Gowers U2 norm as a measure of nonlinearity for Boolean functions and their generalizations

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dc.contributor.authorGangopadhyay, Sugata
dc.contributor.authorRiera, Constanza
dc.contributor.authorStănică, Pantelimon
dc.contributor.departmentApplied Mathematics
dc.date.accessioned2020-03-23T23:39:33Z
dc.date.available2020-03-23T23:39:33Z
dc.date.issued2020
dc.description.abstractIn this paper, we investigate the Gowers U2 norm for generalized Boolean func- tions, and Z-bent functions. The Gowers U2 norm of a function is a measure of its resistance to affine approximation. Although nonlinearity serves the same purpose for the classical Boolean functions, it does not extend easily to generalized Boolean functions. We first pro- vide a framework for employing the Gowers U2 norm in the context of generalized Boolean functions with cryptographic significance, in particular, we give a recurrence rule for the Gowers U2 norms, and an evaluation of the Gowers U2 norm of functions that are affine over spreads. We also give an introduction to Z-bent functions, as proposed by Dobbertin and Leander [8], to provide a recursive framework to study bent functions. In the second part of the paper, we concentrate on Z-bent functions and their U2 norms. As a consequence of one of our results, we give an alternate proof to a known theorem of Dobbertin and Leander, and also find necessary and sufficient conditions for a function obtained by gluing Z-bent functions to be bent, in terms of the Gowers U2 norms of its components.en_US
dc.identifier.citationGangopadhyay, Sugata, Constanza Riera, and Pantelimon Stănică. "Gowers U2 norm as a measure of nonlinearity for Boolean functions and their generalizations." (2020).
dc.identifier.doihttps://doi.org/10.3934/amc.2019038
dc.identifier.urihttps://hdl.handle.net/10945/64448
dc.publisherAmerican Institute of Mathematical Sciences
dc.relation.ispartofseriesFaculty & Researcher Publications
dc.rightsThis publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.en_US
dc.subject.authorGowers normsen_US
dc.subject.authorBoolean functionsen_US
dc.subject.authorbent functionsen_US
dc.subject.authorZ-bent functionsen_US
dc.titleGowers U2 norm as a measure of nonlinearity for Boolean functions and their generalizationsen_US
dc.typeArticleen_US
dspace.entity.typePublication
relation.isSeriesOfPublicationc2c3de57-d1f4-47b1-aa53-6f1c074e4c20
relation.isSeriesOfPublication.latestForDiscoveryc2c3de57-d1f4-47b1-aa53-6f1c074e4c20
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