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.

中文翻译：

---

椭圆曲线 Hessian 模型上的除法多项式

在本文中，我们在椭圆曲线的 Hessian 模型上推导出标量乘以 n 映射的公式，表示为 [n]。这使得能够表征该曲线上的 n 个扭转点。计算涉及多项式 $$P_n$$、$Q_n$$ 和 $$V_n$$ 的三个族，我们展示了这些多项式的系数和次数的一些属性。我们还展示了这些多项式满足的一些函数方程。作为应用，我们提供了一种 Hessian 椭圆曲线的均值定理。