AES Algorithm: State Block Representation and S-Box Transformation

The AES (Advanced Encryption Standard) algorithm uses a 4x4 table to represent a state block. Each cell in the table contains a byte (8 bits) of data. This representation is crucial for performing various transformations during the encryption process. One such transformation is the application of the AES S-box, a substitution table that performs a byte-by-byte substitution of the input block.

(a) AES S-box Transformation:

Let's consider an example to illustrate the application of the AES S-box transformation. Given the following state block:

State: D1 26 B9 3C; 59 C2 AC 42; 15 BC 42 A9; 39 DA D3 26.
D1 59 15 39
26 C2 BC DA
B9 AC 42 D3
3C 42 A9 26

State before transformation

To apply the S-box transformation, we substitute each byte in the state block with a corresponding byte from the S-box lookup table. This is done by splitting each byte into two nibbles (4 bits each), using the first nibble as the row index and the second nibble as the column index to look up the corresponding byte from the S-box table.

For example, the first byte in the state block is D1. This corresponds to row D (13) and column 1. Looking up this value in the S-box table gives us the byte 8F. We perform this substitution for each byte in the state block, resulting in the new state block:

8F 8F E3 0C
C6 26 82 6C
E8 27 0F 89
70 0F 6C C6

Answer: after S-box transformation

The size of the block is 4x4, or 16 bytes in total. This is the standard size for a state block in AES encryption. The AES S-box plays a crucial role in enhancing the security of the AES algorithm by introducing non-linearity into the encryption process, making it more resistant to cryptanalysis.