Studies on Gopala-Hemachandra Codes and their Applications

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.

Department dc:contributor.department

Computer Science

Grantor dc:publisher

East Carolina University

Year dc:date.issued

2020

Author dc:creator

• Childers, Logan

Advisor dc:contributor.advisor

• Gopalakrishnan, Krishnan

• Zeckendorf Representation
• Gopala-Hemachandra Codes
• Data Compression
• Fibonacci Code
• Stream Ciphers
• Cryptanalysis

Language dc:language.iso

en

Handle dc:identifier.uri

http://hdl.handle.net/10342/8803

OAI identifier oai:identifier

oai:thescholarship.ecu.edu:10342/8803