Attack Experiments on Elliptic Curves of Prime and Binary Fields

Abstract

At the beginning the paper describes the basic properties of finite fieldarithmetic and elliptic curve arithmetic over prime and binary fields. Then it discussesthe elliptic curve discrete logarithm problem and its properties. We study the BabyStep, Giant-Step method, Pollard’s rho method and Pohlig–Hellman method, knownas general methods that can exploit the elliptic curve discrete logarithm problem,and describe in detail attack experiments using these methods over prime and binaryfields. Finally, the paper discusses the expected running time of these attacks andsuggests the strong elliptic curves that are not vulnerable to these attacks