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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 : 129998 : uint32_t EncodingConstant(Encoding encoding) {
123 [ + + + - ]: 129998 : assert(encoding == Encoding::BECH32 || encoding == Encoding::BECH32M);
124 : 129998 : 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 : 129916 : 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 : 129916 : uint32_t c = 1;
178 [ + + ]: 7442911 : 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 : 7312995 : 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 : 7312995 : 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 [ + + ]: 7312995 : if (c0 & 1) c ^= 0x3b6a57b2; // k(x) = {29}x^5 + {22}x^4 + {20}x^3 + {21}x^2 + {29}x + {18}
209 [ + + ]: 7312995 : if (c0 & 2) c ^= 0x26508e6d; // {2}k(x) = {19}x^5 + {5}x^4 + x^3 + {3}x^2 + {19}x + {13}
210 [ + + ]: 7312995 : if (c0 & 4) c ^= 0x1ea119fa; // {4}k(x) = {15}x^5 + {10}x^4 + {2}x^3 + {6}x^2 + {15}x + {26}
211 [ + + ]: 7312995 : if (c0 & 8) c ^= 0x3d4233dd; // {8}k(x) = {30}x^5 + {20}x^4 + {4}x^3 + {12}x^2 + {30}x + {29}
212 [ + + ]: 7312995 : 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 : 129916 : 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 : 16 : 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 : 16 : 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 : 16 : 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 [ + + ]: 416 : for (int i = 0; i < 25; ++i) {
275 [ + + ]: 400 : result ^= ((residue >> (5+i)) & 1 ? SYNDROME_CONSTS.at(i) : 0);
276 : 400 : }
277 : 16 : return result;
278 : : }
279 : :
280 : : /** Convert to lower case. */
281 : 757 : inline unsigned char LowerCase(unsigned char c)
282 : : {
283 [ + + + + ]: 757 : return (c >= 'A' && c <= 'Z') ? (c - 'A') + 'a' : c;
284 : : }
285 : :
286 : : /** Return indices of invalid characters in a Bech32 string. */
287 : 179 : bool CheckCharacters(const std::string& str, std::vector<int>& errors)
288 : : {
289 : 179 : bool lower = false, upper = false;
290 [ + + ]: 230562 : for (size_t i = 0; i < str.size(); ++i) {
291 : 230383 : unsigned char c{(unsigned char)(str[i])};
292 [ + + + + ]: 230383 : if (c >= 'a' && c <= 'z') {
293 [ + + ]: 20007 : if (upper) {
294 : 529 : errors.push_back(i);
295 : 529 : } else {
296 : 19478 : lower = true;
297 : : }
298 [ + + + + ]: 230383 : } else if (c >= 'A' && c <= 'Z') {
299 [ + + ]: 5087 : if (lower) {
300 : 4432 : errors.push_back(i);
301 : 4432 : } else {
302 : 655 : upper = true;
303 : : }
304 [ + + + + ]: 210376 : } else if (c < 33 || c > 126) {
305 : 192691 : errors.push_back(i);
306 : 192691 : }
307 : 230383 : }
308 : 179 : return errors.empty();
309 : : }
310 : :
311 : : /** Expand a HRP for use in checksum computation. */
312 : 129916 : data ExpandHRP(const std::string& hrp)
313 : : {
314 : 129916 : data ret;
315 [ + - ]: 129916 : ret.reserve(hrp.size() + 90);
316 [ + - ]: 129916 : ret.resize(hrp.size() * 2 + 1);
317 [ + + ]: 649729 : for (size_t i = 0; i < hrp.size(); ++i) {
318 : 519813 : unsigned char c = hrp[i];
319 : 519813 : ret[i] = c >> 5;
320 : 519813 : ret[i + hrp.size() + 1] = c & 0x1f;
321 : 519813 : }
322 : 129916 : ret[hrp.size()] = 0;
323 : 129916 : return ret;
324 [ + - ]: 129916 : }
325 : :
326 : : /** Verify a checksum. */
327 : 136 : 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 [ + - - + ]: 136 : const uint32_t check = PolyMod(Cat(ExpandHRP(hrp), values));
335 [ + + ]: 136 : if (check == EncodingConstant(Encoding::BECH32)) return Encoding::BECH32;
336 [ + + ]: 82 : if (check == EncodingConstant(Encoding::BECH32M)) return Encoding::BECH32M;
337 : 20 : return Encoding::INVALID;
338 : 136 : }
339 : :
340 : : /** Create a checksum. */
341 : 129764 : data CreateChecksum(Encoding encoding, const std::string& hrp, const data& values)
342 : : {
343 [ + - ]: 129764 : data enc = Cat(ExpandHRP(hrp), values);
344 [ + - ]: 129764 : enc.resize(enc.size() + 6); // Append 6 zeroes
345 [ + - + - ]: 129764 : uint32_t mod = PolyMod(enc) ^ EncodingConstant(encoding); // Determine what to XOR into those 6 zeroes.
346 [ - + ]: 129764 : data ret(6);
347 [ + + ]: 908348 : for (size_t i = 0; i < 6; ++i) {
348 : : // Convert the 5-bit groups in mod to checksum values.
349 : 778584 : ret[i] = (mod >> (5 * (5 - i))) & 31;
350 : 778584 : }
351 : 129764 : return ret;
352 [ + - ]: 129764 : }
353 : :
354 : : } // namespace
355 : :
356 : : /** Encode a Bech32 or Bech32m string. */
357 : 129764 : 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 [ + + + + : 648791 : for (const char& c : hrp) assert(c < 'A' || c > 'Z');
+ - ]
362 : 129764 : data checksum = CreateChecksum(encoding, hrp, values);
363 [ + - + - ]: 129764 : data combined = Cat(values, checksum);
364 [ - + ]: 129764 : std::string ret = hrp + '1';
365 [ + - ]: 129764 : ret.reserve(ret.size() + combined.size());
366 [ + + ]: 6266818 : for (const auto c : combined) {
367 [ + - ]: 6137054 : ret += CHARSET[c];
368 : : }
369 : 129764 : return ret;
370 [ + - ]: 129764 : }
371 : :
372 : : /** Decode a Bech32 or Bech32m string. */
373 : 165 : DecodeResult Decode(const std::string& str) {
374 : 165 : std::vector<int> errors;
375 [ + - + + : 165 : if (!CheckCharacters(str, errors)) return {};
+ - ]
376 : 143 : size_t pos = str.rfind('1');
377 [ + + + + : 143 : if (str.size() > 90 || pos == str.npos || pos == 0 || pos + 7 > str.size()) {
+ - + + ]
378 [ + - ]: 6 : return {};
379 : : }
380 [ + - ]: 137 : data values(str.size() - 1 - pos);
381 [ + + ]: 5653 : for (size_t i = 0; i < str.size() - 1 - pos; ++i) {
382 : 5517 : unsigned char c = str[i + pos + 1];
383 : 5517 : int8_t rev = CHARSET_REV[c];
384 : :
385 [ + + ]: 5517 : if (rev == -1) {
386 [ + - ]: 1 : return {};
387 : : }
388 : 5516 : values[i] = rev;
389 : 5516 : }
390 : 136 : std::string hrp;
391 [ + + ]: 864 : for (size_t i = 0; i < pos; ++i) {
392 [ + - + - ]: 728 : hrp += LowerCase(str[i]);
393 : 728 : }
394 [ + - ]: 136 : Encoding result = VerifyChecksum(hrp, values);
395 [ + + + - ]: 136 : if (result == Encoding::INVALID) return {};
396 [ + - + - ]: 116 : return {result, std::move(hrp), data(values.begin(), values.end() - 6)};
397 : 165 : }
398 : :
399 : : /** Find index of an incorrect character in a Bech32 string. */
400 : 20 : std::pair<std::string, std::vector<int>> LocateErrors(const std::string& str) {
401 : 20 : std::vector<int> error_locations{};
402 : :
403 [ + + ]: 20 : if (str.size() > 90) {
404 [ + - ]: 6 : error_locations.resize(str.size() - 90);
405 [ + - ]: 6 : std::iota(error_locations.begin(), error_locations.end(), 90);
406 [ + - + - ]: 6 : return std::make_pair("Bech32 string too long", std::move(error_locations));
407 : : }
408 : :
409 [ + - + + ]: 14 : if (!CheckCharacters(str, error_locations)){
410 [ + - + - ]: 4 : return std::make_pair("Invalid character or mixed case", std::move(error_locations));
411 : : }
412 : :
413 : 10 : size_t pos = str.rfind('1');
414 [ + + ]: 10 : if (pos == str.npos) {
415 [ + - + - ]: 1 : return std::make_pair("Missing separator", std::vector<int>{});
416 : : }
417 [ + - + + ]: 9 : if (pos == 0 || pos + 7 > str.size()) {
418 [ + - ]: 1 : error_locations.push_back(pos);
419 [ + - + - ]: 1 : return std::make_pair("Invalid separator position", std::move(error_locations));
420 : : }
421 : :
422 : 8 : std::string hrp;
423 [ + + ]: 37 : for (size_t i = 0; i < pos; ++i) {
424 [ + - + - ]: 29 : hrp += LowerCase(str[i]);
425 : 29 : }
426 : :
427 : 8 : size_t length = str.size() - 1 - pos; // length of data part
428 [ + - ]: 8 : data values(length);
429 [ + + ]: 453 : for (size_t i = pos + 1; i < str.size(); ++i) {
430 : 445 : unsigned char c = str[i];
431 : 445 : int8_t rev = CHARSET_REV[c];
432 [ + - ]: 445 : 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 : 445 : values[i - pos - 1] = rev;
437 : 445 : }
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 : 8 : std::optional<Encoding> error_encoding;
442 [ + + ]: 24 : for (Encoding encoding : {Encoding::BECH32, Encoding::BECH32M}) {
443 : 16 : 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 [ + - + - : 16 : 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 [ + - ]: 16 : 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 [ + - ]: 16 : uint32_t syn = Syndrome(residue);
454 : :
455 : : // Unpack the three 10-bit syndrome values
456 : 16 : int s0 = syn & 0x3FF;
457 : 16 : int s1 = (syn >> 10) & 0x3FF;
458 : 16 : int s2 = syn >> 20;
459 : :
460 : : // Get the discrete logs of these values in GF1024 for more efficient computation
461 [ + - ]: 16 : int l_s0 = GF1024_LOG.at(s0);
462 [ + - ]: 16 : int l_s1 = GF1024_LOG.at(s1);
463 [ + - ]: 16 : 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 [ + - + - : 16 : 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 : 2 : 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 : 2 : 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 [ + - + - ]: 2 : 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 [ + - ]: 2 : possible_errors.push_back(str.size() - p1 - 1);
484 : 2 : }
485 : : // Otherwise, suppose there are two errors. Then E(x) = e1*x^p1 + e2*x^p2.
486 : 2 : } else {
487 : : // For all possible first error positions p1
488 [ + + ]: 773 : 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 [ - + + - ]: 761 : int s2_s1p1 = s2 ^ (s1 == 0 ? 0 : GF1024_EXP.at((l_s1 + p1) % 1023));
499 [ + - ]: 761 : if (s2_s1p1 == 0) continue;
500 [ + - ]: 761 : 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 [ + - + - ]: 761 : int s1_s0p1 = s1 ^ (s0 == 0 ? 0 : GF1024_EXP.at((l_s0 + p1) % 1023));
505 [ + + ]: 761 : if (s1_s0p1 == 0) continue;
506 [ + - ]: 760 : 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 : 760 : 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 [ + + - + ]: 760 : 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 [ - + + - ]: 73 : int s1_s0p2 = s1 ^ (s0 == 0 ? 0 : GF1024_EXP.at((l_s0 + p2) % 1023));
520 [ + - ]: 73 : if (s1_s0p2 == 0) continue;
521 [ + - ]: 73 : int l_s1_s0p2 = GF1024_LOG.at(s1_s0p2);
522 : :
523 : : // And compute (the log of) 1/((e)^p1 + (e)^p2))
524 [ + - + - : 73 : 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 : 73 : int l_e2 = l_s1_s0p1 + inv_p1_p2 + (1023 - 997) * p2;
530 : : // Check that e2 is in GF(32)
531 [ + + ]: 73 : 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 : 2 : int l_e1 = l_s1_s0p2 + inv_p1_p2 + (1023 - 997) * p1;
537 : : // Check that e1 is in GF(32)
538 [ - + ]: 2 : 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 [ - + ]: 2 : 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 [ + - ]: 2 : possible_errors.push_back(str.size() - p2 - 1);
547 [ + - ]: 2 : possible_errors.push_back(str.size() - p1 - 1);
548 : : }
549 : 2 : break;
550 : : }
551 : : }
552 : 16 : } else {
553 : : // No errors
554 [ # # # # ]: 0 : return std::make_pair("", std::vector<int>{});
555 : : }
556 : :
557 [ - + # # : 16 : if (error_locations.empty() || (!possible_errors.empty() && possible_errors.size() < error_locations.size())) {
# # ]
558 : 16 : error_locations = std::move(possible_errors);
559 [ + + + - ]: 16 : if (!error_locations.empty()) error_encoding = encoding;
560 : 16 : }
561 [ - + ]: 16 : }
562 [ + - + + : 12 : std::string error_message = error_encoding == Encoding::BECH32M ? "Invalid Bech32m checksum"
+ - ]
563 [ + - ]: 4 : : error_encoding == Encoding::BECH32 ? "Invalid Bech32 checksum"
564 : : : "Invalid checksum";
565 : :
566 [ + - ]: 8 : return std::make_pair(error_message, std::move(error_locations));
567 : 20 : }
568 : :
569 : : } // namespace bech32
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