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

Research output: Contribution to journal › Article › peer-review

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 formulæ for the case of N=3, and show that the resulting algorithms are more efficient than all prior (3, 3)-isogeny algorithms.

Original language	English
Article number	25
Journal	Research in Number Theory
Volume	11
Issue number	1
DOIs	https://doi.org/10.1007/s40993-024-00600-y
Publication status	Published - 1 Mar 2025

Keywords

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

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10.1007/s40993-024-00600-y

Cite this

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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.",

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KW - Genus 2 curves

KW - Isogeny-based cryptography

KW - Kummer surfaces

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

Abstract

Keywords

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