Studies on Gopala-Hemachandra Codes and their Applications
Author
Childers, Logan
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.
Date
2020-11-16
Citation:
APA:
Childers, Logan.
(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.)
MLA:
Childers, Logan.
Studies on Gopala-Hemachandra Codes and their Applications.
Master's Thesis. East Carolina University,
November 2020. The Scholarship.
http://hdl.handle.net/10342/8803.
June 29, 2024.
Chicago:
Childers, Logan,
“Studies on Gopala-Hemachandra Codes and their Applications”
(Master's Thesis., East Carolina University,
November 2020).
AMA:
Childers, Logan.
Studies on Gopala-Hemachandra Codes and their Applications
[Master's Thesis]. Greenville, NC: East Carolina University;
November 2020.
Collections
Publisher
East Carolina University