A large enough quantum computer will break most of the currently deployed public-key cryptography, like RSA or elliptic curve cryptography. To prepare for this, NIST is running a public process to evaluate and standardize one or more of several proposed 'post-quantum' cryptosystems. These cryptosystems are thought to be secure even against an adversary with a quantum computer. One proposal, SIKE, bases its security on the hardness of computing isogenies between supersingular elliptic curves. In this expository talk, I will give a brief introduction to elliptic curve cryptography and to isogeny-based cryptography. Time permitting, I will discuss the security of isogeny based cryptography and how it relates to the problem of computing endomorphism rings of supersingular elliptic curves, and sketch a new algorithm for computing these endomorphism rings. This is joint work with Eisentraeger, Hallgren, Leonardi, and Park.
Before the talk, at 4:10pm, there will be tea and cookies in Wean 6220.
The ACO Seminar (2019–2020)