All Pairings Are in a Group

Chang-An ZHAO
Fangguo ZHANG

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E91-A    No.10    pp.3084-3087
Publication Date: 2008/10/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e91-a.10.3084
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Cryptography and Information Security
pairing-based cryptosystems,  R-ate pairing,  Ate pairing,  elliptic curves,  group,  

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In this paper, we suggest that all pairings are in a group from an abstract angle. Based on the results, some new pairings with the short Miller loop are constructed for great efficiency. It is possible that our observation can be applied into other aspects of pairing-based cryptosystems.