I spent the past academic year studying integer lattices for my honors thesis. I dove into this study with little idea of what I wanted to accomplish other than to gain a better understanding of lattice cryptography, which is a member of the increasingly relevant family called quantum cryptography or post-quantum cryptography. I ended up focusing on the mathematical underpinnings of basis reduction algorithms. These algorithms are used for breaking lattice cryptosystems.
I hope that I have met my goal of making this paper accessible to anyone who has taken linear algebra. Here is the paper for your reading pleasure in all its mathematical rigor, and here is my more high-level talk at the Colby Liberal Arts Symposium 2019.