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Designing Cryptographically Strong S-Boxes with Use of 1D Cellular Automata
Miroslaw Szaban and Franciszek Seredynski

In this paper we use recently proposed cellular automata (CA) – based methodology, to design 6 × 4 S-boxes functionally equivalent to ones used in the cryptographic standard known as DES. Also, we use CA to design 8 × n (n ≤ 8) S-boxes functionally equivalent to S-boxes used in current cryptographic standards. We provide an exhaustive experimental analysis of the proposed CA-based S-boxes in terms of non-linearity and autocorrelation. We also analyze scalability of n × n S-boxes in the sense of non-linearity and autocorrelation, and compare these properties with results related to DES S-boxes and other proposals. We show that the proposed CA-based S-boxes, generally have cryptographic properties comparable with currently offered classical S-box tables.We have shown that the particular CA-based S-boxes are better or much better than classical Sbox tables. The interesting feature of the proposed S-boxes is their dynamic nature, fully functionally realized by CA, while the classical S-boxes are represented by predefined unchangeable table structures.

Keywords: Cellular Automata, S-boxes, Block Cipher, Cryptography, Boolean Functions

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