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. */
PolyMod(const data & v)33 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 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 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 c = ((c & 0x1ffffff) << 5) ^ v_i;
81
82 // Finally, for each set bit n in c0, conditionally add {2^n}k(x):
83 if (c0 & 1) c ^= 0x3b6a57b2; // k(x) = {29}x^5 + {22}x^4 + {20}x^3 + {21}x^2 + {29}x + {18}
84 if (c0 & 2) c ^= 0x26508e6d; // {2}k(x) = {19}x^5 + {5}x^4 + x^3 + {3}x^2 + {19}x + {13}
85 if (c0 & 4) c ^= 0x1ea119fa; // {4}k(x) = {15}x^5 + {10}x^4 + {2}x^3 + {6}x^2 + {15}x + {26}
86 if (c0 & 8) c ^= 0x3d4233dd; // {8}k(x) = {30}x^5 + {20}x^4 + {4}x^3 + {12}x^2 + {30}x + {29}
87 if (c0 & 16) c ^= 0x2a1462b3; // {16}k(x) = {21}x^5 + x^4 + {8}x^3 + {24}x^2 + {21}x + {19}
88 }
89 return c;
90 }
91
92 /** Convert to lower case. */
LowerCase(unsigned char c)93 inline unsigned char LowerCase(unsigned char c)
94 {
95 return (c >= 'A' && c <= 'Z') ? (c - 'A') + 'a' : c;
96 }
97
98 /** Expand a HRP for use in checksum computation. */
ExpandHRP(const std::string & hrp)99 data ExpandHRP(const std::string& hrp)
100 {
101 data ret;
102 ret.reserve(hrp.size() + 90);
103 ret.resize(hrp.size() * 2 + 1);
104 for (size_t i = 0; i < hrp.size(); ++i) {
105 unsigned char c = hrp[i];
106 ret[i] = c >> 5;
107 ret[i + hrp.size() + 1] = c & 0x1f;
108 }
109 ret[hrp.size()] = 0;
110 return ret;
111 }
112
113 /** Verify a checksum. */
VerifyChecksum(const std::string & hrp,const data & values)114 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 return PolyMod(Cat(ExpandHRP(hrp), values)) == 1;
121 }
122
123 /** Create a checksum. */
CreateChecksum(const std::string & hrp,const data & values)124 data CreateChecksum(const std::string& hrp, const data& values)
125 {
126 data enc = Cat(ExpandHRP(hrp), values);
127 enc.resize(enc.size() + 6); // Append 6 zeroes
128 uint32_t mod = PolyMod(enc) ^ 1; // Determine what to XOR into those 6 zeroes.
129 data ret(6);
130 for (size_t i = 0; i < 6; ++i) {
131 // Convert the 5-bit groups in mod to checksum values.
132 ret[i] = (mod >> (5 * (5 - i))) & 31;
133 }
134 return ret;
135 }
136
137 } // namespace
138
139 namespace bech32
140 {
141
142 /** Encode a Bech32 string. */
Encode(const std::string & hrp,const data & values)143 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 for (const char& c : hrp) assert(c < 'A' || c > 'Z');
148 data checksum = CreateChecksum(hrp, values);
149 data combined = Cat(values, checksum);
150 std::string ret = hrp + '1';
151 ret.reserve(ret.size() + combined.size());
152 for (const auto c : combined) {
153 ret += CHARSET[c];
154 }
155 return ret;
156 }
157
158 /** Decode a Bech32 string. */
Decode(const std::string & str)159 std::pair<std::string, data> Decode(const std::string& str) {
160 bool lower = false, upper = false;
161 for (size_t i = 0; i < str.size(); ++i) {
162 unsigned char c = str[i];
163 if (c >= 'a' && c <= 'z') lower = true;
164 else if (c >= 'A' && c <= 'Z') upper = true;
165 else if (c < 33 || c > 126) return {};
166 }
167 if (lower && upper) return {};
168 size_t pos = str.rfind('1');
169 if (str.size() > 90 || pos == str.npos || pos == 0 || pos + 7 > str.size()) {
170 return {};
171 }
172 data values(str.size() - 1 - pos);
173 for (size_t i = 0; i < str.size() - 1 - pos; ++i) {
174 unsigned char c = str[i + pos + 1];
175 int8_t rev = CHARSET_REV[c];
176
177 if (rev == -1) {
178 return {};
179 }
180 values[i] = rev;
181 }
182 std::string hrp;
183 for (size_t i = 0; i < pos; ++i) {
184 hrp += LowerCase(str[i]);
185 }
186 if (!VerifyChecksum(hrp, values)) {
187 return {};
188 }
189 return {hrp, data(values.begin(), values.end() - 6)};
190 }
191
192 } // namespace bech32
193