Botan  2.7.0
Crypto and TLS for C++11
tss.cpp
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1 /*
2 * RTSS (threshold secret sharing)
3 * (C) 2009 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 /**
19 Table for GF(2^8) arithmetic (exponentials)
20 */
21 const uint8_t RTSS_EXP[256] = {
22 0x01, 0x03, 0x05, 0x0F, 0x11, 0x33, 0x55, 0xFF, 0x1A, 0x2E, 0x72,
23 0x96, 0xA1, 0xF8, 0x13, 0x35, 0x5F, 0xE1, 0x38, 0x48, 0xD8, 0x73,
24 0x95, 0xA4, 0xF7, 0x02, 0x06, 0x0A, 0x1E, 0x22, 0x66, 0xAA, 0xE5,
25 0x34, 0x5C, 0xE4, 0x37, 0x59, 0xEB, 0x26, 0x6A, 0xBE, 0xD9, 0x70,
26 0x90, 0xAB, 0xE6, 0x31, 0x53, 0xF5, 0x04, 0x0C, 0x14, 0x3C, 0x44,
27 0xCC, 0x4F, 0xD1, 0x68, 0xB8, 0xD3, 0x6E, 0xB2, 0xCD, 0x4C, 0xD4,
28 0x67, 0xA9, 0xE0, 0x3B, 0x4D, 0xD7, 0x62, 0xA6, 0xF1, 0x08, 0x18,
29 0x28, 0x78, 0x88, 0x83, 0x9E, 0xB9, 0xD0, 0x6B, 0xBD, 0xDC, 0x7F,
30 0x81, 0x98, 0xB3, 0xCE, 0x49, 0xDB, 0x76, 0x9A, 0xB5, 0xC4, 0x57,
31 0xF9, 0x10, 0x30, 0x50, 0xF0, 0x0B, 0x1D, 0x27, 0x69, 0xBB, 0xD6,
32 0x61, 0xA3, 0xFE, 0x19, 0x2B, 0x7D, 0x87, 0x92, 0xAD, 0xEC, 0x2F,
33 0x71, 0x93, 0xAE, 0xE9, 0x20, 0x60, 0xA0, 0xFB, 0x16, 0x3A, 0x4E,
34 0xD2, 0x6D, 0xB7, 0xC2, 0x5D, 0xE7, 0x32, 0x56, 0xFA, 0x15, 0x3F,
35 0x41, 0xC3, 0x5E, 0xE2, 0x3D, 0x47, 0xC9, 0x40, 0xC0, 0x5B, 0xED,
36 0x2C, 0x74, 0x9C, 0xBF, 0xDA, 0x75, 0x9F, 0xBA, 0xD5, 0x64, 0xAC,
37 0xEF, 0x2A, 0x7E, 0x82, 0x9D, 0xBC, 0xDF, 0x7A, 0x8E, 0x89, 0x80,
38 0x9B, 0xB6, 0xC1, 0x58, 0xE8, 0x23, 0x65, 0xAF, 0xEA, 0x25, 0x6F,
39 0xB1, 0xC8, 0x43, 0xC5, 0x54, 0xFC, 0x1F, 0x21, 0x63, 0xA5, 0xF4,
40 0x07, 0x09, 0x1B, 0x2D, 0x77, 0x99, 0xB0, 0xCB, 0x46, 0xCA, 0x45,
41 0xCF, 0x4A, 0xDE, 0x79, 0x8B, 0x86, 0x91, 0xA8, 0xE3, 0x3E, 0x42,
42 0xC6, 0x51, 0xF3, 0x0E, 0x12, 0x36, 0x5A, 0xEE, 0x29, 0x7B, 0x8D,
43 0x8C, 0x8F, 0x8A, 0x85, 0x94, 0xA7, 0xF2, 0x0D, 0x17, 0x39, 0x4B,
44 0xDD, 0x7C, 0x84, 0x97, 0xA2, 0xFD, 0x1C, 0x24, 0x6C, 0xB4, 0xC7,
45 0x52, 0xF6, 0x01 };
46 
47 /**
48 Table for GF(2^8) arithmetic (logarithms)
49 */
50 const uint8_t RTSS_LOG[] = {
51 0x90, 0x00, 0x19, 0x01, 0x32, 0x02, 0x1A, 0xC6, 0x4B, 0xC7, 0x1B,
52 0x68, 0x33, 0xEE, 0xDF, 0x03, 0x64, 0x04, 0xE0, 0x0E, 0x34, 0x8D,
53 0x81, 0xEF, 0x4C, 0x71, 0x08, 0xC8, 0xF8, 0x69, 0x1C, 0xC1, 0x7D,
54 0xC2, 0x1D, 0xB5, 0xF9, 0xB9, 0x27, 0x6A, 0x4D, 0xE4, 0xA6, 0x72,
55 0x9A, 0xC9, 0x09, 0x78, 0x65, 0x2F, 0x8A, 0x05, 0x21, 0x0F, 0xE1,
56 0x24, 0x12, 0xF0, 0x82, 0x45, 0x35, 0x93, 0xDA, 0x8E, 0x96, 0x8F,
57 0xDB, 0xBD, 0x36, 0xD0, 0xCE, 0x94, 0x13, 0x5C, 0xD2, 0xF1, 0x40,
58 0x46, 0x83, 0x38, 0x66, 0xDD, 0xFD, 0x30, 0xBF, 0x06, 0x8B, 0x62,
59 0xB3, 0x25, 0xE2, 0x98, 0x22, 0x88, 0x91, 0x10, 0x7E, 0x6E, 0x48,
60 0xC3, 0xA3, 0xB6, 0x1E, 0x42, 0x3A, 0x6B, 0x28, 0x54, 0xFA, 0x85,
61 0x3D, 0xBA, 0x2B, 0x79, 0x0A, 0x15, 0x9B, 0x9F, 0x5E, 0xCA, 0x4E,
62 0xD4, 0xAC, 0xE5, 0xF3, 0x73, 0xA7, 0x57, 0xAF, 0x58, 0xA8, 0x50,
63 0xF4, 0xEA, 0xD6, 0x74, 0x4F, 0xAE, 0xE9, 0xD5, 0xE7, 0xE6, 0xAD,
64 0xE8, 0x2C, 0xD7, 0x75, 0x7A, 0xEB, 0x16, 0x0B, 0xF5, 0x59, 0xCB,
65 0x5F, 0xB0, 0x9C, 0xA9, 0x51, 0xA0, 0x7F, 0x0C, 0xF6, 0x6F, 0x17,
66 0xC4, 0x49, 0xEC, 0xD8, 0x43, 0x1F, 0x2D, 0xA4, 0x76, 0x7B, 0xB7,
67 0xCC, 0xBB, 0x3E, 0x5A, 0xFB, 0x60, 0xB1, 0x86, 0x3B, 0x52, 0xA1,
68 0x6C, 0xAA, 0x55, 0x29, 0x9D, 0x97, 0xB2, 0x87, 0x90, 0x61, 0xBE,
69 0xDC, 0xFC, 0xBC, 0x95, 0xCF, 0xCD, 0x37, 0x3F, 0x5B, 0xD1, 0x53,
70 0x39, 0x84, 0x3C, 0x41, 0xA2, 0x6D, 0x47, 0x14, 0x2A, 0x9E, 0x5D,
71 0x56, 0xF2, 0xD3, 0xAB, 0x44, 0x11, 0x92, 0xD9, 0x23, 0x20, 0x2E,
72 0x89, 0xB4, 0x7C, 0xB8, 0x26, 0x77, 0x99, 0xE3, 0xA5, 0x67, 0x4A,
73 0xED, 0xDE, 0xC5, 0x31, 0xFE, 0x18, 0x0D, 0x63, 0x8C, 0x80, 0xC0,
74 0xF7, 0x70, 0x07 };
75 
76 uint8_t gfp_mul(uint8_t x, uint8_t y)
77  {
78  if(x == 0 || y == 0)
79  return 0;
80  return RTSS_EXP[(RTSS_LOG[x] + RTSS_LOG[y]) % 255];
81  }
82 
83 uint8_t rtss_hash_id(const std::string& hash_name)
84  {
85  if(hash_name == "SHA-160" || hash_name == "SHA-1" || hash_name == "SHA1")
86  return 1;
87  else if(hash_name == "SHA-256")
88  return 2;
89  else
90  throw Invalid_Argument("RTSS only supports SHA-1 and SHA-256");
91  }
92 
93 std::unique_ptr<HashFunction> get_rtss_hash_by_id(uint8_t id)
94  {
95  if(id == 1)
96  return HashFunction::create_or_throw("SHA-1");
97  else if(id == 2)
98  return HashFunction::create_or_throw("SHA-256");
99  else
100  throw Decoding_Error("Bad RTSS hash identifier");
101  }
102 
103 }
104 
105 RTSS_Share::RTSS_Share(const std::string& hex_input)
106  {
107  m_contents = hex_decode_locked(hex_input);
108  }
109 
110 uint8_t RTSS_Share::share_id() const
111  {
112  if(!initialized())
113  throw Invalid_State("RTSS_Share::share_id not initialized");
114 
115  return m_contents[20];
116  }
117 
118 std::string RTSS_Share::to_string() const
119  {
120  return hex_encode(m_contents.data(), m_contents.size());
121  }
122 
123 std::vector<RTSS_Share>
124 RTSS_Share::split(uint8_t M, uint8_t N,
125  const uint8_t S[], uint16_t S_len,
126  const uint8_t identifier[16],
128  {
129  if(M == 0 || N == 0 || M > N)
130  throw Encoding_Error("RTSS_Share::split: M == 0 or N == 0 or M > N");
131 
132  // always use SHA-256 when generating shares
133  std::unique_ptr<HashFunction> hash = HashFunction::create_or_throw("SHA-256");
134 
135  std::vector<RTSS_Share> shares(N);
136 
137  // Create RTSS header in each share
138  for(uint8_t i = 0; i != N; ++i)
139  {
140  shares[i].m_contents += std::make_pair(identifier, 16);
141  shares[i].m_contents += rtss_hash_id(hash->name());
142  shares[i].m_contents += M;
143  shares[i].m_contents += get_byte(0, S_len);
144  shares[i].m_contents += get_byte(1, S_len);
145  }
146 
147  // Choose sequential values for X starting from 1
148  for(uint8_t i = 0; i != N; ++i)
149  shares[i].m_contents.push_back(i+1);
150 
151  // secret = S || H(S)
152  secure_vector<uint8_t> secret(S, S + S_len);
153  secret += hash->process(S, S_len);
154 
155  for(size_t i = 0; i != secret.size(); ++i)
156  {
157  std::vector<uint8_t> coefficients(M-1);
158  rng.randomize(coefficients.data(), coefficients.size());
159 
160  for(uint8_t j = 0; j != N; ++j)
161  {
162  const uint8_t X = j + 1;
163 
164  uint8_t sum = secret[i];
165  uint8_t X_i = X;
166 
167  for(size_t k = 0; k != coefficients.size(); ++k)
168  {
169  sum ^= gfp_mul(X_i, coefficients[k]);
170  X_i = gfp_mul(X_i, X);
171  }
172 
173  shares[j].m_contents.push_back(sum);
174  }
175  }
176 
177  return shares;
178  }
179 
181 RTSS_Share::reconstruct(const std::vector<RTSS_Share>& shares)
182  {
183  const size_t RTSS_HEADER_SIZE = 20;
184 
185  for(size_t i = 0; i != shares.size(); ++i)
186  {
187  if(shares[i].size() != shares[0].size())
188  throw Decoding_Error("Different sized RTSS shares detected");
189  if(shares[i].share_id() == 0)
190  throw Decoding_Error("Invalid (id = 0) RTSS share detected");
191  if(shares[i].size() < RTSS_HEADER_SIZE)
192  throw Decoding_Error("Missing or malformed RTSS header");
193 
194  if(!same_mem(&shares[0].m_contents[0],
195  &shares[i].m_contents[0], RTSS_HEADER_SIZE))
196  throw Decoding_Error("Different RTSS headers detected");
197  }
198 
199  if(shares.size() < shares[0].m_contents[17])
200  throw Decoding_Error("Insufficient shares to do TSS reconstruction");
201 
202  uint16_t secret_len = make_uint16(shares[0].m_contents[18],
203  shares[0].m_contents[19]);
204 
205  uint8_t hash_id = shares[0].m_contents[16];
206 
207  std::unique_ptr<HashFunction> hash(get_rtss_hash_by_id(hash_id));
208 
209  if(shares[0].size() != secret_len + hash->output_length() + RTSS_HEADER_SIZE + 1)
210  throw Decoding_Error("Bad RTSS length field in header");
211 
212  std::vector<uint8_t> V(shares.size());
213  secure_vector<uint8_t> secret;
214 
215  for(size_t i = RTSS_HEADER_SIZE + 1; i != shares[0].size(); ++i)
216  {
217  for(size_t j = 0; j != V.size(); ++j)
218  V[j] = shares[j].m_contents[i];
219 
220  uint8_t r = 0;
221  for(size_t k = 0; k != shares.size(); ++k)
222  {
223  // L_i function:
224  uint8_t r2 = 1;
225  for(size_t l = 0; l != shares.size(); ++l)
226  {
227  if(k == l)
228  continue;
229 
230  uint8_t share_k = shares[k].share_id();
231  uint8_t share_l = shares[l].share_id();
232 
233  if(share_k == share_l)
234  throw Decoding_Error("Duplicate shares found in RTSS recovery");
235 
236  uint8_t div = RTSS_EXP[(255 +
237  RTSS_LOG[share_l] -
238  RTSS_LOG[share_k ^ share_l]) % 255];
239 
240  r2 = gfp_mul(r2, div);
241  }
242 
243  r ^= gfp_mul(V[k], r2);
244  }
245  secret.push_back(r);
246  }
247 
248  if(secret.size() != secret_len + hash->output_length())
249  throw Decoding_Error("Bad length in RTSS output");
250 
251  hash->update(secret.data(), secret_len);
252  secure_vector<uint8_t> hash_check = hash->final();
253 
254  if(!constant_time_compare(hash_check.data(),
255  &secret[secret_len],
256  hash->output_length()))
257  {
258  throw Decoding_Error("RTSS hash check failed");
259  }
260 
261  return secure_vector<uint8_t>(secret.cbegin(), secret.cbegin() + secret_len);
262  }
263 
264 }
fe X
Definition: ge.cpp:27
void hex_encode(char output[], const uint8_t input[], size_t input_length, bool uppercase)
Definition: hex.cpp:14
static secure_vector< uint8_t > reconstruct(const std::vector< RTSS_Share > &shares)
Definition: tss.cpp:181
static std::unique_ptr< HashFunction > create_or_throw(const std::string &algo_spec, const std::string &provider="")
Definition: hash.cpp:345
bool same_mem(const T *p1, const T *p2, size_t n)
Definition: mem_ops.h:158
RTSS_Share()=default
secure_vector< uint8_t > hex_decode_locked(const char input[], size_t input_length, bool ignore_ws)
Definition: hex.cpp:165
virtual void randomize(uint8_t output[], size_t length)=0
bool constant_time_compare(const uint8_t x[], const uint8_t y[], size_t len)
Definition: mem_ops.cpp:51
uint8_t share_id() const
Definition: tss.cpp:110
std::string to_string() const
Definition: tss.cpp:118
size_t size() const
Definition: tss.h:64
bool initialized() const
Definition: tss.h:69
Definition: alg_id.cpp:13
static std::vector< RTSS_Share > split(uint8_t M, uint8_t N, const uint8_t secret[], uint16_t secret_len, const uint8_t identifier[16], RandomNumberGenerator &rng)
Definition: tss.cpp:124
uint16_t make_uint16(uint8_t i0, uint8_t i1)
Definition: loadstor.h:52
uint8_t get_byte(size_t byte_num, T input)
Definition: loadstor.h:39
std::vector< T, secure_allocator< T > > secure_vector
Definition: secmem.h:88
MechanismType hash