Symmetric Encryption Systems - Contemporary Cryptography - page 260

Algorithm 10.2 The AES encryption algorithm.

( in )
s ← in
s ← AddRoundKey( s, w [0 ,N b − 1])
for r =1to ( N r − 1) do
s ← SubBytes( s )
s ← ShiftRows( s )
s ← MixColumns( s )
s ← AddRoundKey( s, w [ rN b , ( r +1) N b − 1])
s ← SubBytes( s )
s ← ShiftRows( s )
s ← AddRoundKey( s, w [ N r N b , ( N r +1) N b − 1])
out ← s
( out )

Table 10.10
The S-Box of the AES Encryption Algorithm

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

0 63 7C 77 7B F2 6B 6F C5 30 01 67 2B FE D7 AB 76

1 CA 82 C9 7D FA 59 47 F0 AD D4 A2 AF 9C A4 72 C0

2 B7 FD 93 26 36 3F F7 CC 34 A5 E5 F1 71 D8 31 15

3 04 C7 23 C3 18 96 05 9A 07 12 80 E2 EB 27 B2 75

4 09 83 2C 1A 1B 6E 5A A0 52 3B D6 B3 29 E3 2F 84

5 53 D1 00 ED 20 FC B1 5B 6A CB BE 39 4A 4C 58 CF

6 D0 EF AA FB 43 4D 33 85 45 F9 02 7F 50 3C 9F A8

7 51 A3 40 8F 92 9D 38 F5 BC B6 DA 21 10 FF F3 D2

8 CD 0C 13 EC 5F 97 44 17 C4 A7 7E 3D 64 5D 19 73

9 60 81 4F DC 22 2A 90 88 46 EE B8 14 DE 5E 0B DB

A E0 32 3A 0A 49 06 24 5C C2 D3 AC 62 91 95 E4 79

B E7 C8 37 6D 8D D5 4E A9 6C 56 F4 EA 65 7A AE 08

C BA 78 25 2E 1C A6 B4 C6 E8 DD 74 1F 4B BD 8B 8A

D 70 3E B5 66 48 03 F6 0E 61 35 57 B9 86 C1 1D 9E

E E1 F8 98 11 69 D9 8E 94 9B 1E 87 E9 CE 55 28 DF

F 8C A1 89 0D BF E6 42 68 41 99 2D 0F B0 54 BB 16

SubBytes() Transformation

The SubBytes() transformation implements a nonlinear substitution cipher. Each
byte s r,c of the State is substituted with another byte s r,c according to the sub-
stitution table (called S-box ) illustrated in Table 10.10. For input byte 0xXY ,the
high-order byte (i.e., 0xX ) refers to the vertical axis, and the low-order byte (i.e.,
0xY ) refers to the horizontal axis. The output byte is the one found in the S-box in
row 0xX and column 0xY . For example, the input byte 0x52 (i.e., 01010010 )is
mapped to the output byte 0x00 (i.e., 00000000 ).
Contrary to many other symmetric encryption systems (inlcuding, for exam-
ple, the DES), the S-box of the AES has a well-documented design. It is constructed
by composing the following two transformations: