Radu Toma

Automorphic forms in cryptography

I will give a broad overview of how Hecke operators have found applications in the world of cryptography, particularly in lattice-based cryptography. One of the main problems one encounters is: given any lattice, how random does a sublattice of large index look? To answer this so-called equidistribution question, uniformly in all parameters, we can use some geometry of numbers and powerful techniques from the theory of automorphic forms, which I will sketch out. An application of this to cryptanalysis is part of joint work with de Boer, Page and Wesolowski.