Cryptography Reference
In-Depth Information
keys also taken in reverse order. There is also an equivalent algorithm for decryp-
tion in which the sequence of steps is the same as in encryption, with operations
replaced by their inverses and a change in the key schedule, but we shall not go into
the details, which can be seen in [62]. We briefly describe the inverse operations
(obviously,
AddRoundKey
, which computes the bitwise Xor of the state bytes with
the round subkey bytes, is its own inverse).
4.2.3.1 InvSubBytes
The
SubBytes
operation consists of applying to each individual byte in the state
array a permutation defined by the
SBox
table we have constructed before. Thus the
inverse operation,
InvSubBytes
, acts by applying the inverse permutation of the
one defined by
SBox
. In Maple we can easily “invert” the
SBox
array by setting:
> InvSBox := Array(0 .. 255, table([seq(SBox[i] = i,i=0..255)])):
As in the case of the S-box, the inverse S-box may be printed as follows:
> PrintInvSBox := proc()
local t, is;
t := interface(rtablesize = 16);
is := Array(InvSBox, order = C_order);
print(LinearAlgebra:-Map(bytetohex, ArrayTools:-Alias(is, [16, 16])));
interface(rtablesize = t);
NULL
end proc:
PrintInvSbox();
⎡
⎣
⎤
⎦
52 09 6a d5 30 36 a5 38 bf 40 a3 9e 81 f3 d7 fb
7c e3 39 82 9b 2f ff 87 34 8e 43 44 c4 de e9 cb
54 7b 94 32 a6 c2 23 3d ee 4c 95 0b 42 fa c3 4e
08 2e a1 66 28 d9 24 b2 76 5b a2 49 6d 8b d1 25
72 f8 f6 64 86 68 98 16 d4 a4 5c cc 5d 65 b6 92
6c 70 48 50 fd ed b9 da 5e 15 46 57 a7 8d 9d 84
90 d8 ab 00 8c bc d3 0a f7 e4 58 05 b8 b3 45 06
d0 2c 1e 8f ca 3f 0f 02 c1 af bd 03 01 13 8a 6b
3a 91 11 41 4f 67 dc ea 97 f2 cf ce f0 b4 e6 73
96 ac 74 22 e7 ad 35 85 e2 f9 37 e8 1c 75 df 6e
47 f1 1a 71 1d 29 c5 89 6f b7 62 0e aa 18 be 1b
fc 56 3e 4b c6 d2 79 20 9a db c0 fe 78 cd 5a f4
1f dd a8 33 88 07 c7 31 b1 12 10 59 27 80 ec 5f
60 51 7f a9 19 b5 4a 0d 2d e5 7a 9f 93 c9 9c ef
a0 e0 3b 4d ae 2a f5 b0 c8 eb bb 3c 83 53 99 61
17 2b 04 7e ba 77 d6 26 e1 69 14 63 55 21 0c 7d
4.2.3.2 InvShiftRows
The
ShiftRows
operation consists of shifting the rows of the state array by 0, 1,
2, 3 positions to the left, where each row is shifted by the same amount as its index.
Thus the inverse operation just shifts rows right by the same offsets and, if we denote
by
b
i
,
j
,0
≤
,
≤
i
j
3 the state bytes, their values are modified as follows:
