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N* algorithm: Nonlinearity-perfect substitution boxes generation method for robust cryptographic systems

algorithms-and-analysis-of-algorithms
cryptography
optimization-theory-and-computation
security-and-privacy
theory-and-formal-methods

Abstract

Substitution boxes (S-Boxes) are operators/atomic functions in cryptographic methods. They are vital in cryptographic algorithms as they transform a cryptologic model from linear to nonlinear. Therefore, S-Box generation is an important step in creating a powerful encryption method.
This paper introduces the N* algorithm (a sample of the eugenics algorithm), a novel and efficient approach for generating nonlinearity-perfect S-Boxes, addressing gaps in existing methods. Unlike traditional chaotic or metaheuristic models, the N* algorithm employs an iterative displacement method inspired by artificial selection and the principles of the eugenics algorithm, leveraging the Advanced Encryption Standard (AES) S-Box as an anchor.
Initially, by deploying an element-wise displacement technique, more than 168,000 S-Boxes were generated. In the cleaning step, 62,857 unique perfect nonlinear S-Boxes were selected. Moreover, by selecting completely distinct S-Boxes from the AES S-Box, an S-Box+ subset was created, containing 21,601 unique S-Boxes.
All 62,857 generated S-Boxes are 8-bit, and the highest nonlinearity of 112 is reached.
The results demonstrate that the presented N* algorithm provides a new S-Box library that contributes to S-Box generation and cryptology research areas. Moreover, the introduced N* algorithm opens doors to a new level for S-Box generation.
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