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

##### 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.

Available format(s)
Category
Public-key cryptography
Publication info
Preprint.
Keywords
isogeniesabelian surfacespost-quantum cryptographySIDH attack
Contact author(s)
thomas decru @ kuleuven be
sabrina kunzweiler @ math u-bordeaux fr
History
2023-03-16: approved
See all versions
Short URL
https://ia.cr/2023/376

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},
note = {\url{https://eprint.iacr.org/2023/376}},
url = {https://eprint.iacr.org/2023/376}
}

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