333 lines
10 KiB
C++
333 lines
10 KiB
C++
// Copyright (c) 2017 Pieter Wuille
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// Copyright (c) 2017 The Bitcoin developers
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// Distributed under the MIT software license, see the accompanying
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// file COPYING or http://www.opensource.org/licenses/mit-license.php.
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#include "cashaddr.h"
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namespace
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{
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typedef std::vector<uint8_t> data;
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/**
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* The cashaddr character set for encoding.
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*/
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const char *CHARSET = "qpzry9x8gf2tvdw0s3jn54khce6mua7l";
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/**
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* The cashaddr character set for decoding.
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*/
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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,
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-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,
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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,
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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,
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1, 0, 3, 16, 11, 28, 12, 14, 6, 4, 2, -1, -1, -1, -1, -1};
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/**
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* Concatenate two byte arrays.
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*/
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data Cat(data x, const data &y)
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{
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x.insert(x.end(), y.begin(), y.end());
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return x;
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}
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/**
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* This function will compute what 8 5-bit values to XOR into the last 8 input
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* values, in order to make the checksum 0. These 8 values are packed together
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* in a single 40-bit integer. The higher bits correspond to earlier values.
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*/
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uint64_t PolyMod(const data &v)
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{
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/**
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* The input is interpreted as a list of coefficients of a polynomial over F
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* = GF(32), with an implicit 1 in front. If the input is [v0,v1,v2,v3,v4],
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* that polynomial is v(x) = 1*x^5 + v0*x^4 + v1*x^3 + v2*x^2 + v3*x + v4.
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* The implicit 1 guarantees that [v0,v1,v2,...] has a distinct checksum
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* from [0,v0,v1,v2,...].
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*
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* The output is a 40-bit integer whose 5-bit groups are the coefficients of
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* the remainder of v(x) mod g(x), where g(x) is the cashaddr generator, x^8
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* + {19}*x^7 + {3}*x^6 + {25}*x^5 + {11}*x^4 + {25}*x^3 + {3}*x^2 + {19}*x
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* + {1}. g(x) is chosen in such a way that the resulting code is a BCH
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* code, guaranteeing detection of up to 4 errors within a window of 1025
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* characters. Among the various possible BCH codes, one was selected to in
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* fact guarantee detection of up to 5 errors within a window of 160
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* characters and 6 erros within a window of 126 characters. In addition,
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* the code guarantee the detection of a burst of up to 8 errors.
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*
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* Note that the coefficients are elements of GF(32), here represented as
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* decimal numbers between {}. In this finite field, addition is just XOR of
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* the corresponding numbers. For example, {27} + {13} = {27 ^ 13} = {22}.
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* Multiplication is more complicated, and requires treating the bits of
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* values themselves as coefficients of a polynomial over a smaller field,
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* GF(2), and multiplying those polynomials mod a^5 + a^3 + 1. For example,
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* {5} * {26} = (a^2 + 1) * (a^4 + a^3 + a) = (a^4 + a^3 + a) * a^2 + (a^4 +
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* a^3 + a) = a^6 + a^5 + a^4 + a = a^3 + 1 (mod a^5 + a^3 + 1) = {9}.
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*
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* During the course of the loop below, `c` contains the bitpacked
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* coefficients of the polynomial constructed from just the values of v that
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* were processed so far, mod g(x). In the above example, `c` initially
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* corresponds to 1 mod (x), and after processing 2 inputs of v, it
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* corresponds to x^2 + v0*x + v1 mod g(x). As 1 mod g(x) = 1, that is the
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* starting value for `c`.
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*/
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uint64_t c = 1;
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for (uint8_t d : v)
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{
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/**
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* We want to update `c` to correspond to a polynomial with one extra
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* term. If the initial value of `c` consists of the coefficients of
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* c(x) = f(x) mod g(x), we modify it to correspond to
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* c'(x) = (f(x) * x + d) mod g(x), where d is the next input to
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* process.
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*
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* Simplifying:
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* c'(x) = (f(x) * x + d) mod g(x)
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* ((f(x) mod g(x)) * x + d) mod g(x)
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* (c(x) * x + d) mod g(x)
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* If c(x) = c0*x^5 + c1*x^4 + c2*x^3 + c3*x^2 + c4*x + c5, we want to
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* compute
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* c'(x) = (c0*x^5 + c1*x^4 + c2*x^3 + c3*x^2 + c4*x + c5) * x + d
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* mod g(x)
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* = c0*x^6 + c1*x^5 + c2*x^4 + c3*x^3 + c4*x^2 + c5*x + d
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* mod g(x)
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* = c0*(x^6 mod g(x)) + c1*x^5 + c2*x^4 + c3*x^3 + c4*x^2 +
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* c5*x + d
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* If we call (x^6 mod g(x)) = k(x), this can be written as
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* c'(x) = (c1*x^5 + c2*x^4 + c3*x^3 + c4*x^2 + c5*x + d) + c0*k(x)
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*/
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// First, determine the value of c0:
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uint8_t c0 = c >> 35;
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// Then compute c1*x^5 + c2*x^4 + c3*x^3 + c4*x^2 + c5*x + d:
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c = ((c & 0x07ffffffff) << 5) ^ d;
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// Finally, for each set bit n in c0, conditionally add {2^n}k(x):
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if (c0 & 0x01)
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{
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// k(x) = {19}*x^7 + {3}*x^6 + {25}*x^5 + {11}*x^4 + {25}*x^3 +
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// {3}*x^2 + {19}*x + {1}
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c ^= 0x98f2bc8e61;
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}
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if (c0 & 0x02)
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{
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// {2}k(x) = {15}*x^7 + {6}*x^6 + {27}*x^5 + {22}*x^4 + {27}*x^3 +
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// {6}*x^2 + {15}*x + {2}
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c ^= 0x79b76d99e2;
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}
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if (c0 & 0x04)
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{
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// {4}k(x) = {30}*x^7 + {12}*x^6 + {31}*x^5 + {5}*x^4 + {31}*x^3 +
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// {12}*x^2 + {30}*x + {4}
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c ^= 0xf33e5fb3c4;
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}
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if (c0 & 0x08)
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{
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// {8}k(x) = {21}*x^7 + {24}*x^6 + {23}*x^5 + {10}*x^4 + {23}*x^3 +
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// {24}*x^2 + {21}*x + {8}
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c ^= 0xae2eabe2a8;
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}
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if (c0 & 0x10)
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{
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// {16}k(x) = {3}*x^7 + {25}*x^6 + {7}*x^5 + {20}*x^4 + {7}*x^3 +
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// {25}*x^2 + {3}*x + {16}
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c ^= 0x1e4f43e470;
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}
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}
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return c;
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}
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/**
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* Convert to lower case.
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*
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* Assume the input is a character.
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*/
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inline uint8_t LowerCase(uint8_t c)
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{
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// ASCII black magic.
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return c | 0x20;
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}
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/**
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* Expand the address prefix for the checksum computation.
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*/
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data ExpandPrefix(const std::string &prefix)
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{
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data ret;
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ret.resize(prefix.size() + 1);
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for (size_t i = 0; i < prefix.size(); ++i)
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{
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ret[i] = prefix[i] & 0x1f;
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}
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ret[prefix.size()] = 0;
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return ret;
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}
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/**
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* Verify a checksum.
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*/
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bool VerifyChecksum(const std::string &prefix, const data &values)
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{
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/**
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* PolyMod computes what value to xor into the final values to make the
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* checksum 0. However, if we required that the checksum was 0, it would be
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* the case that appending a 0 to a valid list of values would result in a
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* new valid list. For that reason, cashaddr requires the resulting checksum
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* to be 1 instead.
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*/
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return PolyMod(Cat(ExpandPrefix(prefix), values)) == 1;
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}
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/**
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* Create a checksum.
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*/
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data CreateChecksum(const std::string &prefix, const data &values)
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{
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data enc = Cat(ExpandPrefix(prefix), values);
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// Append 8 zeroes.
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enc.resize(enc.size() + 8);
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// Determine what to XOR into those 8 zeroes.
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uint64_t mod = PolyMod(enc) ^ 1;
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data ret(8);
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for (size_t i = 0; i < 8; ++i)
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{
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// Convert the 5-bit groups in mod to checksum values.
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ret[i] = (mod >> (5 * (7 - i))) & 0x1f;
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}
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return ret;
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}
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} // namespace
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namespace cashaddr
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{
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/**
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* Encode a cashaddr string.
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*/
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std::string Encode(const std::string &prefix, const data &values)
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{
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data checksum = CreateChecksum(prefix, values);
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data combined = Cat(values, checksum);
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std::string ret = prefix + ':';
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ret.reserve(ret.size() + combined.size());
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for (uint8_t c : combined)
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{
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ret += CHARSET[c];
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}
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return ret;
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}
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/**
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* Decode a cashaddr string.
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*/
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std::pair<std::string, data> Decode(const std::string &str, const std::string &default_prefix)
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{
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// Go over the string and do some sanity checks.
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bool lower = false, upper = false, hasNumber = false;
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size_t prefixSize = 0;
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for (size_t i = 0; i < str.size(); ++i)
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{
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uint8_t c = str[i];
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if (c >= 'a' && c <= 'z')
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{
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lower = true;
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continue;
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}
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if (c >= 'A' && c <= 'Z')
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{
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upper = true;
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continue;
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}
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if (c >= '0' && c <= '9')
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{
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// We cannot have numbers in the prefix.
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hasNumber = true;
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continue;
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}
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if (c == ':')
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{
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// The separator cannot be the first character, cannot have number
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// and there must not be 2 separators.
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if (hasNumber || i == 0 || prefixSize != 0)
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{
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return {};
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}
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prefixSize = i;
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continue;
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}
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// We have an unexpected character.
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return {};
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}
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// We can't have both upper case and lowercase.
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if (upper && lower)
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{
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return {};
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}
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// Get the prefix.
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std::string prefix;
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if (prefixSize == 0)
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{
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prefix = default_prefix;
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}
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else
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{
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prefix.reserve(prefixSize);
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for (size_t i = 0; i < prefixSize; ++i)
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{
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prefix += LowerCase(str[i]);
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}
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// Now add the ':' in the size.
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prefixSize++;
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}
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// Decode values.
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const size_t valuesSize = str.size() - prefixSize;
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data values(valuesSize);
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for (size_t i = 0; i < valuesSize; ++i)
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{
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uint8_t c = str[i + prefixSize];
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// We have an invalid char in there.
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if (c > 127 || CHARSET_REV[c] == -1)
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{
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return {};
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}
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values[i] = CHARSET_REV[c];
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}
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// Verify the checksum.
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if (!VerifyChecksum(prefix, values))
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{
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return {};
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}
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return {std::move(prefix), data(values.begin(), values.end() - 8)};
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}
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std::vector<uint8_t> EncodingCharset()
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{
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const size_t size = 32;
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return std::vector<uint8_t>(CHARSET, CHARSET + size);
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}
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} // namespace cashaddr
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