On Computable Isomorphisms in Efficient Asymmetric Pairing Based Systems?

Abstract. In this paper we examine the hard problems underlying asymmetric pairings, their precise relationships and how they affect a number of existing protocols. Furthermore, we present a new model for the elliptic curve groups used in asymmetric pairings, which allows both an efficient pairing and an efficiently computable isomorphism. Keywords: Pairing-based cryptography, Tate pairing, elliptic curve 1 Introduction In recent years we have seen the advent of various protocols based on pairings.However, much of the literature uses a confusing array of underlying hard problems and differing notation. This is because the original protocols were defined inthe context of pairings on supersingular curves, in which the pairing is between a group and itself, i.e. G * G-! GT