Further Refinements of Miller Algorithm on Edwards curves

TL;DR

This paper introduces further generic refinements to the Miller algorithm for Edwards curves, enabling faster computation of Weil and Tate pairings on pairing-friendly Edwards curves of any embedding degree.

Contribution

It presents new, more efficient refinements to the Miller algorithm applicable to all pairing-friendly Edwards curves, improving over previous methods.

Findings

Our algorithm is faster than the original Miller algorithm.

It outperforms Xu-Lin's refinements in efficiency.

Applicable to curves of any embedding degree.

Abstract

Recently, Edwards curves have received a lot of attention in the cryptographic community due to their fast scalar multiplication algorithms. Then, many works on the application of these curves to pairing-based cryptography have been introduced. Xu and Lin (CT-RSA, 2010) presented refinements to improve the Miller algorithm that is central role compute pairings on Edwards curves. In this paper, we study further refinements to Miller algorithm. Our approach is generic, hence it allow to compute both Weil and Tate pairings on pairing-friendly Edwards curves of any embedding degree. We analyze and show that our algorithm is faster than the original Miller algorithm and the Xu-Lin's refinements.