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1 : : // Copyright (c) 2017, 2021 Pieter Wuille
2 : : // Copyright (c) 2021-present 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 <cassert>
11 : : #include <optional>
12 : :
13 : : namespace bech32
14 : : {
15 : :
16 : : namespace
17 : : {
18 : :
19 : : typedef std::vector<uint8_t> data;
20 : :
21 : : /** The Bech32 and Bech32m character set for encoding. */
22 : : const char* CHARSET = "qpzry9x8gf2tvdw0s3jn54khce6mua7l";
23 : :
24 : : /** The Bech32 and Bech32m character set for decoding. */
25 : : const int8_t CHARSET_REV[128] = {
26 : : -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
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 : : 15, -1, 10, 17, 21, 20, 26, 30, 7, 5, -1, -1, -1, -1, -1, -1,
30 : : -1, 29, -1, 24, 13, 25, 9, 8, 23, -1, 18, 22, 31, 27, 19, -1,
31 : : 1, 0, 3, 16, 11, 28, 12, 14, 6, 4, 2, -1, -1, -1, -1, -1,
32 : : -1, 29, -1, 24, 13, 25, 9, 8, 23, -1, 18, 22, 31, 27, 19, -1,
33 : : 1, 0, 3, 16, 11, 28, 12, 14, 6, 4, 2, -1, -1, -1, -1, -1
34 : : };
35 : :
36 : : /** We work with the finite field GF(1024) defined as a degree 2 extension of the base field GF(32)
37 : : * The defining polynomial of the extension is x^2 + 9x + 23.
38 : : * Let (e) be a root of this defining polynomial. Then (e) is a primitive element of GF(1024),
39 : : * that is, a generator of the field. Every non-zero element of the field can then be represented
40 : : * as (e)^k for some power k.
41 : : * The array GF1024_EXP contains all these powers of (e) - GF1024_EXP[k] = (e)^k in GF(1024).
42 : : * Conversely, GF1024_LOG contains the discrete logarithms of these powers, so
43 : : * GF1024_LOG[GF1024_EXP[k]] == k.
44 : : * The following function generates the two tables GF1024_EXP and GF1024_LOG as constexprs. */
45 : : constexpr std::pair<std::array<int16_t, 1023>, std::array<int16_t, 1024>> GenerateGFTables()
46 : : {
47 : : // Build table for GF(32).
48 : : // We use these tables to perform arithmetic in GF(32) below, when constructing the
49 : : // tables for GF(1024).
50 : : std::array<int8_t, 31> GF32_EXP{};
51 : : std::array<int8_t, 32> GF32_LOG{};
52 : :
53 : : // fmod encodes the defining polynomial of GF(32) over GF(2), x^5 + x^3 + 1.
54 : : // Because coefficients in GF(2) are binary digits, the coefficients are packed as 101001.
55 : : const int fmod = 41;
56 : :
57 : : // Elements of GF(32) are encoded as vectors of length 5 over GF(2), that is,
58 : : // 5 binary digits. Each element (b_4, b_3, b_2, b_1, b_0) encodes a polynomial
59 : : // b_4*x^4 + b_3*x^3 + b_2*x^2 + b_1*x^1 + b_0 (modulo fmod).
60 : : // For example, 00001 = 1 is the multiplicative identity.
61 : : GF32_EXP[0] = 1;
62 : : GF32_LOG[0] = -1;
63 : : GF32_LOG[1] = 0;
64 : : int v = 1;
65 : : for (int i = 1; i < 31; ++i) {
66 : : // Multiplication by x is the same as shifting left by 1, as
67 : : // every coefficient of the polynomial is moved up one place.
68 : : v = v << 1;
69 : : // If the polynomial now has an x^5 term, we subtract fmod from it
70 : : // to remain working modulo fmod. Subtraction is the same as XOR in characteristic
71 : : // 2 fields.
72 : : if (v & 32) v ^= fmod;
73 : : GF32_EXP[i] = v;
74 : : GF32_LOG[v] = i;
75 : : }
76 : :
77 : : // Build table for GF(1024)
78 : : std::array<int16_t, 1023> GF1024_EXP{};
79 : : std::array<int16_t, 1024> GF1024_LOG{};
80 : :
81 : : GF1024_EXP[0] = 1;
82 : : GF1024_LOG[0] = -1;
83 : : GF1024_LOG[1] = 0;
84 : :
85 : : // Each element v of GF(1024) is encoded as a 10 bit integer in the following way:
86 : : // v = v1 || v0 where v0, v1 are 5-bit integers (elements of GF(32)).
87 : : // The element (e) is encoded as 1 || 0, to represent 1*(e) + 0. Every other element
88 : : // a*(e) + b is represented as a || b (a and b are both GF(32) elements). Given (v),
89 : : // we compute (e)*(v) by multiplying in the following way:
90 : : //
91 : : // v0' = 23*v1
92 : : // v1' = 9*v1 + v0
93 : : // e*v = v1' || v0'
94 : : //
95 : : // Where 23, 9 are GF(32) elements encoded as described above. Multiplication in GF(32)
96 : : // is done using the log/exp tables:
97 : : // e^x * e^y = e^(x + y) so a * b = EXP[ LOG[a] + LOG [b] ]
98 : : // for non-zero a and b.
99 : :
100 : : v = 1;
101 : : for (int i = 1; i < 1023; ++i) {
102 : : int v0 = v & 31;
103 : : int v1 = v >> 5;
104 : :
105 : : int v0n = v1 ? GF32_EXP.at((GF32_LOG.at(v1) + GF32_LOG.at(23)) % 31) : 0;
106 : : int v1n = (v1 ? GF32_EXP.at((GF32_LOG.at(v1) + GF32_LOG.at(9)) % 31) : 0) ^ v0;
107 : :
108 : : v = v1n << 5 | v0n;
109 : : GF1024_EXP[i] = v;
110 : : GF1024_LOG[v] = i;
111 : : }
112 : :
113 : : return std::make_pair(GF1024_EXP, GF1024_LOG);
114 : : }
115 : :
116 : : constexpr auto tables = GenerateGFTables();
117 : : constexpr const std::array<int16_t, 1023>& GF1024_EXP = tables.first;
118 : : constexpr const std::array<int16_t, 1024>& GF1024_LOG = tables.second;
119 : :
120 : : /* Determine the final constant to use for the specified encoding. */
121 : 402598 : uint32_t EncodingConstant(Encoding encoding) {
122 [ - + ]: 402598 : assert(encoding == Encoding::BECH32 || encoding == Encoding::BECH32M);
123 [ + + ]: 402598 : return encoding == Encoding::BECH32 ? 1 : 0x2bc830a3;
124 : : }
125 : :
126 : : /** This function will compute what 6 5-bit values to XOR into the last 6 input values, in order to
127 : : * make the checksum 0. These 6 values are packed together in a single 30-bit integer. The higher
128 : : * bits correspond to earlier values. */
129 : 401976 : uint32_t PolyMod(const data& v)
130 : : {
131 : : // The input is interpreted as a list of coefficients of a polynomial over F = GF(32), with an
132 : : // implicit 1 in front. If the input is [v0,v1,v2,v3,v4], that polynomial is v(x) =
133 : : // 1*x^5 + v0*x^4 + v1*x^3 + v2*x^2 + v3*x + v4. The implicit 1 guarantees that
134 : : // [v0,v1,v2,...] has a distinct checksum from [0,v0,v1,v2,...].
135 : :
136 : : // The output is a 30-bit integer whose 5-bit groups are the coefficients of the remainder of
137 : : // v(x) mod g(x), where g(x) is the Bech32 generator,
138 : : // 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
139 : : // that the resulting code is a BCH code, guaranteeing detection of up to 3 errors within a
140 : : // window of 1023 characters. Among the various possible BCH codes, one was selected to in
141 : : // fact guarantee detection of up to 4 errors within a window of 89 characters.
142 : :
143 : : // Note that the coefficients are elements of GF(32), here represented as decimal numbers
144 : : // between {}. In this finite field, addition is just XOR of the corresponding numbers. For
145 : : // example, {27} + {13} = {27 ^ 13} = {22}. Multiplication is more complicated, and requires
146 : : // treating the bits of values themselves as coefficients of a polynomial over a smaller field,
147 : : // GF(2), and multiplying those polynomials mod a^5 + a^3 + 1. For example, {5} * {26} =
148 : : // (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
149 : : // = a^3 + 1 (mod a^5 + a^3 + 1) = {9}.
150 : :
151 : : // During the course of the loop below, `c` contains the bitpacked coefficients of the
152 : : // polynomial constructed from just the values of v that were processed so far, mod g(x). In
153 : : // the above example, `c` initially corresponds to 1 mod g(x), and after processing 2 inputs of
154 : : // v, it corresponds to x^2 + v0*x + v1 mod g(x). As 1 mod g(x) = 1, that is the starting value
155 : : // for `c`.
156 : :
157 : : // The following Sage code constructs the generator used:
158 : : //
159 : : // B = GF(2) # Binary field
160 : : // BP.<b> = B[] # Polynomials over the binary field
161 : : // F_mod = b**5 + b**3 + 1
162 : : // F.<f> = GF(32, modulus=F_mod, repr='int') # GF(32) definition
163 : : // FP.<x> = F[] # Polynomials over GF(32)
164 : : // E_mod = x**2 + F.fetch_int(9)*x + F.fetch_int(23)
165 : : // E.<e> = F.extension(E_mod) # GF(1024) extension field definition
166 : : // for p in divisors(E.order() - 1): # Verify e has order 1023.
167 : : // assert((e**p == 1) == (p % 1023 == 0))
168 : : // G = lcm([(e**i).minpoly() for i in range(997,1000)])
169 : : // print(G) # Print out the generator
170 : : //
171 : : // It demonstrates that g(x) is the least common multiple of the minimal polynomials
172 : : // of 3 consecutive powers (997,998,999) of a primitive element (e) of GF(1024).
173 : : // That guarantees it is, in fact, the generator of a primitive BCH code with cycle
174 : : // length 1023 and distance 4. See https://en.wikipedia.org/wiki/BCH_code for more details.
175 : :
176 : 401976 : uint32_t c = 1;
177 [ + + ]: 23901978 : for (const auto v_i : v) {
178 : : // We want to update `c` to correspond to a polynomial with one extra term. If the initial
179 : : // value of `c` consists of the coefficients of c(x) = f(x) mod g(x), we modify it to
180 : : // correspond to c'(x) = (f(x) * x + v_i) mod g(x), where v_i is the next input to
181 : : // process. Simplifying:
182 : : // c'(x) = (f(x) * x + v_i) mod g(x)
183 : : // ((f(x) mod g(x)) * x + v_i) mod g(x)
184 : : // (c(x) * x + v_i) mod g(x)
185 : : // If c(x) = c0*x^5 + c1*x^4 + c2*x^3 + c3*x^2 + c4*x + c5, we want to compute
186 : : // c'(x) = (c0*x^5 + c1*x^4 + c2*x^3 + c3*x^2 + c4*x + c5) * x + v_i mod g(x)
187 : : // = c0*x^6 + c1*x^5 + c2*x^4 + c3*x^3 + c4*x^2 + c5*x + v_i mod g(x)
188 : : // = c0*(x^6 mod g(x)) + c1*x^5 + c2*x^4 + c3*x^3 + c4*x^2 + c5*x + v_i
189 : : // If we call (x^6 mod g(x)) = k(x), this can be written as
190 : : // c'(x) = (c1*x^5 + c2*x^4 + c3*x^3 + c4*x^2 + c5*x + v_i) + c0*k(x)
191 : :
192 : : // First, determine the value of c0:
193 : 23500002 : uint8_t c0 = c >> 25;
194 : :
195 : : // Then compute c1*x^5 + c2*x^4 + c3*x^3 + c4*x^2 + c5*x + v_i:
196 : 23500002 : c = ((c & 0x1ffffff) << 5) ^ v_i;
197 : :
198 : : // Finally, for each set bit n in c0, conditionally add {2^n}k(x). These constants can be
199 : : // computed using the following Sage code (continuing the code above):
200 : : //
201 : : // for i in [1,2,4,8,16]: # Print out {1,2,4,8,16}*(g(x) mod x^6), packed in hex integers.
202 : : // v = 0
203 : : // for coef in reversed((F.fetch_int(i)*(G % x**6)).coefficients(sparse=True)):
204 : : // v = v*32 + coef.integer_representation()
205 : : // print("0x%x" % v)
206 : : //
207 [ + + ]: 23500002 : if (c0 & 1) c ^= 0x3b6a57b2; // k(x) = {29}x^5 + {22}x^4 + {20}x^3 + {21}x^2 + {29}x + {18}
208 [ + + ]: 23500002 : if (c0 & 2) c ^= 0x26508e6d; // {2}k(x) = {19}x^5 + {5}x^4 + x^3 + {3}x^2 + {19}x + {13}
209 [ + + ]: 23500002 : if (c0 & 4) c ^= 0x1ea119fa; // {4}k(x) = {15}x^5 + {10}x^4 + {2}x^3 + {6}x^2 + {15}x + {26}
210 [ + + ]: 23500002 : if (c0 & 8) c ^= 0x3d4233dd; // {8}k(x) = {30}x^5 + {20}x^4 + {4}x^3 + {12}x^2 + {30}x + {29}
211 [ + + ]: 23500002 : if (c0 & 16) c ^= 0x2a1462b3; // {16}k(x) = {21}x^5 + x^4 + {8}x^3 + {24}x^2 + {21}x + {19}
212 : :
213 : : }
214 : 401976 : return c;
215 : : }
216 : :
217 : : /** Syndrome computes the values s_j = R(e^j) for j in [997, 998, 999]. As described above, the
218 : : * generator polynomial G is the LCM of the minimal polynomials of (e)^997, (e)^998, and (e)^999.
219 : : *
220 : : * Consider a codeword with errors, of the form R(x) = C(x) + E(x). The residue is the bit-packed
221 : : * result of computing R(x) mod G(X), where G is the generator of the code. Because C(x) is a valid
222 : : * codeword, it is a multiple of G(X), so the residue is in fact just E(x) mod G(x). Note that all
223 : : * of the (e)^j are roots of G(x) by definition, so R((e)^j) = E((e)^j).
224 : : *
225 : : * Let R(x) = r1*x^5 + r2*x^4 + r3*x^3 + r4*x^2 + r5*x + r6
226 : : *
227 : : * To compute R((e)^j), we are really computing:
228 : : * r1*(e)^(j*5) + r2*(e)^(j*4) + r3*(e)^(j*3) + r4*(e)^(j*2) + r5*(e)^j + r6
229 : : *
230 : : * Now note that all of the (e)^(j*i) for i in [5..0] are constants and can be precomputed.
231 : : * But even more than that, we can consider each coefficient as a bit-string.
232 : : * For example, take r5 = (b_5, b_4, b_3, b_2, b_1) written out as 5 bits. Then:
233 : : * 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)
234 : : * where all the (2^i*(e)^j) are constants and can be precomputed.
235 : : *
236 : : * Then we just add each of these corresponding constants to our final value based on the
237 : : * bit values b_i. This is exactly what is done in the Syndrome function below.
238 : : */
239 : : constexpr std::array<uint32_t, 25> GenerateSyndromeConstants() {
240 : : std::array<uint32_t, 25> SYNDROME_CONSTS{};
241 : : for (int k = 1; k < 6; ++k) {
242 : : for (int shift = 0; shift < 5; ++shift) {
243 : : int16_t b = GF1024_LOG.at(size_t{1} << shift);
244 : : int16_t c0 = GF1024_EXP.at((997*k + b) % 1023);
245 : : int16_t c1 = GF1024_EXP.at((998*k + b) % 1023);
246 : : int16_t c2 = GF1024_EXP.at((999*k + b) % 1023);
247 : : uint32_t c = c2 << 20 | c1 << 10 | c0;
248 : : int ind = 5*(k-1) + shift;
249 : : SYNDROME_CONSTS[ind] = c;
250 : : }
251 : : }
252 : : return SYNDROME_CONSTS;
253 : : }
254 : : constexpr std::array<uint32_t, 25> SYNDROME_CONSTS = GenerateSyndromeConstants();
255 : :
256 : : /**
257 : : * Syndrome returns the three values s_997, s_998, and s_999 described above,
258 : : * packed into a 30-bit integer, where each group of 10 bits encodes one value.
259 : : */
260 : 766 : uint32_t Syndrome(const uint32_t residue) {
261 : : // low is the first 5 bits, corresponding to the r6 in the residue
262 : : // (the constant term of the polynomial).
263 : 766 : uint32_t low = residue & 0x1f;
264 : :
265 : : // We begin by setting s_j = low = r6 for all three values of j, because these are unconditional.
266 : 766 : uint32_t result = low ^ (low << 10) ^ (low << 20);
267 : :
268 : : // Then for each following bit, we add the corresponding precomputed constant if the bit is 1.
269 : : // For example, 0x31edd3c4 is 1100011110 1101110100 1111000100 when unpacked in groups of 10
270 : : // bits, corresponding exactly to a^999 || a^998 || a^997 (matching the corresponding values in
271 : : // GF1024_EXP above). In this way, we compute all three values of s_j for j in (997, 998, 999)
272 : : // simultaneously. Recall that XOR corresponds to addition in a characteristic 2 field.
273 [ + + ]: 19916 : for (int i = 0; i < 25; ++i) {
274 [ + + + - ]: 19150 : result ^= ((residue >> (5+i)) & 1 ? SYNDROME_CONSTS.at(i) : 0);
275 : : }
276 : 766 : return result;
277 : : }
278 : :
279 : : /** Convert to lower case. */
280 : 16684 : inline unsigned char LowerCase(unsigned char c)
281 : : {
282 [ + + + + ]: 16684 : return (c >= 'A' && c <= 'Z') ? (c - 'A') + 'a' : c;
283 : : }
284 : :
285 : : /** Return indices of invalid characters in a Bech32 string. */
286 : 2278 : bool CheckCharacters(const std::string& str, std::vector<int>& errors)
287 : : {
288 : 2278 : bool lower = false, upper = false;
289 [ - + + + ]: 1111478 : for (size_t i = 0; i < str.size(); ++i) {
290 [ + + ]: 1109200 : unsigned char c{(unsigned char)(str[i])};
291 [ + + ]: 1109200 : if (c >= 'a' && c <= 'z') {
292 [ + + ]: 521487 : if (upper) {
293 : 371548 : errors.push_back(i);
294 : : } else {
295 : : lower = true;
296 : : }
297 [ + + ]: 587713 : } else if (c >= 'A' && c <= 'Z') {
298 [ + + ]: 223805 : if (lower) {
299 : 180733 : errors.push_back(i);
300 : : } else {
301 : : upper = true;
302 : : }
303 [ + + ]: 363908 : } else if (c < 33 || c > 126) {
304 : 66097 : errors.push_back(i);
305 : : }
306 : : }
307 : 2278 : return errors.empty();
308 : : }
309 : :
310 : 401976 : std::vector<unsigned char> PreparePolynomialCoefficients(const std::string& hrp, const data& values)
311 : : {
312 : 401976 : data ret;
313 [ - + - + : 401976 : ret.reserve(hrp.size() + 1 + hrp.size() + values.size() + CHECKSUM_SIZE);
+ - ]
314 : :
315 : : /** Expand a HRP for use in checksum computation. */
316 [ + - - + : 2025721 : for (size_t i = 0; i < hrp.size(); ++i) ret.push_back(hrp[i] >> 5);
+ + ]
317 [ + - ]: 401976 : ret.push_back(0);
318 [ + - - + : 2025721 : for (size_t i = 0; i < hrp.size(); ++i) ret.push_back(hrp[i] & 0x1f);
+ + ]
319 : :
320 [ + - ]: 401976 : ret.insert(ret.end(), values.begin(), values.end());
321 : :
322 : 401976 : return ret;
323 : 0 : }
324 : :
325 : : /** Verify a checksum. */
326 : 1264 : Encoding VerifyChecksum(const std::string& hrp, const data& values)
327 : : {
328 : : // PolyMod computes what value to xor into the final values to make the checksum 0. However,
329 : : // if we required that the checksum was 0, it would be the case that appending a 0 to a valid
330 : : // list of values would result in a new valid list. For that reason, Bech32 requires the
331 : : // resulting checksum to be 1 instead. In Bech32m, this constant was amended. See
332 : : // https://gist.github.com/sipa/14c248c288c3880a3b191f978a34508e for details.
333 : 1264 : auto enc = PreparePolynomialCoefficients(hrp, values);
334 : 1264 : const uint32_t check = PolyMod(enc);
335 [ + + ]: 1264 : if (check == EncodingConstant(Encoding::BECH32)) return Encoding::BECH32;
336 [ + + ]: 622 : if (check == EncodingConstant(Encoding::BECH32M)) return Encoding::BECH32M;
337 : : return Encoding::INVALID;
338 : 1264 : }
339 : :
340 : : /** Create a checksum. */
341 : 399946 : data CreateChecksum(Encoding encoding, const std::string& hrp, const data& values)
342 : : {
343 : 399946 : auto enc = PreparePolynomialCoefficients(hrp, values);
344 [ + - ]: 399946 : enc.insert(enc.end(), CHECKSUM_SIZE, 0x00);
345 : 399946 : uint32_t mod = PolyMod(enc) ^ EncodingConstant(encoding); // Determine what to XOR into those 6 zeroes.
346 [ + - ]: 399946 : data ret(CHECKSUM_SIZE);
347 [ + + ]: 2799622 : for (size_t i = 0; i < CHECKSUM_SIZE; ++i) {
348 : : // Convert the 5-bit groups in mod to checksum values.
349 : 2399676 : ret[i] = (mod >> (5 * (5 - i))) & 31;
350 : : }
351 : 399946 : return ret;
352 : 399946 : }
353 : :
354 : : } // namespace
355 : :
356 : : /** Encode a Bech32 or Bech32m string. */
357 : 399946 : 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 [ - + - + : 2002083 : for (const char& c : hrp) assert(c < 'A' || c > 'Z');
+ + ]
362 : :
363 [ - + ]: 399946 : std::string ret;
364 [ - + - + : 399946 : ret.reserve(hrp.size() + 1 + values.size() + CHECKSUM_SIZE);
+ - ]
365 [ - + ]: 399946 : ret += hrp;
366 [ + - ]: 399946 : ret += SEPARATOR;
367 [ + - + + ]: 17792771 : for (const uint8_t& i : values) ret += CHARSET[i];
368 [ + - + - : 2799622 : for (const uint8_t& i : CreateChecksum(encoding, hrp, values)) ret += CHARSET[i];
+ + ]
369 : 399946 : return ret;
370 : 0 : }
371 : :
372 : : /** Decode a Bech32 or Bech32m string. */
373 : 1697 : DecodeResult Decode(const std::string& str, CharLimit limit) {
374 : 1697 : std::vector<int> errors;
375 [ + - + + ]: 1697 : if (!CheckCharacters(str, errors)) return {};
376 : 1382 : size_t pos = str.rfind(SEPARATOR);
377 [ - + + + ]: 1382 : if (str.size() > limit) return {};
378 [ + + + + ]: 1361 : if (pos == str.npos || pos == 0 || pos + CHECKSUM_SIZE >= str.size()) {
379 : 65 : return {};
380 : : }
381 [ + - ]: 1296 : data values(str.size() - 1 - pos);
382 [ - + + + ]: 40947 : for (size_t i = 0; i < str.size() - 1 - pos; ++i) {
383 [ + + ]: 39683 : unsigned char c = str[i + pos + 1];
384 : 39683 : int8_t rev = CHARSET_REV[c];
385 : :
386 [ + + ]: 39683 : if (rev == -1) {
387 : 32 : return {};
388 : : }
389 : 39651 : values[i] = rev;
390 : : }
391 [ + - ]: 1264 : std::string hrp;
392 [ + - ]: 1264 : hrp.reserve(pos);
393 [ + + ]: 12540 : for (size_t i = 0; i < pos; ++i) {
394 [ + + + - ]: 23561 : hrp += LowerCase(str[i]);
395 : : }
396 [ + - ]: 1264 : Encoding result = VerifyChecksum(hrp, values);
397 [ + + ]: 1264 : if (result == Encoding::INVALID) return {};
398 [ + - ]: 1744 : return {result, std::move(hrp), data(values.begin(), values.end() - CHECKSUM_SIZE)};
399 : 4257 : }
400 : :
401 : : /** Find index of an incorrect character in a Bech32 string. */
402 : 772 : std::pair<std::string, std::vector<int>> LocateErrors(const std::string& str, CharLimit limit) {
403 : 772 : std::vector<int> error_locations{};
404 : :
405 [ - + + + ]: 772 : if (str.size() > limit) {
406 [ + - ]: 191 : error_locations.push_back(static_cast<int>(limit));
407 [ + - ]: 382 : return std::make_pair("Bech32 string too long", std::move(error_locations));
408 : : }
409 : :
410 [ + - + + ]: 581 : if (!CheckCharacters(str, error_locations)){
411 [ + - ]: 236 : return std::make_pair("Invalid character or mixed case", std::move(error_locations));
412 : : }
413 : :
414 : 463 : size_t pos = str.rfind(SEPARATOR);
415 [ + + ]: 463 : if (pos == str.npos) {
416 [ + - ]: 42 : return std::make_pair("Missing separator", std::vector<int>{});
417 : : }
418 [ + - - + : 442 : if (pos == 0 || pos + CHECKSUM_SIZE >= str.size()) {
+ + ]
419 [ + - ]: 30 : error_locations.push_back(pos);
420 [ + - ]: 60 : return std::make_pair("Invalid separator position", std::move(error_locations));
421 : : }
422 : :
423 [ + - ]: 412 : std::string hrp;
424 [ + - ]: 412 : hrp.reserve(pos);
425 [ + + ]: 5820 : for (size_t i = 0; i < pos; ++i) {
426 [ + + + - ]: 11675 : hrp += LowerCase(str[i]);
427 : : }
428 : :
429 [ - + ]: 412 : size_t length = str.size() - 1 - pos; // length of data part
430 [ + - ]: 412 : data values(length);
431 [ - + + + ]: 9769 : for (size_t i = pos + 1; i < str.size(); ++i) {
432 [ + + ]: 9386 : unsigned char c = str[i];
433 : 9386 : int8_t rev = CHARSET_REV[c];
434 [ + + ]: 9386 : if (rev == -1) {
435 [ + - ]: 29 : error_locations.push_back(i);
436 [ + - ]: 58 : return std::make_pair("Invalid Base 32 character", std::move(error_locations));
437 : : }
438 : 9357 : values[i - pos - 1] = rev;
439 : : }
440 : :
441 : : // We attempt error detection with both bech32 and bech32m, and choose the one with the fewest errors
442 : : // We can't simply use the segwit version, because that may be one of the errors
443 : 383 : std::optional<Encoding> error_encoding;
444 [ + + ]: 1149 : for (Encoding encoding : {Encoding::BECH32, Encoding::BECH32M}) {
445 : 766 : std::vector<int> possible_errors;
446 : : // Recall that (expanded hrp + values) is interpreted as a list of coefficients of a polynomial
447 : : // over GF(32). PolyMod computes the "remainder" of this polynomial modulo the generator G(x).
448 [ + - ]: 766 : auto enc = PreparePolynomialCoefficients(hrp, values);
449 : 766 : uint32_t residue = PolyMod(enc) ^ EncodingConstant(encoding);
450 : :
451 : : // All valid codewords should be multiples of G(x), so this remainder (after XORing with the encoding
452 : : // constant) should be 0 - hence 0 indicates there are no errors present.
453 [ + - ]: 766 : if (residue != 0) {
454 : : // If errors are present, our polynomial must be of the form C(x) + E(x) where C is the valid
455 : : // codeword (a multiple of G(x)), and E encodes the errors.
456 [ + - ]: 766 : uint32_t syn = Syndrome(residue);
457 : :
458 : : // Unpack the three 10-bit syndrome values
459 : 766 : int s0 = syn & 0x3FF;
460 : 766 : int s1 = (syn >> 10) & 0x3FF;
461 : 766 : int s2 = syn >> 20;
462 : :
463 : : // Get the discrete logs of these values in GF1024 for more efficient computation
464 [ + - ]: 766 : int l_s0 = GF1024_LOG.at(s0);
465 [ + - ]: 766 : int l_s1 = GF1024_LOG.at(s1);
466 [ + - ]: 766 : int l_s2 = GF1024_LOG.at(s2);
467 : :
468 : : // First, suppose there is only a single error. Then E(x) = e1*x^p1 for some position p1
469 : : // Then s0 = E((e)^997) = e1*(e)^(997*p1) and s1 = E((e)^998) = e1*(e)^(998*p1)
470 : : // Therefore s1/s0 = (e)^p1, and by the same logic, s2/s1 = (e)^p1 too.
471 : : // Hence, s1^2 == s0*s2, which is exactly the condition we check first:
472 [ + + + + : 766 : if (l_s0 != -1 && l_s1 != -1 && l_s2 != -1 && (2 * l_s1 - l_s2 - l_s0 + 2046) % 1023 == 0) {
+ + ]
473 : : // Compute the error position p1 as l_s1 - l_s0 = p1 (mod 1023)
474 : 64 : size_t p1 = (l_s1 - l_s0 + 1023) % 1023; // the +1023 ensures it is positive
475 : : // Now because s0 = e1*(e)^(997*p1), we get e1 = s0/((e)^(997*p1)). Remember that (e)^1023 = 1,
476 : : // so 1/((e)^997) = (e)^(1023-997).
477 : 64 : int l_e1 = l_s0 + (1023 - 997) * p1;
478 : : // Finally, some sanity checks on the result:
479 : : // - The error position should be within the length of the data
480 : : // - e1 should be in GF(32), which implies that e1 = (e)^(33k) for some k (the 31 non-zero elements
481 : : // of GF(32) form an index 33 subgroup of the 1023 non-zero elements of GF(1024)).
482 [ + + + + ]: 64 : if (p1 < length && !(l_e1 % 33)) {
483 : : // Polynomials run from highest power to lowest, so the index p1 is from the right.
484 : : // We don't return e1 because it is dangerous to suggest corrections to the user,
485 : : // the user should check the address themselves.
486 [ - + + - ]: 20 : possible_errors.push_back(str.size() - p1 - 1);
487 : : }
488 : : // Otherwise, suppose there are two errors. Then E(x) = e1*x^p1 + e2*x^p2.
489 : : } else {
490 : : // For all possible first error positions p1
491 [ + + ]: 15221 : for (size_t p1 = 0; p1 < length; ++p1) {
492 : : // We have guessed p1, and want to solve for p2. Recall that E(x) = e1*x^p1 + e2*x^p2, so
493 : : // s0 = E((e)^997) = e1*(e)^(997^p1) + e2*(e)^(997*p2), and similar for s1 and s2.
494 : : //
495 : : // Consider s2 + s1*(e)^p1
496 : : // = 2e1*(e)^(999^p1) + e2*(e)^(999*p2) + e2*(e)^(998*p2)*(e)^p1
497 : : // = e2*(e)^(999*p2) + e2*(e)^(998*p2)*(e)^p1
498 : : // (Because we are working in characteristic 2.)
499 : : // = e2*(e)^(998*p2) ((e)^p2 + (e)^p1)
500 : : //
501 [ + + + - ]: 14609 : int s2_s1p1 = s2 ^ (s1 == 0 ? 0 : GF1024_EXP.at((l_s1 + p1) % 1023));
502 [ + + ]: 14609 : if (s2_s1p1 == 0) continue;
503 [ + - ]: 14173 : int l_s2_s1p1 = GF1024_LOG.at(s2_s1p1);
504 : :
505 : : // Similarly, s1 + s0*(e)^p1
506 : : // = e2*(e)^(997*p2) ((e)^p2 + (e)^p1)
507 [ + + + - ]: 14173 : int s1_s0p1 = s1 ^ (s0 == 0 ? 0 : GF1024_EXP.at((l_s0 + p1) % 1023));
508 [ + + ]: 14173 : if (s1_s0p1 == 0) continue;
509 [ + - ]: 13643 : int l_s1_s0p1 = GF1024_LOG.at(s1_s0p1);
510 : :
511 : : // So, putting these together, we can compute the second error position as
512 : : // (e)^p2 = (s2 + s1^p1)/(s1 + s0^p1)
513 : : // p2 = log((e)^p2)
514 : 13643 : size_t p2 = (l_s2_s1p1 - l_s1_s0p1 + 1023) % 1023;
515 : :
516 : : // Sanity checks that p2 is a valid position and not the same as p1
517 [ + + ]: 13643 : if (p2 >= length || p1 == p2) continue;
518 : :
519 : : // Now we want to compute the error values e1 and e2.
520 : : // Similar to above, we compute s1 + s0*(e)^p2
521 : : // = e1*(e)^(997*p1) ((e)^p1 + (e)^p2)
522 [ + + + - ]: 1434 : int s1_s0p2 = s1 ^ (s0 == 0 ? 0 : GF1024_EXP.at((l_s0 + p2) % 1023));
523 [ - + ]: 1434 : if (s1_s0p2 == 0) continue;
524 [ + - ]: 1434 : int l_s1_s0p2 = GF1024_LOG.at(s1_s0p2);
525 : :
526 : : // And compute (the log of) 1/((e)^p1 + (e)^p2))
527 [ + - + - : 1434 : int inv_p1_p2 = 1023 - GF1024_LOG.at(GF1024_EXP.at(p1) ^ GF1024_EXP.at(p2));
+ - ]
528 : :
529 : : // Then (s1 + s0*(e)^p1) * (1/((e)^p1 + (e)^p2)))
530 : : // = e2*(e)^(997*p2)
531 : : // Then recover e2 by dividing by (e)^(997*p2)
532 : 1434 : int l_e2 = l_s1_s0p1 + inv_p1_p2 + (1023 - 997) * p2;
533 : : // Check that e2 is in GF(32)
534 [ + + ]: 1434 : if (l_e2 % 33) continue;
535 : :
536 : : // In the same way, (s1 + s0*(e)^p2) * (1/((e)^p1 + (e)^p2)))
537 : : // = e1*(e)^(997*p1)
538 : : // So recover e1 by dividing by (e)^(997*p1)
539 : 203 : int l_e1 = l_s1_s0p2 + inv_p1_p2 + (1023 - 997) * p1;
540 : : // Check that e1 is in GF(32)
541 [ + + ]: 203 : if (l_e1 % 33) continue;
542 : :
543 : : // Again, we do not return e1 or e2 for safety.
544 : : // Order the error positions from the left of the string and return them
545 [ - + ]: 90 : if (p1 > p2) {
546 [ # # # # ]: 0 : possible_errors.push_back(str.size() - p1 - 1);
547 [ # # # # ]: 0 : possible_errors.push_back(str.size() - p2 - 1);
548 : : } else {
549 [ - + + - ]: 90 : possible_errors.push_back(str.size() - p2 - 1);
550 [ - + + - ]: 90 : possible_errors.push_back(str.size() - p1 - 1);
551 : : }
552 : : break;
553 : : }
554 : : }
555 : : } else {
556 : : // No errors
557 [ # # ]: 0 : return std::make_pair("", std::vector<int>{});
558 : : }
559 : :
560 [ + + + + : 775 : if (error_locations.empty() || (!possible_errors.empty() && possible_errors.size() < error_locations.size())) {
- + + + ]
561 : 714 : error_locations = std::move(possible_errors);
562 [ + + ]: 714 : if (!error_locations.empty()) error_encoding = encoding;
563 : : }
564 : 766 : }
565 [ + + ]: 383 : std::string error_message = error_encoding == Encoding::BECH32M ? "Invalid Bech32m checksum"
566 [ + + ]: 386 : : error_encoding == Encoding::BECH32 ? "Invalid Bech32 checksum"
567 [ + - ]: 383 : : "Invalid checksum";
568 : :
569 [ + - ]: 383 : return std::make_pair(error_message, std::move(error_locations));
570 : 1567 : }
571 : :
572 : : } // namespace bech32
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