Abstract
Hu et al. first studied pairing computations on supersingular elliptic curve with odd embedding degree k = 3 and applied them to Identity-based cryptosystems. In this paper, a careful analysis of the pairing computation on this family of supersingular curves is given. Some novel improvements are presented from different points of view and hence speed up the implementation of Identity-based cryptosystems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Barreto, P.S.L.M., Galbraith, S., ÓhÉigeartaigh, C., Scott, M.: Efficient pairing computation on supersingular Abelian varieties. Designs, Codes and Cryptography 42(3), 239–271 (2007)
Barreto, P.S.L.M., Kim, H.Y., Lynn, B., Scott, M.: Efficient algorithms for pairing-based cryptosystems. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 354–368. Springer, Heidelberg (2002)
Blake, I.F., Seroussi, G., Smart, N.P.: Elliptic Curves in Cryptography. Cambridge University Press, New York (1999)
Chung, J., Hasan, M.A.: Asymmetric squaring formulae (2006), http://www.cacr.math.uwaterloo.ca/
Cohen, H., Miyaji, A., Ono, T.: Efficient elliptic curve exponentiation using mixed coordinates. In: Ohta, K., Pei, D. (eds.) ASIACRYPT 1998. LNCS, vol. 1514, pp. 51–65. Springer, Heidelberg (1998)
Boneh, D., Franklin, M.: Identity-based encryption from the Weil pairing. SIAM Journal of Computing 32(3), 586–615 (2003)
Frey, G., Rück, H.-G.: A remark concerning m-divisibility and the discrete logartihm in the divisor class group of curves. Math. Comp. 62(206), 865–874 (1994)
Galbraith, S.D.: Pairings - Advances in Elliptic Curve Cryptography. In: Blake, I., Seroussi, G., Smart, N. (eds.). Cambridge University Press, Cambridge (2005)
Hu, L., Dong, J.-W., Pei, D.-Y.: An implementation of cryptosystems Based on tate pairing. Journal of Computer Science and Technology 20(2), 264–269 (2005)
Hu, L.: Compression of Tate Pairings on Elliptic Curves. Journal of Software in China 18(7), 1799–1805 (2007)
Hess, F., Smart, N.P., Vercauteren, F.: The Eta pairing revisited. IEEE Transactions on Information Theory 52, 4595–4602 (2006)
Lee, E., Lee, H.-S., Park, C.-M.: Efficient and generalized pairing computation on abelian varieties. IEEE Transactions on Information Theory 55(4), 1793–1803 (2009)
Knuth, D.E.: Seminumerical algorithms. Addison-Wesley, Reading (1981)
Miller, V.S.: Short programs for functions on curves (Unpublished manuscript) (1986)
Matsuda, S., Kanayama, N., Hess, F., Okamoto, E.: Optimised versions of the Ate and twisted Ate pairings. In: Galbraith, S.D. (ed.) Cryptography and Coding 2007. LNCS, vol. 4887, pp. 302–312. Springer, Heidelberg (2007)
Silverman, J.H.: The arithmetic of elliptic curves. Graduate Texts in Mathematics, vol. 106. Springer, Heidelberg (1986)
Verheul, E.: Evidence that XTR is more secure than supersingular elliptic curve cryptosystems. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 195–210. Springer, Heidelberg (2001)
Zhao, C.-A., Zhang, F., Huang, J.: A note on the Ate pairing. Internationl Journal of Information Security 7(6), 379–382 (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zhao, CA., Xie, D., Zhang, F., Gao, CZ., Zhang, J. (2009). Improved Implementations of Cryptosystems Based on Tate Pairing. In: Park, J.H., Chen, HH., Atiquzzaman, M., Lee, C., Kim, Th., Yeo, SS. (eds) Advances in Information Security and Assurance. ISA 2009. Lecture Notes in Computer Science, vol 5576. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02617-1_15
Download citation
DOI: https://doi.org/10.1007/978-3-642-02617-1_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02616-4
Online ISBN: 978-3-642-02617-1
eBook Packages: Computer ScienceComputer Science (R0)