Botan  1.10.9
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 
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>
127  const byte S[], u16bit S_len,
128  const byte identifier[16],
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 
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 }
size_t size() const
Definition: tss.h:64
virtual void randomize(byte output[], size_t length)=0
static SecureVector< byte > reconstruct(const std::vector< RTSS_Share > &shares)
Definition: tss.cpp:182
bool same_mem(const T *p1, const T *p2, size_t n)
Definition: mem_ops.h:57
std::string to_string() const
Definition: tss.cpp:120
size_t hex_decode(byte output[], const char input[], size_t input_length, size_t &input_consumed, bool ignore_ws)
Definition: hex.cpp:55
bool initialized() const
Definition: tss.h:69
void push_back(T x)
Definition: secmem.h:143
std::invalid_argument Invalid_Argument
Definition: exceptn.h:20
byte get_byte(size_t byte_num, T input)
Definition: get_byte.h:21
unsigned char byte
Definition: types.h:22
RandomNumberGenerator * rng
Definition: global_rng.cpp:165
unsigned short u16bit
Definition: types.h:27
SecureVector< byte > process(const byte in[], size_t length)
Definition: buf_comp.h:101
size_t size() const
Definition: secmem.h:29
u16bit make_u16bit(byte i0, byte i1)
Definition: loadstor.h:47
BigInt r
Definition: numthry.cpp:26
byte share_id() const
Definition: tss.cpp:112
std::string name() const
Definition: sha2_32.h:43
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
void hex_encode(char output[], const byte input[], size_t input_length, bool uppercase)
Definition: hex.cpp:14