Cryptology ePrint Archive: Report 2006/059

High Security Pairing-Based Cryptography Revisited

R. Granger and D. Page and N.P. Smart

Abstract: The security and performance of pairing based cryptography has provoked a large volume of research, in part because of the exciting new cryptographic schemes that it underpins. We re-examine how one should implement pairings over ordinary elliptic curves for various practical levels of security. We conclude, contrary to prior work, that the Tate pairing is more efficient than the Weil pairing for all such security levels. This is achieved by using efficient exponentiation techniques in the cyclotomic subgroup backed by efficient squaring routines within the same subgroup.

Category / Keywords: public-key cryptography / pairings

Date: received 15 Feb 2006, last revised 16 Feb 2006

Contact author: nigel at cs bris ac uk

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Version: 20060216:180009 (All versions of this report)

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