Some recent applications of elliptic curves in crypto− graphy

Abstract

Since about 1985, the theory of elliptic curves over finite fields has been applied to various problems in cryptography. One of the main reasons for interest in cryptosystems based on elliptic curves is that they can provide (a huge number of) finite abelian groups having a rich algebraic structure. In this paper, we give three recent applications of the Weil-pairing on an elliptic curve in cryptography: the MOV attack (discrete logarithm on a supersingular elliptic curve), the tripartite Diffy-Helmann key exchange, and identity-based cryptography.