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Diffstat (limited to 'src/bech32.cpp')
| -rw-r--r-- | src/bech32.cpp | 191 |
1 files changed, 191 insertions, 0 deletions
diff --git a/src/bech32.cpp b/src/bech32.cpp new file mode 100644 index 0000000000..573eac58bb --- /dev/null +++ b/src/bech32.cpp @@ -0,0 +1,191 @@ +// 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" + +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 (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<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 < 33 || c > 126) return {}; + if (c >= 'a' && c <= 'z') lower = true; + if (c >= 'A' && c <= 'Z') upper = true; + } + 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 = (c < 33 || c > 126) ? -1 : 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 |