## Cryptology ePrint Archive: Report 2008/040

Efficient and Generalized Pairing Computation on Abelian Varieties

Eunjeong Lee, Hyang-Sook Lee, and Cheol-Min Park

Abstract: 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 Ate_i pairing, and also improves efficiency of the pairing computation. Using the R-ate pairing, the loop length in Miller's algorithm can be as small as ${\rm log}(r^{1 / \phi(k)})$ for some pairing-friendly elliptic curves which have not reached this lower bound. Therefore we obtain from 29 % to 69 % savings in overall costs compared to the Ate_i pairing. 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.

Category / Keywords: public-key cryptography / pairing, elliptic curves, hyperelliptic curves, pairing based cryptography, Tate pairing