International Seminar on Automorphic Forms

Radu Toma ( Institut de mathémathiques de Jussieu): Refined equidistribution of Hecke points and cryptography

A classic theorem states that, fixing a Euclidean lattice L, its sublattices 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. Motivated by lattice-based cryptography, we apply the result to show that a computational problem called SIVP is as hard for Haar random module lattices as it is in the worst case.

https://tu-darmstadt.zoom.us/j/68048280736

The password is the first Fourier coefficient of the modular j-function (as digits)