Research
For my Ph.D., I worked with Dr. Ernest Stitzinger on the creation of undergraduate-accessible curriculum for Lattice based Cryptography.
Research Statement: The security of current Public Key Cryptosystems relies on the hardness of their underlying problems. For example, the RSA Cryptosystem relies on the hardness of integer factorization. There is currently not a way for a classical computer to find the prime factors in less than exponential time. However, Shor's algorithm factors integers on a quantum computer in polynomial time. Companies like IBM, Google, and Microsoft have invested billions into the research and development of quantum computers, racing to achieve quantum supremacy. This gives rise to a need for quantum-safe cryptosystems, and constructions based on integer lattices are proving promising.
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The vast majority of university Cryptography courses are housed in graduate programs and assume prior computer programming knowledge. I assert that this content is accessible to undergraduate students who have taken a course in Linear Algebra. The goal of this course is to make introductory lattice-based cryptography accessible to undergraduate students in mathematics, computer science, engineering, and other related fields. By engaging students with the theoretical and practical applications of modern cryptographic algorithms, students will be prepared to enter careers in related fields upon graduation.
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Research Projects: I hope to facilitate undergraduate and graduate research in the area of post-quantum Mathematical Cryptography. In this document, please find potential student research projects.
Student Research Projects
Below, you will find a brief description of the research projects that I have facilitated with undergraduate students at the University of Notre Dame over the last two years.
Jack O'Sullivan
Summer 2023
Jack implemented the NTRUEncrypt Cryptosystem in Python and theoretically analyzed the known and potential attacks on the cryptosytem to make a conclusion about its security.
Emma Luchetti
Fall 2023
Emma studied homomorphic encryption, implementing various cryptosystems in Python and SageMath. She also analyzed the potential for homomorphic encryption in the post-quantum world.
Lina McKimson
Fall 2023
Lina looked mostly at code-based encryption, implementing some cryptosystems and known attacks in SageMath. In particular, she studied the McEliece Cryptosystem and analyzed its security for post quantum cryptography.
Kevin Dougherty
Fall 2023
Kevin began with no exposure to cryptography. He started with the RSA Cryptosystem and worked his way through the NTRUEncrypyt System. He implemented all systems in Python and analyzed the mathematical background of them.
Alberto Garza
Fall 2023
Similar to Kevin, Alberto had no background in cryptography. He began by studying some pre-quantum cryptosystems and implementing them in Python. He also looked at some potential attacks of the systems.
Alberto Garza
Summer 2024
Alberto is continuing his work in cryptography this summer. He will be implementing the NTRUEncrypt and the CRYSTALS-Kyber Cyrptosystems in Python and analyzing their security by studying known and potential attacks on the systems.