Studies on Gopala-Hemachandra Codes and their Applications

ECU Author/Contributor (non-ECU co-authors, if there are any, appear on document)

Logan Childers (Creator)

Institution

East Carolina University (ECU )

Web Site: http://www.ecu.edu/lib/

Abstract: Gopala-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.

Additional Information

Publication

Thesis

Language: English

Date: 2023

Subjects

Zeckendorf Representation;Gopala-Hemachandra Codes

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