Linear Cryptanalysis for a Chaos-Based Stream Cipher

Authors: Ruming Yin, Jian Yuan, Qiuhua Yang, Xiuming Shan, Xiqin Wang

Abstract:

Linear cryptanalysis methods are rarely used to improve the security of chaotic stream ciphers. In this paper, we apply linear cryptanalysis to a chaotic stream cipher which was designed by strictly using the basic design criterion of cryptosystem – confusion and diffusion. We show that this well-designed chaos-based stream cipher is still insecure against distinguishing attack. This distinguishing attack promotes the further improvement of the cipher.

Keywords: Stream cipher, chaos, linear cryptanalysis, distinguishing attack.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1078773

References:

[1] L. Kocarev, "Chaos-based cryptography: A brief overview," IEEE Circuits Syst. Mag., vol. 1, pp. 6-21, 2001.
[2] G. Jakimoski and L. Kocarev, "Chaos and cryptography: Block encryption ciphers based on chaotic maps," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 48, no. 2, pp. 163-169, Feb. 2001.
[3] G. Jakimoski and L. Kocarev, "Differential and Linear Probabilities of a Block-Encryption Cipher", IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 50, no. 1, pp. 121-123, Jan. 2003.
[4] J. M. Amigo and J. Szczepanski, "Approximations of dynamical systems and their applications to cryptography," Int. J. Bifurc. Chaos, vol. 13, pp. 1937-1948, 2003.
[5] J. Szczepanski, J. M. Amigo, T. Michalek, L. Kocarev, "Cryptographically secure substitutions based on the approximation of mixing maps," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 52, no. 2, pp. 443- 453, Feb. 2005.
[6] N. Masuda, G. Jakimoski, K. Aihara, L. Kocarev, "Chaotic Block Ciphers: From Theory to Practical Algorithms," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 53, no. 6, pp. 1341-1352, Jun. 2006.
[7] R. Yin, J. Yuan, Q. Yang, et al., "Discretization of coupled map lattices for a stream cipher," submitted to Physics Letters A, Apr. 2009.
[8] S. Paul, B. Preneel, G. Sekar, "Distinguishing Attacks on the Stream Cipher Py," Fast Software Encryption 2006, M.J.B. Robshaw, ed., vol. 4047, pp. 405-421, Springer Berlin/Heidelberg 2006.
[9] T. Baigneres, P. Junod, S. Vaudenay, "How Far Can We Go Beyond Linear Cryptanalysis?," ASIACRYPT 2004, P.J. Lee, ed., vol. 3329, pp. 432-450, Springer Berlin/Heidelberg 2004.
[10] M. Matsui, "Linear cryptanalysis method for DES ciphers," Advances in Cryptology-Eurocrypt 1993, T. Helleseth, ed., vol. 765, pp. 386-397, Springer Berlin/Heidelberg 1994.
[11] M. Boesgaard, M. Vesterager, T. Pedersen, et al., "Rabbit: A New High-Performance Stream Cipher," Fast Software Encryption 2003, T. Johansson, ed., vol. 2887, pp. 307-329, Springer Berlin/Heidelberg 2003.