Bitcoin Core  22.99.0
P2P Digital Currency
bech32.cpp
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1 // Copyright (c) 2017, 2021 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 #include <util/vector.h>
7 
8 #include <assert.h>
9 
10 namespace bech32
11 {
12 
13 namespace
14 {
15 
16 typedef std::vector<uint8_t> data;
17 
19 const char* CHARSET = "qpzry9x8gf2tvdw0s3jn54khce6mua7l";
20 
22 const int8_t CHARSET_REV[128] = {
23  -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
24  -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
25  -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
26  15, -1, 10, 17, 21, 20, 26, 30, 7, 5, -1, -1, -1, -1, -1, -1,
27  -1, 29, -1, 24, 13, 25, 9, 8, 23, -1, 18, 22, 31, 27, 19, -1,
28  1, 0, 3, 16, 11, 28, 12, 14, 6, 4, 2, -1, -1, -1, -1, -1,
29  -1, 29, -1, 24, 13, 25, 9, 8, 23, -1, 18, 22, 31, 27, 19, -1,
30  1, 0, 3, 16, 11, 28, 12, 14, 6, 4, 2, -1, -1, -1, -1, -1
31 };
32 
33 /* Determine the final constant to use for the specified encoding. */
34 uint32_t EncodingConstant(Encoding encoding) {
35  assert(encoding == Encoding::BECH32 || encoding == Encoding::BECH32M);
36  return encoding == Encoding::BECH32 ? 1 : 0x2bc830a3;
37 }
38 
42 uint32_t PolyMod(const data& v)
43 {
44  // The input is interpreted as a list of coefficients of a polynomial over F = GF(32), with an
45  // implicit 1 in front. If the input is [v0,v1,v2,v3,v4], that polynomial is v(x) =
46  // 1*x^5 + v0*x^4 + v1*x^3 + v2*x^2 + v3*x + v4. The implicit 1 guarantees that
47  // [v0,v1,v2,...] has a distinct checksum from [0,v0,v1,v2,...].
48 
49  // The output is a 30-bit integer whose 5-bit groups are the coefficients of the remainder of
50  // v(x) mod g(x), where g(x) is the Bech32 generator,
51  // 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
52  // that the resulting code is a BCH code, guaranteeing detection of up to 3 errors within a
53  // window of 1023 characters. Among the various possible BCH codes, one was selected to in
54  // fact guarantee detection of up to 4 errors within a window of 89 characters.
55 
56  // Note that the coefficients are elements of GF(32), here represented as decimal numbers
57  // between {}. In this finite field, addition is just XOR of the corresponding numbers. For
58  // example, {27} + {13} = {27 ^ 13} = {22}. Multiplication is more complicated, and requires
59  // treating the bits of values themselves as coefficients of a polynomial over a smaller field,
60  // GF(2), and multiplying those polynomials mod a^5 + a^3 + 1. For example, {5} * {26} =
61  // (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
62  // = a^3 + 1 (mod a^5 + a^3 + 1) = {9}.
63 
64  // During the course of the loop below, `c` contains the bitpacked coefficients of the
65  // polynomial constructed from just the values of v that were processed so far, mod g(x). In
66  // the above example, `c` initially corresponds to 1 mod g(x), and after processing 2 inputs of
67  // v, it corresponds to x^2 + v0*x + v1 mod g(x). As 1 mod g(x) = 1, that is the starting value
68  // for `c`.
69 
70  // The following Sage code constructs the generator used:
71  //
72  // B = GF(2) # Binary field
73  // BP.<b> = B[] # Polynomials over the binary field
74  // F_mod = b**5 + b**3 + 1
75  // F.<f> = GF(32, modulus=F_mod, repr='int') # GF(32) definition
76  // FP.<x> = F[] # Polynomials over GF(32)
77  // E_mod = x**2 + F.fetch_int(9)*x + F.fetch_int(23)
78  // E.<e> = F.extension(E_mod) # GF(1024) extension field definition
79  // for p in divisors(E.order() - 1): # Verify e has order 1023.
80  // assert((e**p == 1) == (p % 1023 == 0))
81  // G = lcm([(e**i).minpoly() for i in range(997,1000)])
82  // print(G) # Print out the generator
83  //
84  // It demonstrates that g(x) is the least common multiple of the minimal polynomials
85  // of 3 consecutive powers (997,998,999) of a primitive element (e) of GF(1024).
86  // That guarantees it is, in fact, the generator of a primitive BCH code with cycle
87  // length 1023 and distance 4. See https://en.wikipedia.org/wiki/BCH_code for more details.
88 
89  uint32_t c = 1;
90  for (const auto v_i : v) {
91  // We want to update `c` to correspond to a polynomial with one extra term. If the initial
92  // value of `c` consists of the coefficients of c(x) = f(x) mod g(x), we modify it to
93  // correspond to c'(x) = (f(x) * x + v_i) mod g(x), where v_i is the next input to
94  // process. Simplifying:
95  // c'(x) = (f(x) * x + v_i) mod g(x)
96  // ((f(x) mod g(x)) * x + v_i) mod g(x)
97  // (c(x) * x + v_i) mod g(x)
98  // If c(x) = c0*x^5 + c1*x^4 + c2*x^3 + c3*x^2 + c4*x + c5, we want to compute
99  // c'(x) = (c0*x^5 + c1*x^4 + c2*x^3 + c3*x^2 + c4*x + c5) * x + v_i mod g(x)
100  // = c0*x^6 + c1*x^5 + c2*x^4 + c3*x^3 + c4*x^2 + c5*x + v_i mod g(x)
101  // = c0*(x^6 mod g(x)) + c1*x^5 + c2*x^4 + c3*x^3 + c4*x^2 + c5*x + v_i
102  // If we call (x^6 mod g(x)) = k(x), this can be written as
103  // c'(x) = (c1*x^5 + c2*x^4 + c3*x^3 + c4*x^2 + c5*x + v_i) + c0*k(x)
104 
105  // First, determine the value of c0:
106  uint8_t c0 = c >> 25;
107 
108  // Then compute c1*x^5 + c2*x^4 + c3*x^3 + c4*x^2 + c5*x + v_i:
109  c = ((c & 0x1ffffff) << 5) ^ v_i;
110 
111  // Finally, for each set bit n in c0, conditionally add {2^n}k(x). These constants can be
112  // computed using the following Sage code (continuing the code above):
113  //
114  // for i in [1,2,4,8,16]: # Print out {1,2,4,8,16}*(g(x) mod x^6), packed in hex integers.
115  // v = 0
116  // for coef in reversed((F.fetch_int(i)*(G % x**6)).coefficients(sparse=True)):
117  // v = v*32 + coef.integer_representation()
118  // print("0x%x" % v)
119  //
120  if (c0 & 1) c ^= 0x3b6a57b2; // k(x) = {29}x^5 + {22}x^4 + {20}x^3 + {21}x^2 + {29}x + {18}
121  if (c0 & 2) c ^= 0x26508e6d; // {2}k(x) = {19}x^5 + {5}x^4 + x^3 + {3}x^2 + {19}x + {13}
122  if (c0 & 4) c ^= 0x1ea119fa; // {4}k(x) = {15}x^5 + {10}x^4 + {2}x^3 + {6}x^2 + {15}x + {26}
123  if (c0 & 8) c ^= 0x3d4233dd; // {8}k(x) = {30}x^5 + {20}x^4 + {4}x^3 + {12}x^2 + {30}x + {29}
124  if (c0 & 16) c ^= 0x2a1462b3; // {16}k(x) = {21}x^5 + x^4 + {8}x^3 + {24}x^2 + {21}x + {19}
125 
126  }
127  return c;
128 }
129 
131 inline unsigned char LowerCase(unsigned char c)
132 {
133  return (c >= 'A' && c <= 'Z') ? (c - 'A') + 'a' : c;
134 }
135 
137 data ExpandHRP(const std::string& hrp)
138 {
139  data ret;
140  ret.reserve(hrp.size() + 90);
141  ret.resize(hrp.size() * 2 + 1);
142  for (size_t i = 0; i < hrp.size(); ++i) {
143  unsigned char c = hrp[i];
144  ret[i] = c >> 5;
145  ret[i + hrp.size() + 1] = c & 0x1f;
146  }
147  ret[hrp.size()] = 0;
148  return ret;
149 }
150 
152 Encoding VerifyChecksum(const std::string& hrp, const data& values)
153 {
154  // PolyMod computes what value to xor into the final values to make the checksum 0. However,
155  // if we required that the checksum was 0, it would be the case that appending a 0 to a valid
156  // list of values would result in a new valid list. For that reason, Bech32 requires the
157  // resulting checksum to be 1 instead. In Bech32m, this constant was amended. See
158  // https://gist.github.com/sipa/14c248c288c3880a3b191f978a34508e for details.
159  const uint32_t check = PolyMod(Cat(ExpandHRP(hrp), values));
160  if (check == EncodingConstant(Encoding::BECH32)) return Encoding::BECH32;
161  if (check == EncodingConstant(Encoding::BECH32M)) return Encoding::BECH32M;
162  return Encoding::INVALID;
163 }
164 
166 data CreateChecksum(Encoding encoding, const std::string& hrp, const data& values)
167 {
168  data enc = Cat(ExpandHRP(hrp), values);
169  enc.resize(enc.size() + 6); // Append 6 zeroes
170  uint32_t mod = PolyMod(enc) ^ EncodingConstant(encoding); // Determine what to XOR into those 6 zeroes.
171  data ret(6);
172  for (size_t i = 0; i < 6; ++i) {
173  // Convert the 5-bit groups in mod to checksum values.
174  ret[i] = (mod >> (5 * (5 - i))) & 31;
175  }
176  return ret;
177 }
178 
179 } // namespace
180 
182 std::string Encode(Encoding encoding, const std::string& hrp, const data& values) {
183  // First ensure that the HRP is all lowercase. BIP-173 and BIP350 require an encoder
184  // to return a lowercase Bech32/Bech32m string, but if given an uppercase HRP, the
185  // result will always be invalid.
186  for (const char& c : hrp) assert(c < 'A' || c > 'Z');
187  data checksum = CreateChecksum(encoding, hrp, values);
188  data combined = Cat(values, checksum);
189  std::string ret = hrp + '1';
190  ret.reserve(ret.size() + combined.size());
191  for (const auto c : combined) {
192  ret += CHARSET[c];
193  }
194  return ret;
195 }
196 
198 DecodeResult Decode(const std::string& str) {
199  bool lower = false, upper = false;
200  for (size_t i = 0; i < str.size(); ++i) {
201  unsigned char c = str[i];
202  if (c >= 'a' && c <= 'z') lower = true;
203  else if (c >= 'A' && c <= 'Z') upper = true;
204  else if (c < 33 || c > 126) return {};
205  }
206  if (lower && upper) return {};
207  size_t pos = str.rfind('1');
208  if (str.size() > 90 || pos == str.npos || pos == 0 || pos + 7 > str.size()) {
209  return {};
210  }
211  data values(str.size() - 1 - pos);
212  for (size_t i = 0; i < str.size() - 1 - pos; ++i) {
213  unsigned char c = str[i + pos + 1];
214  int8_t rev = CHARSET_REV[c];
215 
216  if (rev == -1) {
217  return {};
218  }
219  values[i] = rev;
220  }
221  std::string hrp;
222  for (size_t i = 0; i < pos; ++i) {
223  hrp += LowerCase(str[i]);
224  }
225  Encoding result = VerifyChecksum(hrp, values);
226  if (result == Encoding::INVALID) return {};
227  return {result, std::move(hrp), data(values.begin(), values.end() - 6)};
228 }
229 
230 } // namespace bech32
assert
assert(!tx.IsCoinBase())
bech32::Decode
DecodeResult Decode(const std::string &str)
Decode a Bech32 or Bech32m string.
Definition: bech32.cpp:198
Cat
V Cat(V v1, V &&v2)
Concatenate two vectors, moving elements.
Definition: vector.h:31
bech32::DecodeResult
Definition: bech32.h:34
bech32::Encoding::BECH32
@ BECH32
Bech32 encoding as defined in BIP173.
bech32::Encoding::INVALID
@ INVALID
Failed decoding.
values
static const int64_t values[]
A selection of numbers that do not trigger int64_t overflow when added/subtracted.
Definition: scriptnum_tests.cpp:17
bech32
Definition: bech32.cpp:10
bech32::Encoding
Encoding
Definition: bech32.h:23
bech32::Encoding::BECH32M
@ BECH32M
Bech32m encoding as defined in BIP350.
vector.h
bech32.h
bech32::Encode
std::string Encode(Encoding encoding, const std::string &hrp, const data &values)
Encode a Bech32 or Bech32m string.
Definition: bech32.cpp:182