Parallelizing pairings on Hessian elliptic curves

Abstract

This paper considers the computation of the Ate pairing on the Hessian model of elliptic curves. Due to the many important properties making the model attractive in cryptography, we compute for the first time the Ate pairing on this model and show how both the Tate and the Ate pairings can be parallelized on this curve. We wrote codes in the Sage software to ensure the correctness of formulas in this work. Keywords: Hessian curves, Tate and ate pairings, Parallel computation