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dc.contributor.advisorMedina Rivera, Luis
dc.contributor.authorMolina Salazar, Carlos Andres
dc.date.accessioned2023-11-09T19:33:08Z
dc.date.available2023-11-09T19:33:08Z
dc.date.issued2023-06-28
dc.identifier.urihttps://hdl.handle.net/11721/3464
dc.description.abstractRotation symmetric Boolean functions were introduced by Pieprzyk and Qu in 1999. They proved that these functions have efficient and secured cryptographic implementations. In recent years, a subclass of rotation symmetric Boolean functions have been found in examples of Boolean functions that exceed the bent concatenation bound for odd number of variables. This has sparked the interest of researchers. Members of this subclass of rotation symmetric Boolean functions are known as dihedral symmetric Boolean functions. They are useful, among other things, in the design of fast hashing algorithms with strong cryptographic properties.<br /> <br /> In this work we give an explicit representation of generators of short cycles of monomial rotation symmetric Boolean functions, and we use such representation to count the number of short cycles. We present a study of exponential sums of Boolean functions that are fixed under the action of the Dihedral group and a method to show that sequences of exponential sums of some families of Dihedral invariant Boolean functions are C-finite sequences.en_US
dc.language.isoen_USen_US
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 United States*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/us/*
dc.subjectLinear recurrencesen_US
dc.subjectMonomial rotation symmetric Boolean functionsen_US
dc.subjectShort cyclesen_US
dc.subject.lcshExponential sumsen_US
dc.subject.lcshSymmetric functionsen_US
dc.titleGenerators of monomial rotation symmetric Boolean functions and a characterization of monomial dihedral symmetric Boolean functionsen_US
dc.typeDissertationen_US
dc.rights.holder© 2023 Carlos Andres Molina Salazaren_US
dc.contributor.committeeEmamy, M. Reza
dc.contributor.committeeFigueroa, Raúl
dc.contributor.committeeRubio, Ivelisse
dc.contributor.committeeMoll, Victor H.
dc.contributor.campusUniversity of Puerto Rico, Río Piedras Campusen_US
dc.description.graduationSemesterSummer (3rd Semester)en_US
dc.description.graduationYear2023en_US
thesis.degree.disciplineMathsen_US
thesis.degree.levelPh.D.en_US


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Attribution-NonCommercial-NoDerivs 3.0 United States
Except where otherwise noted, this item's license is described as Attribution-NonCommercial-NoDerivs 3.0 United States