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  • Le 11 mai 2021 à 10:00
  • Séminaire de Théorie Algorithmique des Nombres
    Online
    Weiqiang Wen (Inria Rennes, Irisa)
    On algorithms for solving Euclidean lattice problems in cryptography

    In this talk, we will try to review the state-of-the-art of the algorithms for solving the Euclidean lattice problems underlying cryptography. In more details, this talk contains two parts. In the first part, we will focus on the lattice problems such as approximate Shortest Vector Problem (approx-SVP) and the lattice reduction algorithms as the best known solving algorithms so far. In particular, I will present an improved enumeration-based lattice reduction algorithm, which is shown to be (potentially) relevant to cryptanalysis. In the second part, we will instead consider a quantum problem that is computationally equivalent to approx-SVP. By directly solving a quantum problem, we may expect to have a more powerful use of the quantum computation. However, the best known algorithms for solving approx-SVP via solving this quantum problem, is not better than lattice reduction yet.


  • Le 11 mai 2021 à 15:00
  • Séminaire de Physique Mathématique - EDP
    Salle de Conférences
    Bilbao-Bordeaux-Toulouse Seminar: Eugenia Malinnikova (Stanford and St-Petersbourg)
    On Dirichlet Laplace eigenfunctions in Lipschitz domains with small Lipschitz constant
    We consider bounded domains in the Euclidean space with Lipschitz boundary and locally small Lipschitz constant. We proof the sharp upper bound for the area of the nodal sets of Dirichlet Laplace eigenfunctions in such domains. One of our tools is the analysis of the frequency function of a harmonic function vanishing on a part of the boundary.The talk is based on a joint work with A. Logunov, N. Nadirashvili, and F. Nazarov.

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