Homomorphic encryption (HE) schemes allow to perform computations over encrypted data, opening up endless applications in the world of cryptography. Most standard HE schemes are based on the hardness of the Learning with errors (LWE) problem and its structured variants (e.g., Ring-LWE). The latter can be seen as a lattice problem over a specific family of lattices, called q-ary lattices. In this talk we will first introduce lattices and their associated computational problems, then we will explore how these concepts are used to build a HE scheme, with a focus on BGV-like and GSW-like constructions. In particular, LWE provides a natural trapdoor for random q-ary lattices, but recently Leporati, Rovida and van Woerden (ePrint archive 2025/1171) proposed a generalization of some HE constructions under a lattice perspective, abstracting away from LWE. As a natural consequence, we will additionally sketch a construction of a BGV-like scheme based on the hardness of the Lattice Isomorphism Problem (LIP), which allows to instantiate a scheme over (a rotation of) the trivial lattice Z^n.

From: William Schober <william.schober@usi.ch>
Sent: Tuesday, September 2, 2025 9:34 AM
To: seminar-cqi@lists.usi.ch <seminar-cqi@lists.usi.ch>
Cc: Lorenzo Rovida <lorenzo.rovida@unimib.it>
Subject: [seminar-cqi] CQI Seminar: Lorenzo Rovida

Dear friends,

On Friday, the 5th of September at 10:30 in D5.01, Lorenzo Rovida will visit us to give a talk. Lorenzo is a PhD student in cryptography from L'Università degli Studi di Milano-Bicocca.

Best,

Will Schober