Implementing Tate Pairing

The Weil and Tate pairings have found several new applications in cryptography. To efficiently implement these cryptosystems it is necessary to optimise the computation time for the Tate pairing. This paper provides methods to achieve fast computation of the Tate pairing. We also give division-free formulae for point tripling on a family of elliptic curves in characteristic three. Examples of the running time for these methods are given