Pairing Computation for Elliptic Curves with Embedding Degree 15

Nadia El Mrabet 1, * Sorina Ionica 2
* Corresponding author
1 ARITH - Arithmétique informatique
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : This paper presents the first study of pairing computation on curves with embedding degree $15$. We show that pairing computation on these curves has loop length $r^{1/8}$ and we use a twist of degree 3 to perform most of the operations in $\F_p$ or $\F_{p^5}$. Furthermore, we present an original arithmetic for extension fields of degree $5$.
Document type :
Reports
Complete list of metadatas

https://hal-lirmm.ccsd.cnrs.fr/lirmm-00380549
Contributor : Nadia El Mrabet <>
Submitted on : Saturday, May 2, 2009 - 6:01:58 PM
Last modification on : Thursday, May 24, 2018 - 3:59:21 PM
Long-term archiving on : Thursday, June 10, 2010 - 8:33:04 PM

File

articlek15v6.pdf
Publisher files allowed on an open archive

Identifiers

  • HAL Id : lirmm-00380549, version 1

Collections

Citation

Nadia El Mrabet, Sorina Ionica. Pairing Computation for Elliptic Curves with Embedding Degree 15. RR-09012, 2009, pp.14. ⟨lirmm-00380549⟩

Share

Metrics

Record views

276

Files downloads

558