Tate Pairing Computation on Generalized Hessian Curves

摘要

In this paper, we present explicit formulae for Miller's algorithm to compute the Tate pairing on generalized Hessian curves using projective coordinates. Firstly, we propose the geometric interpretation of the group law and construct Miller function on generalized Hessian curves. The computation of Tate pairing using these functions in Miller's algorithm costs 10m in addition steps and 5m+6s in doubling steps. Finally, we present the parallel algorithm for computing Tate pairing on generalized Hessian curves.