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

SymCrypt24 - Symmetric Cryptography and Boolean functions 2024

Organizers

Marco Calderini (University of Trento, Italy)
George Petrides (University of Cyprus, Cyprus)
Irene Villa (University of Genoa & University of Trento, Italy)

Description

The workshop will be in two interrelated areas. The first one concerns different aspects of symmetric cryptography, such as the design of symmetric ciphers, attacks to these ciphers, as well as countermeasures. The second topic of interest is the theory of Boolean functions applied in cryptography scenarios, particularly in the design of symmetric ciphers. Such functions have found applications as S-boxes of block ciphers and feedback functions in stream ciphers, and the workshop will be focusing on their relevant cryptographic properties, their classification, and construction methods.

Program

September 27th, workshop session
Room C, 10:00 - 11:20

Invited speaker: Sihem Mesnager, University of Paris VIII (France)

September 27th (morning) - Workshop Session
10:00 10:20	Roberto La Scala, University of Bari (Italy) Stream ciphers encoded by difference equations over finite fields and their cryptanalysis Abstract Many stream ciphers of practical interest, such as Trivium and Bluetooth's E0, can be modeled as systems of explicit ordinary difference equations with coefficients and solutions in a finite field. These systems govern the evolution of the internal registers of these so-called "difference ciphers" over discrete time. By leveraging the formalism of difference equations, it is possible to define critical properties of stream ciphers, such as invertibility and periodicity, which are essential for assessing their security. This modeling, coupled with the corresponding cryptanalysis, actively supports the development of new ciphers.
10:20 10:40	Luca Mariot, University of Twente (Netherlands) On the computation of the Walsh-Hadamard Transform using Binomial Trees Abstract In this talk, we investigate a new approach to compute the Walsh- Hadamard transform. The main data structure underlying this method is a binomial tree, where the path back to the root of each node represents a Walsh-Hadamard coefficient, and inductively defines the related scalar prod- uct. We show that the Walsh-Hadamard transform is obtained by visiting such a binomial tree, and consider both a depth-first and a breadth-first search strategy to perform this task. Although the resulting algorithms yield the same O(2^2n ) time complexity of the naive Walsh-Hadamard transform, we experimentally observe that they are faster in practice. We then show how to adapt the BFS-based algorithm to check a Boolean function’s correlation immunity order by requiring only its support as an input. Interestingly, this modified algorithm gives an efficient way to check whether a binary matrix of a large number of columns is an orthogonal array. Such a task cannot be practically accomplished with the Fast Walsh-Hadamard Transform proce- dure, due to the amount of memory required to hold the truth table of the associated Boolean function.
10:40 11:15	Sihem Mesnager, University of Paris VIII (France) (Cryptographic) Functions for Designing Locally Recoverable Codes in Distributed Storage Abstract There is a crucial need for highly scalable and reliable extensive data storage systems due to the rapid growth in data. Distributed storage systems (DSSs) store data on multiple distributed nodes and are widely used in file system storage, ample database storage, backup files, cloud storage, and more. The repair problem in DSSs is a key focus area. Lately, there has been a notable increase in interest and focus on Locally Recoverable Codes (LRCs), highlighting their growing importance in distributed storage systems. In this talk, we will explore function-based codes and present mathematical techniques for creating (optimal) LRC codes from functions and polynomials. Notably, we emphasize the significant role of specific cryptographic functions in the design of LRCs.
11:15 11:20	Closing remarks on SymCrypt24