Elliptic curves are typically defined by Weierstrass equations. Given a kernel, the well-known V Velu'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 an explicit formula for isogenies between elliptic curves in (twisted) Hessian form.
, Dang, T.
, Perez, F.
and Fouotsa, E.
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 December 11, 2023)