Line data Source code
1 : // Copyright (c) 2017 Pieter Wuille
2 : // Distributed under the MIT software license, see the accompanying
3 : // file COPYING or http://www.opensource.org/licenses/mit-license.php.
4 :
5 : #include <bech32.h>
6 : #include <util/vector.h>
7 :
8 : #include <assert.h>
9 :
10 : namespace
11 : {
12 :
13 : typedef std::vector<uint8_t> data;
14 :
15 : /** The Bech32 character set for encoding. */
16 : const char* CHARSET = "qpzry9x8gf2tvdw0s3jn54khce6mua7l";
17 :
18 : /** The Bech32 character set for decoding. */
19 : const int8_t CHARSET_REV[128] = {
20 : -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
21 : -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
22 : -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
23 : 15, -1, 10, 17, 21, 20, 26, 30, 7, 5, -1, -1, -1, -1, -1, -1,
24 : -1, 29, -1, 24, 13, 25, 9, 8, 23, -1, 18, 22, 31, 27, 19, -1,
25 : 1, 0, 3, 16, 11, 28, 12, 14, 6, 4, 2, -1, -1, -1, -1, -1,
26 : -1, 29, -1, 24, 13, 25, 9, 8, 23, -1, 18, 22, 31, 27, 19, -1,
27 : 1, 0, 3, 16, 11, 28, 12, 14, 6, 4, 2, -1, -1, -1, -1, -1
28 : };
29 :
30 : /** This function will compute what 6 5-bit values to XOR into the last 6 input values, in order to
31 : * make the checksum 0. These 6 values are packed together in a single 30-bit integer. The higher
32 : * bits correspond to earlier values. */
33 59315 : uint32_t PolyMod(const data& v)
34 : {
35 : // The input is interpreted as a list of coefficients of a polynomial over F = GF(32), with an
36 : // implicit 1 in front. If the input is [v0,v1,v2,v3,v4], that polynomial is v(x) =
37 : // 1*x^5 + v0*x^4 + v1*x^3 + v2*x^2 + v3*x + v4. The implicit 1 guarantees that
38 : // [v0,v1,v2,...] has a distinct checksum from [0,v0,v1,v2,...].
39 :
40 : // The output is a 30-bit integer whose 5-bit groups are the coefficients of the remainder of
41 : // v(x) mod g(x), where g(x) is the Bech32 generator,
42 : // 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
43 : // that the resulting code is a BCH code, guaranteeing detection of up to 3 errors within a
44 : // window of 1023 characters. Among the various possible BCH codes, one was selected to in
45 : // fact guarantee detection of up to 4 errors within a window of 89 characters.
46 :
47 : // Note that the coefficients are elements of GF(32), here represented as decimal numbers
48 : // between {}. In this finite field, addition is just XOR of the corresponding numbers. For
49 : // example, {27} + {13} = {27 ^ 13} = {22}. Multiplication is more complicated, and requires
50 : // treating the bits of values themselves as coefficients of a polynomial over a smaller field,
51 : // GF(2), and multiplying those polynomials mod a^5 + a^3 + 1. For example, {5} * {26} =
52 : // (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
53 : // = a^3 + 1 (mod a^5 + a^3 + 1) = {9}.
54 :
55 : // During the course of the loop below, `c` contains the bitpacked coefficients of the
56 : // polynomial constructed from just the values of v that were processed so far, mod g(x). In
57 : // the above example, `c` initially corresponds to 1 mod g(x), and after processing 2 inputs of
58 : // v, it corresponds to x^2 + v0*x + v1 mod g(x). As 1 mod g(x) = 1, that is the starting value
59 : // for `c`.
60 : uint32_t c = 1;
61 2941305 : for (const auto v_i : v) {
62 : // We want to update `c` to correspond to a polynomial with one extra term. If the initial
63 : // value of `c` consists of the coefficients of c(x) = f(x) mod g(x), we modify it to
64 : // correspond to c'(x) = (f(x) * x + v_i) mod g(x), where v_i is the next input to
65 : // process. Simplifying:
66 : // c'(x) = (f(x) * x + v_i) mod g(x)
67 : // ((f(x) mod g(x)) * x + v_i) mod g(x)
68 : // (c(x) * x + v_i) mod g(x)
69 : // If c(x) = c0*x^5 + c1*x^4 + c2*x^3 + c3*x^2 + c4*x + c5, we want to compute
70 : // c'(x) = (c0*x^5 + c1*x^4 + c2*x^3 + c3*x^2 + c4*x + c5) * x + v_i mod g(x)
71 : // = c0*x^6 + c1*x^5 + c2*x^4 + c3*x^3 + c4*x^2 + c5*x + v_i mod g(x)
72 : // = c0*(x^6 mod g(x)) + c1*x^5 + c2*x^4 + c3*x^3 + c4*x^2 + c5*x + v_i
73 : // If we call (x^6 mod g(x)) = k(x), this can be written as
74 : // c'(x) = (c1*x^5 + c2*x^4 + c3*x^3 + c4*x^2 + c5*x + v_i) + c0*k(x)
75 :
76 : // First, determine the value of c0:
77 2881990 : uint8_t c0 = c >> 25;
78 :
79 : // Then compute c1*x^5 + c2*x^4 + c3*x^3 + c4*x^2 + c5*x + v_i:
80 2881990 : c = ((c & 0x1ffffff) << 5) ^ v_i;
81 :
82 : // Finally, for each set bit n in c0, conditionally add {2^n}k(x):
83 2881990 : if (c0 & 1) c ^= 0x3b6a57b2; // k(x) = {29}x^5 + {22}x^4 + {20}x^3 + {21}x^2 + {29}x + {18}
84 2881990 : if (c0 & 2) c ^= 0x26508e6d; // {2}k(x) = {19}x^5 + {5}x^4 + x^3 + {3}x^2 + {19}x + {13}
85 2881990 : if (c0 & 4) c ^= 0x1ea119fa; // {4}k(x) = {15}x^5 + {10}x^4 + {2}x^3 + {6}x^2 + {15}x + {26}
86 2881990 : if (c0 & 8) c ^= 0x3d4233dd; // {8}k(x) = {30}x^5 + {20}x^4 + {4}x^3 + {12}x^2 + {30}x + {29}
87 2881990 : if (c0 & 16) c ^= 0x2a1462b3; // {16}k(x) = {21}x^5 + x^4 + {8}x^3 + {24}x^2 + {21}x + {19}
88 : }
89 59315 : return c;
90 : }
91 :
92 : /** Convert to lower case. */
93 68620 : inline unsigned char LowerCase(unsigned char c)
94 : {
95 68620 : return (c >= 'A' && c <= 'Z') ? (c - 'A') + 'a' : c;
96 : }
97 :
98 : /** Expand a HRP for use in checksum computation. */
99 59315 : data ExpandHRP(const std::string& hrp)
100 : {
101 59315 : data ret;
102 59315 : ret.reserve(hrp.size() + 90);
103 59315 : ret.resize(hrp.size() * 2 + 1);
104 296815 : for (size_t i = 0; i < hrp.size(); ++i) {
105 237500 : unsigned char c = hrp[i];
106 237500 : ret[i] = c >> 5;
107 237500 : ret[i + hrp.size() + 1] = c & 0x1f;
108 : }
109 59315 : ret[hrp.size()] = 0;
110 : return ret;
111 59315 : }
112 :
113 : /** Verify a checksum. */
114 17088 : bool VerifyChecksum(const std::string& hrp, const data& values)
115 : {
116 : // PolyMod computes what value to xor into the final values to make the checksum 0. However,
117 : // if we required that the checksum was 0, it would be the case that appending a 0 to a valid
118 : // list of values would result in a new valid list. For that reason, Bech32 requires the
119 : // resulting checksum to be 1 instead.
120 17088 : return PolyMod(Cat(ExpandHRP(hrp), values)) == 1;
121 0 : }
122 :
123 : /** Create a checksum. */
124 42227 : data CreateChecksum(const std::string& hrp, const data& values)
125 : {
126 42227 : data enc = Cat(ExpandHRP(hrp), values);
127 42227 : enc.resize(enc.size() + 6); // Append 6 zeroes
128 42227 : uint32_t mod = PolyMod(enc) ^ 1; // Determine what to XOR into those 6 zeroes.
129 42227 : data ret(6);
130 295589 : for (size_t i = 0; i < 6; ++i) {
131 : // Convert the 5-bit groups in mod to checksum values.
132 253362 : ret[i] = (mod >> (5 * (5 - i))) & 31;
133 : }
134 : return ret;
135 42227 : }
136 :
137 : } // namespace
138 :
139 : namespace bech32
140 : {
141 :
142 : /** Encode a Bech32 string. */
143 42227 : std::string Encode(const std::string& hrp, const data& values) {
144 : // First ensure that the HRP is all lowercase. BIP-173 requires an encoder
145 : // to return a lowercase Bech32 string, but if given an uppercase HRP, the
146 : // result will always be invalid.
147 211107 : for (const char& c : hrp) assert(c < 'A' || c > 'Z');
148 42227 : data checksum = CreateChecksum(hrp, values);
149 42227 : data combined = Cat(values, checksum);
150 42227 : std::string ret = hrp + '1';
151 42227 : ret.reserve(ret.size() + combined.size());
152 1707643 : for (const auto c : combined) {
153 1665416 : ret += CHARSET[c];
154 : }
155 : return ret;
156 42227 : }
157 :
158 : /** Decode a Bech32 string. */
159 17360 : std::pair<std::string, data> Decode(const std::string& str) {
160 1600132 : bool lower = false, upper = false;
161 800066 : for (size_t i = 0; i < str.size(); ++i) {
162 782714 : unsigned char c = str[i];
163 782714 : if (c >= 'a' && c <= 'z') lower = true;
164 204470 : else if (c >= 'A' && c <= 'Z') upper = true;
165 199303 : else if (c < 33 || c > 126) return {};
166 782706 : }
167 17352 : if (lower && upper) return {};
168 17145 : size_t pos = str.rfind('1');
169 17145 : if (str.size() > 90 || pos == str.npos || pos == 0 || pos + 7 > str.size()) {
170 38 : return {};
171 : }
172 17107 : data values(str.size() - 1 - pos);
173 699549 : for (size_t i = 0; i < str.size() - 1 - pos; ++i) {
174 682461 : unsigned char c = str[i + pos + 1];
175 682461 : int8_t rev = CHARSET_REV[c];
176 :
177 682461 : if (rev == -1) {
178 19 : return {};
179 : }
180 682442 : values[i] = rev;
181 682442 : }
182 17088 : std::string hrp;
183 85708 : for (size_t i = 0; i < pos; ++i) {
184 68620 : hrp += LowerCase(str[i]);
185 : }
186 17088 : if (!VerifyChecksum(hrp, values)) {
187 36 : return {};
188 : }
189 17052 : return {hrp, data(values.begin(), values.end() - 6)};
190 34467 : }
191 :
192 : } // namespace bech32
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