Analysis Of The Related Algorithms On The Elliptic Curve Discrete Logarithm Problem

This paper mainly analyzes the related algorithms of the elliptic curve discrete loga-rithm problem.Firstly,in chapter one,I introduce the research background and current situation of the problem.In chapter two,three common algorithms are introduced,in-cluding Baby Step-Giant Step,Pollard algorithm and Index Calculus.In chapter three,I specific analysis the GHS Attack.This algorithm is mainly used to attack ECDLP over some finite field of characteristic two.It could reduce the ECDLP to a high genus hyperelliptic curve discrete logarithm problem over the subfield.Gaudry,Hess and S-mart gave a efficient condition that can estimate the feasibility of using GHS Attack.In this paper,I get a necessary and sufficient condition for GHS,and calculate the number of the elliptic curves that satisfy the new condition.