Cryptology ePrint Archive: Report 2019/1003

Twisted Hessian Isogenies

Thinh Dang and Dustin Moody

Abstract: Elliptic curves are typically defined by Weierstrass equations. Given a kernel, the well-known 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.

Category / Keywords: implementation / Isogeny; Elliptic Curves; Hessian curves

Date: received 4 Sep 2019

Contact author: dustin moody at nist gov

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Version: 20190905:120425 (All versions of this report)

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