Abstract:
This paper begins by describing basic properties of
finite field and elliptic curve cryptography over prime field and
binary field. Then we discuss the discrete logarithm problem for
elliptic curves and its properties. We study the general common
attacks on elliptic curve discrete logarithm problem such as the Baby
Step, Giant Step method, Pollard’s rho method and Pohlig-Hellman
method, and describe in detail experiments of these attacks over
prime field and binary field. The paper finishes by describing
expected running time of the attacks and suggesting strong elliptic
curves that are not susceptible to these attacks.
