Seminario: "How to build a homomorphic encryption scheme using lattices, from scratch" - Lorenzo Rovida
Seminario della serie "Seminari CrypTO", in collaborazione con Telsy SpA, centro di competenza in crittografia e cybersecurity del Gruppo TIM che opera nel perimetro di TIM Enterprise
"How to build a homomorphic encryption scheme using lattices, from scratch"
Lorenzo Rovida
Università di Milano-Bicocca
Martedì 23 Settembre 2025 - ore 11:30
Aula Seminari - Dipartimento di Scienze Matematiche
Politecnico di Torino
Abstract: 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 Zn.
