Counting Solutions to Non-Algebraic Equations Modulo Prime Powers

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dc.contributorSidman, Jessica
dc.contributorDavis, Michael
dc.contributor.advisorRobinson, Margaret
dc.contributor.authorTomarkin, Rae
dc.date.accessioned2021-07-02T13:47:39Z
dc.date.available2021-07-02T13:47:39Z
dc.date.gradyear2021en_US
dc.date.issued2021-07-02
dc.description.abstractIn the digital age, cryptology, always important during conflicts, is becoming more and more significant as cybersecurity influences world affairs. We are interested in studying the mathematical properties of certain functions that are employed to create digital signatures, in particular via the ElGamal Digital Signature Scheme. Using techniques from Holden, Richardson and Robinson [3], we examine the properties of these non-algebraic functions and, more specifically, we count the number of fixed points of these functions modulo any positive power of a prime p. We show explicitly how the singular points of the function (i.e. the points where the derivative is zero modulo p) complicate the solution.en_US
dc.description.sponsorshipMathematics & Statisticsen_US
dc.identifier.urihttp://hdl.handle.net/10166/6314
dc.language.isoen_USen_US
dc.rights.restrictedpublicen_US
dc.subjectNumber Theoryen_US
dc.subjectcryptologyen_US
dc.titleCounting Solutions to Non-Algebraic Equations Modulo Prime Powersen_US
dc.typeThesis
mhc.degreeUndergraduateen_US
mhc.institutionMount Holyoke College

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