Counting Richelot isogenies between superspecial abelian surfaces

Abstract: Castryck, Decru, and Smith used superspecial genus-2 curves and their Richelot isogeny graph for basing genus-2 isogeny cryptography, and recently, Costello and Smith devised an improved isogeny path-finding algorithm in the genus 2 setting. In order to establish a firm ground for the cryptographic construction and analysis, we give a new characterization of decomposed Richelot isogenies in terms of involutive reduced automorphisms of genus-2 curves over a finite field, and explicitly count such decomposed (and non-decomposed) Richelot isogenies between superspecial principally polarized abelian varieties. As a corollary, we give another algebraic geometric proof of Theorem 3 in the paper of Castryck et al.

cryptography and securityalgebraic geometrynumber theory

Audience: researchers in the topic

( chat | paper | slides | video )

Comments: Chairs: Brendan Creutz and Felipe Voloch

---

Algorithmic Number Theory Symposium (ANTS XIV)

Series comments: Registration is now open. Registration is free but required to access the chat and livestream.

This is a hybrid synchronous/asynchronous conference with several ways to participate.

• Click the "paper" link to view contributed papers and posters (open to all).
• Click the "video" link to view pre-recorded talks of accepted papers (open to all).
  These are 15-20 minutes aimed at a general algorithmic number theory audience.
• Click the "slides" link to view slides used in the pre-recorded video when available (open to all).
• Click the "chat" link to access the chat stream related to the talk or poster before, during, and after the live event (registration required).
• Click the "livestream" button to join the live event when it is taking place (registration required and you must be logged in).
  For accepted papers the audience will be expected to have watched the pre-recorded video and have the paper in front of them.

The invited talks will be recorded and made available via the "video" link after the talk is over. None of the other sessions will be recorded.

---