Bitcoin Core  24.99.0
P2P Digital Currency
bech32.cpp
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1 // Copyright (c) 2017, 2021 Pieter Wuille
2 // Copyright (c) 2021 The Bitcoin Core developers
3 // Distributed under the MIT software license, see the accompanying
4 // file COPYING or http://www.opensource.org/licenses/mit-license.php.
5 
6 #include <bech32.h>
7 #include <util/vector.h>
8 
9 #include <array>
10 #include <assert.h>
11 #include <numeric>
12 #include <optional>
13 
14 namespace bech32
15 {
16 
17 namespace
18 {
19 
20 typedef std::vector<uint8_t> data;
21 
23 const char* CHARSET = "qpzry9x8gf2tvdw0s3jn54khce6mua7l";
24 
26 const int8_t CHARSET_REV[128] = {
27  -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
28  -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
29  -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
30  15, -1, 10, 17, 21, 20, 26, 30, 7, 5, -1, -1, -1, -1, -1, -1,
31  -1, 29, -1, 24, 13, 25, 9, 8, 23, -1, 18, 22, 31, 27, 19, -1,
32  1, 0, 3, 16, 11, 28, 12, 14, 6, 4, 2, -1, -1, -1, -1, -1,
33  -1, 29, -1, 24, 13, 25, 9, 8, 23, -1, 18, 22, 31, 27, 19, -1,
34  1, 0, 3, 16, 11, 28, 12, 14, 6, 4, 2, -1, -1, -1, -1, -1
35 };
36 
46 constexpr std::pair<std::array<int16_t, 1023>, std::array<int16_t, 1024>> GenerateGFTables()
47 {
48  // Build table for GF(32).
49  // We use these tables to perform arithmetic in GF(32) below, when constructing the
50  // tables for GF(1024).
51  std::array<int8_t, 31> GF32_EXP{};
52  std::array<int8_t, 32> GF32_LOG{};
53 
54  // fmod encodes the defining polynomial of GF(32) over GF(2), x^5 + x^3 + 1.
55  // Because coefficients in GF(2) are binary digits, the coefficients are packed as 101001.
56  const int fmod = 41;
57 
58  // Elements of GF(32) are encoded as vectors of length 5 over GF(2), that is,
59  // 5 binary digits. Each element (b_4, b_3, b_2, b_1, b_0) encodes a polynomial
60  // b_4*x^4 + b_3*x^3 + b_2*x^2 + b_1*x^1 + b_0 (modulo fmod).
61  // For example, 00001 = 1 is the multiplicative identity.
62  GF32_EXP[0] = 1;
63  GF32_LOG[0] = -1;
64  GF32_LOG[1] = 0;
65  int v = 1;
66  for (int i = 1; i < 31; ++i) {
67  // Multiplication by x is the same as shifting left by 1, as
68  // every coefficient of the polynomial is moved up one place.
69  v = v << 1;
70  // If the polynomial now has an x^5 term, we subtract fmod from it
71  // to remain working modulo fmod. Subtraction is the same as XOR in characteristic
72  // 2 fields.
73  if (v & 32) v ^= fmod;
74  GF32_EXP[i] = v;
75  GF32_LOG[v] = i;
76  }
77 
78  // Build table for GF(1024)
79  std::array<int16_t, 1023> GF1024_EXP{};
80  std::array<int16_t, 1024> GF1024_LOG{};
81 
82  GF1024_EXP[0] = 1;
83  GF1024_LOG[0] = -1;
84  GF1024_LOG[1] = 0;
85 
86  // Each element v of GF(1024) is encoded as a 10 bit integer in the following way:
87  // v = v1 || v0 where v0, v1 are 5-bit integers (elements of GF(32)).
88  // The element (e) is encoded as 1 || 0, to represent 1*(e) + 0. Every other element
89  // a*(e) + b is represented as a || b (a and b are both GF(32) elements). Given (v),
90  // we compute (e)*(v) by multiplying in the following way:
91  //
92  // v0' = 23*v1
93  // v1' = 9*v1 + v0
94  // e*v = v1' || v0'
95  //
96  // Where 23, 9 are GF(32) elements encoded as described above. Multiplication in GF(32)
97  // is done using the log/exp tables:
98  // e^x * e^y = e^(x + y) so a * b = EXP[ LOG[a] + LOG [b] ]
99  // for non-zero a and b.
100 
101  v = 1;
102  for (int i = 1; i < 1023; ++i) {
103  int v0 = v & 31;
104  int v1 = v >> 5;
105 
106  int v0n = v1 ? GF32_EXP.at((GF32_LOG.at(v1) + GF32_LOG.at(23)) % 31) : 0;
107  int v1n = (v1 ? GF32_EXP.at((GF32_LOG.at(v1) + GF32_LOG.at(9)) % 31) : 0) ^ v0;
108 
109  v = v1n << 5 | v0n;
110  GF1024_EXP[i] = v;
111  GF1024_LOG[v] = i;
112  }
113 
114  return std::make_pair(GF1024_EXP, GF1024_LOG);
115 }
116 
117 constexpr auto tables = GenerateGFTables();
118 constexpr const std::array<int16_t, 1023>& GF1024_EXP = tables.first;
119 constexpr const std::array<int16_t, 1024>& GF1024_LOG = tables.second;
120 
121 /* Determine the final constant to use for the specified encoding. */
122 uint32_t EncodingConstant(Encoding encoding) {
123  assert(encoding == Encoding::BECH32 || encoding == Encoding::BECH32M);
124  return encoding == Encoding::BECH32 ? 1 : 0x2bc830a3;
125 }
126 
130 uint32_t PolyMod(const data& v)
131 {
132  // The input is interpreted as a list of coefficients of a polynomial over F = GF(32), with an
133  // implicit 1 in front. If the input is [v0,v1,v2,v3,v4], that polynomial is v(x) =
134  // 1*x^5 + v0*x^4 + v1*x^3 + v2*x^2 + v3*x + v4. The implicit 1 guarantees that
135  // [v0,v1,v2,...] has a distinct checksum from [0,v0,v1,v2,...].
136 
137  // The output is a 30-bit integer whose 5-bit groups are the coefficients of the remainder of
138  // v(x) mod g(x), where g(x) is the Bech32 generator,
139  // x^6 + {29}x^5 + {22}x^4 + {20}x^3 + {21}x^2 + {29}x + {18}. g(x) is chosen in such a way
140  // that the resulting code is a BCH code, guaranteeing detection of up to 3 errors within a
141  // window of 1023 characters. Among the various possible BCH codes, one was selected to in
142  // fact guarantee detection of up to 4 errors within a window of 89 characters.
143 
144  // Note that the coefficients are elements of GF(32), here represented as decimal numbers
145  // between {}. In this finite field, addition is just XOR of the corresponding numbers. For
146  // example, {27} + {13} = {27 ^ 13} = {22}. Multiplication is more complicated, and requires
147  // treating the bits of values themselves as coefficients of a polynomial over a smaller field,
148  // GF(2), and multiplying those polynomials mod a^5 + a^3 + 1. For example, {5} * {26} =
149  // (a^2 + 1) * (a^4 + a^3 + a) = (a^4 + a^3 + a) * a^2 + (a^4 + a^3 + a) = a^6 + a^5 + a^4 + a
150  // = a^3 + 1 (mod a^5 + a^3 + 1) = {9}.
151 
152  // During the course of the loop below, `c` contains the bitpacked coefficients of the
153  // polynomial constructed from just the values of v that were processed so far, mod g(x). In
154  // the above example, `c` initially corresponds to 1 mod g(x), and after processing 2 inputs of
155  // v, it corresponds to x^2 + v0*x + v1 mod g(x). As 1 mod g(x) = 1, that is the starting value
156  // for `c`.
157 
158  // The following Sage code constructs the generator used:
159  //
160  // B = GF(2) # Binary field
161  // BP.<b> = B[] # Polynomials over the binary field
162  // F_mod = b**5 + b**3 + 1
163  // F.<f> = GF(32, modulus=F_mod, repr='int') # GF(32) definition
164  // FP.<x> = F[] # Polynomials over GF(32)
165  // E_mod = x**2 + F.fetch_int(9)*x + F.fetch_int(23)
166  // E.<e> = F.extension(E_mod) # GF(1024) extension field definition
167  // for p in divisors(E.order() - 1): # Verify e has order 1023.
168  // assert((e**p == 1) == (p % 1023 == 0))
169  // G = lcm([(e**i).minpoly() for i in range(997,1000)])
170  // print(G) # Print out the generator
171  //
172  // It demonstrates that g(x) is the least common multiple of the minimal polynomials
173  // of 3 consecutive powers (997,998,999) of a primitive element (e) of GF(1024).
174  // That guarantees it is, in fact, the generator of a primitive BCH code with cycle
175  // length 1023 and distance 4. See https://en.wikipedia.org/wiki/BCH_code for more details.
176 
177  uint32_t c = 1;
178  for (const auto v_i : v) {
179  // We want to update `c` to correspond to a polynomial with one extra term. If the initial
180  // value of `c` consists of the coefficients of c(x) = f(x) mod g(x), we modify it to
181  // correspond to c'(x) = (f(x) * x + v_i) mod g(x), where v_i is the next input to
182  // process. Simplifying:
183  // c'(x) = (f(x) * x + v_i) mod g(x)
184  // ((f(x) mod g(x)) * x + v_i) mod g(x)
185  // (c(x) * x + v_i) mod g(x)
186  // If c(x) = c0*x^5 + c1*x^4 + c2*x^3 + c3*x^2 + c4*x + c5, we want to compute
187  // c'(x) = (c0*x^5 + c1*x^4 + c2*x^3 + c3*x^2 + c4*x + c5) * x + v_i mod g(x)
188  // = c0*x^6 + c1*x^5 + c2*x^4 + c3*x^3 + c4*x^2 + c5*x + v_i mod g(x)
189  // = c0*(x^6 mod g(x)) + c1*x^5 + c2*x^4 + c3*x^3 + c4*x^2 + c5*x + v_i
190  // If we call (x^6 mod g(x)) = k(x), this can be written as
191  // c'(x) = (c1*x^5 + c2*x^4 + c3*x^3 + c4*x^2 + c5*x + v_i) + c0*k(x)
192 
193  // First, determine the value of c0:
194  uint8_t c0 = c >> 25;
195 
196  // Then compute c1*x^5 + c2*x^4 + c3*x^3 + c4*x^2 + c5*x + v_i:
197  c = ((c & 0x1ffffff) << 5) ^ v_i;
198 
199  // Finally, for each set bit n in c0, conditionally add {2^n}k(x). These constants can be
200  // computed using the following Sage code (continuing the code above):
201  //
202  // for i in [1,2,4,8,16]: # Print out {1,2,4,8,16}*(g(x) mod x^6), packed in hex integers.
203  // v = 0
204  // for coef in reversed((F.fetch_int(i)*(G % x**6)).coefficients(sparse=True)):
205  // v = v*32 + coef.integer_representation()
206  // print("0x%x" % v)
207  //
208  if (c0 & 1) c ^= 0x3b6a57b2; // k(x) = {29}x^5 + {22}x^4 + {20}x^3 + {21}x^2 + {29}x + {18}
209  if (c0 & 2) c ^= 0x26508e6d; // {2}k(x) = {19}x^5 + {5}x^4 + x^3 + {3}x^2 + {19}x + {13}
210  if (c0 & 4) c ^= 0x1ea119fa; // {4}k(x) = {15}x^5 + {10}x^4 + {2}x^3 + {6}x^2 + {15}x + {26}
211  if (c0 & 8) c ^= 0x3d4233dd; // {8}k(x) = {30}x^5 + {20}x^4 + {4}x^3 + {12}x^2 + {30}x + {29}
212  if (c0 & 16) c ^= 0x2a1462b3; // {16}k(x) = {21}x^5 + x^4 + {8}x^3 + {24}x^2 + {21}x + {19}
213 
214  }
215  return c;
216 }
217 
240 constexpr std::array<uint32_t, 25> GenerateSyndromeConstants() {
241  std::array<uint32_t, 25> SYNDROME_CONSTS{};
242  for (int k = 1; k < 6; ++k) {
243  for (int shift = 0; shift < 5; ++shift) {
244  int16_t b = GF1024_LOG.at(1 << shift);
245  int16_t c0 = GF1024_EXP.at((997*k + b) % 1023);
246  int16_t c1 = GF1024_EXP.at((998*k + b) % 1023);
247  int16_t c2 = GF1024_EXP.at((999*k + b) % 1023);
248  uint32_t c = c2 << 20 | c1 << 10 | c0;
249  int ind = 5*(k-1) + shift;
250  SYNDROME_CONSTS[ind] = c;
251  }
252  }
253  return SYNDROME_CONSTS;
254 }
255 constexpr std::array<uint32_t, 25> SYNDROME_CONSTS = GenerateSyndromeConstants();
256 
261 uint32_t Syndrome(const uint32_t residue) {
262  // low is the first 5 bits, corresponding to the r6 in the residue
263  // (the constant term of the polynomial).
264  uint32_t low = residue & 0x1f;
265 
266  // We begin by setting s_j = low = r6 for all three values of j, because these are unconditional.
267  uint32_t result = low ^ (low << 10) ^ (low << 20);
268 
269  // Then for each following bit, we add the corresponding precomputed constant if the bit is 1.
270  // For example, 0x31edd3c4 is 1100011110 1101110100 1111000100 when unpacked in groups of 10
271  // bits, corresponding exactly to a^999 || a^998 || a^997 (matching the corresponding values in
272  // GF1024_EXP above). In this way, we compute all three values of s_j for j in (997, 998, 999)
273  // simultaneously. Recall that XOR corresponds to addition in a characteristic 2 field.
274  for (int i = 0; i < 25; ++i) {
275  result ^= ((residue >> (5+i)) & 1 ? SYNDROME_CONSTS.at(i) : 0);
276  }
277  return result;
278 }
279 
281 inline unsigned char LowerCase(unsigned char c)
282 {
283  return (c >= 'A' && c <= 'Z') ? (c - 'A') + 'a' : c;
284 }
285 
287 bool CheckCharacters(const std::string& str, std::vector<int>& errors)
288 {
289  bool lower = false, upper = false;
290  for (size_t i = 0; i < str.size(); ++i) {
291  unsigned char c{(unsigned char)(str[i])};
292  if (c >= 'a' && c <= 'z') {
293  if (upper) {
294  errors.push_back(i);
295  } else {
296  lower = true;
297  }
298  } else if (c >= 'A' && c <= 'Z') {
299  if (lower) {
300  errors.push_back(i);
301  } else {
302  upper = true;
303  }
304  } else if (c < 33 || c > 126) {
305  errors.push_back(i);
306  }
307  }
308  return errors.empty();
309 }
310 
312 data ExpandHRP(const std::string& hrp)
313 {
314  data ret;
315  ret.reserve(hrp.size() + 90);
316  ret.resize(hrp.size() * 2 + 1);
317  for (size_t i = 0; i < hrp.size(); ++i) {
318  unsigned char c = hrp[i];
319  ret[i] = c >> 5;
320  ret[i + hrp.size() + 1] = c & 0x1f;
321  }
322  ret[hrp.size()] = 0;
323  return ret;
324 }
325 
327 Encoding VerifyChecksum(const std::string& hrp, const data& values)
328 {
329  // PolyMod computes what value to xor into the final values to make the checksum 0. However,
330  // if we required that the checksum was 0, it would be the case that appending a 0 to a valid
331  // list of values would result in a new valid list. For that reason, Bech32 requires the
332  // resulting checksum to be 1 instead. In Bech32m, this constant was amended. See
333  // https://gist.github.com/sipa/14c248c288c3880a3b191f978a34508e for details.
334  const uint32_t check = PolyMod(Cat(ExpandHRP(hrp), values));
335  if (check == EncodingConstant(Encoding::BECH32)) return Encoding::BECH32;
336  if (check == EncodingConstant(Encoding::BECH32M)) return Encoding::BECH32M;
337  return Encoding::INVALID;
338 }
339 
341 data CreateChecksum(Encoding encoding, const std::string& hrp, const data& values)
342 {
343  data enc = Cat(ExpandHRP(hrp), values);
344  enc.resize(enc.size() + 6); // Append 6 zeroes
345  uint32_t mod = PolyMod(enc) ^ EncodingConstant(encoding); // Determine what to XOR into those 6 zeroes.
346  data ret(6);
347  for (size_t i = 0; i < 6; ++i) {
348  // Convert the 5-bit groups in mod to checksum values.
349  ret[i] = (mod >> (5 * (5 - i))) & 31;
350  }
351  return ret;
352 }
353 
354 } // namespace
355 
357 std::string Encode(Encoding encoding, const std::string& hrp, const data& values) {
358  // First ensure that the HRP is all lowercase. BIP-173 and BIP350 require an encoder
359  // to return a lowercase Bech32/Bech32m string, but if given an uppercase HRP, the
360  // result will always be invalid.
361  for (const char& c : hrp) assert(c < 'A' || c > 'Z');
362  data checksum = CreateChecksum(encoding, hrp, values);
363  data combined = Cat(values, checksum);
364  std::string ret = hrp + '1';
365  ret.reserve(ret.size() + combined.size());
366  for (const auto c : combined) {
367  ret += CHARSET[c];
368  }
369  return ret;
370 }
371 
373 DecodeResult Decode(const std::string& str) {
374  std::vector<int> errors;
375  if (!CheckCharacters(str, errors)) return {};
376  size_t pos = str.rfind('1');
377  if (str.size() > 90 || pos == str.npos || pos == 0 || pos + 7 > str.size()) {
378  return {};
379  }
380  data values(str.size() - 1 - pos);
381  for (size_t i = 0; i < str.size() - 1 - pos; ++i) {
382  unsigned char c = str[i + pos + 1];
383  int8_t rev = CHARSET_REV[c];
384 
385  if (rev == -1) {
386  return {};
387  }
388  values[i] = rev;
389  }
390  std::string hrp;
391  for (size_t i = 0; i < pos; ++i) {
392  hrp += LowerCase(str[i]);
393  }
394  Encoding result = VerifyChecksum(hrp, values);
395  if (result == Encoding::INVALID) return {};
396  return {result, std::move(hrp), data(values.begin(), values.end() - 6)};
397 }
398 
400 std::pair<std::string, std::vector<int>> LocateErrors(const std::string& str) {
401  std::vector<int> error_locations{};
402 
403  if (str.size() > 90) {
404  error_locations.resize(str.size() - 90);
405  std::iota(error_locations.begin(), error_locations.end(), 90);
406  return std::make_pair("Bech32 string too long", std::move(error_locations));
407  }
408 
409  if (!CheckCharacters(str, error_locations)){
410  return std::make_pair("Invalid character or mixed case", std::move(error_locations));
411  }
412 
413  size_t pos = str.rfind('1');
414  if (pos == str.npos) {
415  return std::make_pair("Missing separator", std::vector<int>{});
416  }
417  if (pos == 0 || pos + 7 > str.size()) {
418  error_locations.push_back(pos);
419  return std::make_pair("Invalid separator position", std::move(error_locations));
420  }
421 
422  std::string hrp;
423  for (size_t i = 0; i < pos; ++i) {
424  hrp += LowerCase(str[i]);
425  }
426 
427  size_t length = str.size() - 1 - pos; // length of data part
428  data values(length);
429  for (size_t i = pos + 1; i < str.size(); ++i) {
430  unsigned char c = str[i];
431  int8_t rev = CHARSET_REV[c];
432  if (rev == -1) {
433  error_locations.push_back(i);
434  return std::make_pair("Invalid Base 32 character", std::move(error_locations));
435  }
436  values[i - pos - 1] = rev;
437  }
438 
439  // We attempt error detection with both bech32 and bech32m, and choose the one with the fewest errors
440  // We can't simply use the segwit version, because that may be one of the errors
441  std::optional<Encoding> error_encoding;
442  for (Encoding encoding : {Encoding::BECH32, Encoding::BECH32M}) {
443  std::vector<int> possible_errors;
444  // Recall that (ExpandHRP(hrp) ++ values) is interpreted as a list of coefficients of a polynomial
445  // over GF(32). PolyMod computes the "remainder" of this polynomial modulo the generator G(x).
446  uint32_t residue = PolyMod(Cat(ExpandHRP(hrp), values)) ^ EncodingConstant(encoding);
447 
448  // All valid codewords should be multiples of G(x), so this remainder (after XORing with the encoding
449  // constant) should be 0 - hence 0 indicates there are no errors present.
450  if (residue != 0) {
451  // If errors are present, our polynomial must be of the form C(x) + E(x) where C is the valid
452  // codeword (a multiple of G(x)), and E encodes the errors.
453  uint32_t syn = Syndrome(residue);
454 
455  // Unpack the three 10-bit syndrome values
456  int s0 = syn & 0x3FF;
457  int s1 = (syn >> 10) & 0x3FF;
458  int s2 = syn >> 20;
459 
460  // Get the discrete logs of these values in GF1024 for more efficient computation
461  int l_s0 = GF1024_LOG.at(s0);
462  int l_s1 = GF1024_LOG.at(s1);
463  int l_s2 = GF1024_LOG.at(s2);
464 
465  // First, suppose there is only a single error. Then E(x) = e1*x^p1 for some position p1
466  // Then s0 = E((e)^997) = e1*(e)^(997*p1) and s1 = E((e)^998) = e1*(e)^(998*p1)
467  // Therefore s1/s0 = (e)^p1, and by the same logic, s2/s1 = (e)^p1 too.
468  // Hence, s1^2 == s0*s2, which is exactly the condition we check first:
469  if (l_s0 != -1 && l_s1 != -1 && l_s2 != -1 && (2 * l_s1 - l_s2 - l_s0 + 2046) % 1023 == 0) {
470  // Compute the error position p1 as l_s1 - l_s0 = p1 (mod 1023)
471  size_t p1 = (l_s1 - l_s0 + 1023) % 1023; // the +1023 ensures it is positive
472  // Now because s0 = e1*(e)^(997*p1), we get e1 = s0/((e)^(997*p1)). Remember that (e)^1023 = 1,
473  // so 1/((e)^997) = (e)^(1023-997).
474  int l_e1 = l_s0 + (1023 - 997) * p1;
475  // Finally, some sanity checks on the result:
476  // - The error position should be within the length of the data
477  // - e1 should be in GF(32), which implies that e1 = (e)^(33k) for some k (the 31 non-zero elements
478  // of GF(32) form an index 33 subgroup of the 1023 non-zero elements of GF(1024)).
479  if (p1 < length && !(l_e1 % 33)) {
480  // Polynomials run from highest power to lowest, so the index p1 is from the right.
481  // We don't return e1 because it is dangerous to suggest corrections to the user,
482  // the user should check the address themselves.
483  possible_errors.push_back(str.size() - p1 - 1);
484  }
485  // Otherwise, suppose there are two errors. Then E(x) = e1*x^p1 + e2*x^p2.
486  } else {
487  // For all possible first error positions p1
488  for (size_t p1 = 0; p1 < length; ++p1) {
489  // We have guessed p1, and want to solve for p2. Recall that E(x) = e1*x^p1 + e2*x^p2, so
490  // s0 = E((e)^997) = e1*(e)^(997^p1) + e2*(e)^(997*p2), and similar for s1 and s2.
491  //
492  // Consider s2 + s1*(e)^p1
493  // = 2e1*(e)^(999^p1) + e2*(e)^(999*p2) + e2*(e)^(998*p2)*(e)^p1
494  // = e2*(e)^(999*p2) + e2*(e)^(998*p2)*(e)^p1
495  // (Because we are working in characteristic 2.)
496  // = e2*(e)^(998*p2) ((e)^p2 + (e)^p1)
497  //
498  int s2_s1p1 = s2 ^ (s1 == 0 ? 0 : GF1024_EXP.at((l_s1 + p1) % 1023));
499  if (s2_s1p1 == 0) continue;
500  int l_s2_s1p1 = GF1024_LOG.at(s2_s1p1);
501 
502  // Similarly, s1 + s0*(e)^p1
503  // = e2*(e)^(997*p2) ((e)^p2 + (e)^p1)
504  int s1_s0p1 = s1 ^ (s0 == 0 ? 0 : GF1024_EXP.at((l_s0 + p1) % 1023));
505  if (s1_s0p1 == 0) continue;
506  int l_s1_s0p1 = GF1024_LOG.at(s1_s0p1);
507 
508  // So, putting these together, we can compute the second error position as
509  // (e)^p2 = (s2 + s1^p1)/(s1 + s0^p1)
510  // p2 = log((e)^p2)
511  size_t p2 = (l_s2_s1p1 - l_s1_s0p1 + 1023) % 1023;
512 
513  // Sanity checks that p2 is a valid position and not the same as p1
514  if (p2 >= length || p1 == p2) continue;
515 
516  // Now we want to compute the error values e1 and e2.
517  // Similar to above, we compute s1 + s0*(e)^p2
518  // = e1*(e)^(997*p1) ((e)^p1 + (e)^p2)
519  int s1_s0p2 = s1 ^ (s0 == 0 ? 0 : GF1024_EXP.at((l_s0 + p2) % 1023));
520  if (s1_s0p2 == 0) continue;
521  int l_s1_s0p2 = GF1024_LOG.at(s1_s0p2);
522 
523  // And compute (the log of) 1/((e)^p1 + (e)^p2))
524  int inv_p1_p2 = 1023 - GF1024_LOG.at(GF1024_EXP.at(p1) ^ GF1024_EXP.at(p2));
525 
526  // Then (s1 + s0*(e)^p1) * (1/((e)^p1 + (e)^p2)))
527  // = e2*(e)^(997*p2)
528  // Then recover e2 by dividing by (e)^(997*p2)
529  int l_e2 = l_s1_s0p1 + inv_p1_p2 + (1023 - 997) * p2;
530  // Check that e2 is in GF(32)
531  if (l_e2 % 33) continue;
532 
533  // In the same way, (s1 + s0*(e)^p2) * (1/((e)^p1 + (e)^p2)))
534  // = e1*(e)^(997*p1)
535  // So recover e1 by dividing by (e)^(997*p1)
536  int l_e1 = l_s1_s0p2 + inv_p1_p2 + (1023 - 997) * p1;
537  // Check that e1 is in GF(32)
538  if (l_e1 % 33) continue;
539 
540  // Again, we do not return e1 or e2 for safety.
541  // Order the error positions from the left of the string and return them
542  if (p1 > p2) {
543  possible_errors.push_back(str.size() - p1 - 1);
544  possible_errors.push_back(str.size() - p2 - 1);
545  } else {
546  possible_errors.push_back(str.size() - p2 - 1);
547  possible_errors.push_back(str.size() - p1 - 1);
548  }
549  break;
550  }
551  }
552  } else {
553  // No errors
554  return std::make_pair("", std::vector<int>{});
555  }
556 
557  if (error_locations.empty() || (!possible_errors.empty() && possible_errors.size() < error_locations.size())) {
558  error_locations = std::move(possible_errors);
559  if (!error_locations.empty()) error_encoding = encoding;
560  }
561  }
562  std::string error_message = error_encoding == Encoding::BECH32M ? "Invalid Bech32m checksum"
563  : error_encoding == Encoding::BECH32 ? "Invalid Bech32 checksum"
564  : "Invalid checksum";
565 
566  return std::make_pair(error_message, std::move(error_locations));
567 }
568 
569 } // namespace bech32
int ret
Encoding
Definition: bech32.h:24
@ INVALID
Failed decoding.
@ BECH32
Bech32 encoding as defined in BIP173.
@ BECH32M
Bech32m encoding as defined in BIP350.
std::string Encode(Encoding encoding, const std::string &hrp, const data &values)
Encode a Bech32 or Bech32m string.
Definition: bech32.cpp:357
DecodeResult Decode(const std::string &str)
Decode a Bech32 or Bech32m string.
Definition: bech32.cpp:373
std::pair< std::string, std::vector< int > > LocateErrors(const std::string &str)
Find index of an incorrect character in a Bech32 string.
Definition: bech32.cpp:400
static const int64_t values[]
A selection of numbers that do not trigger int64_t overflow when added/subtracted.
void PolyMod(const std::vector< typename F::Elem > &mod, std::vector< typename F::Elem > &val, const F &field)
Compute the remainder of a polynomial division of val by mod, putting the result in mod.
Definition: sketch_impl.h:18
assert(!tx.IsCoinBase())
V Cat(V v1, V &&v2)
Concatenate two vectors, moving elements.
Definition: vector.h:32