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
Creative Commons Attribution
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},
      note = {\url{https://eprint.iacr.org/2006/026}},
      url = {https://eprint.iacr.org/2006/026}
}
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