ON SOME ATTACKS OF DISCRETE LOGARITHM PROBLEMS OVER FINITE FIELDS

摘要

The intractability of the discrete logarithm problem over finite fields is the basis of the security of recently mainstream public key cryptosystems such as ElGamel, DSA, Diffie-Hellman and ECC (Elliptic Curve Cryptosystems), etc. In this paper, one has presented, illustrated and analyzed some attack algorithms on the DLP over finite fields, namely Shanks's giant-steps baby-steps algorithm, Pollard field splitting p -algorithm, and Pohlig-Hellman Algorithm. One equally implemented these algorithms for the finite field GF* (3049) using a high-level programming language.