Efficient and generalized pairing computation on Abelian varieties. Cryptology ePrint Archive, Report 2008/040 (2008)
| Citations: | 30 - 0 self |
BibTeX
@MISC{Lee08efficientand,
author = {Eunjeong Lee and Hyang-sook Lee and Cheol-min Park},
title = {Efficient and generalized pairing computation on Abelian varieties. Cryptology ePrint Archive, Report 2008/040},
year = {2008}
}
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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 Atei 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 log(r 1/φ(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 Atei 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. Key words: pairing, elliptic curves, hyperelliptic curves, pairing based cryptography, Tate pairing. 1
