Efficient (3,3)-isogenies on fast Kummer surfaces

Maria Corte-Real Santos; Craig Costello; Benjamin Smith

Paper 2024/144

Efficient (3,3)-isogenies on fast Kummer surfaces

Maria Corte-Real Santos

, University College London

Craig Costello

, Microsoft Research

Benjamin Smith

, French Institute for Research in Computer Science and Automation

Abstract

We give an alternative derivation of (N,N)-isogenies between fast Kummer surfaces which complements existing works based on the theory of theta functions. We use this framework to produce explicit formulae for the case of N = 3, and show that the resulting algorithms are more efficient than all prior (3,3)-isogeny algorithms.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. Sixteenth Algorithmic Number Theory Symposium
Keywords: Isogeny-based cryptography genus 2 isogenies superspecial hash function
Contact author(s): maria santos 20 @ ucl ac uk
craigco @ microsoft com
smith @ lix polytechnique fr
History: 2024-09-05: revised; 2024-02-01: received; See all versions
Short URL: https://ia.cr/2024/144
License: CC BY

BibTeX

@misc{cryptoeprint:2024/144,
      author = {Maria Corte-Real Santos and Craig Costello and Benjamin Smith},
      title = {Efficient (3,3)-isogenies on fast Kummer surfaces},
      howpublished = {Cryptology {ePrint} Archive, Paper 2024/144},
      year = {2024},
      url = {https://eprint.iacr.org/2024/144}
}