Linear Cryptanalysis for a Chaos-Based Stream Cipher
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.
[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.
[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.
@article{"International Journal of Electrical, Electronic and Communication Sciences:61248", author = "Ruming Yin and Jian Yuan and Qiuhua Yang and Xiuming Shan and Xiqin Wang", title = "Linear Cryptanalysis for a Chaos-Based Stream Cipher", 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.", volume = "3", number = "12", pages = "2375-6", }
