// 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 #include namespace { typedef std::vector 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 }; /** 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 (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 (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) { data checksum = CreateChecksum(hrp, values); data combined = Cat(values, checksum); std::string ret = hrp + '1'; ret.reserve(ret.size() + combined.size()); for (auto c : combined) { ret += CHARSET[c]; } return ret; } /** Decode a Bech32 string. */ std::pair 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