Pairings on Hyperelliptic Curves with a Real Model

Authors:
Steven D. Galbraith;Xibin Lin;David J. Mireles Morales
Affiliations:
Mathematics Department Royal Holloway, University of London, United Kingdom;Mathematics Department Royal Holloway, University of London, United Kingdom and School of Mathematics and Computational Science, Sun Yat-Sen University, P.R.China;Mathematics Department Royal Holloway, University of London, United Kingdom
Venue:
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Year:
2008

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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 p2茂戮驴 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.