Moody, D.
, Dang, T.
, Perez, F.
and Fouotsa, E.
(2021),
Isogenies on twisted Hessian curves, Journal of Mathematical Cryptography, [online], https://doi.org/10.1515/jmc-2020-0037, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=929415
(Accessed April 24, 2025)
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Isogenies on twisted Hessian curves
Published
Author(s)
, , Fouazou Lontouo Perez, Emmanuel Fouotsa
Abstract
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 X-affine formula has the lowest cost for processing an input point in affine coordinates.Citation
Journal of Mathematical Cryptography
Volume
15
Issue
1
Pub Type
Journals
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Keywords
Elliptic curves, Isogeny, Hessian curves, Vélu’s formulas
Citation
Issues
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Created March 16, 2021, Updated April 23, 2024