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
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
|
/*
* RTSS (threshold secret sharing)
* (C) 2009 Jack Lloyd
*
* Distributed under the terms of the Botan license
*/
#include <botan/tss.h>
#include <botan/loadstor.h>
#include <botan/pipe.h>
#include <botan/hex.h>
#include <botan/sha2_32.h>
#include <botan/sha160.h>
#include <memory>
namespace Botan {
namespace {
/**
Table for GF(2^8) arithmetic (exponentials)
*/
const byte EXP[256] = {
0x01, 0x03, 0x05, 0x0F, 0x11, 0x33, 0x55, 0xFF, 0x1A, 0x2E, 0x72,
0x96, 0xA1, 0xF8, 0x13, 0x35, 0x5F, 0xE1, 0x38, 0x48, 0xD8, 0x73,
0x95, 0xA4, 0xF7, 0x02, 0x06, 0x0A, 0x1E, 0x22, 0x66, 0xAA, 0xE5,
0x34, 0x5C, 0xE4, 0x37, 0x59, 0xEB, 0x26, 0x6A, 0xBE, 0xD9, 0x70,
0x90, 0xAB, 0xE6, 0x31, 0x53, 0xF5, 0x04, 0x0C, 0x14, 0x3C, 0x44,
0xCC, 0x4F, 0xD1, 0x68, 0xB8, 0xD3, 0x6E, 0xB2, 0xCD, 0x4C, 0xD4,
0x67, 0xA9, 0xE0, 0x3B, 0x4D, 0xD7, 0x62, 0xA6, 0xF1, 0x08, 0x18,
0x28, 0x78, 0x88, 0x83, 0x9E, 0xB9, 0xD0, 0x6B, 0xBD, 0xDC, 0x7F,
0x81, 0x98, 0xB3, 0xCE, 0x49, 0xDB, 0x76, 0x9A, 0xB5, 0xC4, 0x57,
0xF9, 0x10, 0x30, 0x50, 0xF0, 0x0B, 0x1D, 0x27, 0x69, 0xBB, 0xD6,
0x61, 0xA3, 0xFE, 0x19, 0x2B, 0x7D, 0x87, 0x92, 0xAD, 0xEC, 0x2F,
0x71, 0x93, 0xAE, 0xE9, 0x20, 0x60, 0xA0, 0xFB, 0x16, 0x3A, 0x4E,
0xD2, 0x6D, 0xB7, 0xC2, 0x5D, 0xE7, 0x32, 0x56, 0xFA, 0x15, 0x3F,
0x41, 0xC3, 0x5E, 0xE2, 0x3D, 0x47, 0xC9, 0x40, 0xC0, 0x5B, 0xED,
0x2C, 0x74, 0x9C, 0xBF, 0xDA, 0x75, 0x9F, 0xBA, 0xD5, 0x64, 0xAC,
0xEF, 0x2A, 0x7E, 0x82, 0x9D, 0xBC, 0xDF, 0x7A, 0x8E, 0x89, 0x80,
0x9B, 0xB6, 0xC1, 0x58, 0xE8, 0x23, 0x65, 0xAF, 0xEA, 0x25, 0x6F,
0xB1, 0xC8, 0x43, 0xC5, 0x54, 0xFC, 0x1F, 0x21, 0x63, 0xA5, 0xF4,
0x07, 0x09, 0x1B, 0x2D, 0x77, 0x99, 0xB0, 0xCB, 0x46, 0xCA, 0x45,
0xCF, 0x4A, 0xDE, 0x79, 0x8B, 0x86, 0x91, 0xA8, 0xE3, 0x3E, 0x42,
0xC6, 0x51, 0xF3, 0x0E, 0x12, 0x36, 0x5A, 0xEE, 0x29, 0x7B, 0x8D,
0x8C, 0x8F, 0x8A, 0x85, 0x94, 0xA7, 0xF2, 0x0D, 0x17, 0x39, 0x4B,
0xDD, 0x7C, 0x84, 0x97, 0xA2, 0xFD, 0x1C, 0x24, 0x6C, 0xB4, 0xC7,
0x52, 0xF6, 0x01 };
/**
Table for GF(2^8) arithmetic (logarithms)
*/
const byte LOG[] = {
0x90, 0x00, 0x19, 0x01, 0x32, 0x02, 0x1A, 0xC6, 0x4B, 0xC7, 0x1B,
0x68, 0x33, 0xEE, 0xDF, 0x03, 0x64, 0x04, 0xE0, 0x0E, 0x34, 0x8D,
0x81, 0xEF, 0x4C, 0x71, 0x08, 0xC8, 0xF8, 0x69, 0x1C, 0xC1, 0x7D,
0xC2, 0x1D, 0xB5, 0xF9, 0xB9, 0x27, 0x6A, 0x4D, 0xE4, 0xA6, 0x72,
0x9A, 0xC9, 0x09, 0x78, 0x65, 0x2F, 0x8A, 0x05, 0x21, 0x0F, 0xE1,
0x24, 0x12, 0xF0, 0x82, 0x45, 0x35, 0x93, 0xDA, 0x8E, 0x96, 0x8F,
0xDB, 0xBD, 0x36, 0xD0, 0xCE, 0x94, 0x13, 0x5C, 0xD2, 0xF1, 0x40,
0x46, 0x83, 0x38, 0x66, 0xDD, 0xFD, 0x30, 0xBF, 0x06, 0x8B, 0x62,
0xB3, 0x25, 0xE2, 0x98, 0x22, 0x88, 0x91, 0x10, 0x7E, 0x6E, 0x48,
0xC3, 0xA3, 0xB6, 0x1E, 0x42, 0x3A, 0x6B, 0x28, 0x54, 0xFA, 0x85,
0x3D, 0xBA, 0x2B, 0x79, 0x0A, 0x15, 0x9B, 0x9F, 0x5E, 0xCA, 0x4E,
0xD4, 0xAC, 0xE5, 0xF3, 0x73, 0xA7, 0x57, 0xAF, 0x58, 0xA8, 0x50,
0xF4, 0xEA, 0xD6, 0x74, 0x4F, 0xAE, 0xE9, 0xD5, 0xE7, 0xE6, 0xAD,
0xE8, 0x2C, 0xD7, 0x75, 0x7A, 0xEB, 0x16, 0x0B, 0xF5, 0x59, 0xCB,
0x5F, 0xB0, 0x9C, 0xA9, 0x51, 0xA0, 0x7F, 0x0C, 0xF6, 0x6F, 0x17,
0xC4, 0x49, 0xEC, 0xD8, 0x43, 0x1F, 0x2D, 0xA4, 0x76, 0x7B, 0xB7,
0xCC, 0xBB, 0x3E, 0x5A, 0xFB, 0x60, 0xB1, 0x86, 0x3B, 0x52, 0xA1,
0x6C, 0xAA, 0x55, 0x29, 0x9D, 0x97, 0xB2, 0x87, 0x90, 0x61, 0xBE,
0xDC, 0xFC, 0xBC, 0x95, 0xCF, 0xCD, 0x37, 0x3F, 0x5B, 0xD1, 0x53,
0x39, 0x84, 0x3C, 0x41, 0xA2, 0x6D, 0x47, 0x14, 0x2A, 0x9E, 0x5D,
0x56, 0xF2, 0xD3, 0xAB, 0x44, 0x11, 0x92, 0xD9, 0x23, 0x20, 0x2E,
0x89, 0xB4, 0x7C, 0xB8, 0x26, 0x77, 0x99, 0xE3, 0xA5, 0x67, 0x4A,
0xED, 0xDE, 0xC5, 0x31, 0xFE, 0x18, 0x0D, 0x63, 0x8C, 0x80, 0xC0,
0xF7, 0x70, 0x07 };
byte gfp_mul(byte x, byte y)
{
if(x == 0 || y == 0)
return 0;
return EXP[(LOG[x] + LOG[y]) % 255];
}
byte rtss_hash_id(const std::string& hash_name)
{
if(hash_name == "SHA-160")
return 1;
else if(hash_name == "SHA-256")
return 2;
else
throw Invalid_Argument("RTSS only supports SHA-1 and SHA-256");
}
HashFunction* get_rtss_hash_by_id(byte id)
{
if(id == 1)
return new SHA_160;
else if(id == 2)
return new SHA_256;
else
throw Decoding_Error("Bad RTSS hash identifier");
}
}
RTSS_Share::RTSS_Share(const std::string& hex_input)
{
contents = hex_decode(hex_input);
}
byte RTSS_Share::share_id() const
{
if(!initialized())
throw Invalid_State("RTSS_Share::share_id not initialized");
return contents[20];
}
std::string RTSS_Share::to_string() const
{
return hex_encode(&contents[0], contents.size());
}
std::vector<RTSS_Share>
RTSS_Share::split(byte M, byte N,
const byte S[], u16bit S_len,
const byte identifier[16],
RandomNumberGenerator& rng)
{
if(M == 0 || N == 0 || M > N)
throw Encoding_Error("RTSS_Share::split: M == 0 or N == 0 or M > N");
SHA_256 hash; // always use SHA-256 when generating shares
std::vector<RTSS_Share> shares(N);
// Create RTSS header in each share
for(byte i = 0; i != N; ++i)
{
shares[i].contents.append(identifier, 16);
shares[i].contents.append(rtss_hash_id(hash.name()));
shares[i].contents.append(M);
shares[i].contents.append(get_byte(0, S_len));
shares[i].contents.append(get_byte(1, S_len));
}
// Choose sequential values for X starting from 1
for(byte i = 0; i != N; ++i)
shares[i].contents.append(i+1);
// secret = S || H(S)
SecureVector<byte> secret(S, S_len);
secret.append(hash.process(S, S_len));
for(size_t i = 0; i != secret.size(); ++i)
{
std::vector<byte> coefficients(M-1);
rng.randomize(&coefficients[0], coefficients.size());
for(byte j = 0; j != N; ++j)
{
const byte X = j + 1;
byte sum = secret[i];
byte X_i = X;
for(size_t k = 0; k != coefficients.size(); ++k)
{
sum ^= gfp_mul(X_i, coefficients[k]);
X_i = gfp_mul(X_i, X);
}
shares[j].contents.append(sum);
}
}
return shares;
}
SecureVector<byte>
RTSS_Share::reconstruct(const std::vector<RTSS_Share>& shares)
{
const u32bit RTSS_HEADER_SIZE = 20;
for(size_t i = 0; i != shares.size(); ++i)
{
if(shares[i].size() != shares[0].size())
throw Decoding_Error("Different sized RTSS shares detected");
if(shares[i].share_id() == 0)
throw Decoding_Error("Invalid (id = 0) RTSS share detected");
if(shares[i].size() < RTSS_HEADER_SIZE)
throw Decoding_Error("Missing or malformed RTSS header");
if(!same_mem(&shares[0].contents[0],
&shares[i].contents[0], RTSS_HEADER_SIZE))
throw Decoding_Error("Different RTSS headers detected");
}
if(shares.size() < shares[0].contents[17])
throw Decoding_Error("Insufficient shares to do TSS reconstruction");
u16bit secret_len = make_u16bit(shares[0].contents[18],
shares[0].contents[19]);
byte hash_id = shares[0].contents[16];
std::auto_ptr<HashFunction> hash(get_rtss_hash_by_id(hash_id));
if(shares[0].size() != secret_len + hash->OUTPUT_LENGTH + RTSS_HEADER_SIZE + 1)
throw Decoding_Error("Bad RTSS length field in header");
std::vector<byte> V(shares.size());
SecureVector<byte> secret;
for(size_t i = RTSS_HEADER_SIZE + 1; i != shares[0].size(); ++i)
{
for(size_t j = 0; j != V.size(); ++j)
V[j] = shares[j].contents[i];
byte r = 0;
for(size_t k = 0; k != shares.size(); ++k)
{
// L_i function:
byte r2 = 1;
for(size_t l = 0; l != shares.size(); ++l)
{
if(k == l)
continue;
byte share_k = shares[k].share_id();
byte share_l = shares[l].share_id();
if(share_k == share_l)
throw Decoding_Error("Duplicate shares found in RTSS recovery");
byte div = EXP[(255 + LOG[share_l] - LOG[share_k ^ share_l]) % 255];
r2 = gfp_mul(r2, div);
}
r ^= gfp_mul(V[k], r2);
}
secret.append(r);
}
if(secret.size() != secret_len + hash->OUTPUT_LENGTH)
throw Decoding_Error("Bad length in RTSS output");
hash->update(&secret[0], secret_len);
SecureVector<byte> hash_check = hash->final();
if(!same_mem(&hash_check[0],
&secret[secret_len], hash->OUTPUT_LENGTH))
throw Decoding_Error("RTSS hash check failed");
return SecureVector<byte>(&secret[0], secret_len);
}
}
|
