Botan: src/constructs/tss/tss.cpp Source File

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tss.cpp
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1 /*
2 * RTSS (threshold secret sharing)
3 * (C) 2009 Jack Lloyd
4 *
5 * Distributed under the terms of the Botan license
6 */
7
8 #include <botan/tss.h>
9 #include <botan/loadstor.h>
10 #include <botan/pipe.h>
11 #include <botan/hex.h>
12 #include <botan/sha2_32.h>
13 #include <botan/sha160.h>
14 #include <memory>
15
16 namespace Botan {
17
18 namespace {
19
20 /**
21 Table for GF(2^8) arithmetic (exponentials)
22 */
23 const byte RTSS_EXP[256] = {
24 0x01, 0x03, 0x05, 0x0F, 0x11, 0x33, 0x55, 0xFF, 0x1A, 0x2E, 0x72,
25 0x96, 0xA1, 0xF8, 0x13, 0x35, 0x5F, 0xE1, 0x38, 0x48, 0xD8, 0x73,
26 0x95, 0xA4, 0xF7, 0x02, 0x06, 0x0A, 0x1E, 0x22, 0x66, 0xAA, 0xE5,
27 0x34, 0x5C, 0xE4, 0x37, 0x59, 0xEB, 0x26, 0x6A, 0xBE, 0xD9, 0x70,
28 0x90, 0xAB, 0xE6, 0x31, 0x53, 0xF5, 0x04, 0x0C, 0x14, 0x3C, 0x44,
29 0xCC, 0x4F, 0xD1, 0x68, 0xB8, 0xD3, 0x6E, 0xB2, 0xCD, 0x4C, 0xD4,
30 0x67, 0xA9, 0xE0, 0x3B, 0x4D, 0xD7, 0x62, 0xA6, 0xF1, 0x08, 0x18,
31 0x28, 0x78, 0x88, 0x83, 0x9E, 0xB9, 0xD0, 0x6B, 0xBD, 0xDC, 0x7F,
32 0x81, 0x98, 0xB3, 0xCE, 0x49, 0xDB, 0x76, 0x9A, 0xB5, 0xC4, 0x57,
33 0xF9, 0x10, 0x30, 0x50, 0xF0, 0x0B, 0x1D, 0x27, 0x69, 0xBB, 0xD6,
34 0x61, 0xA3, 0xFE, 0x19, 0x2B, 0x7D, 0x87, 0x92, 0xAD, 0xEC, 0x2F,
35 0x71, 0x93, 0xAE, 0xE9, 0x20, 0x60, 0xA0, 0xFB, 0x16, 0x3A, 0x4E,
36 0xD2, 0x6D, 0xB7, 0xC2, 0x5D, 0xE7, 0x32, 0x56, 0xFA, 0x15, 0x3F,
37 0x41, 0xC3, 0x5E, 0xE2, 0x3D, 0x47, 0xC9, 0x40, 0xC0, 0x5B, 0xED,
38 0x2C, 0x74, 0x9C, 0xBF, 0xDA, 0x75, 0x9F, 0xBA, 0xD5, 0x64, 0xAC,
39 0xEF, 0x2A, 0x7E, 0x82, 0x9D, 0xBC, 0xDF, 0x7A, 0x8E, 0x89, 0x80,
40 0x9B, 0xB6, 0xC1, 0x58, 0xE8, 0x23, 0x65, 0xAF, 0xEA, 0x25, 0x6F,
41 0xB1, 0xC8, 0x43, 0xC5, 0x54, 0xFC, 0x1F, 0x21, 0x63, 0xA5, 0xF4,
42 0x07, 0x09, 0x1B, 0x2D, 0x77, 0x99, 0xB0, 0xCB, 0x46, 0xCA, 0x45,
43 0xCF, 0x4A, 0xDE, 0x79, 0x8B, 0x86, 0x91, 0xA8, 0xE3, 0x3E, 0x42,
44 0xC6, 0x51, 0xF3, 0x0E, 0x12, 0x36, 0x5A, 0xEE, 0x29, 0x7B, 0x8D,
45 0x8C, 0x8F, 0x8A, 0x85, 0x94, 0xA7, 0xF2, 0x0D, 0x17, 0x39, 0x4B,
46 0xDD, 0x7C, 0x84, 0x97, 0xA2, 0xFD, 0x1C, 0x24, 0x6C, 0xB4, 0xC7,
47 0x52, 0xF6, 0x01 };
48
49 /**
50 Table for GF(2^8) arithmetic (logarithms)
51 */
52 const byte RTSS_LOG[] = {
53 0x90, 0x00, 0x19, 0x01, 0x32, 0x02, 0x1A, 0xC6, 0x4B, 0xC7, 0x1B,
54 0x68, 0x33, 0xEE, 0xDF, 0x03, 0x64, 0x04, 0xE0, 0x0E, 0x34, 0x8D,
55 0x81, 0xEF, 0x4C, 0x71, 0x08, 0xC8, 0xF8, 0x69, 0x1C, 0xC1, 0x7D,
56 0xC2, 0x1D, 0xB5, 0xF9, 0xB9, 0x27, 0x6A, 0x4D, 0xE4, 0xA6, 0x72,
57 0x9A, 0xC9, 0x09, 0x78, 0x65, 0x2F, 0x8A, 0x05, 0x21, 0x0F, 0xE1,
58 0x24, 0x12, 0xF0, 0x82, 0x45, 0x35, 0x93, 0xDA, 0x8E, 0x96, 0x8F,
59 0xDB, 0xBD, 0x36, 0xD0, 0xCE, 0x94, 0x13, 0x5C, 0xD2, 0xF1, 0x40,
60 0x46, 0x83, 0x38, 0x66, 0xDD, 0xFD, 0x30, 0xBF, 0x06, 0x8B, 0x62,
61 0xB3, 0x25, 0xE2, 0x98, 0x22, 0x88, 0x91, 0x10, 0x7E, 0x6E, 0x48,
62 0xC3, 0xA3, 0xB6, 0x1E, 0x42, 0x3A, 0x6B, 0x28, 0x54, 0xFA, 0x85,
63 0x3D, 0xBA, 0x2B, 0x79, 0x0A, 0x15, 0x9B, 0x9F, 0x5E, 0xCA, 0x4E,
64 0xD4, 0xAC, 0xE5, 0xF3, 0x73, 0xA7, 0x57, 0xAF, 0x58, 0xA8, 0x50,
65 0xF4, 0xEA, 0xD6, 0x74, 0x4F, 0xAE, 0xE9, 0xD5, 0xE7, 0xE6, 0xAD,
66 0xE8, 0x2C, 0xD7, 0x75, 0x7A, 0xEB, 0x16, 0x0B, 0xF5, 0x59, 0xCB,
67 0x5F, 0xB0, 0x9C, 0xA9, 0x51, 0xA0, 0x7F, 0x0C, 0xF6, 0x6F, 0x17,
68 0xC4, 0x49, 0xEC, 0xD8, 0x43, 0x1F, 0x2D, 0xA4, 0x76, 0x7B, 0xB7,
69 0xCC, 0xBB, 0x3E, 0x5A, 0xFB, 0x60, 0xB1, 0x86, 0x3B, 0x52, 0xA1,
70 0x6C, 0xAA, 0x55, 0x29, 0x9D, 0x97, 0xB2, 0x87, 0x90, 0x61, 0xBE,
71 0xDC, 0xFC, 0xBC, 0x95, 0xCF, 0xCD, 0x37, 0x3F, 0x5B, 0xD1, 0x53,
72 0x39, 0x84, 0x3C, 0x41, 0xA2, 0x6D, 0x47, 0x14, 0x2A, 0x9E, 0x5D,
73 0x56, 0xF2, 0xD3, 0xAB, 0x44, 0x11, 0x92, 0xD9, 0x23, 0x20, 0x2E,
74 0x89, 0xB4, 0x7C, 0xB8, 0x26, 0x77, 0x99, 0xE3, 0xA5, 0x67, 0x4A,
75 0xED, 0xDE, 0xC5, 0x31, 0xFE, 0x18, 0x0D, 0x63, 0x8C, 0x80, 0xC0,
76 0xF7, 0x70, 0x07 };
77
78 byte gfp_mul(byte x, byte y)
79 {
80 if(x == 0 || y == 0)
81 return 0;
82 return RTSS_EXP[(RTSS_LOG[x] + RTSS_LOG[y]) % 255];
83 }
84
85 byte rtss_hash_id(const std::string& hash_name)
86 {
87 if(hash_name == "SHA-160")
88 return 1;
89 else if(hash_name == "SHA-256")
90 return 2;
91 else
92 throw Invalid_Argument("RTSS only supports SHA-1 and SHA-256");
93 }
94
95 HashFunction* get_rtss_hash_by_id(byte id)
96 {
97 if(id == 1)
98 return new SHA_160;
99 else if(id == 2)
100 return new SHA_256;
101 else
102 throw Decoding_Error("Bad RTSS hash identifier");
103 }
104
105 }
106
107 RTSS_Share::RTSS_Share(const std::string& hex_input)
108 {
109 contents = hex_decode(hex_input);
110 }
111
112 byte RTSS_Share::share_id() const
113 {
114 if(!initialized())
115 throw Invalid_State("RTSS_Share::share_id not initialized");
116
117 return contents[20];
118 }
119
120 std::string RTSS_Share::to_string() const
121 {
122 return hex_encode(&contents[0], contents.size());
123 }
124
125 std::vector<RTSS_Share>
126 RTSS_Share::split(byte M, byte N,
127 const byte S[], u16bit S_len,
128 const byte identifier[16],
129 RandomNumberGenerator& rng)
130 {
131 if(M == 0 || N == 0 || M > N)
132 throw Encoding_Error("RTSS_Share::split: M == 0 or N == 0 or M > N");
133
134 SHA_256 hash; // always use SHA-256 when generating shares
135
136 std::vector<RTSS_Share> shares(N);
137
138 // Create RTSS header in each share
139 for(byte i = 0; i != N; ++i)
140 {
141 shares[i].contents += std::make_pair(identifier, 16);
142 shares[i].contents += rtss_hash_id(hash.name());
143 shares[i].contents += M;
144 shares[i].contents += get_byte(0, S_len);
145 shares[i].contents += get_byte(1, S_len);
146 }
147
148 // Choose sequential values for X starting from 1
149 for(byte i = 0; i != N; ++i)
150 shares[i].contents.push_back(i+1);
151
152 // secret = S || H(S)
153 SecureVector<byte> secret(S, S_len);
154 secret += hash.process(S, S_len);
155
156 for(size_t i = 0; i != secret.size(); ++i)
157 {
158 std::vector<byte> coefficients(M-1);
159 rng.randomize(&coefficients[0], coefficients.size());
160
161 for(byte j = 0; j != N; ++j)
162 {
163 const byte X = j + 1;
164
165 byte sum = secret[i];
166 byte X_i = X;
167
168 for(size_t k = 0; k != coefficients.size(); ++k)
169 {
170 sum ^= gfp_mul(X_i, coefficients[k]);
171 X_i = gfp_mul(X_i, X);
172 }
173
174 shares[j].contents.push_back(sum);
175 }
176 }
177
178 return shares;
179 }
180
181 SecureVector<byte>
182 RTSS_Share::reconstruct(const std::vector<RTSS_Share>& shares)
183 {
184 const size_t RTSS_HEADER_SIZE = 20;
185
186 for(size_t i = 0; i != shares.size(); ++i)
187 {
188 if(shares[i].size() != shares[0].size())
189 throw Decoding_Error("Different sized RTSS shares detected");
190 if(shares[i].share_id() == 0)
191 throw Decoding_Error("Invalid (id = 0) RTSS share detected");
192 if(shares[i].size() < RTSS_HEADER_SIZE)
193 throw Decoding_Error("Missing or malformed RTSS header");
194
195 if(!same_mem(&shares[0].contents[0],
196 &shares[i].contents[0], RTSS_HEADER_SIZE))
197 throw Decoding_Error("Different RTSS headers detected");
198 }
199
200 if(shares.size() < shares[0].contents[17])
201 throw Decoding_Error("Insufficient shares to do TSS reconstruction");
202
203 u16bit secret_len = make_u16bit(shares[0].contents[18],
204 shares[0].contents[19]);
205
206 byte hash_id = shares[0].contents[16];
207
208 std::auto_ptr<HashFunction> hash(get_rtss_hash_by_id(hash_id));
209
210 if(shares[0].size() != secret_len + hash->output_length() + RTSS_HEADER_SIZE + 1)
211 throw Decoding_Error("Bad RTSS length field in header");
212
213 std::vector<byte> V(shares.size());
214 SecureVector<byte> secret;
215
216 for(size_t i = RTSS_HEADER_SIZE + 1; i != shares[0].size(); ++i)
217 {
218 for(size_t j = 0; j != V.size(); ++j)
219 V[j] = shares[j].contents[i];
220
221 byte r = 0;
222 for(size_t k = 0; k != shares.size(); ++k)
223 {
224 // L_i function:
225 byte r2 = 1;
226 for(size_t l = 0; l != shares.size(); ++l)
227 {
228 if(k == l)
229 continue;
230
231 byte share_k = shares[k].share_id();
232 byte share_l = shares[l].share_id();
233
234 if(share_k == share_l)
235 throw Decoding_Error("Duplicate shares found in RTSS recovery");
236
237 byte div = RTSS_EXP[(255 +
238 RTSS_LOG[share_l] -
239 RTSS_LOG[share_k ^ share_l]) % 255];
240
241 r2 = gfp_mul(r2, div);
242 }
243
244 r ^= gfp_mul(V[k], r2);
245 }
246 secret.push_back(r);
247 }
248
249 if(secret.size() != secret_len + hash->output_length())
250 throw Decoding_Error("Bad length in RTSS output");
251
252 hash->update(&secret[0], secret_len);
253 SecureVector<byte> hash_check = hash->final();
254
255 if(!same_mem(&hash_check[0],
256 &secret[secret_len], hash->output_length()))
257 throw Decoding_Error("RTSS hash check failed");
258
259 return SecureVector<byte>(&secret[0], secret_len);
260 }
261
262 }
Botan::RTSS_Share::size
size_t size() const
Definition: tss.h:64
Botan::RandomNumberGenerator::randomize
virtual void randomize(byte output[], size_t length)=0
Botan::RTSS_Share::reconstruct
static SecureVector< byte > reconstruct(const std::vector< RTSS_Share > &shares)
Definition: tss.cpp:182
Botan::same_mem
bool same_mem(const T *p1, const T *p2, size_t n)
Definition: mem_ops.h:57
Botan::RTSS_Share::to_string
std::string to_string() const
Definition: tss.cpp:120
Botan::RandomNumberGenerator
Definition: rng.h:20
Botan::hex_decode
size_t hex_decode(byte output[], const char input[], size_t input_length, size_t &input_consumed, bool ignore_ws)
Definition: hex.cpp:55
Botan::RTSS_Share::initialized
bool initialized() const
Definition: tss.h:69
Botan::MemoryRegion::push_back
void push_back(T x)
Definition: secmem.h:143
Botan::Invalid_State
Definition: exceptn.h:25
Botan::Invalid_Argument
std::invalid_argument Invalid_Argument
Definition: exceptn.h:20
Botan::get_byte
byte get_byte(size_t byte_num, T input)
Definition: get_byte.h:21
Botan::byte
unsigned char byte
Definition: types.h:22
Botan::u16bit
unsigned short u16bit
Definition: types.h:27
Botan::Decoding_Error
Definition: exceptn.h:138
Botan::Buffered_Computation::process
SecureVector< byte > process(const byte in[], size_t length)
Definition: buf_comp.h:101
Botan::MemoryRegion::size
size_t size() const
Definition: secmem.h:29
Botan
Definition: algo_base.h:14
Botan::make_u16bit
u16bit make_u16bit(byte i0, byte i1)
Definition: loadstor.h:47
Botan::RTSS_Share::share_id
byte share_id() const
Definition: tss.cpp:112
Botan::SHA_256::name
std::string name() const
Definition: sha2_32.h:43
Botan::SecureVector< byte >
Botan::RTSS_Share::RTSS_Share
RTSS_Share()
Definition: tss.h:44
Botan::Encoding_Error
Definition: exceptn.h:129
Botan::SHA_256
Definition: sha2_32.h:40
Botan::RTSS_Share::split
static std::vector< RTSS_Share > split(byte M, byte N, const byte secret[], u16bit secret_len, const byte identifier[16], RandomNumberGenerator &rng)
Definition: tss.cpp:126
Botan::hex_encode
void hex_encode(char output[], const byte input[], size_t input_length, bool uppercase)
Definition: hex.cpp:14