An Algorithmic Approach to (2, 2)-isogenies in the Theta Model and Applications to Isogeny-based Cryptography
DARTOIS, Pierrick
Institut de Mathématiques de Bordeaux [IMB]
Analyse cryptographique et arithmétique [CANARI]
Lithe and fast algorithmic number theory [LFANT]
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Institut de Mathématiques de Bordeaux [IMB]
Analyse cryptographique et arithmétique [CANARI]
Lithe and fast algorithmic number theory [LFANT]
DARTOIS, Pierrick
Institut de Mathématiques de Bordeaux [IMB]
Analyse cryptographique et arithmétique [CANARI]
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
Analyse cryptographique et arithmétique [CANARI]
Lithe and fast algorithmic number theory [LFANT]
ROBERT, Damien
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]
Analyse cryptographique et arithmétique [CANARI]
< Leer menos
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]
Analyse cryptographique et arithmétique [CANARI]
Idioma
en
Document de travail - Pré-publication
Resumen en inglés
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 ...Leer más >
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.< Leer menos
Palabras clave en inglés
Post-Quantum Cryptography
Isogenies
Theta coordinates
Dimension 2
Proyecto ANR
Cryptographie, isogenies et variété abéliennes surpuissantes - ANR-19-CE48-0008
Post-quantum padlock for web browser - ANR-22-PETQ-0008
Post-quantum padlock for web browser - ANR-22-PETQ-0008
Orígen
Importado de HalCentros de investigación