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