Construction and Optimization of Dynamic S-Boxes Based on Gaussian Distribution

• Published in: IEEE access 2023, Vol.11, p.35818-35829
• Main Authors: Alharbi, Adel R., Jamal, Sajjad Shaukat, Khan, Muhammad Fahad, Gondal, Mohammad Asif, Abbasi, Aaqif Afzaal
• Format: Article
• Language: English
• Subjects: Approximation; block cipher; Boxes; Chaos theory; Chaotic communication; Ciphers; Criteria; Cryptography; Encryption; Gaussian distribution; genetic algorithm; Genetic algorithms; Mathematical analysis; Nonlinearity; Normal distribution; Optimization; PRNG; Pseudorandom sequences; Randomness; S-Box construction; S-Box optimization; Security; Statistical analysis; Symmetric cipher
• ISSN: 2169-3536; 2169-3536
• DOI: 10.1109/ACCESS.2023.3262313

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.