Research Day 2023: Friday, November 3

Dr. LeGrow will give a departmental colloquium at 4 pm, with a reception beginning at 3:30.

Title: Isogeny-Based Post-Quantum Cryptography

Abstract: Quantum computers threaten the security of digital communications. In particular, Shor’s algorithm for factoring and discrete logarithms render many ubiquitous cryptographic protocols insecure. To ensure that modern communication channels remain secure and reliable in a future with quantum adversaries, we must develop protocols which run on classical computers, but which are nonetheless resistant to attacks using quantum computers—these protocols are called post-quantum. Post-quantum cryptographic protocols can be classified by the nature of the hard computational problems that underlie their security—for instance, problems in lattice theory, coding theory, and the theory of elliptic curves have all been used to construct post-quantum schemes. In this talk we will introduce the mathematics of isogeny-based cryptography and discuss fundamental isogeny-based protocols, before diving into the Commutative Supersingular Isogeny Diffie-Hellman (CSIDH) framework and detailing some recently-addressed problems in this area. We will also see some open problems, avenues for future research, and connections with other branches of post-quantum cryptography.

*prerecorded talks