Online seminars
These seminars provide a platform for members of the UMI Crittografia e Codici group to share insights and ideas on the mathematical aspects of cryptography and coding theory. They facilitate collaboration, innovation, and the exchange of cutting-edge research within the field, fostering interdisciplinary connections and advancing our understanding of these areas.
Thursday 27 06 2024 at 17:00
Speaker: Albert Garreta (Basque Center of Applied Mathematics (BCAM) and Nethermind)
Title: New narratives in the zk space: commitments, lookups, and folding
Abstract:
I will present an overview of the main driving narratives in the area of zk-proofs from the past couple years, providing an introduction to the most relevant topics along the way. I will also outline some of our contributions on these topics.
Monday 27 05 2024 at 17:00
Speaker: Giovanni Longobardi (Università degli Studi di Napoli Federico II)
Title: On the vertices of maximum scattered linear sets of PG(1,q^n) and MRD codes
Abstract:
It is known that every linear set of the projective space is either a subgeometry or a projection of a subgeometry [G. Lunardon, O. Polverino: Translation ovoids of orthogonal polar spaces, Forum Math. 16 (2004) 663-669]. In the last years, it was described how the properties of the projection vertex reflect in those of the linear set, especially with regard to those contained in the projective line PG(1, q^n). If n is less or equal than 4, this approach led to a complete classification of them.
In this talk, I will give an overview of what has been done so far in this direction, I will show a recently developed method to reconstruct a projecting vertex for a class of linear sets of rank n(r-1) in PG(r-1,q^n) and some geometrical characterization of the families of maximum scattered linear sets of the projective line PG(1,q^n) introduced from 2018 onward. Moreover, using various techniques borrowed from linear algebra, projective geometry, algebraic geometry over finite fields, I will provide a classification result for scattered linear sets of maximum size in PG(1,q^5).
Finally, I will stress the implications of the above mentioned results for a class of maximum rank distance codes (MRD for short) with length n and minimum distance n-1.
This is a joint work with G.G. Grimaldi, S. Gupta, S. Lia, R. Trombetti and C. Zanella.
Wednesday 18 04 2024 at 16:30
Speaker: María Isabel González Vasco (Universidad Carlos III de Madrid)
Title: Q-Alice and C-Bob need to talk
Abstract:
Advances in quantum computation have led to the development of numerous cryptographic tools that are potentially robust to attacks implemented with quantum hardware. These constructions, called post-quantum tools, are implemented using classical technology and their security is proved using standard security models.
On the other hand, cryptographic constructions built exploiting the potential of quantum technology are built and formalized in a very different way. For instance, for the case of key exchange schemes, the "classical" established security models are not useful for analysing the security of so-called QKD (Quantum Key Distribution) schemes. While there have been proposals for new security models in this scenario, the situation for which several (more than two) users interact, and, moreover, some of these users use quantum technology while others are essentially classical has hardly been investigated.
In this talk, we will present the formal challenges we face in evaluating this such "hybrid" constructions, and discuss the kind of solutions we are developing in the framework of a project funded by NATO's Science for Peace and Security programme.
Organizers
Daniele Bartoli (Università degli Studi di Perugia)
Michela Ceria (Politecnico di Bari)
Marialaura Noce (Università degli Studi di Salerno)
Marco Timpanella (Università degli Studi di Perugia)
Ferdinando Zullo (Università degli Studi della Campania "Luigi Vanvitelli")