LCOV - code coverage report
Current view: top level - src - bech32.cpp (source / functions) Hit Total Coverage
Test: fuzz_coverage.info Lines: 138 184 75.0 %
Date: 2024-01-03 14:57:27 Functions: 9 11 81.8 %
Branches: 136 292 46.6 %

           Branch data     Line data    Source code
       1                 :            : // Copyright (c) 2017, 2021 Pieter Wuille
       2                 :            : // Copyright (c) 2021-2022 The Bitcoin Core developers
       3                 :            : // Distributed under the MIT software license, see the accompanying
       4                 :            : // file COPYING or http://www.opensource.org/licenses/mit-license.php.
       5                 :            : 
       6                 :            : #include <bech32.h>
       7                 :            : #include <util/vector.h>
       8                 :            : 
       9                 :            : #include <array>
      10                 :            : #include <assert.h>
      11                 :            : #include <numeric>
      12                 :            : #include <optional>
      13                 :            : 
      14                 :            : namespace bech32
      15                 :            : {
      16                 :            : 
      17                 :            : namespace
      18                 :            : {
      19                 :            : 
      20                 :            : typedef std::vector<uint8_t> data;
      21                 :            : 
      22                 :            : /** The Bech32 and Bech32m character set for encoding. */
      23                 :            : const char* CHARSET = "qpzry9x8gf2tvdw0s3jn54khce6mua7l";
      24                 :            : 
      25                 :            : /** The Bech32 and Bech32m character set for decoding. */
      26                 :            : const int8_t CHARSET_REV[128] = {
      27                 :            :     -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
      28                 :            :     -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
      29                 :            :     -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
      30                 :            :     15, -1, 10, 17, 21, 20, 26, 30,  7,  5, -1, -1, -1, -1, -1, -1,
      31                 :            :     -1, 29, -1, 24, 13, 25,  9,  8, 23, -1, 18, 22, 31, 27, 19, -1,
      32                 :            :      1,  0,  3, 16, 11, 28, 12, 14,  6,  4,  2, -1, -1, -1, -1, -1,
      33                 :            :     -1, 29, -1, 24, 13, 25,  9,  8, 23, -1, 18, 22, 31, 27, 19, -1,
      34                 :            :      1,  0,  3, 16, 11, 28, 12, 14,  6,  4,  2, -1, -1, -1, -1, -1
      35                 :            : };
      36                 :            : 
      37                 :            : /** We work with the finite field GF(1024) defined as a degree 2 extension of the base field GF(32)
      38                 :            :  * The defining polynomial of the extension is x^2 + 9x + 23.
      39                 :            :  * Let (e) be a root of this defining polynomial. Then (e) is a primitive element of GF(1024),
      40                 :            :  * that is, a generator of the field. Every non-zero element of the field can then be represented
      41                 :            :  * as (e)^k for some power k.
      42                 :            :  * The array GF1024_EXP contains all these powers of (e) - GF1024_EXP[k] = (e)^k in GF(1024).
      43                 :            :  * Conversely, GF1024_LOG contains the discrete logarithms of these powers, so
      44                 :            :  * GF1024_LOG[GF1024_EXP[k]] == k.
      45                 :            :  * The following function generates the two tables GF1024_EXP and GF1024_LOG as constexprs. */
      46                 :            : constexpr std::pair<std::array<int16_t, 1023>, std::array<int16_t, 1024>> GenerateGFTables()
      47                 :            : {
      48                 :            :     // Build table for GF(32).
      49                 :            :     // We use these tables to perform arithmetic in GF(32) below, when constructing the
      50                 :            :     // tables for GF(1024).
      51                 :            :     std::array<int8_t, 31> GF32_EXP{};
      52                 :            :     std::array<int8_t, 32> GF32_LOG{};
      53                 :            : 
      54                 :            :     // fmod encodes the defining polynomial of GF(32) over GF(2), x^5 + x^3 + 1.
      55                 :            :     // Because coefficients in GF(2) are binary digits, the coefficients are packed as 101001.
      56                 :            :     const int fmod = 41;
      57                 :            : 
      58                 :            :     // Elements of GF(32) are encoded as vectors of length 5 over GF(2), that is,
      59                 :            :     // 5 binary digits. Each element (b_4, b_3, b_2, b_1, b_0) encodes a polynomial
      60                 :            :     // b_4*x^4 + b_3*x^3 + b_2*x^2 + b_1*x^1 + b_0 (modulo fmod).
      61                 :            :     // For example, 00001 = 1 is the multiplicative identity.
      62                 :            :     GF32_EXP[0] = 1;
      63                 :            :     GF32_LOG[0] = -1;
      64                 :            :     GF32_LOG[1] = 0;
      65                 :            :     int v = 1;
      66                 :            :     for (int i = 1; i < 31; ++i) {
      67                 :            :         // Multiplication by x is the same as shifting left by 1, as
      68                 :            :         // every coefficient of the polynomial is moved up one place.
      69                 :            :         v = v << 1;
      70                 :            :         // If the polynomial now has an x^5 term, we subtract fmod from it
      71                 :            :         // to remain working modulo fmod. Subtraction is the same as XOR in characteristic
      72                 :            :         // 2 fields.
      73                 :            :         if (v & 32) v ^= fmod;
      74                 :            :         GF32_EXP[i] = v;
      75                 :            :         GF32_LOG[v] = i;
      76                 :            :     }
      77                 :            : 
      78                 :            :     // Build table for GF(1024)
      79                 :            :     std::array<int16_t, 1023> GF1024_EXP{};
      80                 :            :     std::array<int16_t, 1024> GF1024_LOG{};
      81                 :            : 
      82                 :            :     GF1024_EXP[0] = 1;
      83                 :            :     GF1024_LOG[0] = -1;
      84                 :            :     GF1024_LOG[1] = 0;
      85                 :            : 
      86                 :            :     // Each element v of GF(1024) is encoded as a 10 bit integer in the following way:
      87                 :            :     // v = v1 || v0 where v0, v1 are 5-bit integers (elements of GF(32)).
      88                 :            :     // The element (e) is encoded as 1 || 0, to represent 1*(e) + 0. Every other element
      89                 :            :     // a*(e) + b is represented as a || b (a and b are both GF(32) elements). Given (v),
      90                 :            :     // we compute (e)*(v) by multiplying in the following way:
      91                 :            :     //
      92                 :            :     // v0' = 23*v1
      93                 :            :     // v1' = 9*v1 + v0
      94                 :            :     // e*v = v1' || v0'
      95                 :            :     //
      96                 :            :     // Where 23, 9 are GF(32) elements encoded as described above. Multiplication in GF(32)
      97                 :            :     // is done using the log/exp tables:
      98                 :            :     // e^x * e^y = e^(x + y) so a * b = EXP[ LOG[a] + LOG [b] ]
      99                 :            :     // for non-zero a and b.
     100                 :            : 
     101                 :            :     v = 1;
     102                 :            :     for (int i = 1; i < 1023; ++i) {
     103                 :            :         int v0 = v & 31;
     104                 :            :         int v1 = v >> 5;
     105                 :            : 
     106                 :            :         int v0n = v1 ? GF32_EXP.at((GF32_LOG.at(v1) + GF32_LOG.at(23)) % 31) : 0;
     107                 :            :         int v1n = (v1 ? GF32_EXP.at((GF32_LOG.at(v1) + GF32_LOG.at(9)) % 31) : 0) ^ v0;
     108                 :            : 
     109                 :            :         v = v1n << 5 | v0n;
     110                 :            :         GF1024_EXP[i] = v;
     111                 :            :         GF1024_LOG[v] = i;
     112                 :            :     }
     113                 :            : 
     114                 :            :     return std::make_pair(GF1024_EXP, GF1024_LOG);
     115                 :            : }
     116                 :            : 
     117                 :            : constexpr auto tables = GenerateGFTables();
     118                 :            : constexpr const std::array<int16_t, 1023>& GF1024_EXP = tables.first;
     119                 :            : constexpr const std::array<int16_t, 1024>& GF1024_LOG = tables.second;
     120                 :            : 
     121                 :            : /* Determine the final constant to use for the specified encoding. */
     122                 :         65 : uint32_t EncodingConstant(Encoding encoding) {
     123 [ +  + ][ +  - ]:         65 :     assert(encoding == Encoding::BECH32 || encoding == Encoding::BECH32M);
     124                 :         65 :     return encoding == Encoding::BECH32 ? 1 : 0x2bc830a3;
     125                 :            : }
     126                 :            : 
     127                 :            : /** This function will compute what 6 5-bit values to XOR into the last 6 input values, in order to
     128                 :            :  *  make the checksum 0. These 6 values are packed together in a single 30-bit integer. The higher
     129                 :            :  *  bits correspond to earlier values. */
     130                 :         49 : uint32_t PolyMod(const data& v)
     131                 :            : {
     132                 :            :     // The input is interpreted as a list of coefficients of a polynomial over F = GF(32), with an
     133                 :            :     // implicit 1 in front. If the input is [v0,v1,v2,v3,v4], that polynomial is v(x) =
     134                 :            :     // 1*x^5 + v0*x^4 + v1*x^3 + v2*x^2 + v3*x + v4. The implicit 1 guarantees that
     135                 :            :     // [v0,v1,v2,...] has a distinct checksum from [0,v0,v1,v2,...].
     136                 :            : 
     137                 :            :     // The output is a 30-bit integer whose 5-bit groups are the coefficients of the remainder of
     138                 :            :     // v(x) mod g(x), where g(x) is the Bech32 generator,
     139                 :            :     // 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
     140                 :            :     // that the resulting code is a BCH code, guaranteeing detection of up to 3 errors within a
     141                 :            :     // window of 1023 characters. Among the various possible BCH codes, one was selected to in
     142                 :            :     // fact guarantee detection of up to 4 errors within a window of 89 characters.
     143                 :            : 
     144                 :            :     // Note that the coefficients are elements of GF(32), here represented as decimal numbers
     145                 :            :     // between {}. In this finite field, addition is just XOR of the corresponding numbers. For
     146                 :            :     // example, {27} + {13} = {27 ^ 13} = {22}. Multiplication is more complicated, and requires
     147                 :            :     // treating the bits of values themselves as coefficients of a polynomial over a smaller field,
     148                 :            :     // GF(2), and multiplying those polynomials mod a^5 + a^3 + 1. For example, {5} * {26} =
     149                 :            :     // (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
     150                 :            :     // = a^3 + 1 (mod a^5 + a^3 + 1) = {9}.
     151                 :            : 
     152                 :            :     // During the course of the loop below, `c` contains the bitpacked coefficients of the
     153                 :            :     // polynomial constructed from just the values of v that were processed so far, mod g(x). In
     154                 :            :     // the above example, `c` initially corresponds to 1 mod g(x), and after processing 2 inputs of
     155                 :            :     // v, it corresponds to x^2 + v0*x + v1 mod g(x). As 1 mod g(x) = 1, that is the starting value
     156                 :            :     // for `c`.
     157                 :            : 
     158                 :            :     // The following Sage code constructs the generator used:
     159                 :            :     //
     160                 :            :     // B = GF(2) # Binary field
     161                 :            :     // BP.<b> = B[] # Polynomials over the binary field
     162                 :            :     // F_mod = b**5 + b**3 + 1
     163                 :            :     // F.<f> = GF(32, modulus=F_mod, repr='int') # GF(32) definition
     164                 :            :     // FP.<x> = F[] # Polynomials over GF(32)
     165                 :            :     // E_mod = x**2 + F.fetch_int(9)*x + F.fetch_int(23)
     166                 :            :     // E.<e> = F.extension(E_mod) # GF(1024) extension field definition
     167                 :            :     // for p in divisors(E.order() - 1): # Verify e has order 1023.
     168                 :            :     //    assert((e**p == 1) == (p % 1023 == 0))
     169                 :            :     // G = lcm([(e**i).minpoly() for i in range(997,1000)])
     170                 :            :     // print(G) # Print out the generator
     171                 :            :     //
     172                 :            :     // It demonstrates that g(x) is the least common multiple of the minimal polynomials
     173                 :            :     // of 3 consecutive powers (997,998,999) of a primitive element (e) of GF(1024).
     174                 :            :     // That guarantees it is, in fact, the generator of a primitive BCH code with cycle
     175                 :            :     // length 1023 and distance 4. See https://en.wikipedia.org/wiki/BCH_code for more details.
     176                 :            : 
     177                 :         49 :     uint32_t c = 1;
     178         [ +  + ]:       5279 :     for (const auto v_i : v) {
     179                 :            :         // We want to update `c` to correspond to a polynomial with one extra term. If the initial
     180                 :            :         // value of `c` consists of the coefficients of c(x) = f(x) mod g(x), we modify it to
     181                 :            :         // correspond to c'(x) = (f(x) * x + v_i) mod g(x), where v_i is the next input to
     182                 :            :         // process. Simplifying:
     183                 :            :         // c'(x) = (f(x) * x + v_i) mod g(x)
     184                 :            :         //         ((f(x) mod g(x)) * x + v_i) mod g(x)
     185                 :            :         //         (c(x) * x + v_i) mod g(x)
     186                 :            :         // If c(x) = c0*x^5 + c1*x^4 + c2*x^3 + c3*x^2 + c4*x + c5, we want to compute
     187                 :            :         // c'(x) = (c0*x^5 + c1*x^4 + c2*x^3 + c3*x^2 + c4*x + c5) * x + v_i mod g(x)
     188                 :            :         //       = c0*x^6 + c1*x^5 + c2*x^4 + c3*x^3 + c4*x^2 + c5*x + v_i mod g(x)
     189                 :            :         //       = c0*(x^6 mod g(x)) + c1*x^5 + c2*x^4 + c3*x^3 + c4*x^2 + c5*x + v_i
     190                 :            :         // If we call (x^6 mod g(x)) = k(x), this can be written as
     191                 :            :         // c'(x) = (c1*x^5 + c2*x^4 + c3*x^3 + c4*x^2 + c5*x + v_i) + c0*k(x)
     192                 :            : 
     193                 :            :         // First, determine the value of c0:
     194                 :       5230 :         uint8_t c0 = c >> 25;
     195                 :            : 
     196                 :            :         // Then compute c1*x^5 + c2*x^4 + c3*x^3 + c4*x^2 + c5*x + v_i:
     197                 :       5230 :         c = ((c & 0x1ffffff) << 5) ^ v_i;
     198                 :            : 
     199                 :            :         // Finally, for each set bit n in c0, conditionally add {2^n}k(x). These constants can be
     200                 :            :         // computed using the following Sage code (continuing the code above):
     201                 :            :         //
     202                 :            :         // for i in [1,2,4,8,16]: # Print out {1,2,4,8,16}*(g(x) mod x^6), packed in hex integers.
     203                 :            :         //     v = 0
     204                 :            :         //     for coef in reversed((F.fetch_int(i)*(G % x**6)).coefficients(sparse=True)):
     205                 :            :         //         v = v*32 + coef.integer_representation()
     206                 :            :         //     print("0x%x" % v)
     207                 :            :         //
     208         [ +  + ]:       5230 :         if (c0 & 1)  c ^= 0x3b6a57b2; //     k(x) = {29}x^5 + {22}x^4 + {20}x^3 + {21}x^2 + {29}x + {18}
     209         [ +  + ]:       5230 :         if (c0 & 2)  c ^= 0x26508e6d; //  {2}k(x) = {19}x^5 +  {5}x^4 +     x^3 +  {3}x^2 + {19}x + {13}
     210         [ +  + ]:       5230 :         if (c0 & 4)  c ^= 0x1ea119fa; //  {4}k(x) = {15}x^5 + {10}x^4 +  {2}x^3 +  {6}x^2 + {15}x + {26}
     211         [ +  + ]:       5230 :         if (c0 & 8)  c ^= 0x3d4233dd; //  {8}k(x) = {30}x^5 + {20}x^4 +  {4}x^3 + {12}x^2 + {30}x + {29}
     212         [ +  + ]:       5230 :         if (c0 & 16) c ^= 0x2a1462b3; // {16}k(x) = {21}x^5 +     x^4 +  {8}x^3 + {24}x^2 + {21}x + {19}
     213                 :            : 
     214                 :            :     }
     215                 :         49 :     return c;
     216                 :            : }
     217                 :            : 
     218                 :            : /** Syndrome computes the values s_j = R(e^j) for j in [997, 998, 999]. As described above, the
     219                 :            :  * generator polynomial G is the LCM of the minimal polynomials of (e)^997, (e)^998, and (e)^999.
     220                 :            :  *
     221                 :            :  * Consider a codeword with errors, of the form R(x) = C(x) + E(x). The residue is the bit-packed
     222                 :            :  * result of computing R(x) mod G(X), where G is the generator of the code. Because C(x) is a valid
     223                 :            :  * codeword, it is a multiple of G(X), so the residue is in fact just E(x) mod G(x). Note that all
     224                 :            :  * of the (e)^j are roots of G(x) by definition, so R((e)^j) = E((e)^j).
     225                 :            :  *
     226                 :            :  * Let R(x) = r1*x^5 + r2*x^4 + r3*x^3 + r4*x^2 + r5*x + r6
     227                 :            :  *
     228                 :            :  * To compute R((e)^j), we are really computing:
     229                 :            :  * r1*(e)^(j*5) + r2*(e)^(j*4) + r3*(e)^(j*3) + r4*(e)^(j*2) + r5*(e)^j + r6
     230                 :            :  *
     231                 :            :  * Now note that all of the (e)^(j*i) for i in [5..0] are constants and can be precomputed.
     232                 :            :  * But even more than that, we can consider each coefficient as a bit-string.
     233                 :            :  * For example, take r5 = (b_5, b_4, b_3, b_2, b_1) written out as 5 bits. Then:
     234                 :            :  * r5*(e)^j = b_1*(e)^j + b_2*(2*(e)^j) + b_3*(4*(e)^j) + b_4*(8*(e)^j) + b_5*(16*(e)^j)
     235                 :            :  * where all the (2^i*(e)^j) are constants and can be precomputed.
     236                 :            :  *
     237                 :            :  * Then we just add each of these corresponding constants to our final value based on the
     238                 :            :  * bit values b_i. This is exactly what is done in the Syndrome function below.
     239                 :            :  */
     240                 :            : constexpr std::array<uint32_t, 25> GenerateSyndromeConstants() {
     241                 :            :     std::array<uint32_t, 25> SYNDROME_CONSTS{};
     242                 :            :     for (int k = 1; k < 6; ++k) {
     243                 :            :         for (int shift = 0; shift < 5; ++shift) {
     244                 :            :             int16_t b = GF1024_LOG.at(size_t{1} << shift);
     245                 :            :             int16_t c0 = GF1024_EXP.at((997*k + b) % 1023);
     246                 :            :             int16_t c1 = GF1024_EXP.at((998*k + b) % 1023);
     247                 :            :             int16_t c2 = GF1024_EXP.at((999*k + b) % 1023);
     248                 :            :             uint32_t c = c2 << 20 | c1 << 10 | c0;
     249                 :            :             int ind = 5*(k-1) + shift;
     250                 :            :             SYNDROME_CONSTS[ind] = c;
     251                 :            :         }
     252                 :            :     }
     253                 :            :     return SYNDROME_CONSTS;
     254                 :            : }
     255                 :            : constexpr std::array<uint32_t, 25> SYNDROME_CONSTS = GenerateSyndromeConstants();
     256                 :            : 
     257                 :            : /**
     258                 :            :  * Syndrome returns the three values s_997, s_998, and s_999 described above,
     259                 :            :  * packed into a 30-bit integer, where each group of 10 bits encodes one value.
     260                 :            :  */
     261                 :         32 : uint32_t Syndrome(const uint32_t residue) {
     262                 :            :     // low is the first 5 bits, corresponding to the r6 in the residue
     263                 :            :     // (the constant term of the polynomial).
     264                 :         32 :     uint32_t low = residue & 0x1f;
     265                 :            : 
     266                 :            :     // We begin by setting s_j = low = r6 for all three values of j, because these are unconditional.
     267                 :         32 :     uint32_t result = low ^ (low << 10) ^ (low << 20);
     268                 :            : 
     269                 :            :     // Then for each following bit, we add the corresponding precomputed constant if the bit is 1.
     270                 :            :     // For example, 0x31edd3c4 is 1100011110 1101110100 1111000100 when unpacked in groups of 10
     271                 :            :     // bits, corresponding exactly to a^999 || a^998 || a^997 (matching the corresponding values in
     272                 :            :     // GF1024_EXP above). In this way, we compute all three values of s_j for j in (997, 998, 999)
     273                 :            :     // simultaneously. Recall that XOR corresponds to addition in a characteristic 2 field.
     274         [ +  + ]:        832 :     for (int i = 0; i < 25; ++i) {
     275         [ +  + ]:        800 :         result ^= ((residue >> (5+i)) & 1 ? SYNDROME_CONSTS.at(i) : 0);
     276                 :        800 :     }
     277                 :         32 :     return result;
     278                 :            : }
     279                 :            : 
     280                 :            : /** Convert to lower case. */
     281                 :       1454 : inline unsigned char LowerCase(unsigned char c)
     282                 :            : {
     283 [ +  + ][ -  + ]:       1454 :     return (c >= 'A' && c <= 'Z') ? (c - 'A') + 'a' : c;
     284                 :            : }
     285                 :            : 
     286                 :            : /** Return indices of invalid characters in a Bech32 string. */
     287                 :         34 : bool CheckCharacters(const std::string& str, std::vector<int>& errors)
     288                 :            : {
     289                 :         34 :     bool lower = false, upper = false;
     290         [ +  + ]:       2425 :     for (size_t i = 0; i < str.size(); ++i) {
     291                 :       2391 :         unsigned char c{(unsigned char)(str[i])};
     292 [ +  + ][ +  + ]:       2391 :         if (c >= 'a' && c <= 'z') {
     293         [ +  + ]:       1173 :             if (upper) {
     294                 :        148 :                 errors.push_back(i);
     295                 :        148 :             } else {
     296                 :       1025 :                 lower = true;
     297                 :            :             }
     298 [ +  + ][ +  + ]:       2391 :         } else if (c >= 'A' && c <= 'Z') {
     299         [ -  + ]:        143 :             if (lower) {
     300                 :          0 :                 errors.push_back(i);
     301                 :          0 :             } else {
     302                 :        143 :                 upper = true;
     303                 :            :             }
     304 [ +  - ][ -  + ]:       1218 :         } else if (c < 33 || c > 126) {
     305                 :          0 :             errors.push_back(i);
     306                 :          0 :         }
     307                 :       2391 :     }
     308                 :         34 :     return errors.empty();
     309                 :            : }
     310                 :            : 
     311                 :            : /** Expand a HRP for use in checksum computation. */
     312                 :         49 : data ExpandHRP(const std::string& hrp)
     313                 :            : {
     314                 :         49 :     data ret;
     315         [ +  - ]:         49 :     ret.reserve(hrp.size() + 90);
     316         [ +  - ]:         49 :     ret.resize(hrp.size() * 2 + 1);
     317         [ +  + ]:       2216 :     for (size_t i = 0; i < hrp.size(); ++i) {
     318                 :       2167 :         unsigned char c = hrp[i];
     319                 :       2167 :         ret[i] = c >> 5;
     320                 :       2167 :         ret[i + hrp.size() + 1] = c & 0x1f;
     321                 :       2167 :     }
     322                 :         49 :     ret[hrp.size()] = 0;
     323                 :         49 :     return ret;
     324         [ +  - ]:         49 : }
     325                 :            : 
     326                 :            : /** Verify a checksum. */
     327                 :         17 : Encoding VerifyChecksum(const std::string& hrp, const data& values)
     328                 :            : {
     329                 :            :     // PolyMod computes what value to xor into the final values to make the checksum 0. However,
     330                 :            :     // if we required that the checksum was 0, it would be the case that appending a 0 to a valid
     331                 :            :     // list of values would result in a new valid list. For that reason, Bech32 requires the
     332                 :            :     // resulting checksum to be 1 instead. In Bech32m, this constant was amended. See
     333                 :            :     // https://gist.github.com/sipa/14c248c288c3880a3b191f978a34508e for details.
     334 [ +  - ][ -  + ]:         17 :     const uint32_t check = PolyMod(Cat(ExpandHRP(hrp), values));
     335         [ +  + ]:         17 :     if (check == EncodingConstant(Encoding::BECH32)) return Encoding::BECH32;
     336         [ -  + ]:         16 :     if (check == EncodingConstant(Encoding::BECH32M)) return Encoding::BECH32M;
     337                 :         16 :     return Encoding::INVALID;
     338                 :         17 : }
     339                 :            : 
     340                 :            : /** Create a checksum. */
     341                 :          0 : data CreateChecksum(Encoding encoding, const std::string& hrp, const data& values)
     342                 :            : {
     343         [ #  # ]:          0 :     data enc = Cat(ExpandHRP(hrp), values);
     344         [ #  # ]:          0 :     enc.resize(enc.size() + 6); // Append 6 zeroes
     345 [ #  # ][ #  # ]:          0 :     uint32_t mod = PolyMod(enc) ^ EncodingConstant(encoding); // Determine what to XOR into those 6 zeroes.
     346         [ #  # ]:          0 :     data ret(6);
     347         [ #  # ]:          0 :     for (size_t i = 0; i < 6; ++i) {
     348                 :            :         // Convert the 5-bit groups in mod to checksum values.
     349                 :          0 :         ret[i] = (mod >> (5 * (5 - i))) & 31;
     350                 :          0 :     }
     351                 :          0 :     return ret;
     352         [ #  # ]:          0 : }
     353                 :            : 
     354                 :            : } // namespace
     355                 :            : 
     356                 :            : /** Encode a Bech32 or Bech32m string. */
     357                 :          0 : std::string Encode(Encoding encoding, const std::string& hrp, const data& values) {
     358                 :            :     // First ensure that the HRP is all lowercase. BIP-173 and BIP350 require an encoder
     359                 :            :     // to return a lowercase Bech32/Bech32m string, but if given an uppercase HRP, the
     360                 :            :     // result will always be invalid.
     361 [ #  # ][ #  # ]:          0 :     for (const char& c : hrp) assert(c < 'A' || c > 'Z');
                 [ #  # ]
     362                 :          0 :     data checksum = CreateChecksum(encoding, hrp, values);
     363 [ #  # ][ #  # ]:          0 :     data combined = Cat(values, checksum);
     364         [ #  # ]:          0 :     std::string ret = hrp + '1';
     365         [ #  # ]:          0 :     ret.reserve(ret.size() + combined.size());
     366         [ #  # ]:          0 :     for (const auto c : combined) {
     367         [ #  # ]:          0 :         ret += CHARSET[c];
     368                 :            :     }
     369                 :          0 :     return ret;
     370         [ #  # ]:          0 : }
     371                 :            : 
     372                 :            : /** Decode a Bech32 or Bech32m string. */
     373                 :         18 : DecodeResult Decode(const std::string& str) {
     374                 :         18 :     std::vector<int> errors;
     375 [ +  - ][ +  + ]:         18 :     if (!CheckCharacters(str, errors)) return {};
                 [ +  - ]
     376                 :         17 :     size_t pos = str.rfind('1');
     377 [ +  - ][ +  - ]:         17 :     if (str.size() > 90 || pos == str.npos || pos == 0 || pos + 7 > str.size()) {
         [ +  - ][ -  + ]
     378         [ #  # ]:          0 :         return {};
     379                 :            :     }
     380         [ +  - ]:         17 :     data values(str.size() - 1 - pos);
     381         [ +  + ]:        310 :     for (size_t i = 0; i < str.size() - 1 - pos; ++i) {
     382                 :        293 :         unsigned char c = str[i + pos + 1];
     383                 :        293 :         int8_t rev = CHARSET_REV[c];
     384                 :            : 
     385         [ +  - ]:        293 :         if (rev == -1) {
     386         [ #  # ]:          0 :             return {};
     387                 :            :         }
     388                 :        293 :         values[i] = rev;
     389                 :        293 :     }
     390                 :         17 :     std::string hrp;
     391         [ +  + ]:        758 :     for (size_t i = 0; i < pos; ++i) {
     392 [ +  - ][ +  - ]:        741 :         hrp += LowerCase(str[i]);
     393                 :        741 :     }
     394         [ +  - ]:         17 :     Encoding result = VerifyChecksum(hrp, values);
     395 [ +  + ][ +  - ]:         17 :     if (result == Encoding::INVALID) return {};
     396 [ +  - ][ +  - ]:          1 :     return {result, std::move(hrp), data(values.begin(), values.end() - 6)};
     397                 :         18 : }
     398                 :            : 
     399                 :            : /** Find index of an incorrect character in a Bech32 string. */
     400                 :         17 : std::pair<std::string, std::vector<int>> LocateErrors(const std::string& str) {
     401                 :         17 :     std::vector<int> error_locations{};
     402                 :            : 
     403         [ +  + ]:         17 :     if (str.size() > 90) {
     404         [ +  - ]:          1 :         error_locations.resize(str.size() - 90);
     405         [ +  - ]:          1 :         std::iota(error_locations.begin(), error_locations.end(), 90);
     406 [ +  - ][ +  - ]:          1 :         return std::make_pair("Bech32 string too long", std::move(error_locations));
     407                 :            :     }
     408                 :            : 
     409 [ +  - ][ -  + ]:         16 :     if (!CheckCharacters(str, error_locations)){
     410 [ #  # ][ #  # ]:          0 :         return std::make_pair("Invalid character or mixed case", std::move(error_locations));
     411                 :            :     }
     412                 :            : 
     413                 :         16 :     size_t pos = str.rfind('1');
     414         [ +  - ]:         16 :     if (pos == str.npos) {
     415 [ #  # ][ #  # ]:          0 :         return std::make_pair("Missing separator", std::vector<int>{});
     416                 :            :     }
     417 [ +  - ][ -  + ]:         16 :     if (pos == 0 || pos + 7 > str.size()) {
     418         [ #  # ]:          0 :         error_locations.push_back(pos);
     419 [ #  # ][ #  # ]:          0 :         return std::make_pair("Invalid separator position", std::move(error_locations));
     420                 :            :     }
     421                 :            : 
     422                 :         16 :     std::string hrp;
     423         [ +  + ]:        729 :     for (size_t i = 0; i < pos; ++i) {
     424 [ +  - ][ +  - ]:        713 :         hrp += LowerCase(str[i]);
     425                 :        713 :     }
     426                 :            : 
     427                 :         16 :     size_t length = str.size() - 1 - pos; // length of data part
     428         [ +  - ]:         16 :     data values(length);
     429         [ +  + ]:        293 :     for (size_t i = pos + 1; i < str.size(); ++i) {
     430                 :        277 :         unsigned char c = str[i];
     431                 :        277 :         int8_t rev = CHARSET_REV[c];
     432         [ +  - ]:        277 :         if (rev == -1) {
     433         [ #  # ]:          0 :             error_locations.push_back(i);
     434 [ #  # ][ #  # ]:          0 :             return std::make_pair("Invalid Base 32 character", std::move(error_locations));
     435                 :            :         }
     436                 :        277 :         values[i - pos - 1] = rev;
     437                 :        277 :     }
     438                 :            : 
     439                 :            :     // We attempt error detection with both bech32 and bech32m, and choose the one with the fewest errors
     440                 :            :     // We can't simply use the segwit version, because that may be one of the errors
     441                 :         16 :     std::optional<Encoding> error_encoding;
     442         [ +  + ]:         48 :     for (Encoding encoding : {Encoding::BECH32, Encoding::BECH32M}) {
     443                 :         32 :         std::vector<int> possible_errors;
     444                 :            :         // Recall that (ExpandHRP(hrp) ++ values) is interpreted as a list of coefficients of a polynomial
     445                 :            :         // over GF(32). PolyMod computes the "remainder" of this polynomial modulo the generator G(x).
     446 [ +  - ][ +  - ]:         32 :         uint32_t residue = PolyMod(Cat(ExpandHRP(hrp), values)) ^ EncodingConstant(encoding);
         [ +  - ][ +  - ]
     447                 :            : 
     448                 :            :         // All valid codewords should be multiples of G(x), so this remainder (after XORing with the encoding
     449                 :            :         // constant) should be 0 - hence 0 indicates there are no errors present.
     450         [ +  - ]:         32 :         if (residue != 0) {
     451                 :            :             // If errors are present, our polynomial must be of the form C(x) + E(x) where C is the valid
     452                 :            :             // codeword (a multiple of G(x)), and E encodes the errors.
     453         [ +  - ]:         32 :             uint32_t syn = Syndrome(residue);
     454                 :            : 
     455                 :            :             // Unpack the three 10-bit syndrome values
     456                 :         32 :             int s0 = syn & 0x3FF;
     457                 :         32 :             int s1 = (syn >> 10) & 0x3FF;
     458                 :         32 :             int s2 = syn >> 20;
     459                 :            : 
     460                 :            :             // Get the discrete logs of these values in GF1024 for more efficient computation
     461         [ +  - ]:         32 :             int l_s0 = GF1024_LOG.at(s0);
     462         [ +  - ]:         32 :             int l_s1 = GF1024_LOG.at(s1);
     463         [ +  - ]:         32 :             int l_s2 = GF1024_LOG.at(s2);
     464                 :            : 
     465                 :            :             // First, suppose there is only a single error. Then E(x) = e1*x^p1 for some position p1
     466                 :            :             // Then s0 = E((e)^997) = e1*(e)^(997*p1) and s1 = E((e)^998) = e1*(e)^(998*p1)
     467                 :            :             // Therefore s1/s0 = (e)^p1, and by the same logic, s2/s1 = (e)^p1 too.
     468                 :            :             // Hence, s1^2 == s0*s2, which is exactly the condition we check first:
     469 [ +  - ][ +  - ]:         32 :             if (l_s0 != -1 && l_s1 != -1 && l_s2 != -1 && (2 * l_s1 - l_s2 - l_s0 + 2046) % 1023 == 0) {
         [ +  - ][ +  - ]
     470                 :            :                 // Compute the error position p1 as l_s1 - l_s0 = p1 (mod 1023)
     471                 :          0 :                 size_t p1 = (l_s1 - l_s0 + 1023) % 1023; // the +1023 ensures it is positive
     472                 :            :                 // Now because s0 = e1*(e)^(997*p1), we get e1 = s0/((e)^(997*p1)). Remember that (e)^1023 = 1,
     473                 :            :                 // so 1/((e)^997) = (e)^(1023-997).
     474                 :          0 :                 int l_e1 = l_s0 + (1023 - 997) * p1;
     475                 :            :                 // Finally, some sanity checks on the result:
     476                 :            :                 // - The error position should be within the length of the data
     477                 :            :                 // - e1 should be in GF(32), which implies that e1 = (e)^(33k) for some k (the 31 non-zero elements
     478                 :            :                 // of GF(32) form an index 33 subgroup of the 1023 non-zero elements of GF(1024)).
     479 [ #  # ][ #  # ]:          0 :                 if (p1 < length && !(l_e1 % 33)) {
     480                 :            :                     // Polynomials run from highest power to lowest, so the index p1 is from the right.
     481                 :            :                     // We don't return e1 because it is dangerous to suggest corrections to the user,
     482                 :            :                     // the user should check the address themselves.
     483         [ #  # ]:          0 :                     possible_errors.push_back(str.size() - p1 - 1);
     484                 :          0 :                 }
     485                 :            :             // Otherwise, suppose there are two errors. Then E(x) = e1*x^p1 + e2*x^p2.
     486                 :          0 :             } else {
     487                 :            :                 // For all possible first error positions p1
     488         [ +  + ]:        586 :                 for (size_t p1 = 0; p1 < length; ++p1) {
     489                 :            :                     // We have guessed p1, and want to solve for p2. Recall that E(x) = e1*x^p1 + e2*x^p2, so
     490                 :            :                     // s0 = E((e)^997) = e1*(e)^(997^p1) + e2*(e)^(997*p2), and similar for s1 and s2.
     491                 :            :                     //
     492                 :            :                     // Consider s2 + s1*(e)^p1
     493                 :            :                     //          = 2e1*(e)^(999^p1) + e2*(e)^(999*p2) + e2*(e)^(998*p2)*(e)^p1
     494                 :            :                     //          = e2*(e)^(999*p2) + e2*(e)^(998*p2)*(e)^p1
     495                 :            :                     //    (Because we are working in characteristic 2.)
     496                 :            :                     //          = e2*(e)^(998*p2) ((e)^p2 + (e)^p1)
     497                 :            :                     //
     498 [ +  - ][ +  - ]:        554 :                     int s2_s1p1 = s2 ^ (s1 == 0 ? 0 : GF1024_EXP.at((l_s1 + p1) % 1023));
     499         [ +  + ]:        554 :                     if (s2_s1p1 == 0) continue;
     500         [ +  - ]:        553 :                     int l_s2_s1p1 = GF1024_LOG.at(s2_s1p1);
     501                 :            : 
     502                 :            :                     // Similarly, s1 + s0*(e)^p1
     503                 :            :                     //          = e2*(e)^(997*p2) ((e)^p2 + (e)^p1)
     504 [ +  - ][ +  - ]:        553 :                     int s1_s0p1 = s1 ^ (s0 == 0 ? 0 : GF1024_EXP.at((l_s0 + p1) % 1023));
     505         [ +  + ]:        553 :                     if (s1_s0p1 == 0) continue;
     506         [ +  - ]:        551 :                     int l_s1_s0p1 = GF1024_LOG.at(s1_s0p1);
     507                 :            : 
     508                 :            :                     // So, putting these together, we can compute the second error position as
     509                 :            :                     // (e)^p2 = (s2 + s1^p1)/(s1 + s0^p1)
     510                 :            :                     // p2 = log((e)^p2)
     511                 :        551 :                     size_t p2 = (l_s2_s1p1 - l_s1_s0p1 + 1023) % 1023;
     512                 :            : 
     513                 :            :                     // Sanity checks that p2 is a valid position and not the same as p1
     514 [ +  + ][ -  + ]:        551 :                     if (p2 >= length || p1 == p2) continue;
     515                 :            : 
     516                 :            :                     // Now we want to compute the error values e1 and e2.
     517                 :            :                     // Similar to above, we compute s1 + s0*(e)^p2
     518                 :            :                     //          = e1*(e)^(997*p1) ((e)^p1 + (e)^p2)
     519 [ +  - ][ +  - ]:         20 :                     int s1_s0p2 = s1 ^ (s0 == 0 ? 0 : GF1024_EXP.at((l_s0 + p2) % 1023));
     520         [ +  - ]:         20 :                     if (s1_s0p2 == 0) continue;
     521         [ +  - ]:         20 :                     int l_s1_s0p2 = GF1024_LOG.at(s1_s0p2);
     522                 :            : 
     523                 :            :                     // And compute (the log of) 1/((e)^p1 + (e)^p2))
     524 [ +  - ][ +  - ]:         20 :                     int inv_p1_p2 = 1023 - GF1024_LOG.at(GF1024_EXP.at(p1) ^ GF1024_EXP.at(p2));
                 [ +  - ]
     525                 :            : 
     526                 :            :                     // Then (s1 + s0*(e)^p1) * (1/((e)^p1 + (e)^p2)))
     527                 :            :                     //         = e2*(e)^(997*p2)
     528                 :            :                     // Then recover e2 by dividing by (e)^(997*p2)
     529                 :         20 :                     int l_e2 = l_s1_s0p1 + inv_p1_p2 + (1023 - 997) * p2;
     530                 :            :                     // Check that e2 is in GF(32)
     531         [ +  + ]:         20 :                     if (l_e2 % 33) continue;
     532                 :            : 
     533                 :            :                     // In the same way, (s1 + s0*(e)^p2) * (1/((e)^p1 + (e)^p2)))
     534                 :            :                     //         = e1*(e)^(997*p1)
     535                 :            :                     // So recover e1 by dividing by (e)^(997*p1)
     536                 :          1 :                     int l_e1 = l_s1_s0p2 + inv_p1_p2 + (1023 - 997) * p1;
     537                 :            :                     // Check that e1 is in GF(32)
     538         [ +  - ]:          1 :                     if (l_e1 % 33) continue;
     539                 :            : 
     540                 :            :                     // Again, we do not return e1 or e2 for safety.
     541                 :            :                     // Order the error positions from the left of the string and return them
     542         [ #  # ]:          0 :                     if (p1 > p2) {
     543         [ #  # ]:          0 :                         possible_errors.push_back(str.size() - p1 - 1);
     544         [ #  # ]:          0 :                         possible_errors.push_back(str.size() - p2 - 1);
     545                 :          0 :                     } else {
     546         [ #  # ]:          0 :                         possible_errors.push_back(str.size() - p2 - 1);
     547         [ #  # ]:          0 :                         possible_errors.push_back(str.size() - p1 - 1);
     548                 :            :                     }
     549                 :          0 :                     break;
     550                 :            :                 }
     551                 :            :             }
     552                 :         32 :         } else {
     553                 :            :             // No errors
     554 [ #  # ][ #  # ]:          0 :             return std::make_pair("", std::vector<int>{});
     555                 :            :         }
     556                 :            : 
     557 [ -  + ][ #  # ]:         32 :         if (error_locations.empty() || (!possible_errors.empty() && possible_errors.size() < error_locations.size())) {
                 [ #  # ]
     558                 :         32 :             error_locations = std::move(possible_errors);
     559         [ +  - ]:         32 :             if (!error_locations.empty()) error_encoding = encoding;
     560                 :         32 :         }
     561         [ -  + ]:         32 :     }
     562 [ +  - ][ +  - ]:         32 :     std::string error_message = error_encoding == Encoding::BECH32M ? "Invalid Bech32m checksum"
                 [ +  - ]
     563         [ +  - ]:         16 :                               : error_encoding == Encoding::BECH32 ? "Invalid Bech32 checksum"
     564                 :            :                               : "Invalid checksum";
     565                 :            : 
     566         [ +  - ]:         16 :     return std::make_pair(error_message, std::move(error_locations));
     567                 :         17 : }
     568                 :            : 
     569                 :            : } // namespace bech32

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