New Generation Computing, 23(2005)201-218
Ohmsha, Ltd. and Springer

Multi-objective Optimisation of Bijective S-boxes

Joanne FULLER, William MILLAN and Ed DAWSON
ISRC, QUT
GPO Box 2434, Brisbane 4001, Qld, Australia
{j.fuller, b.millan, e.dawson}@qut.edu.au

Received 29 March 2004
Revised manuscript received 1 July 2004

Abstract

In this paper we investigate the heuristic construction of bijective s-boxes that satisfy a wide range of cryptographic criteria including algebraic complexity, high nonlinearity, low autocorrelation and have none of the known weaknesses including linear structures, fixed points or linear redundancy. We demonstrate that the power mappings can be evolved (by iterated mutation operators alone) to generate bijective s-boxes with the best known tradeoffs among the considered criteria. The s-boxes found are suitable for use directly in modern encryption algorithms.

Keywords:Cryptography, Bijective S-boxes, Nonlinearity, Autocorrelation, Linear Redundancy, Finite Field, Heuristic Construction.

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