Abstract
A directed signature scheme allows a designated verifier to directly verify a signature issued to him, and a third party to check the signature validity with the help of the signer or the designated verifier as well. In this paper, starting from the Vercauteren’s work on optimal pairings, we describe how to exploit the action of the 23mth power Verschiebung in order to reduce the loop length of Miller’s algorithm even further brief than the genus − 2η T approach. At the same time, we propose an efficient identity-based directed signature scheme from Optimal Eta Pairing on Supersingular Genus-2 Binary Hyperelliptic Curves.
Keywords
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Shamir, A.: Identity-Based Cryptosystems and Signature Schemes. In: Blakely, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 47–53. Springer, Heidelberg (1985)
Sun, X., Li, J.-H., Chen, G.-L., Yung, S.-T.: Identity-Based Directed Signature Scheme from Bilinear Pairings, http://eprint.iacr.org/2008/305.pdf
Bellare, M., Namprempre, C., Neven, G.: Security Proofs for Identity-Based Identification and Signature Schemes. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 268–286. Springer, Heidelberg (2004)
Libert, B., Quisquater, J.J.: The exact security of an Identity based signature and its applications, http://eprint.iacr.org/2004/102
Zhang, J., Yang, Y., Niu, X.: Efficient Provable Secure ID-Based Directed Signature Scheme without Random Oracle. In: Yu, W., He, H., Zhang, N. (eds.) ISNN 2009, Part III. LNCS, vol. 5553, pp. 318–327. Springer, Heidelberg (2009)
Waters, B.: Efficient Identity-Based Encryption Without Random Oracles. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 114–127. Springer, Heidelberg (2005)
Miller, V.: The Weil pairing, and its efficient calculation. J. Cryptol. 17(4), 235–261 (2004)
Hess, F.: Efficient identity based signature schemes based on pairings. In: Nyberg, K., Heys, H.M. (eds.) SAC 2002. LNCS, vol. 2595, pp. 310–324. Springer, Heidelberg (2003)
Barreto, M., et al.: Efficient pairing computation on supersingular Abelian varieties. Des. Codes Crypt. 42, 239–271 (2007)
Hess, F., Smart, N., Vercauteren, F.: The Eta pairing revisited. IEEE Trans. Inf. Theory 52(10), 4595–4602 (2006)
Granger, R., Hess, F., Oyono, R., Thériault, N., Vercauteren, F.: Ate Pairing on Hyperelliptic Curves. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 430–447. Springer, Heidelberg (2007)
Hess, F.: Pairing Lattices. In: Galbraith, S.D., Paterson, K.G. (eds.) Pairing 2008. LNCS, vol. 5209, pp. 18–38. Springer, Heidelberg (2008)
Galbraith, S., Paterson, K., Smart, N.: Pairings for cryptographers. Discrete Applied Mathematics 156, 3113–3121 (2008)
Menezes, A., Okamoto, T., Vanstone, S.: Reducing elliptic curves logarithms to logarithms in a finite field. IEEE Trans. Inf. Theory 39(5), 1639–1646 (1993)
Estibals, N.: Compact Hardware for Computing the Tate Pairing over 128-Bit-Security Supersingular Curves. In: Joye, M., Miyaji, A., Otsuka, A. (eds.) Pairing 2010. LNCS, vol. 6487, pp. 397–416. Springer, Heidelberg (2010)
Aranha, D.F., López, J., Hankerson, D.: High-Speed Parallel Software Implementation of the η_T Pairing. In: Pieprzyk, J. (ed.) CT-RSA 2010. LNCS, vol. 5985, pp. 89–105. Springer, Heidelberg (2010)
Galbraith, S.D.: Supersingular Curves in Cryptography. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 495–513. Springer, Heidelberg (2001)
Vercauteren, F.: Optimal pairings. IEEE Trans. Inf. Theory 56(1), 455–461 (2010)
Cantor, D.: Computing in the Jacobian of a hyperelliptic curve. Math. Comput. 48(177), 95–101 (1987)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ku, J., Yun, D., Zheng, B., Wei, S. (2012). An Efficient ID-Based Directed Signature Scheme from Optimal Eta Pairing. In: Li, Z., Li, X., Liu, Y., Cai, Z. (eds) Computational Intelligence and Intelligent Systems. ISICA 2012. Communications in Computer and Information Science, vol 316. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34289-9_49
Download citation
DOI: https://doi.org/10.1007/978-3-642-34289-9_49
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-34288-2
Online ISBN: 978-3-642-34289-9
eBook Packages: Computer ScienceComputer Science (R0)