Fast computation of higher dimensional isogenies for cryptographic applications

par Pierrick Dartois

jeudi 21 nov. 2024, 14:00 → 15:00 Europe/Paris

The search for compact quantum resistant cryptographic schemes made isogeny-based cryptography relevant. Before 2022, most practical cryptographic applications used elliptic curve isogenies and isogenies between higher dimensional abelian varieties were deemed inefficient. However, attacks against the isogeny-based scheme SIDH using isogenies of dimension 2, 4 (or 8) and a result due to Ernst Kani completely shifted this paradigm. This attack quickly became a constructive tool. Ever since, higher dimensional isogenies have been widely used in isogeny based cryptography.

 

This motivated the search for fast algorithms to compute these higher dimensional isogenies. In this talk, we present recent algorithms to compute chains of 2-isogenies with level 2 theta coordinates between abelian varieties of any dimension. Our implementation of these algorithms in dimensions 2 and 4 show encouraging results which are already leveraged by recent cryptographic protocols.