Security of a key agreement protocol based on chaotic maps. (English) Zbl 1146.94304

Summary: Kacorev et al. proposed new public key encryption scheme using chaotic maps. Subsequently, Bergamo et al. has broken Kacorev and Tasev’s encryption scheme and then applied the attack on a key agreement protocol based on Kacorev et al.’s system. In order to address Bergamo et al.’ attack, Xiao et al. proposed a novel key agreement protocol. In this paper, we will present two attacks on Xiao et al.’s key agreement protocol using chaotic maps. Our new attack method is different from the one that Bergamo et al. developed. The proposed attacks work in a way that an adversary can prevent the user and the server from establishing a shared session key even though the adversary cannot get any private information from the user and the server’s communications.


94A62 Authentication, digital signatures and secret sharing
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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[1] Alvarez, G., Security problems with a chaos-based deniable authentication scheme, Chaos, solitons & fractals, 26, 7-11, (2005) · Zbl 1077.94019
[2] Bergamo, P.; D’Arco, P.; Santis, A.; Kocarev, L., Security of public key cryptosystems based on Chebyshev polynomials, IEEE trans circ syst-I, 52, 7, 1382-1393, (2005) · Zbl 1374.94775
[3] Dachselt, F.; Schwarz, W., Chaos and cryptography, IEEE trans circ syst-I, fundam theory, 48, 12, 1498-1509, (2001) · Zbl 0999.94030
[4] Fridrich, G., Symmetric ciphers based on two-dimensional chaotic maps, Int J bifur chaos, 8, 1259-1284, (1998) · Zbl 0935.94019
[5] Pecorra, T.L.; Carroll, T.L., Driving systems with chaotic signals, Phys rev A, 44, 4, 2374-2383, (1991)
[6] Kocarev, L., Chaos-based cryptography: a brief overview, IEEE circ syst mag, 1, 6-21, (2001)
[7] Kocarev, L.; Tasev, Z., Public-key encryption based on Chebyshev maps, Proc IEEE symp circ syst (ISCAS’03), 3, 28-31, (2003)
[8] Menezes, A.; van Oorschot, P.; Vanstone, S., Handbook of applied cryptography, (1997), CRC Press Boca Raton · Zbl 0868.94001
[9] Xiao, D.; Liao, X.; Wong, K., An efficient entire chaos-based scheme for deniable authentication, Chaos, solitons & fractals, 23, 1327-1331, (2005) · Zbl 1070.94023
[10] Xiao, D.; Liao, X.; Deng, S., One-way hash function construction based on the chaotic map with changeable-parameter, Chaos, solitons & fractals, 24, 65-71, (2005) · Zbl 1068.94019
[11] Xiao, D.; Liao, XF.; Deng, SJ., A novel key agreement protocol based on chaotic maps, Inform sci, (2006)
[12] Grassi, G.; Mascolo, S., IEEE trans circ syst I: fundam theory appl, 46, 1135, (1999)
[13] Wong, K.W., A fast chaotic cryptographic scheme with dynamic look-up table, Phys lett A, 298, 238-242, (2002) · Zbl 0995.94029
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