Wouter Castryck

COSIC, KU Leuven

Introduction talk: Key recovery attack on the Supersingular Isogeny Diffie-Hellman protocol (3/3)

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Research talk: The isogeny interpolation problem

It is not hard to prove that a degree-d isogeny f between two elliptic curves E and E' is completely determined by the images of any 4d + 1 points. In this talk we will study the algorithmic problem of evaluating f at a given point P on E, merely upon input of such "interpolation data". The attacks on SIDH solve this problem in case the interpolation points generate a group containing E[N] such that N^2 > 4d is smooth and coprime to d and the field characteristic. But what about the general problem? We will explain how to get rid of many of these conditions, and also publicize some unsolved cases.

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Sabrina Kunzweiler

INRIA Bordeaux, Institut de mathématiques de Bordeaux

Introduction talk: Isogenies in higher dimension (2/3)

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Research talk: Computing modular polynomials

The techniques used in the SIDH attack have not only found applications in the design of new cryptographic protocols, but they also inspired new algorithms to solve number theoretical problems. This talk will focus on a novel algorithm for computing modular polynomials, which is based on the ideas from the attack and deformations. We will discuss a heuristic version of the algorithm which works with isogenies in dimension 2, and an unconditional version which requires working in dimension 8.

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Benjamin Wesolowski

Unité de Mathématiques pures et appliquées, ENS Lyon

Introduction talk: Isogeny-based cryptography (1/3)

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Research talk: SQIsignHD

The algorithmic breakthrough underlying the attack on SIDH has rapidly found constructive applications. In this talk, we will illustrate the power of these new tools through SQIsignHD, a new post-quantum digital signature scheme inspired by SQISign. Exploiting the new machinery, SQIsignHD overcomes the main drawbacks of SQISign, improving its scalability, signing efficiency, and the security proof.

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