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 26686 : 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 (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 26686 : uint32_t c = 1;
61 4473144 : for (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 4446451 : 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 4446451 : c = ((c & 0x1ffffff) << 5) ^ v_i;
81 :
82 : // Finally, for each set bit n in c0, conditionally add {2^n}k(x):
83 4446451 : if (c0 & 1) c ^= 0x3b6a57b2; // k(x) = {29}x^5 + {22}x^4 + {20}x^3 + {21}x^2 + {29}x + {18}
84 4446451 : if (c0 & 2) c ^= 0x26508e6d; // {2}k(x) = {19}x^5 + {5}x^4 + x^3 + {3}x^2 + {19}x + {13}
85 4446451 : if (c0 & 4) c ^= 0x1ea119fa; // {4}k(x) = {15}x^5 + {10}x^4 + {2}x^3 + {6}x^2 + {15}x + {26}
86 4446451 : if (c0 & 8) c ^= 0x3d4233dd; // {8}k(x) = {30}x^5 + {20}x^4 + {4}x^3 + {12}x^2 + {30}x + {29}
87 4446451 : if (c0 & 16) c ^= 0x2a1462b3; // {16}k(x) = {21}x^5 + x^4 + {8}x^3 + {24}x^2 + {21}x + {19}
88 : }
89 26686 : return c;
90 : }
91 :
92 : /** Convert to lower case. */
93 119360 : inline unsigned char LowerCase(unsigned char c)
94 : {
95 119360 : return (c >= 'A' && c <= 'Z') ? (c - 'A') + 'a' : c;
96 : }
97 :
98 : /** Expand a HRP for use in checksum computation. */
99 26686 : data ExpandHRP(const std::string& hrp)
100 : {
101 26686 : data ret;
102 26686 : ret.reserve(hrp.size() + 90);
103 26686 : ret.resize(hrp.size() * 2 + 1);
104 326119 : for (size_t i = 0; i < hrp.size(); ++i) {
105 299433 : unsigned char c = hrp[i];
106 299433 : ret[i] = c >> 5;
107 299433 : ret[i + hrp.size() + 1] = c & 0x1f;
108 : }
109 26686 : ret[hrp.size()] = 0;
110 26686 : return ret;
111 : }
112 :
113 : /** Verify a checksum. */
114 8601 : 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 17202 : return PolyMod(Cat(ExpandHRP(hrp), values)) == 1;
121 : }
122 :
123 : /** Create a checksum. */
124 18085 : data CreateChecksum(const std::string& hrp, const data& values)
125 : {
126 18085 : data enc = Cat(ExpandHRP(hrp), values);
127 18085 : enc.resize(enc.size() + 6); // Append 6 zeroes
128 18085 : uint32_t mod = PolyMod(enc) ^ 1; // Determine what to XOR into those 6 zeroes.
129 18085 : data ret(6);
130 126595 : for (size_t i = 0; i < 6; ++i) {
131 : // Convert the 5-bit groups in mod to checksum values.
132 108510 : ret[i] = (mod >> (5 * (5 - i))) & 31;
133 : }
134 36170 : return ret;
135 : }
136 :
137 : } // namespace
138 :
139 : namespace bech32
140 : {
141 :
142 : /** Encode a Bech32 string. */
143 18085 : std::string Encode(const std::string& hrp, const data& values) {
144 36170 : data checksum = CreateChecksum(hrp, values);
145 36170 : data combined = Cat(values, checksum);
146 36170 : std::string ret = hrp + '1';
147 18085 : ret.reserve(ret.size() + combined.size());
148 2367257 : for (auto c : combined) {
149 2349616 : if (c >= 32) {
150 446 : return "";
151 : }
152 2349166 : ret += CHARSET[c];
153 : }
154 35724 : return ret;
155 : }
156 :
157 : /** Decode a Bech32 string. */
158 9554 : std::pair<std::string, data> Decode(const std::string& str) {
159 9554 : bool lower = false, upper = false;
160 1638811 : for (size_t i = 0; i < str.size(); ++i) {
161 1629261 : unsigned char c = str[i];
162 1629261 : if (c < 33 || c > 126) return {};
163 1629261 : if (c >= 'a' && c <= 'z') lower = true;
164 1629261 : if (c >= 'A' && c <= 'Z') upper = true;
165 : }
166 9550 : if (lower && upper) return {};
167 8608 : size_t pos = str.rfind('1');
168 8608 : if (str.size() > 1023 || pos == str.npos || pos == 0 || pos + 7 > str.size()) {
169 6 : return {};
170 : }
171 18156 : data values(str.size() - 1 - pos);
172 1460930 : for (size_t i = 0; i < str.size() - 1 - pos; ++i) {
173 1452338 : unsigned char c = str[i + pos + 1];
174 1452338 : int8_t rev = (c < 33 || c > 126) ? -1 : CHARSET_REV[c];
175 1452338 : if (rev == -1) {
176 1 : return {};
177 : }
178 1452328 : values[i] = rev;
179 : }
180 17203 : std::string hrp;
181 127961 : for (size_t i = 0; i < pos; ++i) {
182 119362 : hrp += LowerCase(str[i]);
183 : }
184 8601 : if (!VerifyChecksum(hrp, values)) {
185 8601 : return {};
186 : }
187 17192 : return {hrp, data(values.begin(), values.end() - 6)};
188 : }
189 :
190 : } // namespace bech32
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