- Christina Boura (Université de Versailles-St Quentin)
Differential cryptanalysis : An old but still powerful technique Slides
Differential cryptanalysis, introduced in 1990 by Biham and Shamir, is a powerful cryptanalysis technique against symmetric primitives. It is based on the existence of an input difference that propagates through the different layers of the cipher to an output difference with high probability. Although the central idea of this technique is quite simple to understand, mounting an optimal differential attack against a given cipher is a highly non-trivial task. The difficulty is two-fold. First, finding good differentials and accurately estimating their probability is a difficult computational problem. Second, performing a key recovery based on the existence of a good differential is a hard optimization task. In this talk we will revisit the differential cryptanalysis technique and present recent advances for treating the two exposed problems.
Most of the the results that will be presented are joint work with Nicolas David, Patrick Derbez, Margot Funk, Rachelle Heim and María Naya-Plasencia.
- Alice Pellet-Mary (CNRS, Université de Bordeaux)
Lattices in cryptography: cryptanalysis, constructions and reductions Slides
In this talk, we will review different aspects of lattice-based cryptography. The first part of the talk will be dedicated to cryptanalysis. We will see (supposedly) hard lattice problems, such as the shortest vector problem, and discuss about algorithms that solve these problems (such as the LLL or the BKZ algorithms).
In a second part, we will see how one can construct a signature scheme based on the supposed hardness of the problems seen in the first part.
Finally, in the last part, we will focus on the following question: how do we generate a random lattice in which the shortest vector problem is hard with overwhelming probability?
- Damien Vergnaud (Sorbonne Université)
Calcul distribué « dans la tête » : techniques et applications Slides
Les preuves à divulgation nulle de connaissance permettent à un prouveur de convaincre un vérifieur de la validité d'une assertion mathématique sans révéler quoi que ce soit d'autre. Cette primitive se trouve au cœur de nombreux protocoles modernes de préservation de la vie privée et, de manière plus générale, joue un rôle essentiel en cryptographie. Le paradigme du calcul distribué « dans la tête », également connu sous le nom de MPC-in-the-head, a été introduit par Ishai, Kushilevitz, Ostrovsky et Sahai en 2007 et a suscité un intérêt important ces dernières années. Cette approche permet notamment de construire des protocoles de signature numérique efficaces dont la sécurité repose sur la difficulté de résoudre des problèmes algorithmiques variés (y compris par d'éventuels ordinateurs quantiques). Dans cet exposé, nous présenterons les principes théoriques de ce paradigme ainsi que plusieurs techniques récemment introduites pour en améliorer l’efficacité. Nous illustrerons ces techniques en explorant plusieurs applications en cryptographie post-quantique et anté-quantique.
- Gilles Zémor (Université de Bordeaux)
Recent constructions of asymptotically good quantum LDPC codes Slides
It is commonly thought that large-scale quantum computers
will require the use of quantum LDPC codes. Until relatively recently,
it was not known whether quantum LDPC codes with a minimum distance that
behave significantly better than the square root of the number of
qubits exist. The discovery of quantum LDPC codes with not only linear
distance but also non-vanishing rate was therefore quite a breakthrough.
We will discuss such a construction together with the relevant algebraic
tools, after presenting some background on quantum LDPC codes.
