# Current

The seminar is held on Tuesdays from 10 to 11 and is organized by Razvan Barbulescu and Wessel van Woerden. When on site, it takes place in room 2 of IMB. To get announcements, you can subscribe to the lfant-seminar mailing list.- 2023-03-2810:00Salle 2Shane Gibbons (CWI, Netherlands)Hull attacks on the Lattice Isomorphism Problem
The lattice isomorphism problem (LIP) asks one to find an isometry between two lattices. It has recently been proposed as a foundation for cryptography in independent works. This problem is the lattice variant of the code equivalence problem, on which the notion of the hull of a code can lead to devastating attacks. In this talk I will present the cryptanalytic role of an adaptation of the hull to the lattice setting, which we call the s-hull. Specifically, we show that the hull can be helpful for geometric attacks, for certain lattices the minimal distance of the hull is relatively smaller than that of the original lattice, and this can be exploited. The attack cost remains exponential, but the constant in the exponent is halved.

Our results suggests that one should be very considerate about the geometry of hulls when instantiating LIP for cryptography. They also point to unimodular lattices as attractive options, as they are equal to their own hulls. Remarkably, this is already the case in proposed instantiations, namely the trivial lattice $\mathbb{Z}^n$ and the Barnes-Wall lattices. - 2023-04-0410:00Salle 2Jean Gillibert (Université de Toulouse 2)Finite subgroups of $\mathrm{PGL}_2(\mathbb{Q})$ and number fields with large class groups
For each finite subgroup $G$ of $\mathrm{PGL}_2(\mathbb{Q})$, and for each integer $n$ coprime to $6$, we construct explicitly infinitely many Galois extensions of $\mathbb{Q}$ with group $G$ and whose ideal class group has $n$-rank at least $\#G-1$. This gives new $n$-rank records for class groups of number fields.

- 2023-04-1110:00Salle 2Henry Bambury (ENS Ulm)An inverse problem for isogeny volcanoes
Supersingular isogeny graphs are very complicated and intricate, and are used extensively by cryptographers. On the other side of things, the structure of ordinary isogeny graphs is well understood connected components look like volcanoes. Throughout this talk we will explore the ordinary $\ell$-isogeny graph over $\mathbb{F}_p$ for various prime numbers $\ell$ and $p$, and answer the following question, given a volcano-shaped graph, can we always find an isogeny graph in which our volcano lives as a connected component?

- 2023-04-2510:00zoom 839 4179 5223 retransmited in room 2Alessandro Languasco (University of Padova, Italy)Computing $L'(1,\chi)/L(1,\chi)$ using special functions, their reflection formulae and the Fast Fourier Transform
We will show how to combine the Fast Fourier Transform algorithm with the reflection formulae of the special functions involved in the computation of the values of $L(1,\chi)$ and $L’(1,\chi)$, where $\chi$ runs over the Dirichlet characters modulo an odd prime number $q$. In this way, we will be able to reduce the memory requirements and to improve the computational cost of the whole procedure.

Several applications to number-theoretic problems will be mentioned, like the study of the distribution of the Euler-Kronecker constants for the cyclotomic field and its subfields, the behaviour of $\min_{\chi\ne \chi_0} | L’(1,\chi)/L(1,\chi) |$, the study of the Kummer ratio for the first factor of the class number of the cyclotomic field and the ``Landau vs. Ramanujan’’ problem for divisor sums and coefficients of cusp forms.

Towards the end of the seminar we will tackle open problems both of theoretical and implementative nature. - 2023-05-0210:00Salle 2Sorina Ionica (Université de Picardie)TBA
- 2023-05-0910:00Salle 2Sabrina Kunzweiler (IMB)TBA
- 2023-05-1610:00Salle 2Matthieu Lequesne (CWI, Netherlands)TBA
- 2023-05-2310:00Salle 2Boris Fuoutsa (EPFL, Switzerland)TBA
- 2023-05-3010:00Salle 2Sarah Arpin (University of Leinden, Netherlands)Adding Level Structure to Supersingular Elliptic Curve Isogeny Graphs
The classical Deuring correspondence provides a roadmap between supersingular elliptic curves and the maximal orders which are isomorphic to their endomorphism rings. Building on this idea, we add the information of a cyclic subgroup of prime order N to supersingular elliptic curves, and prove a generalisation of the Deuring correspondence for these objects. We also study the resulting ell-isogeny graphs supersingular elliptic curve with level-N structure, and the corresponding graphs in the realm of quaternion algebras. The structure of the supersingular elliptic curve ell-isogeny graph underlies the security of a new zero-knowledge proof of isogeny knowledge [Basso-Codogni-Connolly-De Feo-Fouotsa-Lido-Morrison-Panny-Patranabis-Wesolowski 2022].

- 2023-06-0610:00Salle 2Daan van Gent (University of Leinden, Netherlands)TBA
- 2023-06-1310:00Salle 2TBATBA
- 2023-06-2010:00Salle 2TBATBA
- 2023-06-2710:00Salle 2Agathe Houzelot (Labri)TBA