Security analysis of chaotic communication systems based on Volterra–Wiener–Korenberg model

Pseudo-randomicity is an important cryptological characteristic for proof of encryption algorithms. This paper proposes a nonlinear detecting method based on Volterra–Wiener–Korenberg model and suggests an autocorrelation function to analyze the pseudo-randomicity of chaotic secure systems under different sampling interval. The results show that: (1) the increase of the order of the chaotic transmitter will not necessarily result in a high degree of security; (2) chaotic secure systems have higher and stronger pseudo-randomicity at sparse sampling interval due to the similarity of chaotic time series to the noise; (3) Volterra–Wiener–Korenberg method can also give a further appropriate sparse sampling interval for improving the security of chaotic secure communication systems. For unmasking chaotic communication systems, the Volterra–Wiener–Korenberg technique can be applied to analyze the chaotic time series with surrogate data.

[1]  Xianfa Jiao,et al.  Some Advance in Nonlinear Stochastic Evolution Models for Phase Resetting Dynamics on Populations of Neuronal Oscillators , 2003 .

[2]  Mauricio Barahona,et al.  Detection of nonlinear dynamics in short, noisy time series , 1996, Nature.

[3]  Kevin M. Short,et al.  Signal Extraction from Chaotic Communications , 1997 .

[4]  Akio Matsumoto.  Let it be: chaotic price instability can be beneficial , 2003 .

[5]  A. Irving.  Stochastic sensitivity analysis , 1992 .

[6]  Tao Yang,et al.  Application of neural networks to unmasking chaotic secure communication , 1998 .

[7]  Chi-Sang Poon,et al.  Decrease of cardiac chaos in congestive heart failure , 1997, Nature.

[8]  Hongguang Li,et al.  Chaotic behaviors of a bilinear hysteretic oscillator , 2002 .

[9]  Ljupco Kocarev,et al.  Analysis of some recently proposed chaos-based encryption algo-rithms , 2001 .

[10]  L. Kocarev,et al.  Chaos and cryptography: block encryption ciphers based on chaotic maps , 2001 .

[11]  Lei Min.  The Volterra Wiener Korenberg Model Nonlinear Test Method , 2003 .

[12]  Fraser,et al.  Independent coordinates for strange attractors from mutual information. , 1986, Physical review. A, General physics.

[13]  J. Yorke,et al.  Period Three Implies Chaos , 1975 .

[14]  W. Schwarz,et al.  Chaos and cryptography , 2001 .

[15]  Miguel Romera,et al.  Cryptanalyzing a discrete-time chaos synchronization secure communication system , 2003, nlin/0311046.

[16]  Kwok-Wo Wong,et al.  An efficient entire chaos-based scheme for deniable authentication , 2005 .

[17]  U. Parlitz,et al.  Using Surrogate Data Analysis for Unmasking Chaotic Communication Systems , 1997 .

[18]  Steven R. Bishop,et al.  Chaotic Behaviour in a Nonlinear Delay System , 2001 .

[19]  Ta-lun Yang,et al.  Breaking chaotic secure communication using a spectrogram , 1998 .

[20]  Mauricio Barahona,et al.  Titration of chaos with added noise , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[21]  T. Dewson,et al.  Determining mixed linear-nonlinear coupled differential equations from multivariate discrete time series sequences , 1997 .

[22]  A d'Anjou,et al.  Parameter-adaptive identical synchronization disclosing Lorenz chaotic masking. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Min Lei,et al.  Detecting Nonlinearity of Sunspot Number , 2004 .

[24]  Jun-an Lu,et al.  Synchronization of a unified chaotic system and the application in secure communication , 2002 .

[25]  T. Dewson,et al.  Volterra Functional Secure Communication Systems , 2003, Int. J. Bifurc. Chaos.

[26]  H. Sakaguchi.  Parameter evaluation from time sequences using chaos synchronization. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  Mingshu Peng,et al.  Rich dynamics of discrete delay ecological models , 2005 .

[28]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[29]  Xie Kun.  The Encryption Analysis on the Chaotic System Based on Sub- Nyquist , 2004 .

[30]  Ravi Prakash,et al.  Quasi-periodic, Subharmonic and Chaotic Motions of a Rotor Bearing System , 2003 .

[31]  Bing-Hong Wang,et al.  Improving the security of chaotic encryption by using a simple modulating method , 2004 .

[32]  Baier,et al.  Design of hyperchaotic flows. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[33]  Wei Huang,et al.  Unmasking Chaotic mask by a Wavelet Multiscale Decomposition Algorithm , 2001, Int. J. Bifurc. Chaos.