Division polynomials on the Hessian model of elliptic curves

In this paper we derive formulas for the scalar multiplication by n map, denoted [ n ], on the Hessian model of elliptic curve. This enables to characterize n -torsion points on this curve. The computation involves three families of polynomials P n , Q n and V n and we show some properties on the coefficients and degrees of these polynomials. We also show some functional equations satisfied by these polynomials. As application we provide a type of mean-value theorem for the Hessian elliptic curve.