Lorenzo Rovida
Homomorphic Encryption from the Lattice Isomorphism Problem
Abstract:
Homomorphic encryption (HE) is a strong cryptographic primitive that enables computations on encrypted data.
Currently, the security of most HE schemes is based on the hardness of the Learning with Errors (LWE) problem. In this talk, we define the foundations to switch the problem underlying a HE cryptosystem from LWE to the Lattice Isomorphism Problem (LIP), and we will show how to apply this approach to construct two types of schemes: BGV and GSW.
This framework is flexible enough to support the instantiation over any lattice, and we show how to instantiate the schemes over (a rotation of) the Z^n lattice, as opposed to the random q-ary lattices used in LWE. This proposal might lead to a more secure (even against quantum adversaries), conceptually simpler perspective of HE.
This talk will introduce the topics of HE and lattice-based cryptography, and it will offer a high-level overview of how HE can be achieved through the lens of the LIP framework.
Short bio:
Lorenzo Rovida is a third year PhD student working in the field of security and, in particular, of homomorphic encryption and lattice-based cryptography.
Alessandro Riva
Geometric prior for transformers in non-rigid point cloud matching.
Abstract:
Current data-driven methodologies for point cloud matching demand extensive training time and computational resources, presenting significant challenges for model deployment and application.
Transformers have been applied to some 3D tasks with good results. However, the application of such architectures in the context of 3D data remains an open problem due to the lack of a sequential structure and, while a number of different solutions exist, a standard accepted procedure is missing.
In the point cloud matching task, recent advancements with an encoder-only Transformer architecture have revealed the emergence of semantically meaningful patterns in the attention heads, particularly resembling Gaussian functions centered on each point of the input shape.
In this talk some ideas about the use of these patterns as priors for the attention mechanism are presented.
Particular focus will be given to the unique challenges 3D data presents and how the additional information provided by these patterns can help address them with the aid of the Transformer architecture.
Short bio:
Alessandro Riva is a PhD student in computer science at the University of Milano-Bicocca. His main research fields are computer vision and graphics, focusing on the use of deep-learning methods to tackle the challenges of 3D data.
Alessandro obtained his master’s degree in computer science from the University of Milano-Bicocca in 2024, where he also received his bachelor’s degree.
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