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The design of S-boxes by simulated annealing

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Substitution boxes (S-boxes) are important components in many modern-day symmetric key ciphers. Their study has attracted a great deal of attention over many years. The emergence of a variety of cryptosystem attacks has shown that substitutions must be designed with great care. Some general criteria such as high non-linearity and low autocorrelation have been proposed (providing some protection against attacks such as linear cryptanalysis and differential cryptanalysis). The design of appropriate S-boxes is a difficult task; several criteria must be traded off and the design space is huge. There has been little application of evolutionary search to the development of S-boxes. In this paper we show how a cost function that has found excellent single-out put Boolean functions can be generalised to provide improved results for small S-boxes.

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Correspondence to John A. Clark.

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John A. Clark: He is Professor of Critical Systems at the University of York, where he leads the software testing, security and cryptography work. Much of this has been concerned with the application of meta-heuristic search.

Jeremy L. Jacob: He has a BSc. in Mathematics from the University of Hull, England, M.Sc. and D. Phil. in Computation from the University of Oxford, England and now works for the Univerity of York. His research interests include modelling secure systems and software engineering practices for secure systems.

Susan Stepney: She is Professor of computer Science at the University of York, and leads the Non-Standard Computation research group there. She is a member of the ACM, Fellow of the British Computer Society, and moderator of the UKCRC Grand Challenge in Non-Classical Computation. Her main research interests include novel applications of nature-inspired computation, modelling self-organising complex systems and designing and reasoning about emergent properties.

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Clark, J.A., Jacob, J.L. & Stepney, S. The design of S-boxes by simulated annealing. New Gener Comput 23, 219–231 (2005).

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