xa9,
0xab,0x0c,0x15,0xe1,0x36,0x5f,0xf8,0xd5,0x92,0x4e,0xa6,0x04,0x30,0x88,0x2b,
0x1e,0x16,0x67,0x45,0x93,0x38,0x23,0x68,0x8c,0x81,0x1a,0x25,0x61,0x13,0xc1,
0xcb,0x63,0x97,0x0e,0x37,0x41,0x24,0x57,0xca,0x5b,0xb9,0xc4,0x17,0x4d,0x52,
0x8d,0xef,0xb3,0x20,0xec,0x2f,0x32,0x28,0xd1,0x11,0xd9,0xe9,0xfb,0xda,0x79,
0xdb,0x77,0x06,0xbb,0x84,0xcd,0xfe,0xfc,0x1b,0x54,0xa1,0x1d,0x7c,0xcc,0xe4,
0xb0,0x49,0x31,0x27,0x2d,0x53,0x69,0x02,0xf5,0x18,0xdf,0x44,0x4f,0x9b,0xbc,
0x0f,0x5c,0x0b,0xdc,0xbd,0x94,0xac,0x09,0xc7,0xa2,0x1c,0x82,0x9f,0xc6,0x34,
0xc2,0x46,0x05,0xce,0x3b,0x0d,0x3c,0x9c,0x08,0xbe,0xb7,0x87,0xe5,0xee,0x6b,
0xeb,0xf2,0xbf,0xaf,0xc5,0x64,0x07,0x7b,0x95,0x9a,0xae,0xb6,0x12,0x59,0xa5,
0x35,0x65,0xb8,0xa3,0x9e,0xd2,0xf7,0x62,0x5a,0x85,0x7d,0xa8,0x3a,0x29,0x71,
0xc8,0xf6,0xf9,0x43,0xd7,0xd6,0x10,0x73,0x76,0x78,0x99,0x0a,0x19,0x91,0x14,
0x3f,0xe6,0xf0,0x86,0xb1,0xe2,0xf1,0xfa,0x74,0xf3,0xb4,0x6d,0x21,0xb2,0x6a,
0xe3,0xe7,0xb5,0xea,0x03,0x8f,0xd3,0xc9,0x42,0xd4,0xe8,0x75,0x7f,0xff,0x7e,
0xfd
};
uint8_t
ECC_GF28_multiply(uint8_t a, uint8_t b)
{
if (a == 0 || b == 0)
return 0;
if (a == 1)
return b;
if (b == 1)
return a;
//
// Use the discrete logarithm table to make multiplicaton an O(1)
// operation.
//
return kPowAlpha[(kLogAlpha[a] + kLogAlpha[b]) % 255];
}
uint8_t
ECC_GF28_invert(uint8_t a)
{
return kInverse[a];
}
//
// Evaluate the value of a polynomial in x when x is a specific value.
//
uint8_t
ECC_GF28_evaluate(const uint8_t p[], uint8_t x, size_t n)
{
uint8_t y = 1;
uint8_t res = 0;
for (size_t i = 0; i < n; i++) {
res ^= ECC_GF28_multiply(p[i], y);
y = ECC_GF28_multiply(y, x);
}
return res;
}
//
// Return a specific power of the generator, alpha.
//
uint8_t
ECC_GF28_pow_alpha(uint8_t n)
{
if (n > 254)
n = 0;
return kPowAlpha[n];
}