## Cryptology ePrint Archive: Report 2008/250

Pairings on hyperelliptic curves with a real model

Steven Galbraith and Xibin Lin and David Mireles

Abstract: We analyse the efficiency of pairing computations on hyperelliptic curves given by a real model using a balanced divisor at infinity. Several optimisations are proposed and analysed. Genus two curves given by a real model arise when considering pairing friendly groups of order dividing $p^{2}-p+1$. We compare the performance of pairings on such groups in both elliptic and hyperelliptic versions. We conclude that pairings can be efficiently computable in real models of hyperelliptic curves.

Category / Keywords: implementation / hyperelliptic curves, pairings, real models