Performance of S-Boxes Constructed by Irreducible Polynomials on GF(28)

Substitution boxes are a crucial component of the Rijndael algorithm, a modern block cipher like AES. The security and efficiency of these ciphers depend on the algebraic construction of the substitution boxes. This paper analyzes the algebraic construction of substitution boxes for AES, exploring various irreducible polynomials. The focus is on understanding different methods of constructing substitution boxes and evaluating their cryptographic security. Properties such as Strict Avalanche Criterion (SAC), Bit Independence Criterion (BIC), and Nonlinearity (NL) are considered. The results show that the use of alternative irreducible polynomial equations can improve security compared to the standard ones in AES. Furthermore, it's shown that substitution boxes in AES can be created with different irreducible polynomial equations. According to the SAC criterion, the S-box with IP Hex Code 13F consistently demonstrates more favorable values compared to the other codes in Table IX. It has mean and median values of SAC exactly 0.5, as well as closer interquartile distances. All S-boxes have the same value of 112 for the BIC criteria. Regarding the NL criteria, three S-boxes have a value of112: those with IP Hex Code 11B, 163, and 1F3, as shown in Table X.