Improving the Quality of AES S-box by Modifications Irreducible Polynomial and Affine Matrix

Abstract

$S$-box plays an important role in the process of secure data transmission over the internet. The proposed S-box uses the results of various modifications, i.e., a combination of an irreducible polynomial and an affine matrix. Irreducible polynomial modification is done by taking the 3 best irreducible polynomials based on previous research. Affine matrix modification is done by a Boolean operation XOR for each affine matrix element of the AES S-box. The combination results of these modifications are used to build several quality S-boxes. To determine the best S-box quality, nonlinearity, strict avalanche criterion, bit independence criterion-nonlinearity, and bit independence criterion-strict avalanche criterion testing were used. The test results show that the best quality S-box has scores of 112, 0.5015, 112, and 0.4997 for the nonlinearity, strict avalanche criterion, bit independence criterion-nonlinearity, and bit independence criterion-strict avalanche criterion, respectively. The test results are implemented using a predetermined mathematical formulation to obtain the S-box value. The results of the calculation show that the S-box value in this study is 16.0017. This result indicates that the proposed S-box has better quality than the S-boxes produced in previous studies.