An Algorithmic Approach to (2, 2)-isogenies in the Theta Model and Applications to Isogeny-based Cryptography - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

An Algorithmic Approach to (2, 2)-isogenies in the Theta Model and Applications to Isogeny-based Cryptography

Résumé

In this paper, we describe an algorithm to compute chains of (2, 2)-isogenies between products of elliptic curves in the theta model. The description of the algorithm is split into various subroutines to allow for a precise field operation counting. We present a constant time implementation of our algorithm in Rust and an alternative implementation in SageMath. Our work in SageMath runs ten times faster than a comparable implementation of an isogeny chain using the Richelot correspondence. The Rust implementation runs up to forty times faster than the equivalent isogeny in SageMath and has been designed to be portable for future research in higher-dimensional isogeny-based cryptography.
Fichier principal
Vignette du fichier
2023-1747.pdf (668.38 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04297088 , version 1 (21-11-2023)

Identifiants

  • HAL Id : hal-04297088 , version 1

Citer

Pierrick Dartois, Luciano Maino, Giacomo Pope, Damien Robert. An Algorithmic Approach to (2, 2)-isogenies in the Theta Model and Applications to Isogeny-based Cryptography. 2023. ⟨hal-04297088⟩
18 Consultations
30 Téléchargements

Partager

Gmail Facebook X LinkedIn More