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src/cashaddr.cpp
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// Copyright (c) 2017 Pieter Wuille | |||||
// Copyright (c) 2017 The Bitcoin developers | |||||
// Distributed under the MIT software license, see the accompanying | |||||
// file COPYING or http://www.opensource.org/licenses/mit-license.php. | |||||
#include "cashaddr.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 infact 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) { | |||||
// k(x) = {29}x^5 + {22}x^4 + {20}x^3 + {21}x^2 + {29}x + {18} | |||||
c ^= 0x3b6a57b2; | |||||
} | |||||
if (c0 & 2) { | |||||
// {2}k(x) = {19}x^5 + {5}x^4 + x^3 + {3}x^2 + {19}x + {13} | |||||
c ^= 0x26508e6d; | |||||
} | |||||
if (c0 & 4) { | |||||
// {4}k(x) = {15}x^5 + {10}x^4 + {2}x^3 + {6}x^2 + {15}x + {26} | |||||
c ^= 0x1ea119fa; | |||||
} | |||||
if (c0 & 8) { | |||||
// {8}k(x) = {30}x^5 + {20}x^4 + {4}x^3 + {12}x^2 + {30}x + {29} | |||||
c ^= 0x3d4233dd; | |||||
} | |||||
if (c0 & 16) { | |||||
// {16}k(x) = {21}x^5 + x^4 + {8}x^3 + {24}x^2 + {21}x + {19} | |||||
c ^= 0x2a1462b3; | |||||
} | |||||
} | |||||
return c; | |||||
} | |||||
/** Convert to lower case. */ | |||||
inline uint8_t LowerCase(uint8_t c) { | |||||
return (c >= 'A' && c <= 'Z') ? (c - 'A') + 'a' : c; | |||||
} | |||||
/** Expand a prefix for use in checksum computation. */ | |||||
data ExpandPrefix(const std::string &prefix) { | |||||
data ret; | |||||
ret.reserve(prefix.size() + 90); | |||||
ret.resize(prefix.size() * 2 + 1); | |||||
for (size_t i = 0; i < prefix.size(); ++i) { | |||||
uint8_t c = prefix[i]; | |||||
ret[i] = c >> 5; | |||||
ret[i + prefix.size() + 1] = c & 0x1f; | |||||
} | |||||
ret[prefix.size()] = 0; | |||||
return ret; | |||||
} | |||||
/** Verify a checksum. */ | |||||
bool VerifyChecksum(const std::string &prefix, 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(ExpandPrefix(prefix), values)) == 1; | |||||
} | |||||
/** Create a checksum. */ | |||||
data CreateChecksum(const std::string &prefix, const data &values) { | |||||
data enc = Cat(ExpandPrefix(prefix), values); | |||||
enc.resize(enc.size() + 8); // Append 8 zeroes | |||||
uint64_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 cashaddr { | |||||
/** Encode a Cash Address string. */ | |||||
std::string Encode(const std::string &prefix, const data &values) { | |||||
data checksum = CreateChecksum(prefix, values); | |||||
data combined = Cat(values, checksum); | |||||
std::string ret = prefix + ':'; | |||||
ret.reserve(ret.size() + combined.size()); | |||||
for (auto c : combined) { | |||||
ret += CHARSET[c]; | |||||
} | |||||
return ret; | |||||
} | |||||
/** Decode a Cash Address 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) { | |||||
uint8_t c = str[i]; | |||||
if (c != ':' && (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(':'); | |||||
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) { | |||||
uint8_t 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 prefix; | |||||
for (size_t i = 0; i < pos; ++i) { | |||||
prefix += LowerCase(str[i]); | |||||
} | |||||
if (!VerifyChecksum(prefix, values)) { | |||||
return {}; | |||||
} | |||||
return {prefix, data(values.begin(), values.end() - 6)}; | |||||
} | |||||
} // namespace cashaddr |