Iteration functions for Pollard's rho on elliptic curve groups

dc.contributor.committeeChairMonico, Christopher J.
dc.contributor.committeeMemberChristensen, Lars Winther
dc.contributor.committeeMemberLedet, Arne
dc.creatorBishop, Katie Lynn
dc.date.accessioned2016-06-27T19:49:44Z
dc.date.available2016-06-27T19:49:44Z
dc.date.created2016-05
dc.date.issued2016-05
dc.date.submittedMay 2016
dc.date.updated2016-06-27T19:49:44Z
dc.description.abstractPollard's Rho method is one way to solve the discrete log problem (DLP) in Elliptic Curve Groups. It relies on the use of an iterative mapping that behaves like a random mapping. In this paper, we will discuss some alternative iteration functions to Pollard's original suggestion. We will then compare the different iteration functions to Pollard's by examining the expected value of the number of iterations, or steps, each iteration function requires for completion in elliptic curve groups of prime order $\approx 10^4, \; 10^5, \; \text{and} \; 10^6$. We will compare the expected value of each iteration function to the performance expected of an iteration function chosen at random. This analysis will be performed in order to identify possible iteration functions that may perform better than Pollard's original, the random case, or both most of the time. Finally, we then describe an algorithm to compute Pollard's Rho in parallel, which dramatically decreases the run time to solve the DLP in large elliptic curve groups.
dc.format.mimetypeapplication/pdf
dc.identifier.urihttp://hdl.handle.net/2346/67068
dc.language.isoeng
dc.subjectCryptography
dc.subjectCryptology
dc.subjectPollard
dc.subjectPollard's rho
dc.subjectElliptic curve group
dc.subjectElliptic curve groups
dc.subjectElliptic curve
dc.subjectIteration functions
dc.subjectRandom walk
dc.titleIteration functions for Pollard's rho on elliptic curve groups
dc.typeThesis
dc.type.materialtext
thesis.degree.departmentMathematics and Statistics
thesis.degree.disciplineMathematics
thesis.degree.grantorTexas Tech University
thesis.degree.levelMasters
thesis.degree.nameMaster of Science

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