AES Algorithm: State Block Representation and S-box Transformation

The Advanced Encryption Standard (AES) algorithm operates on a state block, typically represented as a 4x4 matrix of bytes. This article focuses on the AES S-box transformation and how it alters the state block.

(a) AES S-box Transformation

Consider the following state block, where each 4-tuple represents a column:

'D1 26 B9 3C' '59 C2 AC 42' '15 BC 42 A9' '39 DA D3 26'

State before transformation:

'D1 59 15 39' '26 C2 BC DA' 'B9 AC 42 D3' '3C 42 A9 26'

The AES S-box transformation replaces each byte in the state block with a new byte value based on a predefined lookup table. The lookup table, a fixed 16x16 matrix, maps every possible byte value (from 0x00 to 0xFF) to a unique output byte. This transformation is applied independently to each byte within the state block.

After applying the S-box transformation, the state block becomes:

'8F 9F EA 1B' 'D4 F7 3D AE' 'AD 44 95 38' 'C8 AE 1B D4'

Understanding the Transformation

The state block is divided into four columns, each containing four bytes. The S-box transformation replaces each byte in the original state block with a new value from the lookup table. The resulting state block maintains the same 4x4 table format, but with the transformed byte values.

Example:

The original byte 'D1' in the top-left corner of the state block is transformed to '8F' after the S-box operation. Similarly, '26' in the second row, first column, is transformed to 'D4'. This process is repeated for every byte in the state block.

The AES S-box transformation is a crucial component of the AES algorithm, contributing significantly to the algorithm's security and diffusion properties.