Wåhlin Christopher: Pairing based attacks against elliptic curve cryptography      

Abstract: In this paper we describe attacks on the elliptic curve discrete logarithm problem with focus on the pairing based attacks, MOV and FR, that use the Weil and the Tate-Lichenbaum pairing respectively. They reduce the problem to a discrete logarithm in GF(q) where more efficient algorithms are known. The pairings can be calculated using Miller’s algorithm, which we have implemented in SageMath together with an example of the FR attack. We will also briefly describe common attacks on the discrete logarithm problem of an arbitrary group and give an outline of index calculus.