Hybrid-Key Agreement Protocol based on Chebyshev Polynomials
Main Article Content
Abstract
This paper presented implementation of the Chebyshev permutation polynomials on hardware. The experimental results demonstrate that this is an efficient way to calculate the Chebyshev polynomials in a prime field. According to the hardware structure of the Chebyshev polynomial, a Hybrid-Key Agreement Protocol is proposed. The purpose of our protocol is to enable two end-users exchanging a secret session key using both the key distribution center and the Chebyshev-based public key encryption. Advantage of public-key encryption is authentic and confidential for delivering secret keys, the addition of KDCs serves a widely distributed set of users. The proposed key agreement protocol offers satisfactory security and can be implemented hardware efficiently suitable for the low resource utilization.
Keywords
Public key, Chebyshev, FPGA
Article Details
References
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[2] Dong Hwi Seo and P. Sweeney, Simple authenticated key agreement algorithm, Electronics Letters, vol. 35, pp. 1073–1074, June 1999.
[3] P. E. Abi-Char, A. Mhamed, and B. El-Hassan, A secure authenticated key agreement protocol based on elliptic curve cryptography, in Third International Symposium on Information Assurance and Security, pp. 89–94, Aug 2007.
[4] C. Boyd and A. Mathuria, Key Agreement Protocols, pp. 137–199. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003.
[5] C. Adams, Kerberos Authentication Protocol, pp. 674–675. Boston, MA: Springer US, 2011.
[6] G. Maze, Algebraic methods for constructing one-way trapdoor functions. PhD thesis, University of Notre Dame Notre Dame, 2003.
[7] L. Kocarev and S. Lian, Chaos-based Cryptography. Springer, 2011.
[8] S. Vairachilai, M. K. Kavithadevi, and R. Gnanaejayaraman, Public key cryptosystems using chebyshev polynomials based on edge information, in 2014 World Congress on Computing and Communication Technologies, pp. 243–245, Feb 2014.
[9] P. Bergamo, P. D’Arco, A. De Santis, and L. Kocarev, Security of public-key cryptosystems based on chebyshev polynomials, IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 52, pp. 1382–1393, July 2005.
[10] T. T. K. Hue, T. M. Hoang, and A. Braeken, Lightweight signcryption scheme based on discrete chebyshev maps, in 2017 12th International Conference for Internet Technology and Secured Transactions (ICITST), pp. 43–47, Dec 2017.
[11] A. Braeken, P. Kumar, M. Liyange, and T. T. K. Hue, An efficient anonymous authentication protocol in multiple server communication networks (easm), The Journal of Supercomputing, vol. 74, pp. 1695–1714, Apr 2018.
[12] G. J. Fee and M. B. Monagan, Cryptography using chebyshev polynomials, in Laurier University, Waterloo, pp. 1–15, 2004.
[13] J. Liu, D. Yang, H. Zhou, and S. Chen, A digital image encryption algorithm based on bit-planes and an improved logistic map, Multimedia Tools and Applications, p. 1, Nov. 2017.
[14] R. Bronson and G. B. Costa, 7 - matrix calculus, in Matrix Methods (Third Edition) (R. Bronson and G. B. Costa, eds.), pp. 213 – 255, Boston: Academic Press, third edition ed., 2009.
[15] D. Yoshioka, Properties of chebyshev polynomials modulo p^k, IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 65, pp. 386–390, March 2018.