Pairing computation on Edwards curves with high-degree twists

Liangze Li, Hongfeng Wu, and Fan Zhang

Abstract

In this paper, we propose an elaborate geometry approach to explain the group law on twisted Edwards curves which are seen as the intersection of quadric surfaces in place. Using the geometric interpretation of the group law we obtain the Miller function for Tate pairing computation on twisted Edwards curves. Then we present the explicit formulae for pairing computation on twisted Edwards curves. Our formulae for the doubling step are a littler faster than that proposed by Arene et.al.. Finally, to improve the efficiency of pairing computation we present twists of degree 4 and 6 on twisted Edwards curves.

Available format(s)
Category
Public-key cryptography
Publication info
Published elsewhere. Unknown where it was published
Keywords
Edwards curvesTate pairingMiller functionsCryptography
Contact author(s)
whfmath @ gmail com
History
2012-09-27: last of 2 revisions
See all versions
Short URL
https://ia.cr/2012/532

CC BY

BibTeX

@misc{cryptoeprint:2012/532,
author = {Liangze Li and Hongfeng Wu and Fan Zhang},
title = {Pairing computation on Edwards curves with high-degree twists},
howpublished = {Cryptology ePrint Archive, Paper 2012/532},
year = {2012},
note = {\url{https://eprint.iacr.org/2012/532}},
url = {https://eprint.iacr.org/2012/532}
}

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