Lattice-Based Cryptography

My undergraduate Mathematics Capstone project puts forth the theory of lattices as a viable source of quantum-resistant cryptographic problems. In it, I discuss the GGH and NTRU lattice-based cryptosystems as well as their mathematical background. I also introduce the LLL lattice reduction algorithm as a tool for cryptanalysis on lattices. As part of this project, I coded a version of the LLL algorithm (in the C language) and presented my results to the Mathematics Honors Program at my university.

Timeline: January - May 2021
Keywords: Lattices, Post-quantum Cryptography, Lattice Reduction
Link: A Mathematical Introduction to Lattice-Based Cryptography

Usability of Authentication

“You’re only as strong as your weakest link”. Too often companies rely on security training and password complexity requirements to ensure proper use of authentication mechanisms. However, this overexposure to training bombardment can lead to security fatigue. This paper argues that usability is a better approach to achieving security goals while reducing friction in the user experience. I address usability in the context of password management, multi-factor authentication, security questions, and mobile authentication.

Timeline: September - December 2022
Keywords: Usability, MFA, Password Management, Human Factors
Link: A Usability Approach to The Authentication Problem

Cybersecurity of Critical Infrastructure

The U.S. government has adopted a voluntary, nonregulatory, incentive-based framework for protecting the various critical infrastructure sectors. This has led to a jumble of incentives and a general lack of legislation. I this paper, I lay out an agenda for increasing adoption of the NIST Cybersecurity Framework and expanding the role of the CISA information sharing program while taking into account the economic, social, and moral incentives at play. I also advocate for a reassessment of the definition for “commercial information technology product”.

Timeline: September - December 2022
Keywords: Critical Infrastructure, NIST Cybersecurity Framework, CISA, Law
Link: An Agenda for Improving the Cybersecurity of Critical Infrastructure

Diffie-Hellman Key Exchange

The seminal 1976 paper New Directions in Cryptography by Whitfield Diffie and Martin Hellman laid out the foundation for public-key cryptography. This collaborative paper examines the mathematics behind the Diffie-Hellman Key Exchange. We provide an algebraic background to the discrete logarithm problem and a concrete example of the algorithm in action. Additionally, we discuss computational difficulties in implementing it and explain how the Binary Exponential Algorithm solves these problems.

Timeline: January - May 2021
Keywords: Key-exchange, Discrete Logarithm, Binary Exponential Algorithm
Link: The Diffie-Hellman Key Exchange