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Efficient and Generalized Pairing Computation on Abelian Varieties
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| Abstract: | In this paper, we propose a new method for constructing a bilinear pairing over (hyper)elliptic curves, which we call the R-ate pairing. This pairing is a generalization of the Ate and Ate_i pairing, and also improves efficiency of the pairing computation. Using the R-ate pairing, the loop length in Miller's algorithm can be as small as ${\rm log}(r^{1 / \phi(k)})$ for some pairing-friendly elliptic curves which have not reached this lower bound. Therefore we obtain from 29 % to 69 % savings in overall costs compared to the Ate_i pairing. On supersingular hyperelliptic curves of genus 2, we show that this approach makes the loop length in Miller's algorithm shorter than that of the Ate pairing. |
BibTeX
@misc{eprint-2008-17717,
title={Efficient and Generalized Pairing Computation on Abelian Varieties},
booktitle={IACR Eprint archive},
keywords={public-key cryptography / pairing, elliptic curves, hyperelliptic curves, pairing based cryptography, Tate pairing},
url={http://eprint.iacr.org/2008/040},
note={ ejlee@kias.re.kr 13906 received 28 Jan 2008},
author={Eunjeong Lee and Hyang-Sook Lee and Cheol-Min Park},
year=2008
}