Paper 2008/040 Original: eprint.iacr.org/2008/040 ↗
Efficient and Generalized Pairing Computation on Abelian Varieties
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.
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2008-01-28: last updated
- 2008-01-28: published
- Short URL
- https://ia.cr/2008/040
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2008/040,
author = {Eunjeong Lee and Hyang-Sook Lee and Cheol-Min Park},
title = {Efficient and Generalized Pairing Computation on Abelian Varieties},
howpublished = {Cryptology {ePrint} Archive, Paper 2008/040},
year = {2008},
url = {https://eprint.iacr.org/2008/040}
}