An improved key agreement protocol based on chaos. (English) Zbl 1222.94039

Summary: Cryptography based on chaos theory has developed fast in the past few years, but most of the researches focus on secret key cryptography. There are few public key encryption algorithms and cryptographic protocols based on chaos, which are also of great importance for network security. We introduce an enhanced key agreement protocol based on Chebyshev chaotic map. Utilizing the semi-group property of Chebyshev polynomials, the proposed key exchange algorithm works like Diffie–Hellman algorithm. The improved protocol overcomes the drawbacks of several previously proposed chaotic key agreement protocols. Both analytical and experimental results show that it is effective and secure.


94A60 Cryptography
33C90 Applications of hypergeometric functions
Full Text: DOI


[1] Schneier, B., Applied cryptography, () · Zbl 0789.94001
[2] Menezes, A.; van Oorschot, P.; Vanstone, S., Handbook of applied cryptography, (1997), CRC Press Boca Raton (FL) · Zbl 0868.94001
[3] Stallings, W., Cryptography and network security: principles and practice, (2002), Publishing House of Electronics Industry Beijing
[4] Liu, B.; Peng, J., Nonlinear dynamics, (2004), High Education Press Beijing
[5] Baptista, M.S., Cryptography with chaos, Phys lett A, 240, 50-54, (1998) · Zbl 0936.94013
[6] Wong, K.W., A fast chaotic cryptographic scheme with dynamic look-up table, Phys lett A, 298, 238-242, (2002) · Zbl 0995.94029
[7] Behnia, S.; Akhshani, A.; Ahadpour, S.; Mahmodi, H.; Akhavan, A., A fast chaotic encryption scheme based on piecewise nonlinear chaotic maps, Phys lett A, 366, 391-396, (2007)
[8] Guan, Z.H.; Huang, F.; Guan, W., Chaos-based image encryption algorithm, Phys lett A, 346, 153-157, (2005) · Zbl 1195.94056
[9] Wong, K.W.; Kwok, B.S.H.; Law, W.S., A fast image encryption scheme based on chaotic standard map, Phys lett A, 372, 2645-2652, (2008) · Zbl 1220.94044
[10] Gao, T.; Chen, Z., A new image encryption algorithm based on hyper-chaos, Phys lett A, 372, 394-400, (2008) · Zbl 1217.94096
[11] Wang, S.; Liu, W.; Lu, H.; Kuang, J.; Hu, G., Periodicity of chaotic trajectories in realizations of finite computer precisions and its implication in chaos communications, Int J mod phys B, 18, 2617-2622, (2004)
[12] Wang, X.; Zhan, M.; Lai, C.-H.; Gang, H., Error function attack of chaos synchronization based encryption schemes, Chaos, 14, 128-137, (2004)
[13] Kocarev L, Tasev Z. Public-key encryption based on Chebyshev maps. In: Proc IEEE Symp Circ Syst (ISCAS’03), vol. 3. 2003. p. 28-31.
[14] Bergamo, P.; D’Arco, P.; Santis, A.; Kocarev, L., Security of public key cryptosystems based on Chebyshev polynomials, IEEE trans circ syst - I, 52, 1382-1393, (2005) · Zbl 1374.94775
[15] Bose, R., Novel public key encryption technique based on multiple chaotic systems, Phys rev lett, 95, 098702, (2005)
[16] Wang, K.; Pei, W.; Zhou, L.; Cheung, Y.; He, Z., Security of public key encryption technique based on multiple chaotic system, Phys lett A, 360, 259-262, (2006) · Zbl 1236.94068
[17] Zhang, L., Cryptanalysis of the public key encryption based on multiple chaotic systems, Chaos solitons fract, 37, 669-674, (2008) · Zbl 1134.94371
[18] Xiao, D.; Liao, X.; Deng, S., A novel key agreement protocol based on chaotic maps, Inform sci, 177, 1136-1142, (2007)
[19] Han, S., Security of a key agreement protocol based on chaotic maps, Chaos solitons fract, 38, 764-768, (2008) · Zbl 1146.94304
[20] Chang E, Han S. Using passphrase to construct key agreement. CBS-IS-2006, Technical report, Curtin University of Technology.
[21] Han, S.; Chang, E., Chaotic map based key agreement with/out clock synchronization, Chaos solitons fract, 39, 1283-1289, (2009) · Zbl 1197.94190
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.