Efficient pairing computation on supersingular Abelian varieties

We present a general technique for the efficient computation of pairings on supersingular Abelian varieties. This formulation, which we call the eta pairing, generalises results of Duursma and Lee for computing the Tate pairing on supersingular elliptic curves in characteristic three. We then show how our general technique leads to a new algorithm which is about twice as fast as the Duursma-Lee method. These ideas are then used for elliptic and hyperelliptic curves in characteristic 2 with very efficient results. In particular, the hyperelliptic case is faster than all previously known pairing algorithms.