Computing $2$-isogenies between Kummer lines
ROBERT, Damien
Institut de Mathématiques de Bordeaux [IMB]
Analyse cryptographique et arithmétique [CANARI]
Institut de Mathématiques de Bordeaux [IMB]
Analyse cryptographique et arithmétique [CANARI]
SARKIS, Nicolas
Institut de Mathématiques de Bordeaux [IMB]
Analyse cryptographique et arithmétique [CANARI]
Institut de Mathématiques de Bordeaux [IMB]
Analyse cryptographique et arithmétique [CANARI]
ROBERT, Damien
Institut de Mathématiques de Bordeaux [IMB]
Analyse cryptographique et arithmétique [CANARI]
Institut de Mathématiques de Bordeaux [IMB]
Analyse cryptographique et arithmétique [CANARI]
SARKIS, Nicolas
Institut de Mathématiques de Bordeaux [IMB]
Analyse cryptographique et arithmétique [CANARI]
< Reduce
Institut de Mathématiques de Bordeaux [IMB]
Analyse cryptographique et arithmétique [CANARI]
Language
en
Document de travail - Pré-publication
This item was published in
2024-01-09
English Abstract
We use theta groups to study $2$-isogenies between Kummer lines, with a particular focus on the Montgomery model. This allows us to recover known formula, along with more efficient forms for translated isogenies, which ...Read more >
We use theta groups to study $2$-isogenies between Kummer lines, with a particular focus on the Montgomery model. This allows us to recover known formula, along with more efficient forms for translated isogenies, which require only $2S+2m_0$ for evaluation. We leverage these translated isogenies to build a hybrid ladder for scalar multiplication on Montgomery curves with rational $2$-torsion which cost $3M+6S+2m_0$ by bits, compared to $5M+4S+1m_0$ for the standard Montgomery ladder.Read less <
English Keywords
Elliptic curves cryptography
Kummer lines
Isogenies
Scalar multiplication
Montgomery ladder
Origin
Hal imported