1 /*
2 * RTSS (threshold secret sharing)
3 * (C) 2009,2018 Jack Lloyd
4 *
5 * Botan is released under the Simplified BSD License (see license.txt)
6 */
7
8 #include <botan/tss.h>
9 #include <botan/rng.h>
10 #include <botan/hash.h>
11 #include <botan/loadstor.h>
12 #include <botan/hex.h>
13
14 namespace Botan {
15
16 namespace {
17
18 const size_t RTSS_HEADER_SIZE = 20;
19
20 /**
21 Table for GF(2^8) arithmetic (exponentials)
22 */
23 const uint8_t 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 uint8_t 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
gfp_mul(uint8_t x,uint8_t y)78 uint8_t gfp_mul(uint8_t x, uint8_t y)
79 {
80 if(x == 0 || y == 0)
81 return 0;
82 return RTSS_EXP[(RTSS_LOG[x] + RTSS_LOG[y]) % 255];
83 }
84
rtss_hash_id(const std::string & hash_name)85 uint8_t rtss_hash_id(const std::string& hash_name)
86 {
87 if(hash_name == "None")
88 return 0;
89 else if(hash_name == "SHA-160" || hash_name == "SHA-1" || hash_name == "SHA1")
90 return 1;
91 else if(hash_name == "SHA-256")
92 return 2;
93 else
94 throw Invalid_Argument("RTSS only supports SHA-1 and SHA-256");
95 }
96
get_rtss_hash_by_id(uint8_t id)97 std::unique_ptr<HashFunction> get_rtss_hash_by_id(uint8_t id)
98 {
99 if(id == 0)
100 return std::unique_ptr<HashFunction>();
101 if(id == 1)
102 return HashFunction::create_or_throw("SHA-1");
103 else if(id == 2)
104 return HashFunction::create_or_throw("SHA-256");
105 else
106 throw Decoding_Error("Unknown RTSS hash identifier");
107 }
108
109 }
110
RTSS_Share(const std::string & hex_input)111 RTSS_Share::RTSS_Share(const std::string& hex_input)
112 {
113 m_contents = hex_decode_locked(hex_input);
114 }
115
RTSS_Share(const uint8_t bin[],size_t len)116 RTSS_Share::RTSS_Share(const uint8_t bin[], size_t len)
117 {
118 m_contents.assign(bin, bin + len);
119 }
120
share_id() const121 uint8_t RTSS_Share::share_id() const
122 {
123 if(!initialized())
124 throw Invalid_State("RTSS_Share::share_id not initialized");
125
126 if(m_contents.size() < RTSS_HEADER_SIZE + 1)
127 throw Decoding_Error("RTSS_Share::share_id invalid share data");
128
129 return m_contents[20];
130 }
131
to_string() const132 std::string RTSS_Share::to_string() const
133 {
134 return hex_encode(m_contents.data(), m_contents.size());
135 }
136
137 std::vector<RTSS_Share>
split(uint8_t M,uint8_t N,const uint8_t S[],uint16_t S_len,const uint8_t identifier[16],RandomNumberGenerator & rng)138 RTSS_Share::split(uint8_t M, uint8_t N,
139 const uint8_t S[], uint16_t S_len,
140 const uint8_t identifier[16],
141 RandomNumberGenerator& rng)
142 {
143 return RTSS_Share::split(M, N, S, S_len,
144 std::vector<uint8_t>(identifier, identifier + 16),
145 "SHA-256",
146 rng);
147 }
148
149 std::vector<RTSS_Share>
split(uint8_t M,uint8_t N,const uint8_t S[],uint16_t S_len,const std::vector<uint8_t> & identifier,const std::string & hash_fn,RandomNumberGenerator & rng)150 RTSS_Share::split(uint8_t M, uint8_t N,
151 const uint8_t S[], uint16_t S_len,
152 const std::vector<uint8_t>& identifier,
153 const std::string& hash_fn,
154 RandomNumberGenerator& rng)
155 {
156 if(M <= 1 || N <= 1 || M > N || N >= 255)
157 throw Invalid_Argument("RTSS_Share::split: Invalid N or M");
158
159 if(identifier.size() > 16)
160 throw Invalid_Argument("RTSS_Share::split Invalid identifier size");
161
162 const uint8_t hash_id = rtss_hash_id(hash_fn);
163
164 std::unique_ptr<HashFunction> hash;
165 if(hash_id > 0)
166 hash = HashFunction::create_or_throw(hash_fn);
167
168 // secret = S || H(S)
169 secure_vector<uint8_t> secret(S, S + S_len);
170 if(hash)
171 secret += hash->process(S, S_len);
172
173 if(secret.size() >= 0xFFFE)
174 throw Encoding_Error("RTSS_Share::split secret too large for TSS format");
175
176 // +1 byte for the share ID
177 const uint16_t share_len = static_cast<uint16_t>(secret.size() + 1);
178
179 secure_vector<uint8_t> share_header(RTSS_HEADER_SIZE);
180 copy_mem(&share_header[0], identifier.data(), identifier.size());
181 share_header[16] = hash_id;
182 share_header[17] = M;
183 share_header[18] = get_byte(0, share_len);
184 share_header[19] = get_byte(1, share_len);
185
186 // Create RTSS header in each share
187 std::vector<RTSS_Share> shares(N);
188
189 for(uint8_t i = 0; i != N; ++i)
190 {
191 shares[i].m_contents.reserve(share_header.size() + share_len);
192 shares[i].m_contents = share_header;
193 }
194
195 // Choose sequential values for X starting from 1
196 for(uint8_t i = 0; i != N; ++i)
197 shares[i].m_contents.push_back(i+1);
198
199 for(size_t i = 0; i != secret.size(); ++i)
200 {
201 std::vector<uint8_t> coefficients(M-1);
202 rng.randomize(coefficients.data(), coefficients.size());
203
204 for(uint8_t j = 0; j != N; ++j)
205 {
206 const uint8_t X = j + 1;
207
208 uint8_t sum = secret[i];
209 uint8_t X_i = X;
210
211 for(size_t k = 0; k != coefficients.size(); ++k)
212 {
213 sum ^= gfp_mul(X_i, coefficients[k]);
214 X_i = gfp_mul(X_i, X);
215 }
216
217 shares[j].m_contents.push_back(sum);
218 }
219 }
220
221 return shares;
222 }
223
224 secure_vector<uint8_t>
reconstruct(const std::vector<RTSS_Share> & shares)225 RTSS_Share::reconstruct(const std::vector<RTSS_Share>& shares)
226 {
227 if(shares.size() <= 1)
228 throw Decoding_Error("Insufficient shares to do TSS reconstruction");
229
230 for(size_t i = 0; i != shares.size(); ++i)
231 {
232 if(shares[i].size() < RTSS_HEADER_SIZE + 1)
233 throw Decoding_Error("Missing or malformed RTSS header");
234
235 if(shares[i].share_id() == 0)
236 throw Decoding_Error("Invalid (id = 0) RTSS share detected");
237
238 if(i > 0)
239 {
240 if(shares[i].size() != shares[0].size())
241 throw Decoding_Error("Different sized RTSS shares detected");
242
243 if(!same_mem(&shares[0].m_contents[0],
244 &shares[i].m_contents[0], RTSS_HEADER_SIZE))
245 throw Decoding_Error("Different RTSS headers detected");
246 }
247 }
248
249 const uint8_t N = shares[0].m_contents[17];
250
251 if(shares.size() < N)
252 throw Decoding_Error("Insufficient shares to do TSS reconstruction");
253
254 const uint16_t share_len = make_uint16(shares[0].m_contents[18],
255 shares[0].m_contents[19]);
256
257 const uint8_t hash_id = shares[0].m_contents[16];
258 std::unique_ptr<HashFunction> hash(get_rtss_hash_by_id(hash_id));
259 const size_t hash_len = (hash ? hash->output_length() : 0);
260
261 if(shares[0].size() != RTSS_HEADER_SIZE + share_len)
262 {
263 /*
264 * This second (laxer) check accomodates a bug in TSS that was
265 * fixed in 2.9.0 - previous versions used the length of the
266 * *secret* here, instead of the length of the *share*, which is
267 * precisely 1 + hash_len longer.
268 */
269 if(shares[0].size() <= RTSS_HEADER_SIZE + 1 + hash_len)
270 throw Decoding_Error("Bad RTSS length field in header");
271 }
272
273 std::vector<uint8_t> V(shares.size());
274 secure_vector<uint8_t> recovered;
275
276 for(size_t i = RTSS_HEADER_SIZE + 1; i != shares[0].size(); ++i)
277 {
278 for(size_t j = 0; j != V.size(); ++j)
279 V[j] = shares[j].m_contents[i];
280
281 uint8_t r = 0;
282 for(size_t k = 0; k != shares.size(); ++k)
283 {
284 // L_i function:
285 uint8_t r2 = 1;
286 for(size_t l = 0; l != shares.size(); ++l)
287 {
288 if(k == l)
289 continue;
290
291 uint8_t share_k = shares[k].share_id();
292 uint8_t share_l = shares[l].share_id();
293
294 if(share_k == share_l)
295 throw Decoding_Error("Duplicate shares found in RTSS recovery");
296
297 uint8_t div = RTSS_EXP[(255 +
298 RTSS_LOG[share_l] -
299 RTSS_LOG[share_k ^ share_l]) % 255];
300
301 r2 = gfp_mul(r2, div);
302 }
303
304 r ^= gfp_mul(V[k], r2);
305 }
306 recovered.push_back(r);
307 }
308
309 if(hash)
310 {
311 if(recovered.size() < hash->output_length())
312 throw Decoding_Error("RTSS recovered value too short to be valid");
313
314 const size_t secret_len = recovered.size() - hash->output_length();
315
316 hash->update(recovered.data(), secret_len);
317 secure_vector<uint8_t> hash_check = hash->final();
318
319 if(!constant_time_compare(hash_check.data(),
320 &recovered[secret_len],
321 hash->output_length()))
322 {
323 throw Decoding_Error("RTSS hash check failed");
324 }
325
326 // remove the trailing hash value
327 recovered.resize(secret_len);
328 }
329
330 return recovered;
331 }
332
333 }
334