## CryptoDB

### Paper: Delaying Mismatched Field Multiplications in Pairing Computations

Authors: Craig Costello Juan Manuel Gonzalez Nieto Colin Boyd Kenneth Koon-Ho Wong URL: http://eprint.iacr.org/2010/123 Search ePrint Search Google 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.
##### BibTeX
@misc{eprint-2010-23024,
title={Delaying Mismatched Field Multiplications in Pairing Computations},
booktitle={IACR Eprint archive},
keywords={Pairings, Millers algorithm, finite field arithmetic, Tate pairing, ate pairing.},
url={http://eprint.iacr.org/2010/123},
note={ craig.costello@qut.edu.au 14707 received 5 Mar 2010, last revised 7 Apr 2010},
author={Craig Costello and Juan Manuel Gonzalez Nieto and Colin Boyd and Kenneth Koon-Ho Wong},
year=2010
}