Refinement of miller's algorithm over edwards curves

Authors:
Lei Xu;Dongdai Lin
Affiliations:
State Key Laboratory of Information Security, Institute of Software, Chinese Academy of Sciences, Beijing, China;State Key Laboratory of Information Security, Institute of Software, Chinese Academy of Sciences, Beijing, China
Venue:
CT-RSA'10 Proceedings of the 2010 international conference on Topics in Cryptology
Year:
2010

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Abstract

Edwards gave a new form of elliptic curves in [1], and these curves were introduced to cryptography by Bernstein and Lange in [2]. The Edwards curves enjoy faster addition and doubling operations, so they are very attractive for elliptic curve cryptography. In 2006, Blake, Murty and Xu proposed three refinements to Millers algorithm for computing Weil/Tate pairings over Weierstraß curves. In this paper we extend their method to Edwards curve and propose a faster algorithm for computing pairings with Edwards coordinates, which comes from the analysis of divisors of rational functions.