PROBLEMS MOTIVATED BY CRYPTOLOGY: COUNTING FIXED POINTS AND TWO-CYCLES OF THE DISCRETE LAMBERT MAP

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dc.contributorPollatsek, Harriet
dc.contributor.advisorRobinson, Margaret
dc.contributor.authorZirlin, Dara
dc.date.accessioned2015-06-30T17:30:10Z
dc.date.available2015-06-30T17:30:10Z
dc.date.gradyear2015en_US
dc.date.issued2015-06-30
dc.description.abstractIn this thesis, we begin with a brief introduction to some relevant number theory and to digital signature schemes (DSS). We explain how information about the discrete Lambert map (DLM) [2] relates to DSS security. Next we introduce results from p-adic analysis. We summarize the results from previous work on the DLM and extend these results to p = 2. In the main part of this thesis we explain our results counting fi xed points and two-cycles of the DLM. That is, for a fi xed prime p and a nonzero integer g where p does not divide g and e is a positive integer, we will count the number of fi xed points or solutions to xgx ≡x (mod p^e) and the number of two cycles or simultaneous solutions to xgx ≡y (mod p^e) and ygy ≡x (mod p^e) where x and y range through appropriate sets of integers. This work is a continuation of work started by Holden and Robinson in [7] and their students from the 2014 Mount Holyoke summer REU program: Anne Waldo and Caiyun Zhu [10], Yu Liu [8], and Abigail Mann and Adelyn Yeoh [9].en_US
dc.description.sponsorshipMathematics & Statisticsen_US
dc.identifier.urihttp://hdl.handle.net/10166/3671
dc.language.isoen_USen_US
dc.rights.restrictedpublicen_US
dc.subjectp-adic analysisen_US
dc.subjectDigital signature schemesen_US
dc.subjectDiscrete Lambert Mapen_US
dc.titlePROBLEMS MOTIVATED BY CRYPTOLOGY: COUNTING FIXED POINTS AND TWO-CYCLES OF THE DISCRETE LAMBERT MAPen_US
dc.typeThesis
mhc.degreeUndergraduateen_US
mhc.institutionMount Holyoke College

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