Refinements of Miller's algorithm for computing the Weil/Tate pairing

Ian F. Blake, V. Kumar Murty, Guangwu Xu
2006 Journal of Algorithms  
In this paper we propose three refinements to Miller's algorithm for computing Weil/Tate Pairing. The first one is an overall improvement and achieves its optimal behavior if the binary expansion of the involved integer has more zeros. If more ones are presented in the binary expansion, second improvement is suggested. The third one is especially efficient in the case base three. We also have some performance analysis. keywords: algorithm, elliptic curve, cryptography, Weil/Tate pairing Recent
more » ... ork on parings in cryptography has considered their use in the definition and implementation of certain new and potentially very useful protocols. Boneh and Franklin [3] used pairings to develop an efficient identity-based encryption (IBE) system, the first such system since the notion of IBE was first described by Shamir [14]. In such a system a user's public information such as his identity, email address etc.
doi:10.1016/j.jalgor.2005.01.009 fatcat:sahhckccpvc5rpgzkaii7ddb3a