Optimised Versions of the Ate and Twisted Ate Pairings

Seiichi MATSUDA  Naoki KANAYAMA  Florian HESS  Eiji OKAMOTO  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E92-A   No.7   pp.1660-1667
Publication Date: 2009/07/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E92.A.1660
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Cryptography and Information Security
Keyword: 
tate pairing,  eta pairing,  ate pairing,  twisted ate pairing,  

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Summary: 
We observe a natural generalisation of the ate and twisted ate pairings, which allow for performance improvements in non standard applications of pairings to cryptography like composite group orders. We also give a performance comparison of our pairings and the Tate, ate and twisted ate pairings for certain polynomial families based on operation count estimations and on an implementation, showing that our pairings can achieve a speedup of a factor of up to two over the other pairings.