Date of Award

12-2013

Degree Type

Honors College Thesis

Department

Mathematics

First Advisor

James Lambers, Ph.D.

Second Advisor

Samuel Jeremy Lyle, Ph.D.

Advisor Department

Mathematics

Abstract

Cryptography is the study of a centuries–old technique of secretly transferring information between parties. Linear recurrences were the chosen method of encryption and decryption in the thesis. The Fibonacci sequence, with its Zeckendorf representation, allows for the flexibility of encoding any number desired based on a particular encoding technique used in the film Sherlock Holmes: A Game of Shadows. The main goal is to find other linear recurrences that possess characteristics similar to the Fibonacci sequence to use as suitable substitutes for encoding. Different sequences were analyzed based on a number of criteria. In order for a sequence to be a candidate, it had to be first deemed a possible sequence based on the nature of the roots of its characteristic equation. Once it passed this test, a particular method was developed for showing that a sequence could be used to encode a set of numbers. This method was applied to various sequences, showing which sequences satisfy the desired encryption method.

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