Fighting the Symmetries: The Structure of Cryptographic Boolean Function Spaces

Date

2015

Authors

Picek, Stjepan
McKay, Robert Ian
Santana, Roberto
Gedeon, Tamas (Tom)

Journal Title

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Publisher

Association for Computing Machinery (ACM)

Abstract

We explore the problem space of maximum nonlinearity problems for balanced Boolean functions, examining the symmetry structure and fitness landscapes in the most common (bit string) representation. We present theoretical analyses of well understood aspects, together with detailed enumeration of the 4-bit problem, sampling of the 6-bit problem based on known optima, and sampling of the 8-bit problem based on its fittest known solutions. We show that these problems have many more symmetries than is generally noted, with implications for crossover and for distributional methods. We explore the large-scale plateau structure of the problem, with similar implications for local search. We show that symmetries yield additional information that may yield more effective search methods

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Citation

Source

GECCO '15 Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation

Type

Conference paper

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Restricted until

2037-12-31