Current Topics in Lattice-Based Cryptography, Math Club 10/17/2025, Julia VanLandingham speaking.

This is a very interesting (and "hot off the presses") talk about some research in lattice-based cryptography. The talk begins with some history of the subject and then gets into a nice overview of lattice-based cryptography. It builds to the climax of introducing some new research directions that are being explored as we speak. The original abstract is below. --------------------------------------------- While means of encryption date back thousands of years, mathematical algorithms used by modern systems are shockingly recent. We will explore some of these modern systems, recent changes in cryptography, and an avenue of ongoing research. We will mainly feature lattice-based cryptography, but no prior knowledge of cryptography or lattices is required.