GF256
in package
FinalYes
This class contains utility methods for performing mathematical operations over the Galois Fields. Operations use a given primitive polynomial in calculations.
Throughout this package, elements of the GF are represented as an int for convenience and speed (but at the cost of memory).
Tags
Table of Contents
Constants
- expTable = [1, 2, 4, 8, 16, 32, 64, 128, 29, 58, 116, 232, 205, 135, 19, 38, 76, 152, 45, 90, 180, 117, 234, 201, 143, 3, 6, 12, 24, 48, 96, 192, 157, 39, 78, 156, 37, 74, 148, 53, 106, 212, 181, 119, 238, 193, 159, 35, 70, 140, 5, 10, 20, 40, 80, 160, 93, 186, 105, 210, 185, 111, 222, 161, 95, 190, 97, 194, 153, 47, 94, 188, 101, 202, 137, 15, 30, 60, 120, 240, 253, 231, 211, 187, 107, 214, 177, 127, 254, 225, 223, 163, 91, 182, 113, 226, 217, 175, 67, 134, 17, 34, 68, 136, 13, 26, 52, 104, 208, 189, 103, 206, 129, 31, 62, 124, 248, 237, 199, 147, 59, 118, 236, 197, 151, 51, 102, 204, 133, 23, 46, 92, 184, 109, 218, 169, 79, 158, 33, 66, 132, 21, 42, 84, 168, 77, 154, 41, 82, 164, 85, 170, 73, 146, 57, 114, 228, 213, 183, 115, 230, 209, 191, 99, 198, 145, 63, 126, 252, 229, 215, 179, 123, 246, 241, 255, 227, 219, 171, 75, 150, 49, 98, 196, 149, 55, 110, 220, 165, 87, 174, 65, 130, 25, 50, 100, 200, 141, 7, 14, 28, 56, 112, 224, 221, 167, 83, 166, 81, 162, 89, 178, 121, 242, 249, 239, 195, 155, 43, 86, 172, 69, 138, 9, 18, 36, 72, 144, 61, 122, 244, 245, 247, 243, 251, 235, 203, 139, 11, 22, 44, 88, 176, 125, 250, 233, 207, 131, 27, 54, 108, 216, 173, 71, 142, 1]
- logTable = [ 0, // the first value is never returned, index starts at 1 0, 1, 25, 2, 50, 26, 198, 3, 223, 51, 238, 27, 104, 199, 75, 4, 100, 224, 14, 52, 141, 239, 129, 28, 193, 105, 248, 200, 8, 76, 113, 5, 138, 101, 47, 225, 36, 15, 33, 53, 147, 142, 218, 240, 18, 130, 69, 29, 181, 194, 125, 106, 39, 249, 185, 201, 154, 9, 120, 77, 228, 114, 166, 6, 191, 139, 98, 102, 221, 48, 253, 226, 152, 37, 179, 16, 145, 34, 136, 54, 208, 148, 206, 143, 150, 219, 189, 241, 210, 19, 92, 131, 56, 70, 64, 30, 66, 182, 163, 195, 72, 126, 110, 107, 58, 40, 84, 250, 133, 186, 61, 202, 94, 155, 159, 10, 21, 121, 43, 78, 212, 229, 172, 115, 243, 167, 87, 7, 112, 192, 247, 140, 128, 99, 13, 103, 74, 222, 237, 49, 197, 254, 24, 227, 165, 153, 119, 38, 184, 180, 124, 17, 68, 146, 217, 35, 32, 137, 46, 55, 63, 209, 91, 149, 188, 207, 205, 144, 135, 151, 178, 220, 252, 190, 97, 242, 86, 211, 171, 20, 42, 93, 158, 132, 60, 57, 83, 71, 109, 65, 162, 31, 45, 67, 216, 183, 123, 164, 118, 196, 23, 73, 236, 127, 12, 111, 246, 108, 161, 59, 82, 41, 157, 85, 170, 251, 96, 134, 177, 187, 204, 62, 90, 203, 89, 95, 176, 156, 169, 160, 81, 11, 245, 22, 235, 122, 117, 44, 215, 79, 174, 213, 233, 230, 231, 173, 232, 116, 214, 244, 234, 168, 80, 88, 175, ]
- irreducible polynomial whose coefficients are represented by the bits of an int, where the least-significant bit represents the constant coefficient
Methods
- addOrSubtract() : int
- Implements both addition and subtraction -- they are the same in GF(size).
- buildMonomial() : GenericGFPoly
- exp() : int
- inverse() : int
- log() : int
- multiply() : int
Constants
expTable
private
mixed
expTable
= [1, 2, 4, 8, 16, 32, 64, 128, 29, 58, 116, 232, 205, 135, 19, 38, 76, 152, 45, 90, 180, 117, 234, 201, 143, 3, 6, 12, 24, 48, 96, 192, 157, 39, 78, 156, 37, 74, 148, 53, 106, 212, 181, 119, 238, 193, 159, 35, 70, 140, 5, 10, 20, 40, 80, 160, 93, 186, 105, 210, 185, 111, 222, 161, 95, 190, 97, 194, 153, 47, 94, 188, 101, 202, 137, 15, 30, 60, 120, 240, 253, 231, 211, 187, 107, 214, 177, 127, 254, 225, 223, 163, 91, 182, 113, 226, 217, 175, 67, 134, 17, 34, 68, 136, 13, 26, 52, 104, 208, 189, 103, 206, 129, 31, 62, 124, 248, 237, 199, 147, 59, 118, 236, 197, 151, 51, 102, 204, 133, 23, 46, 92, 184, 109, 218, 169, 79, 158, 33, 66, 132, 21, 42, 84, 168, 77, 154, 41, 82, 164, 85, 170, 73, 146, 57, 114, 228, 213, 183, 115, 230, 209, 191, 99, 198, 145, 63, 126, 252, 229, 215, 179, 123, 246, 241, 255, 227, 219, 171, 75, 150, 49, 98, 196, 149, 55, 110, 220, 165, 87, 174, 65, 130, 25, 50, 100, 200, 141, 7, 14, 28, 56, 112, 224, 221, 167, 83, 166, 81, 162, 89, 178, 121, 242, 249, 239, 195, 155, 43, 86, 172, 69, 138, 9, 18, 36, 72, 144, 61, 122, 244, 245, 247, 243, 251, 235, 203, 139, 11, 22, 44, 88, 176, 125, 250, 233, 207, 131, 27, 54, 108, 216, 173, 71, 142, 1]
logTable
irreducible polynomial whose coefficients are represented by the bits of an int, where the least-significant bit represents the constant coefficient
private
mixed
logTable
= [
0,
// the first value is never returned, index starts at 1
0,
1,
25,
2,
50,
26,
198,
3,
223,
51,
238,
27,
104,
199,
75,
4,
100,
224,
14,
52,
141,
239,
129,
28,
193,
105,
248,
200,
8,
76,
113,
5,
138,
101,
47,
225,
36,
15,
33,
53,
147,
142,
218,
240,
18,
130,
69,
29,
181,
194,
125,
106,
39,
249,
185,
201,
154,
9,
120,
77,
228,
114,
166,
6,
191,
139,
98,
102,
221,
48,
253,
226,
152,
37,
179,
16,
145,
34,
136,
54,
208,
148,
206,
143,
150,
219,
189,
241,
210,
19,
92,
131,
56,
70,
64,
30,
66,
182,
163,
195,
72,
126,
110,
107,
58,
40,
84,
250,
133,
186,
61,
202,
94,
155,
159,
10,
21,
121,
43,
78,
212,
229,
172,
115,
243,
167,
87,
7,
112,
192,
247,
140,
128,
99,
13,
103,
74,
222,
237,
49,
197,
254,
24,
227,
165,
153,
119,
38,
184,
180,
124,
17,
68,
146,
217,
35,
32,
137,
46,
55,
63,
209,
91,
149,
188,
207,
205,
144,
135,
151,
178,
220,
252,
190,
97,
242,
86,
211,
171,
20,
42,
93,
158,
132,
60,
57,
83,
71,
109,
65,
162,
31,
45,
67,
216,
183,
123,
164,
118,
196,
23,
73,
236,
127,
12,
111,
246,
108,
161,
59,
82,
41,
157,
85,
170,
251,
96,
134,
177,
187,
204,
62,
90,
203,
89,
95,
176,
156,
169,
160,
81,
11,
245,
22,
235,
122,
117,
44,
215,
79,
174,
213,
233,
230,
231,
173,
232,
116,
214,
244,
234,
168,
80,
88,
175,
]
Methods
addOrSubtract()
Implements both addition and subtraction -- they are the same in GF(size).
public
static addOrSubtract(int $a, int $b) : int
Parameters
- $a : int
- $b : int
Return values
int —sum/difference of a and b
buildMonomial()
public
static buildMonomial(int $degree, int $coefficient) : GenericGFPoly
Parameters
- $degree : int
- $coefficient : int
Tags
Return values
GenericGFPoly —the monomial representing coefficient * x^degree
exp()
public
static exp(int $a) : int
Parameters
- $a : int
Return values
int —2 to the power of $a in GF(size)
inverse()
public
static inverse(int $a) : int
Parameters
- $a : int
Tags
Return values
int —multiplicative inverse of a
log()
public
static log(int $a) : int
Parameters
- $a : int
Tags
Return values
int —base 2 log of $a in GF(size)
multiply()
public
static multiply(int $a, int $b) : int
Parameters
- $a : int
- $b : int
Return values
int —product of a and b in GF(size)