## Cryptology ePrint Archive: Report 2010/123

Delaying Mismatched Field Multiplications in Pairing Computations

Craig Costello and Colin Boyd and Juan Manuel Gonzalez Nieto and Kenneth Koon-Ho Wong

Abstract: Miller's algorithm for computing pairings involves performing multiplications between elements that belong to different finite fields. Namely, elements in the full extension field $\mathbb{F}_{p^k}$ are multiplied by elements contained in proper subfields $\mathbb{F}_{p^{k/d}}$, and by elements in the base field $\mathbb{F}_{p}$. We show that significant speedups in pairing computations can be achieved by delaying these mismatched'' multiplications for an optimal number of iterations. Importantly, we show that our technique can be easily integrated into traditional pairing algorithms; implementers can exploit the computational savings herein by applying only minor changes to existing pairing code.

Category / Keywords: Pairings, Miller’s algorithm, finite field arithmetic, Tate pairing, ate pairing.

Date: received 5 Mar 2010, last revised 7 Apr 2010

Contact author: craig costello at qut edu au

Available format(s): PDF | BibTeX Citation

Short URL: ia.cr/2010/123

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