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    Studies on Gopala-Hemachandra Codes and their Applications.

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    Author
    Childers, Logan Gray
    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.
    URI
    http://hdl.handle.net/10342/8803
    Subject
     Data Compression; Zeckendorf Representation; Fibonacci Code; Gopala-Hemachandra Codes; Stream Ciphers; Cryptanalysis 
    Date
    2020-11-16
    Citation:
    APA:
    Childers, Logan Gray. (November 2020). Studies on Gopala-Hemachandra Codes and their Applications. (Master's Thesis, East Carolina University). Retrieved from the Scholarship. (http://hdl.handle.net/10342/8803.)

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    MLA:
    Childers, Logan Gray. Studies on Gopala-Hemachandra Codes and their Applications.. Master's Thesis. East Carolina University, November 2020. The Scholarship. http://hdl.handle.net/10342/8803. January 15, 2021.
    Chicago:
    Childers, Logan Gray, “Studies on Gopala-Hemachandra Codes and their Applications.” (Master's Thesis., East Carolina University, November 2020).
    AMA:
    Childers, Logan Gray. Studies on Gopala-Hemachandra Codes and their Applications. [Master's Thesis]. Greenville, NC: East Carolina University; November 2020.
    Collections
    • Master's Theses
    Publisher
    East Carolina University

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