Cryptology ePrint Archive: Report 2010/342

Fixed Argument Pairings

Craig Costello and Douglas Stebila

Abstract: A common scenario in many pairing-based cryptographic protocols is that one argument in the pairing is fixed as a long term secret key or a constant parameter in the system. In these situations, the runtime of Millerís algorithm can be significantly reduced by storing precomputed values that depend on the fixed argument, prior to the input or existence of the second argument. In light of recent developments in pairing computation, we show that the computation of the Miller loop can be sped up by up to 37% if precomputation is employed, with our method being up to 19.5% faster than the previous precomputation techniques.

Category / Keywords: Pairings, Millerís algorithm, Tate pairing, ate pairing, precomputation.

Date: received 15 Jun 2010, last revised 15 Jun 2010

Contact author: craig costello at qut edu au

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Version: 20100618:183424 (All versions of this report)

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