Isogenies on twisted Hessian curves

Elliptic curves are typically defined by Weierstrass equations. Given a kernel, the well-known Vélu's formula shows how to explicitly write down an isogeny between Weierstrass curves. However, it is not clear how to do the same on other forms of elliptic curves without isomorphisms mapping to a...

Full description

Saved in:
Bibliographic Details
Published inJournal of mathematical cryptology Vol. 15; no. 1; pp. 345 - 358
Main Authors Perez Broon, Fouazou Lontouo, Dang, Thinh, Fouotsa, Emmanuel, Moody, Dustin
Format Journal Article
LanguageEnglish
Published Berlin De Gruyter 01.01.2021
Walter de Gruyter GmbH
Subjects
14H52
14K02
Curves
Elliptic curves
Hessian curves
Isogeny
Isomorphism
Kernels
Vélu's formulas
Online AccessGet full text

Cover

More Information
Summary:Elliptic curves are typically defined by Weierstrass equations. Given a kernel, the well-known Vélu's formula shows how to explicitly write down an isogeny between Weierstrass curves. However, it is not clear how to do the same on other forms of elliptic curves without isomorphisms mapping to and from the Weierstrass form. Previous papers have shown some isogeny formulas for (twisted) Edwards, Huff, and Montgomery forms of elliptic curves. Continuing this line of work, this paper derives explicit formulas for isogenies between elliptic curves in (twisted) Hessian form. In addition, we examine the numbers of operations in the base field to compute the formulas. In comparison with other isogeny formulas, we note that our formulas for twisted Hessian curves have the lowest costs for processing the kernel and our -affine formula has the lowest cost for processing an input point in affine coordinates.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:1862-2976
1862-2984
1862-2984
DOI:10.1515/jmc-2020-0037