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Fighting the Symmetries: The Structure of Cryptographic Boolean Function Spaces

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

Description

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...[Show more]

dc.contributor.authorPicek, Stjepan
dc.contributor.authorMcKay, Robert Ian
dc.contributor.authorSantana, Roberto
dc.contributor.authorGedeon, Tamas (Tom)
dc.coverage.spatialMadrid, Spain
dc.date.accessioned2016-06-14T23:21:04Z
dc.date.created11-15 July 2015
dc.identifier.isbn9781450334723
dc.identifier.urihttp://hdl.handle.net/1885/103700
dc.description.abstractWe 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
dc.publisherAssociation for Computing Machinery (ACM)
dc.relation.ispartofseries2015 Annual Conference on Genetic and Evolutionary Computation (GECCO'15)
dc.sourceGECCO '15 Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation
dc.titleFighting the Symmetries: The Structure of Cryptographic Boolean Function Spaces
dc.typeConference paper
local.description.notesImported from ARIES
local.description.refereedYes
dc.date.issued2015
local.identifier.absfor080100 - ARTIFICIAL INTELLIGENCE AND IMAGE PROCESSING
local.identifier.ariespublicationu4056230xPUB557
local.type.statusPublished Version
local.contributor.affiliationPicek, Stjepan, University of Zagreb
local.contributor.affiliationMcKay, Robert Ian, Seoul National University
local.contributor.affiliationSantana, Roberto, University of the Basque Country
local.contributor.affiliationGedeon, Tamas (Tom), College of Engineering and Computer Science, ANU
local.description.embargo2037-12-31
local.bibliographicCitation.startpage457
local.bibliographicCitation.lastpage464
local.identifier.doi10.1145/2739480.2754739
local.identifier.absseo970108 - Expanding Knowledge in the Information and Computing Sciences
dc.date.updated2016-06-14T08:58:33Z
CollectionsANU Research Publications

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