Number Theory Seminar: Radu Toma

Title: Hecke operators and equidistribution in post-quantum cryptography

Speaker: Radu Toma (Jussieu, Paris, France)

Abstract: Fix a Euclidean lattice L. A classic theorem, often called the equidistribution of Hecke points, states that the sublattices of L of large index equidistribute in the space of lattices. The literature leaves open the question: how does the rate of equidistribution depend on L? In joint work with de Boer, Page, and Wesolowski, we answer this using automorphic theory and geometry of numbers. We then apply this result to a problem motivated by lattice-based cryptography: we show that the computational problem SIVP is as hard for Haar random module lattices as it is in the worst case.