求解迹1椭圆曲线上的离散对数

Solving the discrete logarithm on elliptic curve of trace one

自Nigel Smart首次提出迹1的椭圆曲线是不安全的,针对迹1椭圆曲线的理论研究逐渐多了起来,这些研究成果对于椭圆曲线的应用起到了积极作用,然而对迹1椭圆曲线的实践研究却很少有学者关注。为了较好地理解迹1椭圆曲线的理论成果,了解算法的实施过程和效果,给出了求解离散对数的方法.利用Hensel提升理论,在Q_(p)域上通过约减和形式对数的方法求解离散对数,同时分析了该方法的计算效率,最后通过实例验证了该方法的正确性和有效性。

Since Nigel Smart firstly put forword that elliptic curve of trace one is unsafe,more researches on the theory of trace one have been conducted and these research results has played a positive role.However few scholars have focused on practical research on elliptic curve of trace one.In order to better understand elliptic curve theory achievement,to understand the algorithm attack process and effect,this paper put forward the concrete method to solve discrete logarithm.The method of solving the discrete logarithm is given,using the theory of Hensel lifting,in the Q_(p)domain by subtract and formal logarithmic method.At the same time,the computational efficiency of the method is analyzed.Finally,an example is given to verify the correctness and effectiveness of the method.