Analysis and algebraic construction of S-Box for AES algorithm using irreducible polynomials

Abstract

Substitution Boxes play a vital role in the Rijndael algorithm of modern block ciphers. The security and efficiency of these ciphers mainly depend upon the algebraic construction of their Substitution Boxes. In this paper, the algebraic construction of the Substitution Boxes for the AES algorithm is analyzed with different irreducible polynomials. This paper emphasizes on the study of the ways of constructing the Substitution Boxes and the other important feature of a Substitution Box is how secure it is cryptographically. The cryptographic properties namely correlation immunity bias, strict avalanche criteria, non-linearity and entropy are used to evaluate the level of security for Substitution Boxes. The results show that the other irreducible polynomial equation offer better level of security compared to that of standard polynomial equation used in Advanced Encryption Standard algorithm. Moreover, the Substitution Box used in AES can be constructed with different irreducible polynomial equations.