Term of Award
Fall 2021
Degree Name
Master of Science in Mathematics (M.S.)
Document Type and Release Option
Thesis (open access)
Copyright Statement / License for Reuse
This work is licensed under a Creative Commons Attribution 4.0 License.
Department
Department of Mathematical Sciences
Committee Chair
Yan Wu
Committee Member 1
Martha Abell
Committee Member 2
Yongki Lee
Abstract
As our world becomes increasingly digital, data security becomes key. Data must be encrypted such that it can be easily encrypted only by the intended recipient. Arnold Transformations are a useful tool in this because of its unpredictable periodicity. Our goal is to outline a method for choosing an Arnold Transformation that is both secure and easy to implement. We find the necessary and sufficient condition that a key matrix has periodicity. The chosen key matrix has a random structure, and it has a periodicity that is sufficiently high. We apply this method to several image and data string examples to evaluate its effectiveness.
OCLC Number
1290885196
Catalog Permalink
https://galileo-georgiasouthern.primo.exlibrisgroup.com/permalink/01GALI_GASOUTH/1r4bu70/alma9916470448302950
Recommended Citation
Anderson, Haley N., "Arnold Transformations as Applied to Data Encryption" (2021). Electronic Theses and Dissertations. 2323.
https://digitalcommons.georgiasouthern.edu/etd/2323
Research Data and Supplementary Material
No
Included in
Information Security Commons, Numerical Analysis and Computation Commons, Other Applied Mathematics Commons
