## Cryptology ePrint Archive: Report 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.

Category / Keywords: implementation /

Publication Info: student paper