Divisor class group arithmetic on non-hyperelliptic genus 3 curves

Abstract: We present novel explicit formulas for arithmetic in the divisor class group of a $C_{3,4}$ curve. Our formulas handle all cases of inputs and outputs without having to fall back on a generic method. We also improve on the most commonly occurring case by reducing the number of required field inversions to one at the cost of a small number of additional field operations, resulting in running times that are 11-13% faster than the prior state-of-the-art.

cryptography and securityalgebraic geometrynumber theory

Audience: researchers in the topic

( chat | paper | slides | video )

Comments: The slides used in the pre-recorded video can be found here.

Chairs: Tom Fisher and Jen Paulhus

---

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.

---