Advanced Research Workshop : Isogeny based post-quantum cryptography,
Directors Tony Shaska, Shaul Zemel
Program Committee R. Donagi, R. Livne, T. Shaska, S. Zemel
Motivation
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 (n,n)-split Jacobian. However, isogeny based cryptography is not dead and other approaches are explored.
The goal of this conference is explore the isogeny based cryptography for Abelian varieties of dimension >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 workshop is to bring together mathematicians who are experts in the area of Abelian varieties and cryptographers who are focused on isogeny based cryptography.Â
TopicsÂ
While this is a conference focused on cryptography, other topics related to Abelian varieties are welcome:
Endomorphisms and isogenies of Abelian varietiesÂ
Isogenies and correspondencies
Genus 2 and genus 3 cryptography, including implementations
Galois properties of torsion points, Tate modules
Heights, weighted moduli heights
Height bounds and height conjectures
Zeta functions of algebraic varieties
Hyperelliptic/superelliptic Jacobians, and their endomorphism rings
Computing isogenies effectively
Brauer group of abelian varieties, K3 surfaces and generalized Kummer varieties
Minimal models, models of curves with minimal weighted moduli height
Brauer-Siegel theorem in arithmetic geometry
Abelian varieties and the Mordell-Lang conjecture
Effective computation of the Mordell-Weil group and set of rational points
othersÂ
Speakers
Speakers will be announced before the conference. If you are interested to give a talk please fill out the form below (including a title/abstract). Please keep in mind that we are strictly looking for talks focus on topics of the conference (isogenies of Abelian varieties and applications to post-quantum cryptography).
    https://forms.gle/cnLccSz8nS7njwnz9
Proceedings
The results of the Workshop will be published in the SPS Science Series. All speakers at the Workshop are expected to contribute a paper for the proceedings.Â
Registration
Registration is now open. Please fill the form
