Description
Nous verrons comment certifier algorithmiquement des calculs de représentations galoisiennes associés à des formes modulaires, en nous appuyant notamment sur le théorème de Khare-Wintenberger (ex conjecture de modularité de Serre) et des calculs de cohomologie des groupes afin de déterminer le groupe de Galois de certains polynômes.
Prochains exposés
-
Attacking the Supersingular Isogeny Problem: From the Delfs–Galbraith algorithm to oriented graphs
Orateur : Arthur Herlédan Le Merdy - COSIC, KU Leuven
The threat of quantum computers motivates the introduction of new hard problems for cryptography.One promising candidate is the Isogeny problem: given two elliptic curves, compute a “nice’’ map between them, called an isogeny.In this talk, we study classical attacks on this problem, specialised to supersingular elliptic curves, on which the security of current isogeny-based cryptography relies. In[…]-
Cryptography
-
-
Verification of Rust Cryptographic Implementations with Aeneas
Orateur : Aymeric Fromherz - Inria
From secure communications to online banking, cryptography is the cornerstone of most modern secure applications. Unfortunately, cryptographic design and implementation is notoriously error-prone, with a long history of design flaws, implementation bugs, and high-profile attacks. To address this issue, several projects proposed the use of formal verification techniques to statically ensure the[…] -
Endomorphisms via Splittings
Orateur : Min-Yi Shen - No Affiliation
One of the fundamental hardness assumptions underlying isogeny-based cryptography is the problem of finding a non-trivial endomorphism of a given supersingular elliptic curve. In this talk, we show that the problem is related to the problem of finding a splitting of a principally polarised superspecial abelian surface. In particular, we provide formal security reductions and a proof-of-concept[…]-
Cryptography
-