Beginning Lecture Course
Toni Bluher, NSA, "Mathematics in Cryptography"
Abstract: This introductory course aims to convey the evolutionary nature of cryptography and the central role of mathematics in this story. Topics include substitution ciphers and how to defeat them, WWII cryptography, symmetric cryptography and electronic codebooks, authentication, public key cryptography, mathematical underpinnings of internet security, and the future.
Advanced Lecture Course
Kristin Lauter, Microsoft Research, "The Mathematics of Post-Quantum Cryptography"
Abstract: This course will cover some of the mathematics behind current proposals for Post-Quantum Cryptography (PQC). In 2017, the National Institute of Standards and Technology launched a multi-year international competition to select new post-quantum cryptographic systems, based on hard problems in mathematics for which there are no known polynomial time quantum algorithms. These lectures will cover some of the mathematics of lattice-based cryptography, code-based cryptography, homomorphic encryption, and Supersingular Isogeny Graphs, and will highlight some of the deep connections with number theory.