## Cryptology ePrint Archive: Report 2012/632

Pairings on Generalized Huff Curves

Abdoul Aziz Ciss and Djiby Sow

Abstract: This paper presents the Tate pairing computation on generalized Huff curves proposed by Wu and Feng in \cite{Wu}. In fact, we extend the results of the Tate pairing computation on the standard Huff elliptic curves done previously by Joye, Tibouchi and Vergnaud in \cite{Joux}. We show that the addition step of the Miller loop can be performed in $1\mathbf{M}+(k+15)\mathbf{m}+2\mathbf{c}$ and the doubling one in $1\mathbf{M} + 1\mathbf{S} + (k + 12) \mathbf{m} + 5\mathbf{s} + 2\mathbf{c}$ on the generalized Huff curve.

Category / Keywords: foundations / Tate pairing, elliptic curves, Huff curves, Miller algorithm