Date of Completion

2021

Document Type

Honors College Thesis

Department

Mathematics and Statistics

Thesis Type

Honors College

First Advisor

Dr. Christelle Vincent

Keywords

mathematics, cryptography, quantum computing

Abstract

This thesis studies how a chosen set of parameters for a Ring Learning With Errors (RLWE) cryptographic instance affects its ability to withstand a certain type of attack. We begin with some non-technical motivation on the specific qualities of RLWE that support its candidacy as a post-quantum cryptographic protocol, and why such protocols are necessary due to recent developments in computing. We then discuss some of the context for RLWE, providing some overview on important concepts in algebraic number theory that underpin the mathematical structure of RLWE. We define several variants of RLWE which researchers in this field have analyzed, provide some detail on how these variants relate to each other, and cover some of the types of attacks against these variants. Following this overview, we introduce the experimental phase of this thesis project and cover the functionality of a program used to simulate a RLWE attack. Finally, we analyze some data generated as a result of tests run on our program and briefly discuss how it relates to previous hypotheses on how a RLWE instance's security should be characterized.

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.

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