Paper 2009/370

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

Nadia El Mrabet and 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 $\rho~1.5$ 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.