Bitcoin Core  0.18.99
P2P Digital Currency
bech32.cpp
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1 // Copyright (c) 2017 Pieter Wuille
2 // Distributed under the MIT software license, see the accompanying
3 // file COPYING or http://www.opensource.org/licenses/mit-license.php.
4 
5 #include <bech32.h>
6 
7 namespace
8 {
9 
10 typedef std::vector<uint8_t> data;
11 
13 const char* CHARSET = "qpzry9x8gf2tvdw0s3jn54khce6mua7l";
14 
16 const int8_t CHARSET_REV[128] = {
17  -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
18  -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
19  -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
20  15, -1, 10, 17, 21, 20, 26, 30, 7, 5, -1, -1, -1, -1, -1, -1,
21  -1, 29, -1, 24, 13, 25, 9, 8, 23, -1, 18, 22, 31, 27, 19, -1,
22  1, 0, 3, 16, 11, 28, 12, 14, 6, 4, 2, -1, -1, -1, -1, -1,
23  -1, 29, -1, 24, 13, 25, 9, 8, 23, -1, 18, 22, 31, 27, 19, -1,
24  1, 0, 3, 16, 11, 28, 12, 14, 6, 4, 2, -1, -1, -1, -1, -1
25 };
26 
28 data Cat(data x, const data& y)
29 {
30  x.insert(x.end(), y.begin(), y.end());
31  return x;
32 }
33 
37 uint32_t PolyMod(const data& v)
38 {
39  // The input is interpreted as a list of coefficients of a polynomial over F = GF(32), with an
40  // implicit 1 in front. If the input is [v0,v1,v2,v3,v4], that polynomial is v(x) =
41  // 1*x^5 + v0*x^4 + v1*x^3 + v2*x^2 + v3*x + v4. The implicit 1 guarantees that
42  // [v0,v1,v2,...] has a distinct checksum from [0,v0,v1,v2,...].
43 
44  // The output is a 30-bit integer whose 5-bit groups are the coefficients of the remainder of
45  // v(x) mod g(x), where g(x) is the Bech32 generator,
46  // 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
47  // that the resulting code is a BCH code, guaranteeing detection of up to 3 errors within a
48  // window of 1023 characters. Among the various possible BCH codes, one was selected to in
49  // fact guarantee detection of up to 4 errors within a window of 89 characters.
50 
51  // Note that the coefficients are elements of GF(32), here represented as decimal numbers
52  // between {}. In this finite field, addition is just XOR of the corresponding numbers. For
53  // example, {27} + {13} = {27 ^ 13} = {22}. Multiplication is more complicated, and requires
54  // treating the bits of values themselves as coefficients of a polynomial over a smaller field,
55  // GF(2), and multiplying those polynomials mod a^5 + a^3 + 1. For example, {5} * {26} =
56  // (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
57  // = a^3 + 1 (mod a^5 + a^3 + 1) = {9}.
58 
59  // During the course of the loop below, `c` contains the bitpacked coefficients of the
60  // polynomial constructed from just the values of v that were processed so far, mod g(x). In
61  // the above example, `c` initially corresponds to 1 mod (x), and after processing 2 inputs of
62  // v, it corresponds to x^2 + v0*x + v1 mod g(x). As 1 mod g(x) = 1, that is the starting value
63  // for `c`.
64  uint32_t c = 1;
65  for (const auto v_i : v) {
66  // We want to update `c` to correspond to a polynomial with one extra term. If the initial
67  // value of `c` consists of the coefficients of c(x) = f(x) mod g(x), we modify it to
68  // correspond to c'(x) = (f(x) * x + v_i) mod g(x), where v_i is the next input to
69  // process. Simplifying:
70  // c'(x) = (f(x) * x + v_i) mod g(x)
71  // ((f(x) mod g(x)) * x + v_i) mod g(x)
72  // (c(x) * x + v_i) mod g(x)
73  // If c(x) = c0*x^5 + c1*x^4 + c2*x^3 + c3*x^2 + c4*x + c5, we want to compute
74  // c'(x) = (c0*x^5 + c1*x^4 + c2*x^3 + c3*x^2 + c4*x + c5) * x + v_i mod g(x)
75  // = c0*x^6 + c1*x^5 + c2*x^4 + c3*x^3 + c4*x^2 + c5*x + v_i mod g(x)
76  // = c0*(x^6 mod g(x)) + c1*x^5 + c2*x^4 + c3*x^3 + c4*x^2 + c5*x + v_i
77  // If we call (x^6 mod g(x)) = k(x), this can be written as
78  // c'(x) = (c1*x^5 + c2*x^4 + c3*x^3 + c4*x^2 + c5*x + v_i) + c0*k(x)
79 
80  // First, determine the value of c0:
81  uint8_t c0 = c >> 25;
82 
83  // Then compute c1*x^5 + c2*x^4 + c3*x^3 + c4*x^2 + c5*x + v_i:
84  c = ((c & 0x1ffffff) << 5) ^ v_i;
85 
86  // Finally, for each set bit n in c0, conditionally add {2^n}k(x):
87  if (c0 & 1) c ^= 0x3b6a57b2; // k(x) = {29}x^5 + {22}x^4 + {20}x^3 + {21}x^2 + {29}x + {18}
88  if (c0 & 2) c ^= 0x26508e6d; // {2}k(x) = {19}x^5 + {5}x^4 + x^3 + {3}x^2 + {19}x + {13}
89  if (c0 & 4) c ^= 0x1ea119fa; // {4}k(x) = {15}x^5 + {10}x^4 + {2}x^3 + {6}x^2 + {15}x + {26}
90  if (c0 & 8) c ^= 0x3d4233dd; // {8}k(x) = {30}x^5 + {20}x^4 + {4}x^3 + {12}x^2 + {30}x + {29}
91  if (c0 & 16) c ^= 0x2a1462b3; // {16}k(x) = {21}x^5 + x^4 + {8}x^3 + {24}x^2 + {21}x + {19}
92  }
93  return c;
94 }
95 
97 inline unsigned char LowerCase(unsigned char c)
98 {
99  return (c >= 'A' && c <= 'Z') ? (c - 'A') + 'a' : c;
100 }
101 
103 data ExpandHRP(const std::string& hrp)
104 {
105  data ret;
106  ret.reserve(hrp.size() + 90);
107  ret.resize(hrp.size() * 2 + 1);
108  for (size_t i = 0; i < hrp.size(); ++i) {
109  unsigned char c = hrp[i];
110  ret[i] = c >> 5;
111  ret[i + hrp.size() + 1] = c & 0x1f;
112  }
113  ret[hrp.size()] = 0;
114  return ret;
115 }
116 
118 bool VerifyChecksum(const std::string& hrp, const data& values)
119 {
120  // PolyMod computes what value to xor into the final values to make the checksum 0. However,
121  // if we required that the checksum was 0, it would be the case that appending a 0 to a valid
122  // list of values would result in a new valid list. For that reason, Bech32 requires the
123  // resulting checksum to be 1 instead.
124  return PolyMod(Cat(ExpandHRP(hrp), values)) == 1;
125 }
126 
128 data CreateChecksum(const std::string& hrp, const data& values)
129 {
130  data enc = Cat(ExpandHRP(hrp), values);
131  enc.resize(enc.size() + 6); // Append 6 zeroes
132  uint32_t mod = PolyMod(enc) ^ 1; // Determine what to XOR into those 6 zeroes.
133  data ret(6);
134  for (size_t i = 0; i < 6; ++i) {
135  // Convert the 5-bit groups in mod to checksum values.
136  ret[i] = (mod >> (5 * (5 - i))) & 31;
137  }
138  return ret;
139 }
140 
141 } // namespace
142 
143 namespace bech32
144 {
145 
147 std::string Encode(const std::string& hrp, const data& values) {
148  data checksum = CreateChecksum(hrp, values);
149  data combined = Cat(values, checksum);
150  std::string ret = hrp + '1';
151  ret.reserve(ret.size() + combined.size());
152  for (const auto c : combined) {
153  ret += CHARSET[c];
154  }
155  return ret;
156 }
157 
159 std::pair<std::string, data> Decode(const std::string& str) {
160  bool lower = false, upper = false;
161  for (size_t i = 0; i < str.size(); ++i) {
162  unsigned char c = str[i];
163  if (c >= 'a' && c <= 'z') lower = true;
164  else if (c >= 'A' && c <= 'Z') upper = true;
165  else if (c < 33 || c > 126) return {};
166  }
167  if (lower && upper) return {};
168  size_t pos = str.rfind('1');
169  if (str.size() > 90 || pos == str.npos || pos == 0 || pos + 7 > str.size()) {
170  return {};
171  }
172  data values(str.size() - 1 - pos);
173  for (size_t i = 0; i < str.size() - 1 - pos; ++i) {
174  unsigned char c = str[i + pos + 1];
175  int8_t rev = CHARSET_REV[c];
176 
177  if (rev == -1) {
178  return {};
179  }
180  values[i] = rev;
181  }
182  std::string hrp;
183  for (size_t i = 0; i < pos; ++i) {
184  hrp += LowerCase(str[i]);
185  }
186  if (!VerifyChecksum(hrp, values)) {
187  return {};
188  }
189  return {hrp, data(values.begin(), values.end() - 6)};
190 }
191 
192 } // namespace bech32
std::pair< std::string, data > Decode(const std::string &str)
Decode a Bech32 string.
Definition: bech32.cpp:159
std::string Encode(const std::string &hrp, const data &values)
Encode a Bech32 string.
Definition: bech32.cpp:147