An Authenticated Key Agreement Protocol Using Isogenies Between Elliptic Curves

Debiao He, Jianhua Chen, Jin Hu

Abstract


All the current public-key cryptosystems will become insecure when size of a quantum register is sufficient. An authenticated key agreement protocol, which is against the attack of quantum computer, is proposed. The proposed protocol can provide the security properties known session key security, forward security, resistance to key-compromise impersonation attack and to unknown key-share attack, key control. We also prove its security in a widely accepted model.

Keywords


public-key cryptosystem; quantum computer; isogeny; elliptic curve; key agreement protocol

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References


W. Diffie and M. Hellman, New directions in cryptography, IEEE Trans. Info. TH, vol. 22, pp.644-654, 1976.
http://dx.doi.org/10.1109/TIT.1976.1055638

Boneh D., Lipton R. Quantum cryptanalysis of hidden linear functions. Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology (LNCS 963), 1995:424-437.
http://dx.doi.org/10.1007/3-540-44750-4_34

Rostovtesv A. and Stolbunov A., Public-key cryptosystem based on isogenies. Cryptology ePrint Archive, Report 2006/145, 2006. http://eprint.iacr.org/.

Couveignes J. M., Dewaghe L., Morain F. Isogeny cycles and the schoof-elkies-atkin algorithm. Ecole polytechnique, France, 1996.

Elkies N., Elliptic and modular curves over finite fields and related computational issues, Proceedings of a Conference in Honor of A.O.L. Atkin, AMS International Press, 1998, pp.21- 76.

Muller V., Ein Algorithmus zur Bestimmung der Punktanzahl elliptisher Kurven uber endlichen Korpern der Charakteristik groser drei, 1995. http://www.informatik.tudarmstadt. de/ti/forschung/ecc.

F.Morain, E.Schost, Fast Algorithms for Computing Isogenies between Elliptic Curves. http://www.lix.polytechnique.fr/ morain/jcomp.pdf, 2006.

S. Galbraith. Constructing isogenies between elliptic curves over finite fields, Journal of Computational Mathematics, vol. 2, pp.118-138, 1999.
http://dx.doi.org/10.1112/s1461157000000097

S. Blake-Wilson, D. Johnson and A. Menezes, Key Agreement Protocols and Their Security Analysis, Proceedings of Sixth IMA International Conference on Cryptography and Coding, Cirencester, UK, 1997, pp. 30-45.
http://dx.doi.org/10.1007/bfb0024447

H. Pan, J.-F. Li, Q.-S. Zheng, A Provable-Security Mutual Authenticated Key Agreement Protocol for Mobile Communication, The 4th International Conference on Wireless Communications, Networking and Mobile Computing, 2008, pp.1-4.




DOI: https://doi.org/10.15837/ijccc.2011.2.2174



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