Efficient computation of $(3^n,3^n)$-isogenies

Thomas Decru; Sabrina Kunzweiler

Paper 2023/376

Efficient computation of $(3^n,3^n)$-isogenies

Thomas Decru

, imec-COSIC, KU Leuven, Belgium

Sabrina Kunzweiler

, Univ. Bordeaux, CNRS, Bordeaux INP, Inria, France

Abstract

The parametrization of $(3,3)$-isogenies by Bruin, Flynn and Testa requires over 37.500 multiplications if one wants to evaluate a single isogeny in a point. We simplify their formulae and reduce the amount of required multiplications by 94%. Further we deduce explicit formulae for evaluating $(3,3)$-splitting and gluing maps in the framework of the parametrization by Bröker, Howe, Lauter and Stevenhagen. We provide implementations to compute $(3^n,3^n)$-isogenies between principally polarized abelian surfaces with a focus on cryptographic application. Our implementation can retrieve Alice's secret isogeny in 11 seconds for the SIKEp751 parameters, which were aimed at NIST level 5 security.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. AfricaCrypt 2023
Keywords: isogenies abelian surfaces post-quantum cryptography SIDH attack
Contact author(s): thomas decru @ kuleuven be
sabrina kunzweiler @ math u-bordeaux fr
History: 2023-05-12: revised; 2023-03-15: received; See all versions
Short URL: https://ia.cr/2023/376
License: CC BY

BibTeX

@misc{cryptoeprint:2023/376,
      author = {Thomas Decru and Sabrina Kunzweiler},
      title = {Efficient computation of $(3^n,3^n)$-isogenies},
      howpublished = {Cryptology {ePrint} Archive, Paper 2023/376},
      year = {2023},
      url = {https://eprint.iacr.org/2023/376}
}