Symmetric Encryption Systems - Contemporary Cryptography - page 267

shift ( r, N b ) bytes (note that the shift function is the same for both the encryption
and decryption algorithms). Similar to (10.5), the InvShiftRows() transformation can
be specified as

s r, ( c + shif t ( r,N b )) mod N b = s r,c

for 0 ≤ r< 4 and 0 ≤ c<N b =4. It is illustrated in Figure 10.8.

I

+

+ +1

+ +1 + +3

+3

+ +1 + + +3

+ +3 +1

3+1

3+ 3+ 3+1 3+3 3+

3+3 3+

1+ 1+ 1+3 1+

1+ 1+3 1+1 1+1

Figure 10.8 The InvShiftRows() transformation of the AES decryption algorithm.

Table 10.11
The Inverse S-Box of the AES Decryption Algorithm

0 1 2 3 4 5 6 7 8 9 A B C D E F

0 52 09 6A D5 30 36 A5 38 BF 40 A3 9E 81 F3 D7 FB

1 7C E3 39 82 9B 2F FF 87 34 8E 43 44 C4 DE E9 CB

2 54 7B 94 32 A6 C2 23 3D EE 4C 95 0B 42 FA C3 4E

3 08 2E A1 66 28 D9 24 B2 76 5B A2 49 6D 8B D1 25

4 72 F8 F6 64 86 68 98 16 D4 A4 5C CC 5D 65 B6 92

5 6C 70 48 50 FD ED B9 DA 5E 15 46 57 A7 8D 9D 84

6 90 D8 AB 00 8C BC D3 0A F7 E4 58 05 B8 B3 45 06

7 D0 2C 1E 8F CA 3F 0F 02 C1 AF BD 03 01 13 8A 6B

8 3A 91 11 41 4F 67 DC EA 97 F2 CF CE F0 B4 E6 73

9 96 AC 74 22 E7 AD 35 85 E2 F9 37 E8 1C 75 DF 6E

A 47 F1 1A 71 1D 29 C5 89 6F B7 62 0E AA 18 BE 1B

b FC 56 3E 4B C6 D2 79 20 9A DB C0 FE 78 CD 5A F4

C 1F DD A8 33 88 07 C7 31 B1 12 10 59 27 80 EC 5F

D 60 51 7F A9 19 B5 4A 0D 2D E5 7A 9F 93 C9 9C EF

E A0 E0 3B 4D AE 2A F5 B0 C8 EB BB 3C 83 53 99 61

F 17 2B 04 7E BA 77 D6 26 E1 69 14 63 55 21 0C 7D

InvSubBytes() Transformation

The InvSubBytes() transformation is the inverse of the SubBytes() transformation. It
is obtained by applying the inverse of the affine transformation specified in 10.2.2.3,