Studies on Gopala-Hemachandra Codes and their Applications
dc.access.option | Open Access | |
dc.contributor.advisor | Gopalakrishnan, Krishnan | |
dc.contributor.author | Childers, Logan | |
dc.contributor.department | Computer Science | |
dc.date.accessioned | 2020-12-18T15:48:08Z | |
dc.date.available | 2020-12-18T15:48:08Z | |
dc.date.created | 2020-12 | |
dc.date.issued | 2020-11-16 | |
dc.date.submitted | December 2020 | |
dc.date.updated | 2020-12-18T14:31:31Z | |
dc.degree.department | Computer Science | |
dc.degree.discipline | MS-Computer Science | |
dc.degree.grantor | East Carolina University | |
dc.degree.level | Masters | |
dc.degree.name | M.S. | |
dc.description.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. | |
dc.format.mimetype | application/pdf | |
dc.identifier.uri | http://hdl.handle.net/10342/8803 | |
dc.language.iso | en | |
dc.publisher | East Carolina University | |
dc.subject | Zeckendorf Representation | |
dc.subject | Gopala-Hemachandra Codes | |
dc.subject | Data Compression | |
dc.subject | Fibonacci Code | |
dc.subject | Stream Ciphers | |
dc.subject | Cryptanalysis | |
dc.subject.lcsh | Fibonacci numbers | |
dc.subject.lcsh | Data compression (Computer science) | |
dc.subject.lcsh | Stream ciphers | |
dc.subject.lcsh | Cryptography | |
dc.title | Studies on Gopala-Hemachandra Codes and their Applications | |
dc.type | Master's Thesis | |
dc.type.material | text |
Files
Original bundle
1 - 1 of 1
Loading...
- Name:
- CHILDERS-MASTERSTHESIS-2020.pdf
- Size:
- 244.66 KB
- Format:
- Adobe Portable Document Format