A study of pairing computation for elliptic curves with embedding degree 15

Nadia El Mrabet; Nicolas Guillermin; Sorina Ionica

Paper 2009/370

A study of pairing computation for elliptic curves with embedding degree 15

Nadia El Mrabet, Nicolas Guillermin, and Sorina Ionica

Abstract

This paper presents the first study of pairing computation on curves with embedding degree $15$ . We compute the Ate and the twisted Ate pairing for a family of curves with parameter $ρ 1.5$ and embedding degree $15$ . We use a twist of degree 3 to perform most of the operations in $\F_{p}$ or $\F_{p^{5}}$ . Furthermore, we present a new arithmetic for extension fields of degree $5$ . Our computations show that these curves give very efficient implementations for pairing-based cryptography at high security levels.

Metadata

Available format(s): PDF PS
Category: Implementation
Publication info: Published elsewhere. student paper
Contact author(s): nadia elmrabet @ lirmm fr
sorina ionica @ m4x org
History: 2009-07-31: received
Short URL: https://ia.cr/2009/370
License: CC BY

BibTeX

@misc{cryptoeprint:2009/370,
      author = {Nadia El Mrabet and Nicolas Guillermin and Sorina Ionica},
      title = {A study of pairing computation for elliptic curves with embedding degree 15},
      howpublished = {Cryptology {ePrint} Archive, Paper 2009/370},
      year = {2009},
      url = {https://eprint.iacr.org/2009/370}
}