CIFRIS24 - an event by De Cifris

Venue: Banca d'Italia, Centro D. Menichella, Largo Guido Carli 1, Frascati (Roma)
Social dinner: September 25th, Satiricus, Via dei Corridori 58, Roma
September 25th, 26th, 27th 2024

CodeMath24 - Coding Theory and Discrete Mathematics 2024

Organizers

Massimo Giulietti (Università degli Studi di Perugia, Italy)
Giuseppe Marino (Università degli studi di Napoli Federico II, Italy)
Olga Polverino (Università degli Studi della Campania “Luigi Vanvitelli”, Italy)
Ferdinando Zullo (Università degli Studi della Campania “Luigi Vanvitelli”, Italy)

Description

The aim of the workshop is to create a collaborative environment that promotes research and innovation in these fields, to facilitate networking opportunities for participants to engage with peers, industry experts, and researchers, and to showcase the practical applications of coding theory and discrete mathematics in areas such as error correction and cryptography.
Subjects of interest for the Workshop will be: Algebraic Foundations of Coding theory (Finite fields, Polynomial algebras, Algebraic Varieties and their applications in coding), Advanced Topics in Coding Theory (such as turbo codes and LDPC codes; network coding and its applications; quantum error correction), Cryptography and its relation to Coding theory and Finite Geometry, Current trends and challenges in coding theory and discrete mathematics.

Program

September 27th, workshop session
Room C, 11:20 - 13:00

Invited speaker: Gilles Zémor, Institut de Mathématiques de Bordeaux (France)

September 27th (morning) - Workshop Session
11:40 12:00	Gilles Zémor, Institut de Mathématiques de Bordeaux (France) Hadamard products of codes: an Additive Combinatorics perspective Abstract The Hadamard (or Schur) product of two linear codes C and D is the linear code generated by all coordinate-wise products of a codeword of C with a codeword of D. Code products that have an unusually small dimension have found numerous applications in coding theory and beyond: they are relevant to algebraic decoding, to cryptanalysis of code-based cryptosystems, to secret-sharing for multiparty computation and many other topics. There is a strong connection between structural results for code products of small dimension and theorems of Additive Combinatorics that characterise sets of elements of an abelian group with small sumsets. We will highlight part of this correspondence, with emphasis on Kneser's Addition Theorem, and give some applications.
12:00 12:20	Daniele Bartoli, Università degli Studi di Perugia (Italy) Recent results on scattered spaces and MRD codes Abstract Linear sets have numerous applications in various areas of mathematics, in- cluding finite geometry and coding theory. In particular, scattered linear sets are of special interest due to their unique properties and the role they play in these fields. One of the most effective methods to describe and analyze these scattered linear sets is through the use of linearized polynomials that are particularly useful because they allow us to leverage techniques from both algebraic geom- etry and group theory. By employing these techniques, one can gain deeper insights into the properties of scattered linear sets and their applications. In this talk, I will present recent advances in the study of exceptional scattered polynomials and their generalizations (scattered sequences). Furthermore, I will explore the connection between these concepts and maximum rank distance (MRD) codes.
12:20 12:40	Luca Giuzzi, Università degli Studi di Brescia (Italy) Cryptographic uses of (polar) Grassmannians Abstract Embeddings of (polar) Grassmannians determine error correcting codes with high length and nice minimum distance. In this talk we shall propose the use of punctured Grassmann codes in a McEliece-like cryptosystem. The security of the scheme is based on hiding from potential attackers the point-line structure of the geometry of the Grassmannian, as this structure is essential in order to provide efficient decoding algorithms. This is a Joint work with Ilaria Cardinali.
12:40 13:00	Violetta Weger, Technical University of Munich (Germany) CROSS: a signature scheme with restricted errors Abstract The additional call for signature schemes by NIST has shifted the focus of the cryptographic community considerably. One of the main strategies to construct code-based signatures is through Zero-Knowledge (ZK) protocols. This strategy has been deemed impractical for many years due to the large resulting sizes. This size is dominated by the linear transitive maps on the set of possible secret keys and by the number of rounds. Several proposals to NIST thus change the ZK protocol and employ Multi-Party Computations. This approach reduces the number of rounds and in turn the signature sizes. However, this comes at the cost of a slower scheme. CROSS is using a different solution: instead of changing the ZK protocol, we change the underlying problem. In this talk I will introduce restricted errors, and the Restricted Syndrome Decoding Problem used in CROSS. We will explore the mathematical properties of restricted errors and show that they are perfectly suited for code-based ZK protocols as they achieve the theoretical minimum in communication costs.