Simplified isogeny formulas on twisted Jacobi quartic curves
type: Item
instance of: scholarly article
title: Simplified isogeny formulas on twisted Jacobi quartic curves
zbMATH Open document ID: 1487.14078
author: Zhi Hu
author: Zhe Liu
author: Lin Wang
author: Zijian Zhou
published in: Finite Fields and their Applications
publication date: 2022-01-14T00:00:00Z
review text: The authors introduce a \(w\)-coordinate system on Jacobi quartic curves and prove Montgomery-like group law formulas on such curves. Also, they give the connection between such \(w\)-coordinate and the projection map to some Kummer line. Explicit formulas for 2-isogenies and odd degree isogenies between Jacobi quartic curves are presented in the paper, too. The new derived formulas, especially those of curve parameters in odd degree isogenies, are simple to express in low algebraic complexity. The author also give the simple isogeny formulas based on the \(w\)-coordinate on Jacobi quartic curve, which share the similar forms as those on Montgomery curves (with only \(x\)-coordinate).
Mathematics Subject Classification ID: 14H52
Mathematics Subject Classification ID: 14K02
Mathematics Subject Classification ID: 11T71
zbMATH DE Number: 7457369
zbMATH Keywords: elliptic curve
zbMATH Keywords: isogenies
zbMATH Keywords: Jacobi quartic model
zbMATH Keywords: fast computation
reviewed by: Nikolai L. Manev
describes a project that uses: SIDH
MaRDI profile type: Publication
full work available at URL: j.ffa.2021.101981
OpenAlex ID: W4200295827
Wikidata QID: Q113874194
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DOI: 10.1016/J.FFA.2021.101981
description: scientific article; zbMATH DE number 7457369