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Studies on Gopala-Hemachandra Codes and their Applications

dc.access.optionOpen Access
dc.contributor.advisorGopalakrishnan, Krishnan
dc.contributor.authorChilders, Logan
dc.contributor.departmentComputer Science
dc.date.accessioned2020-12-18T15:48:08Z
dc.date.available2020-12-18T15:48:08Z
dc.date.created2020-12
dc.date.issued2020-11-16
dc.date.submittedDecember 2020
dc.date.updated2020-12-18T14:31:31Z
dc.degree.departmentComputer Science
dc.degree.disciplineMS-Computer Science
dc.degree.grantorEast Carolina University
dc.degree.levelMasters
dc.degree.nameM.S.
dc.description.abstractGopala-Hemachandra codes are a variation of the Fibonacci universal code and have applications in data compression and cryptography. We study a specific parameterization of Gopala-Hemachandra codes and present several results pertaining to these codes. We show that GH_{a}(n) always exists for any n >= 1, when -2 >= a >= -4, meaning that these are universal codes. We develop two new algorithms to determine whether a GH code exists for a given a and n, and to construct them if they exist. We also prove that when a = -(4+k), where k >= 1, that there are at most k consecutive integers for which GH codes do not exist. In 2014, Nalli and Ozyilmaz proposed a stream cipher based on GH codes. We show that this cipher is insecure and provide experimental results on the performance of our program that cracks this cipher.
dc.format.mimetypeapplication/pdf
dc.identifier.urihttp://hdl.handle.net/10342/8803
dc.language.isoen
dc.publisherEast Carolina University
dc.subjectZeckendorf Representation
dc.subjectGopala-Hemachandra Codes
dc.subjectData Compression
dc.subjectFibonacci Code
dc.subjectStream Ciphers
dc.subjectCryptanalysis
dc.subject.lcshFibonacci numbers
dc.subject.lcshData compression (Computer science)
dc.subject.lcshStream ciphers
dc.subject.lcshCryptography
dc.titleStudies on Gopala-Hemachandra Codes and their Applications
dc.typeMaster's Thesis
dc.type.materialtext

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