Pairing computation on Edwards curves with high-degree twists

Liangze Li; Hongfeng Wu; Fan Zhang

Paper 2012/532

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.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Keywords: Edwards curves Tate pairing Miller functions Cryptography
Contact author(s): whfmath @ gmail com
History: 2012-09-27: last of 2 revisions; 2012-09-20: received; See all versions
Short URL: https://ia.cr/2012/532
License: 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},
      url = {https://eprint.iacr.org/2012/532}
}