椭圆曲线密码的计算与分析研究

本项目主要研究椭圆曲线的离散对数问题的深层次理论背景，力图用群表示和代数几何的相关理论给出该问题新的阐述和表达。我们将尝试构造针对该问题有效的计算方法。特别地，我们将考察计算该问题的新的并行策略，并在一些高性能计算平台以及局域网上来实现具体的攻击。同时研究与此关联的椭圆曲线的计算问题，我们重点研究椭圆曲线上点乘和双线性配对的快速计算方法以及相关实现，并将这些方法和技术推广到底亏格的代数曲线上去。

In this program, we focus on the theory of elliptic curve discrete logarithm problem, and try to give some new description on this problem by using theories of group representation and algebriac geometry. We will try to construct some efficient computation method. Especially, we will do some research on the parallel computing strategy,and realize the attack on high performance platform and local network. On the related computation on elliptic curves, we pay much attention to fast computation for elliptic curve point multiplication and bilinear pairing, and generalize these methods and technologies to algebraic curves with small genus.