src/bech32.cpp

   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
  12 /** The Bech32 character set for encoding. */
  13 const char* CHARSET = "qpzry9x8gf2tvdw0s3jn54khce6mua7l";
  14
  15 /** The Bech32 character set for decoding. */
  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
  27 /** Concatenate two byte arrays. */
  28 data Cat(data x, const data& y)
  29 {
  30     x.insert(x.end(), y.begin(), y.end());
  31     return x;
  32 }
  33
  34 /** This function will compute what 6 5-bit values to XOR into the last 6 input values, in order to
  35  *  make the checksum 0. These 6 values are packed together in a single 30-bit integer. The higher
  36  *  bits correspond to earlier values. */
  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 (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
  96 /** Convert to lower case. */
  97 inline unsigned char LowerCase(unsigned char c)
  98 {
  99     return (c >= 'A' && c <= 'Z') ? (c - 'A') + 'a' : c;
 100 }
 101
 102 /** Expand a HRP for use in checksum computation. */
 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
 117 /** Verify a checksum. */
 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
 127 /** Create a checksum. */
 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
 146 /** Encode a Bech32 string. */
 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 (auto c : combined) {
 153         ret += CHARSET[c];
 154     }
 155     return ret;
 156 }
 157
 158 /** Decode a Bech32 string. */
 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 < 33 || c > 126) return {};
 164         if (c >= 'a' && c <= 'z') lower = true;
 165         if (c >= 'A' && c <= 'Z') upper = true;
 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 = (c < 33 || c > 126) ? -1 : CHARSET_REV[c];
 176         if (rev == -1) {
 177             return {};
 178         }
 179         values[i] = rev;
 180     }
 181     std::string hrp;
 182     for (size_t i = 0; i < pos; ++i) {
 183         hrp += LowerCase(str[i]);
 184     }
 185     if (!VerifyChecksum(hrp, values)) {
 186         return {};
 187     }
 188     return {hrp, data(values.begin(), values.end() - 6)};
 189 }
 190
 191 } // namespace bech32