text: // Copyright (c) 2017 Pieter Wuille
  // Distributed under the MIT software license, see the accompanying
  // file COPYING or http://www.opensource.org/licenses/mit-license.php.
  
  #include <bech32.h>
  
  #include <assert.h>
  
  namespace
  {
  
  typedef std::vector<uint8_t> data;
  
  /** The Bech32 character set for encoding. */
  const char* CHARSET = "qpzry9x8gf2tvdw0s3jn54khce6mua7l";
  
  /** The Bech32 character set for decoding. */
  const int8_t CHARSET_REV[128] = {
      -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
      -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
      -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
      15, -1, 10, 17, 21, 20, 26, 30,  7,  5, -1, -1, -1, -1, -1, -1,
      -1, 29, -1, 24, 13, 25,  9,  8, 23, -1, 18, 22, 31, 27, 19, -1,
       1,  0,  3, 16, 11, 28, 12, 14,  6,  4,  2, -1, -1, -1, -1, -1,
      -1, 29, -1, 24, 13, 25,  9,  8, 23, -1, 18, 22, 31, 27, 19, -1,
       1,  0,  3, 16, 11, 28, 12, 14,  6,  4,  2, -1, -1, -1, -1, -1
  };
  
  /** Concatenate two byte arrays. */
  data Cat(data x, const data& y)
  {
      x.insert(x.end(), y.begin(), y.end());
      return x;
  }
  
  /** This function will compute what 6 5-bit values to XOR into the last 6 input values, in order to
   *  make the checksum 0. These 6 values are packed together in a single 30-bit integer. The higher
   *  bits correspond to earlier values. */
  uint32_t PolyMod(const data& v)
  {
      // The input is interpreted as a list of coefficients of a polynomial over F = GF(32), with an
      // implicit 1 in front. If the input is [v0,v1,v2,v3,v4], that polynomial is v(x) =
      // 1*x^5 + v0*x^4 + v1*x^3 + v2*x^2 + v3*x + v4. The implicit 1 guarantees that
      // [v0,v1,v2,...] has a distinct checksum from [0,v0,v1,v2,...].
  
      // The output is a 30-bit integer whose 5-bit groups are the coefficients of the remainder of
      // v(x) mod g(x), where g(x) is the Bech32 generator,
      // 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
      // that the resulting code is a BCH code, guaranteeing detection of up to 3 errors within a
      // window of 1023 characters. Among the various possible BCH codes, one was selected to in
      // fact guarantee detection of up to 4 errors within a window of 89 characters.
  
      // Note that the coefficients are elements of GF(32), here represented as decimal numbers
      // between {}. In this finite field, addition is just XOR of the corresponding numbers. For
      // example, {27} + {13} = {27 ^ 13} = {22}. Multiplication is more complicated, and requires
      // treating the bits of values themselves as coefficients of a polynomial over a smaller field,
      // GF(2), and multiplying those polynomials mod a^5 + a^3 + 1. For example, {5} * {26} =
      // (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
      // = a^3 + 1 (mod a^5 + a^3 + 1) = {9}.
  
      // During the course of the loop below, `c` contains the bitpacked coefficients of the
      // polynomial constructed from just the values of v that were processed so far, mod g(x). In
      // the above example, `c` initially corresponds to 1 mod g(x), and after processing 2 inputs of
      // v, it corresponds to x^2 + v0*x + v1 mod g(x). As 1 mod g(x) = 1, that is the starting value
      // for `c`.
      uint32_t c = 1;
      for (const auto v_i : v) {
          // We want to update `c` to correspond to a polynomial with one extra term. If the initial
          // value of `c` consists of the coefficients of c(x) = f(x) mod g(x), we modify it to
          // correspond to c'(x) = (f(x) * x + v_i) mod g(x), where v_i is the next input to
          // process. Simplifying:
          // c'(x) = (f(x) * x + v_i) mod g(x)
          //         ((f(x) mod g(x)) * x + v_i) mod g(x)
          //         (c(x) * x + v_i) mod g(x)
          // If c(x) = c0*x^5 + c1*x^4 + c2*x^3 + c3*x^2 + c4*x + c5, we want to compute
          // c'(x) = (c0*x^5 + c1*x^4 + c2*x^3 + c3*x^2 + c4*x + c5) * x + v_i mod g(x)
          //       = c0*x^6 + c1*x^5 + c2*x^4 + c3*x^3 + c4*x^2 + c5*x + v_i mod g(x)
          //       = c0*(x^6 mod g(x)) + c1*x^5 + c2*x^4 + c3*x^3 + c4*x^2 + c5*x + v_i
          // If we call (x^6 mod g(x)) = k(x), this can be written as
          // c'(x) = (c1*x^5 + c2*x^4 + c3*x^3 + c4*x^2 + c5*x + v_i) + c0*k(x)
  
          // First, determine the value of c0:
          uint8_t c0 = c >> 25;
  
          // Then compute c1*x^5 + c2*x^4 + c3*x^3 + c4*x^2 + c5*x + v_i:
          c = ((c & 0x1ffffff) << 5) ^ v_i;
  
          // Finally, for each set bit n in c0, conditionally add {2^n}k(x):
          if (c0 & 1)  c ^= 0x3b6a57b2; //     k(x) = {29}x^5 + {22}x^4 + {20}x^3 + {21}x^2 + {29}x + {18}
          if (c0 & 2)  c ^= 0x26508e6d; //  {2}k(x) = {19}x^5 +  {5}x^4 +     x^3 +  {3}x^2 + {19}x + {13}
          if (c0 & 4)  c ^= 0x1ea119fa; //  {4}k(x) = {15}x^5 + {10}x^4 +  {2}x^3 +  {6}x^2 + {15}x + {26}
          if (c0 & 8)  c ^= 0x3d4233dd; //  {8}k(x) = {30}x^5 + {20}x^4 +  {4}x^3 + {12}x^2 + {30}x + {29}
          if (c0 & 16) c ^= 0x2a1462b3; // {16}k(x) = {21}x^5 +     x^4 +  {8}x^3 + {24}x^2 + {21}x + {19}
      }
      return c;
  }
  
  /** Convert to lower case. */
  inline unsigned char LowerCase(unsigned char c)
  {
      return (c >= 'A' && c <= 'Z') ? (c - 'A') + 'a' : c;
  }
  
  /** Expand a HRP for use in checksum computation. */
  data ExpandHRP(const std::string& hrp)
  {
      data ret;
      ret.reserve(hrp.size() + 90);
      ret.resize(hrp.size() * 2 + 1);
      for (size_t i = 0; i < hrp.size(); ++i) {
          unsigned char c = hrp[i];
          ret[i] = c >> 5;
          ret[i + hrp.size() + 1] = c & 0x1f;
      }
      ret[hrp.size()] = 0;
      return ret;
  }
  
  /** Verify a checksum. */
  bool VerifyChecksum(const std::string& hrp, const data& values)
  {
      // PolyMod computes what value to xor into the final values to make the checksum 0. However,
      // if we required that the checksum was 0, it would be the case that appending a 0 to a valid
      // list of values would result in a new valid list. For that reason, Bech32 requires the
      // resulting checksum to be 1 instead.
      return PolyMod(Cat(ExpandHRP(hrp), values)) == 1;
  }
  
  /** Create a checksum. */
  data CreateChecksum(const std::string& hrp, const data& values)
  {
      data enc = Cat(ExpandHRP(hrp), values);
      enc.resize(enc.size() + 6); // Append 6 zeroes
      uint32_t mod = PolyMod(enc) ^ 1; // Determine what to XOR into those 6 zeroes.
      data ret(6);
      for (size_t i = 0; i < 6; ++i) {
          // Convert the 5-bit groups in mod to checksum values.
          ret[i] = (mod >> (5 * (5 - i))) & 31;
      }
      return ret;
  }
  
  } // namespace
  
  namespace bech32
  {
  
  /** Encode a Bech32 string. */
  std::string Encode(const std::string& hrp, const data& values) {
      // First ensure that the HRP is all lowercase. BIP-173 requires an encoder
      // to return a lowercase Bech32 string, but if given an uppercase HRP, the
      // result will always be invalid.
      for (const char& c : hrp) assert(c < 'A' || c > 'Z');
      data checksum = CreateChecksum(hrp, values);
      data combined = Cat(values, checksum);
      std::string ret = hrp + '1';
      ret.reserve(ret.size() + combined.size());
      for (const auto c : combined) {
          ret += CHARSET[c];
      }
      return ret;
  }
  
  /** Decode a Bech32 string. */
  std::pair<std::string, data> Decode(const std::string& str) {
      bool lower = false, upper = false;
      for (size_t i = 0; i < str.size(); ++i) {
          unsigned char c = str[i];
          if (c >= 'a' && c <= 'z') lower = true;
          else if (c >= 'A' && c <= 'Z') upper = true;
          else if (c < 33 || c > 126) return {};
      }
      if (lower && upper) return {};
      size_t pos = str.rfind('1');
      if (str.size() > 90 || pos == str.npos || pos == 0 || pos + 7 > str.size()) {
          return {};
      }
      data values(str.size() - 1 - pos);
      for (size_t i = 0; i < str.size() - 1 - pos; ++i) {
          unsigned char c = str[i + pos + 1];
          int8_t rev = CHARSET_REV[c];
  
          if (rev == -1) {
              return {};
          }
          values[i] = rev;
      }
      std::string hrp;
      for (size_t i = 0; i < pos; ++i) {
          hrp += LowerCase(str[i]);
      }
      if (!VerifyChecksum(hrp, values)) {
          return {};
      }
      return {hrp, data(values.begin(), values.end() - 6)};
  }
  
  } // namespace bech32
  