Construction and Optimization of Dynamic S-Boxes Based on Gaussian Distribution
Adel R. Alharbi, Sajjad Shaukat Jamal, Muhammad Fahad Khan, Muhammad Asif Gondal, Aaqif Afzaal Abbasi
Abstract
Block ciphers are widely used for securing data and are known for their resistance to various types of attacks. The strength of a block cipher against these attacks often depends on the S-boxes used in the cipher. There are many chaotic map-based techniques in the literature for constructing the dynamic S-Boxes. While chaos-based approaches have certain attractive properties for this purpose, they also have some inherent weaknesses, including finite precision effect, dynamical degradation of chaotic systems, non-uniform distribution, discontinuity in chaotic sequences. These weaknesses can limit the effectiveness of chaotic map-based substitution boxes. In this paper, we propose an innovative approach for constructing dynamic S-boxes using Gaussian distribution-based pseudo-random sequences. The proposed technique overcomes the weaknesses of existing chaos-based S-box techniques by leveraging the strength of pseudo-randomness sequences. However, one of the main drawbacks of using Gaussian distribution-based pseudo-random sequences is the low nonlinearity of the resulting S-boxes. To address this limitation, we introduce the use of genetic algorithms (GA) to optimize the nonlinearity of Gaussian distribution-based S-boxes while preserving a high level of randomness. The proposed technique is evaluated using standard S-box performance criteria, including nonlinearity, bit independence criterion (BIC), linear approximation probability (LP), strict avalanche criterion (SAC), and differential approximation probability (DP). Results demonstrate that the proposed technique achieves a maximum nonlinearity of 112, which is comparable to the ASE algorithm.