Efficient generation of quadratic cyclotomic classes for shortest quadratic decompositions of polynomials

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dc.contributor.authorOtal, Kamil
dc.contributor.authorTekin, Eda
dc.date.accessioned2024-09-29T15:54:34Z
dc.date.available2024-09-29T15:54:34Z
dc.date.issued2021
dc.departmentKarabük Üniversitesien_US
dc.description.abstractNikova et al. investigated the decomposition problem of power permutations over finite fields F-2n in (Cryptogr. Commun. 11:379-384, 2019). In particular, they provided an algorithm to give a decomposition of a power permutation into quadratic power permutations. Their algorithm has a precomputation step that finds all cyclotomic classes of F-2n and then use the quadratic ones. In this paper, we provide an efficient and systematic method to generate the representatives of quadratic cyclotomic classes and hence reduce the complexity of the precomputation step drastically. We then apply our method to extend their results on shortest quadratic decompositions of x(2n-2) from 3 <= n <= 16 to 3 <= n <= 24 and correct a typo (for n = 11). We also give two explicit formulas for the time complexity of the adaptive search to understand its efficiency with respect to the parameters.en_US
dc.identifier.doi10.1007/s12095-021-00512-z
dc.identifier.endpage845en_US
dc.identifier.issn1936-2447
dc.identifier.issn1936-2455
dc.identifier.issue5en_US
dc.identifier.scopus2-s2.0-85110709756en_US
dc.identifier.scopusqualityQ1en_US
dc.identifier.startpage837en_US
dc.identifier.urihttps://doi.org/10.1007/s12095-021-00512-z
dc.identifier.urihttps://hdl.handle.net/20.500.14619/4160
dc.identifier.volume13en_US
dc.identifier.wosWOS:000673022800001en_US
dc.identifier.wosqualityQ2en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherSpringeren_US
dc.relation.ispartofCryptography and Communications-Discrete-Structures Boolean Functions and Sequencesen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectBoolean functionsen_US
dc.subjectS-boxesen_US
dc.subjectPower permutationsen_US
dc.titleEfficient generation of quadratic cyclotomic classes for shortest quadratic decompositions of polynomialsen_US
dc.typeArticleen_US

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