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.

Tuesday 16 12 2025 at 15:00

Speaker: Giulia Cavicchioni (German Aerospace Center DLR)

Title: Information Set Decoding for Ring-Linear Codes

Abstract: Decoding a random linear code is a computationally hard problem and is considered  one of the main problems in coding theory. Because of this,  it is the basis of many code-based cryptosystems. One of the families of decoders used to solve this problem is Information Set Decoding (ISD), which is a set of generic algorithms that can be applied to decode any input code. An ISD algorithm can recover the message from a corrupted codeword or identify the error vector. ISD Decoding algorithms still  represent the main method for decoding random linear codes in the Hamming metric, especially when the problem has only a small number of solutions. In this talk, we discuss the behavior of ISD algorithms in the not-so-well-studied regimes of codes the over integer residue ring Z/p^sZ equipped with the Hamming, Lee and Rank metric. In this framework, ISD algorithms can adapt to the underlying structure and exploit it to their advantage to obtain significantly lower complexity. In particular, projecting the instance of the problem over the base field Z/pZ  and then tracing it back to a solution over Z/p^sZ is more efficient than applying ISD to the original instance directly.

Thursday 20 11 2025 at 15:00

Speaker: Sebastian Bitzer (Technical University of Munich)

Title: Honey, I Shrunk the Ciphertext: Compressing HQC 

Abstract: The code-based KEM Hamming Quasi-Cyclic (HQC), recently selected by NIST for standardization, does not employ ciphertext compression — a standard post-processing step in lattice-based schemes. In this talk, we address this gap by developing techniques to reduce ciphertext sizes in schemes defined over the Hamming metric. Building on a generalized decryption failure rate (DFR) analysis, we introduce two ciphertext compression mechanisms that are transparent with respect to security. For HQC parameters from the round-4 submission, these techniques reduce HQC ciphertext sizes by up to 4.3% without noticeable efficiency loss. Reductions of up to 10% are achievable through a trade-off with public-key size.

Joint work with Jean-Christophe Deneuville, Emma Munisamy, Bharath Purtipli, Stefan Ritterhoff, and Antonia Wachter-Zeh.

Thursday 30 10 2025 at 15:00

Speaker: Anurag Bishnoi (TU Delft)

Title: The trifference problem and its variations  

Abstract: What is the largest possible size T(n) of a family of ternary strings of length n such that among any three strings there is a coordinate where they take three distinct symbols? This is the famous trifference problem from information theory, introduced in the 1970s. Despite considerable effort, the exact value remains unknown; the best bounds are roughly 1.158^n < T(n) < 1.5^n. In this talk, we discuss the linear version of the problem, where we have recently obtained improved upper bounds together with lower bounds that match the non-linear version. We also present new connections between the linear trifference problem, minimal codes, and strong blocking sets, and we outline further generalizations.  

Monday 22 09 2025 at 15:00

Speaker: Andrea Sanguineti (Università di Genova)

Title: Algebraic modelings of the Supersingular Isogeny Problem

Abstract: We construct algebraic models for the Supersingular Isogeny Problem, for isogenies of degree powers of 2 and 3, using modular polynomials and explicit formulae from the works of Burdges, DeFeo, Renes, Costello, and Hisil. These constructions yield multivariate polynomial systems which we study through tools from computational algebra, including Gröbner bases and related techniques in commutative algebra. We further present experimental results that estimate the maximum step degree observed during the solution process, providing insight into the complexity and feasibility of solving these systems in practice. 

This is an ongoing joint work with Alessio Caminata (Università di Genova) and Silvia Sconza (University of Zurich).

Tuesday 24 06 2025 at 15:00

Speaker: Andrea Gangemi (Politecnico di Torino)

Title: Advances in Non-Interactive Commitments from Cryptographic Group Actions

Abstract: We present recent advances in non-interactive commitment schemes starting from group actions. D’Alconzo, Flamini, and Gangemi (ASIACRYPT 2023) initiate this line of work by proposing a commitment scheme based on non-transitive group actions, using tensor rank as an orbit invariant. Their construction achieves computational hiding, perfect binding, and introduces a novel linkability property. Later, Gilchrist et al. (CRYPTO 2024) demonstrate that this scheme is vulnerable: by exploiting low-rank structure in special orbits, they break the hiding property. They then repair the scheme by moving to the general Tensor Isomorphism Problem, which eliminates the exploitable structure and restores security. Building on these foundations, Jiang et al. (EUROCRYPT 2025) introduce a novel commitment framework called Re-randomize and Extract. They show how these techniques can significantly facilitate the construction of commitment schemes, providing a flexible framework for constructing either perfectly hiding or perfectly binding commitments, depending on the type of extractor involved. Their construction is then instantiated using lattice-based group actions. This framework not only generalizes prior tensor-based approaches but also supports more versatile commitment functionalities.

Wednesday 14 05 2025 at 15:00

Speaker: Flavio Salizzoni (Max Planck Institute for Mathematics in the Sciences, Leipzig (MIS))

Title: Combinatorial objects in coding theory

Abstract: 

In this talk, we will focus on a combinatorial object, called latroid, which simultaneously generalizes the concepts of matroid, q-matroid, and q-polymatorid. After a brief introduction on these topics, we will see how the classical invariants of linear codes can be recovered from the Tutte polynomial of the associated latroid, even in the case of codes over rings. In particular, we show that it determines the weight distribution of the code under suitable assumptions.

This talk is based on a joint work with Elisa Gorla.

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

Rocco Mora - CISPA (Helmholtz Center for Information Security) - Chair

Paolo Santini - Università Politecnica delle Marche - Chair

Chiara Castello -  Università degli Studi della Campania "Luigi Vanvitelli"

Federico di Concilio - Università degli Studi di Salerno

Rosa Fera - Università degli Studi di Cassino e del Lazio Meridionale

Giovanni Giuseppe Grimaldi - Università degli Studi di Perugia

Giovanni Longobardi - Università degli studi di Napoli "Federico II"

Paolo Santonastaso - Politecnico di Bari

Valentino Smaldore - Università degli Studi di Padova

Martina Vigorito - Università degli Studi di Salerno

Irene Villa - Università degli Studi di Trento

In collaboration with:

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"