Faster Pairing Computation
Christophe Arène, Tanja Lange, Michael Naehrig, Christophe Ritzenthaler · arXiv (Cornell University) · 2009
Abstract. This paper proposes new explicit formulas for the doubling and addition step in Miller’s algorithm to compute pairings. For Edwards curves the formulas come from a new way of seeing the arithmetic. We state the first geometric interpretation of the group law on Edwards curves by presenting the functions which arise in the addition and doubling. Computing the coefficients of the functions and the sum or double of the points is faster than with all previously proposed formulas for pairings on Edwards curves. They are even competitive with all published formulas for pairing computation on Weierstrass curves. We also speed up pairing computation on Weierstrass curves in Jacobian coordinates. Finally, we present examples of pairing-friendly twisted Edwards curves with embedding degree k = 6.