# Current

The seminar is held on Tuesdays from 11 to 12 and is organised by Razvan Barbulescu and Wessel van Woerden. Unless otherwise stated it takes place in room 2 of IMB. To get announcements, you can subscribe to the mailing list of the Bordeaux number theory seminars. Last minute changes may appear first on the IMB website.

- 2024-02-2711:00Salle 2Pierre Briaud (Simula UiB)Variants of the Decoding Problem and algebraic cryptanalysisThe intractability of decoding generic linear codes is at the core of an important branch of post-quantum cryptography. In this context, the code is random by design or it is assumed to be so in the security reduction. This talk will focus on versions of the Decoding Problem where the error vector is structured, in general to achieve better performance. While combinatorial techniques such as Information Set Decoding are often the method of choice to attack these versions, I will describe the potential of algebraic algorithms. I will mostly consider the Regular Syndrome Decoding Problem and a paper presented at Eurocrypt 2023. I will also mention ongoing work on an assumption used in the CROSS submission to new call for signature schemes launched by NIST.
- 2024-03-0511:00Salle 2Yuri Bilu (IMB)Skolem meets SchanuelA linear recurrence of order r over a number field K is a map U:Z→K satisfying a relation of the form U(n+r)=a_{r−1}U(n)+⋯+a_0U(n)(n∈Z), where a_0,…,a_{r−1}∈K and a_0≠0. A linear recurrence is called simple if the characteristic polynomial X^r−a_{r−1}X^{r−1}−…−a_0 has only simple roots, and non-degenerate if λ/λ′ is not a root of unity for any two distinct roots λ,λ′ of the characteristic polynomial. The classical Theorem of Skolem-Mahler-Lech asserts that a non-degenerate linear recurrence may have at most finitely many zeros. However, all known proofs of this theorem are non-effective and do not produce any tool to determine the zeros. In this talk I will describe a simple algorithm that, when terminates, produces the rigorously certified list of zeros of a given simple linear recurrence. This algorithm always terminates subject to two celebrated conjectures: the p-adic Schanuel Conjecture, and the Exponential Local-Global Principle. We do not give any running time bound (even conditional to some conjectures), but the algorithm performs well in practice, and was implemented in the Skolem tool https://skolem.mpi-sws.org/ that I will demonstrate. This is a joint work with Florian Luca, Joris Nieuwveld, Joël Ouaknine, David Purser and James Worrell.
- 2024-03-1211:00Salle 2Olivier Ruatta (Université de Limoges)Polynômes linéarisés et cryptographie en métrique rang
- 2024-03-1911:00Salle 2Rocco Mora (CISPA)TBA
- 2024-03-2611:00Salle 2Bastien Pacifico (LIRMM, Université de Montpellier)TBA