Isogeny based cryptography is based on computing isogenies among Abelian varieties. More isogenies an Abelian variety has the harder it is to "guess" another Abelian variety isogenous to the first one. So naturally one is interested on Abelian varieties with large endomorphism rings.  The most basic case is that of elliptic curves which gives rise to SIDH (Supersingular Isogeny Diffee Hellman) and SIKE (Supersingular Isogeny Key Exchange). SIKE was broken in the Summer 2022 by  glueing of two elliptic curves E_1 and E_2 into a genus 2 curve C and then checking if this genus 2 curve has (3,3)-split Jacobian. However, isogeny based cryptography is not dead and provides one of the most promising methods for post-quantum cryptography.

The goal of this conference is explore the isogeny based cryptography for Abelian varieties of dimension $\geq 1$.  One of the main reasons that it took over ten years to break SIKE was because there was a disconnect between cryptographers and mathematicians with expertise in the area.  The aim of this conference is to bring together mathematicians who are experts in the area of Abelian varieties and cryptographers who are focused on isogeny based cryptography. 

We expect all participants to be familiar with basic concepts of Abalian variaties and cryptography on the level of:

• Curves, Jacobians, and cryptography, G. Frey, T. Shaska, Contemp. Math, vol. 724,   AMS,  (2019), pg. 279--344

Topics 

While this is a conference focused on cryptography, other topics related to Abelian varieties are welcome: