Date on Master's Thesis/Doctoral Dissertation

8-2019

Document Type

Doctoral Dissertation

Degree Name

Ph. D.

Department

Mathematics

Degree Program

Applied and Industrial Mathematics, PhD

Committee Chair

Smith-Tone, Daniel

Committee Co-Chair (if applicable)

Brown, David

Committee Member

Brown, David

Committee Member

Kulosman, Hamid

Committee Member

Li, Jinjia

Committee Member

Seif, Steven

Author's Keywords

Post quantum cryptography; multivariate cryptograpy

Abstract

As the world grapples with the possibility of widespread quantum computing, the cryptosystems of the day need to be up to date. Multivariate Public Key Cryptography is a leading option for security in a post quantum society. One goal of this work is to classify the security of multivariate schemes, especially C*variants. We begin by introducing Multivariate Public Key Cryptography and will then discuss different multivariate schemes and the main types of attacks that have been proven effective against multivariate schemes. Once we have developed an appropriate background, we analyze security of different schemes against particular attacks. Specifically, we will analyze differential security of HFEv- and PFLASH schemes. We then introduce a variant of C* that may be used as an encryption scheme, not just as a signature scheme. Finally, we will analyze the security and efficiency of a (n,d,s,a,p,t) scheme in general. This allows for individuals to generally discuss security and performance of any C* variant.

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