On computable isomorphisms in efficient asymmetric pairing-based systemsNigel Smart, Fre Vercauteren, On computable isomorphisms in efficient asymmetric pairing-based systems. Discrete Applied Mathematics, 155(4), pp. 538–547. February 2007. No electronic version available.
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.