## Cryptology ePrint Archive: Report 2019/1480

Analogue of Vélu's Formulas for Computing Isogenies over Hessian Model of Elliptic Curves

Fouazou Lontouo Perez Broon and Emmanuel Fouotsa

Abstract: Vélu's formulas for computing isogenies over Weierstrass model of elliptic curves has been extended to other models of elliptic curves such as the Huff model, the Edwards model and the Jacobi model of elliptic curves. This work continues this line of research by providing efficient formulas for computing isogenies over elliptic curves of Hessian form. We provide explicit formulas for computing isogenies of degree 3 and isogenies of degree l not divisible by 3. The theoretical cost of computing these maps in this case is slightly faster than the case with other curves. We also extend the formulas to obtain isogenies over twisted and generalized Hessian forms of elliptic curves. The formulas in this work have been verified with the Sage software and are faster than previous results on the same curve.

Category / Keywords: public-key cryptography / Elliptic curves, Isogeny , Hessian curves and Vélu's formulas