Here is a discussion thread for the 6th session of The Isogeny Club, where Sabrina Kunzweiler presents her talk titled: Genus 2 Isogenies
Elliptic curves are abelian varieties of dimension one. It is only natural to consider generalizations of isogeny-based cryptographic protocols to higher dimensions. Apart from mathematical curiosity, the recent attacks on SIDH have shown that it is essential to study such generalizations in order to understand the security of elliptic curve based protocols.
This talk gives an introduction to Jacobians of genus-2 curves (abelian varieties of dimension 2) and isogenies in this setting. The focus lies on the computation of Richelot isogenies.