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// Copyright (c) 2017 Pieter Wuille
// Distributed under the MIT software license, see the accompanying
// file COPYING or https://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) {
if (c >= 32) {
return "";
}
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() > 1023 || 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
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