Dense and smooth lattices in any genusMPIM

by Wessel van Woerden (University of Bordeaux)

Thursday Dec 5, 2024, 3:00 PM → 4:00 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

https://www.mpim-bonn.mpg.de/node/13685 

MPI-Oberseminar and Conference on "The Mathematics of Post-Quantum Cryptography"

 

The Lattice Isomorphism Problem (LIP) was recently introduced as a new hardness assumption for post-quantum cryptography. The strongest known efficiently computable invariant for LIP is the genus of a lattice. To instantiate LIP-based schemes one often requires the existence of a lattice that (1) lies in some fixed genus, and (2) has some good geometric properties such as a high packing density or a small smoothness parameter.

In this talk I will show that such lattices exist. In particular, building upon classical results by Siegel (1935), we will see that essentially any genus contains a lattice with a close to optimal packing density, smoothing parameter and covering radius.