Date on Master's Thesis/Doctoral Dissertation

8-2024

Document Type

Doctoral Dissertation

Degree Name

Ph. D.

Department

Mathematics

Degree Program

Applied and Industrial Mathematics, PhD

Committee Chair

Smith-Tone, Daniel

Committee Member

Larson, Lee

Committee Member

Seif, Steve

Committee Member

Lauf, Adrian

Author's Keywords

Post quantum cryptography; multivariate cryptography; lattice based cryptography; algebraic geometry

Abstract

As the world edges closer to widespread quantum computing, cryptosystems need to be able to withstand attacks from new adversaries. Classical public key cryptosystems that currently protect the digital world will no longer be secure in the post-quantum setting. Two of the leading options for public key post-quantum cryptography are multivariate and lattice-based cryptography. One goal of this work is to introduce and classify the security of the multivariate cryptosystems from the C∗ and Oil and Vinegar families, and attacks that have proven successful against them. We begin by outlining the growth of multivariate cryptography from C∗ and its linage. Once we have developed an appropriate background, we analyze the security of HFERP when faced with novel attacks. Further, we will analyze the increased security of Rainbow against the simple attack when restructured in a new iteration of the cryptosystem called IPRainbow. We further will analyze the security of the multivariate 2F cryptosystem when faced with attacks known to lattice based cryptography.

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