Cryptography Reference
In-Depth Information
99 124 119 123 242 107 111 197
48 1 103 43 254 215 171 118
202 130 201 125 250 89 71 240
173 212 162 175 156 164 114 192
183 253 147 38 54 63 247 204
52 165 229 241 113 216 49 21
4 199 35 195 24 150 5 154
7 18 128 226 235 39 178 117
9 131 44 26 27 110 90 160
82 59 214 179 41 227 47 132
83 209 0 237 32 252 177 91
106 203 190 57 74 76 88 207
208 239 170 251 67 77 51 133
69 249 2 127 80 60 59 168
81 163 64 143 146 157 56 245
188 182 218 33 16 255 243 210
205 12 19 236 95 151 68 23
196 167 126 61 100 93 25 115
96 129 79 220 34 42 144 136
70 238 184 20 222 94 11 219
224 50 58 10 73 6 36 92
194 211 172 98 145 149 228 121
231 200 55 109 141 213 78 169
108 86 244 234 101 122 174 8
186 120 37 46 28 166 180 198
232 221 116 31 75 189 139 138
112 62 181 102 72 3 246 14
97 53 87 185 134 193 29 158
225 248 152 17 105 217 142 148
155 30 135 233 206 85 40 223
140 161 137 13 191 230 66 104
65 153 45 15 176 84 187 22
AES Mix Column (MC) Algorithm
In this step of the AES cipher, the columns in the state matrix are treated
as polynomials
a
(
x
)over
F
2
8
=
F
2
[
x
]
/
(
m
(
x
)), where
m
(
x
)=
x
8
+
x
4
+
x
3
+
x
+1
is the irreducible Rijndael polynomial (see construction of the S-Box earlier).
Then
a
(
x
) is multiplied modulo
M
(
x
)=
x
4
+ 1 with a fixed invertible polyno-
mial,
c
(
x
)=3
x
3
+
x
2
+
x
+2
,
denoted by
a
(
x
)
.
Here multiplying modulo
x
4
+ 1 means that
c
(
x
)
⊗
x
i
(mod
x
4
+1)=
x
i
(mod 4)
.
It can be shown that if
a
j
(
x
)=
a
3
,j
x
3
+
a
2
,j
x
2
+
a
1
,j
x
+
a
0
,j
Search WWH ::
Custom Search