Efficient and Generalized Pairing Computation on Abelian Varieties

In this paper, we propose a new method for constructing a bilinear pairing over (hyper)elliptic curves, which we call the R-ate pairing. This pairing is a generalization of the Ate and Ateipairing, and can be computed more efficiently. Using the R-ate pairing, the loop length in Miller's algorithm can be as small as log (r1/phi(k)) some pairing-friendly elliptic curves which have not reached this lower bound. Therefore, we obtain savings of between 29% and 69% in overall costs compared to the Ateipairing. On supersingular hyperelliptic curves of genus 2, we show that this approach makes the loop length in Miller's algorithm shorter than that of the Ate pairing.