A new look in the representation of AES like S-box

Abstract— Substitution box plays an essential role in block ciphers as their main non-linear component in the round function, providing confusion. In this paper, it will be proven how the action of any substitution box on every fixed element can be represented through an affine transformation using an invertible matrix in a finite field. Furthermore, a particular way to represent the action of permutations on every element through a modular addition is given. An analysis of the AES substitution box is conducted based on the theoretical results obtained.