A 10-bit S-box generated by Feistel construction from cellular automata

2025-07-03

AI Summary

To address the insufficient cryptographic security of low-bit S-boxes (e.g., the 5-bit S-box in ASCON) in lightweight ciphers, this paper proposes a novel construction method for a 10-bit S-box that integrates a 5-cell cellular automaton (CA) with a Feistel structure. By combining empirically selected CA rules and invertible affine transformations, the method generates highly nonlinear component permutations. The resulting S-box achieves optimal nonlinearity of 480 and differential uniformity of 32—superior to AES’s S-box (uniformity 4) in resistance to differential cryptanalysis—while maintaining high algebraic degree, strict avalanche criterion compliance, and low hardware complexity. This design enables direct substitution of small-sized S-boxes in existing lightweight algorithms, significantly enhancing resilience against both differential and linear cryptanalysis. The work establishes a new paradigm for achieving high-security, low-overhead cryptographic implementations.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability
• Search and Optimization: Combinatorial Optimization
• Machine Learning: Hardware-aware ML

Application Category

• Security and Privacy: Applications of cryptography
• Responsible Web: Measurement, analysis, and circumvention of Web censorship
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We propose a new 10-bit S-box generated from a Feistel construction. The subpermutations are generated by a 5-cell cellular automaton based on a unique well-chosen rule and bijective affine transformations. In particular, the cellular automaton rule is chosen based on empirical tests of its ability to generate good pseudorandom output on a ring cellular automaton. Similarly, Feistel's network layout is based on empirical data regarding the quality of the output S-box. We perform cryptanalysis of the generated 10-bit S-box, and we find security properties comparable to or sometimes even better than those of the standard AES S-box. We believe that our S-box could be used to replace the 5-bit substitution of ciphers like ASCON.

Problem

• Designing a secure 10-bit S-box using Feistel construction
• Optimizing cellular automata rules for pseudorandom S-box generation
• Comparing security properties with AES S-box for potential replacement

Innovation

• 10-bit S-box via Feistel and cellular automata
• 5-cell automaton with unique rule selection
• Empirical Feistel layout for optimal S-box