The discrete logarithm problem

In this work, the discrete logarithm problem and solutions of this problem are disscused and the algorithms are given to reduce the elliptic curve discrete algorithm problem to an easier discrete logarithm problem. In the first chapter, some fundamental concepts on the theory of algebra and number theory and cryptography are given. In the second chapter, the discrete logarithm problem and the algorithms that used for the solutions of this problem are discussed. Firstly,Diffie-Hellman key exchange algorithm is considered and the El-Gamal public key cryptosystem is discussed. Then some algorithms are given for solving the discrete logarithm problem. In the third chapter, elliptic curves and elliptic curve discrete logarithm problem are considered. In this chapter, some algorithms are given to reduce the elliptic curve discrete logarithm problem to a discrete logarithm problem. In the fourth chapter, similar algorithms are given by using the division polynomials of an elliptic curve.