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Séminaire de Théorie Algorithmique des Nombres

Dense and smooth lattices in any genus

Wessel van Woerden

( PQShield )

Salle 2

13 mai 2025 à 11:00

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.