Paper 2006/026
Constructing Pairing-Friendly Elliptic Curves with Embedding Degree 10
David Freeman
Abstract
We present a general framework for constructing families of elliptic curves of prime order with prescribed embedding degree. We demonstrate this method by constructing curves with embedding degree k = 10, which solves an open problem posed by Boneh, Lynn, and Shacham. We show that our framework incorporates existing constructions for k = 3, 4, 6, and 12, and we give evidence that the method is unlikely to produce infinite families of curves with embedding degree k > 12.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Published elsewhere. Unknown where it was published
- Keywords
- elliptic curvesembedding degreepairings
- Contact author(s)
- dfreeman @ math berkeley edu
- History
- 2006-01-27: received
- Short URL
- https://ia.cr/2006/026
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2006/026,
author = {David Freeman},
title = {Constructing Pairing-Friendly Elliptic Curves with Embedding Degree 10},
howpublished = {Cryptology {ePrint} Archive, Paper 2006/026},
year = {2006},
url = {https://eprint.iacr.org/2006/026}
}
