@inproceedings{0cdaaf3566664ab98e312db53f4378c2,
title = "Fighting the symmetries: The structure of cryptographic boolean function spaces",
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.",
keywords = "Cryptographic boolean function, Evolutionary computation, Fitness landscape, Symmetry",
author = "Stjepan Picek and McKay, {R. I.} and Roberto Santana and Gedeon, {Tom D.}",
note = "Publisher Copyright: {\textcopyright} 2015 ACM.; 16th Genetic and Evolutionary Computation Conference, GECCO 2015 ; Conference date: 11-07-2015 Through 15-07-2015",
year = "2015",
month = jul,
day = "11",
doi = "10.1145/2739480.2754739",
language = "English",
series = "GECCO 2015 - Proceedings of the 2015 Genetic and Evolutionary Computation Conference",
publisher = "Association for Computing Machinery (ACM)",
pages = "457--464",
editor = "Sara Silva",
booktitle = "GECCO 2015 - Proceedings of the 2015 Genetic and Evolutionary Computation Conference",
address = "United States",
}