论文标题
特征两个特征的椭圆曲线同基因的快速计算
Fast computation of elliptic curve isogenies in characteristic two
论文作者
论文摘要
我们提出了一种算法，该算法在$ \ mathbb {q} _2 $上定义的椭圆曲线之间计算同基因。它在于有效地解决$ 2 $ - adiC精度的对数损失的一阶微分方程所满足的一阶微分方程。 我们提供了一些应用，尤其是在椭圆形曲线和不可减少多项式的特征性的2个同基因的有限场上计算，这均在该程度的准线性时间中。
We propose an algorithm that calculates isogenies between elliptic curves defined over an extension $K$ of $\mathbb{Q}_2$. It consists in efficiently solving with a logarithmic loss of $2$-adic precision the first order differential equation satisfied by the isogeny. We give some applications, especially computing over finite fields of characteristic 2 isogenies of elliptic curves and irreducible polynomials, both in quasi-linear time in the degree.
