An Algorithmic Approach to (2, 2)-isogenies in the Theta Model and Applications to Isogeny-based Cryptography
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| hal.structure.identifier | Analyse cryptographique et arithmétique [CANARI] | |
| hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
| dc.contributor.author | DARTOIS, Pierrick | |
| hal.structure.identifier | University of Bristol [Bristol] | |
| dc.contributor.author | MAINO, Luciano | |
| hal.structure.identifier | NCC Group | |
| hal.structure.identifier | University of Bristol [Bristol] | |
| dc.contributor.author | POPE, Giacomo | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
| hal.structure.identifier | Analyse cryptographique et arithmétique [CANARI] | |
| dc.contributor.author | ROBERT, Damien | |
| dc.date.accessioned | 2024-04-04T02:32:26Z | |
| dc.date.available | 2024-04-04T02:32:26Z | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190386 | |
| dc.description.abstractEn | 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. | |
| dc.description.sponsorship | Cryptographie, isogenies et variété abéliennes surpuissantes - ANR-19-CE48-0008 | |
| dc.description.sponsorship | Post-quantum padlock for web browser - ANR-22-PETQ-0008 | |
| dc.language.iso | en | |
| dc.subject.en | Post-Quantum Cryptography | |
| dc.subject.en | Isogenies | |
| dc.subject.en | Theta coordinates | |
| dc.subject.en | Dimension 2 | |
| dc.title.en | An Algorithmic Approach to (2, 2)-isogenies in the Theta Model and Applications to Isogeny-based Cryptography | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math] | |
| dc.subject.hal | Informatique [cs] | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-04297088 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-04297088v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=DARTOIS,%20Pierrick&MAINO,%20Luciano&POPE,%20Giacomo&ROBERT,%20Damien&rft.genre=preprint |
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