Computing isogenies through graph theory: faster, simpler, broader

par Max Duparc

jeudi 22 oct. 2026, 14:00 → 19:00 Europe/Paris

The death of SIDH in 2022 has propelled higher dimensional isogenies to the forefront of research in isogeny based cryptography. In 2026, they are a key part of most major cryptographic schemes of the field (SQIsign, MIKE, POKÉ, qt-Pegasis,…). Implementing such schemes thus requires methods to compute isogenies between abelian varieties that are fast and sound.  
In this talk, we will show that, thanks to the theta model, we can cast the problem of computing 2-isogenies as graph theory problems. This point of view is a powerful one, as it naturally provides the simplest and fastest isogeny formulae. Additionally, we will show how this method can be extended to isogenies between special varieties (Scholten, Weil-type), leading to further speedups.   

This presentation is based on:
[1] Chasing Rabbits Through Hypercubes: Better algorithms for higher dimensional 2-isogeny computations, with Pierrick Dartois
[2] MIKE: a fast and compact post-quantum NIKE, with the MIKE team