Efficient (3, 3)-isogenies on fast Kummer surfaces

Maria Corte-Real Santos; Craig Costello; Benjamin Smith

doi:10.1007/s40993-024-00600-y

Efficient (3, 3)-isogenies on fast Kummer surfaces

Maria Corte-Real Santos
, Craig Costello
, Benjamin Smith

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

We give an alternative derivation of (N, N)-isogenies between fast Kummer surfaces which complements existing works based on the theory of theta functions. We use this framework to produce explicit formulæ for the case of N=3, and show that the resulting algorithms are more efficient than all prior (3, 3)-isogeny algorithms.

langue originale	Anglais
Numéro d'article	25
journal	Research in Number Theory
Volume	11
Numéro de publication	1
Les DOIs	https://doi.org/10.1007/s40993-024-00600-y
état	Publié - 1 mars 2025

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10.1007/s40993-024-00600-y

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title = "Efficient (3, 3)-isogenies on fast Kummer surfaces",

abstract = "We give an alternative derivation of (N, N)-isogenies between fast Kummer surfaces which complements existing works based on the theory of theta functions. We use this framework to produce explicit formul{\ae} for the case of N=3, and show that the resulting algorithms are more efficient than all prior (3, 3)-isogeny algorithms.",

keywords = "(3, 3)-Isogenies, Genus 2 curves, Isogeny-based cryptography, Kummer surfaces",

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KW - (3, 3)-Isogenies

KW - Genus 2 curves

KW - Isogeny-based cryptography

KW - Kummer surfaces

UR - https://www.scopus.com/pages/publications/85218199128

U2 - 10.1007/s40993-024-00600-y

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Efficient (3, 3)-isogenies on fast Kummer surfaces

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