Physical-layer secrecy in AWGN via a class of chaotic DS/SS systems: analysis and design

We study a class of pseudo-chaotic spread spectrum systems for secure communication over additive white Gaussian noise (AWGN) channels, whereby a symbol stream is linearly modulated on a spreading sequence generated by iterating an initial condition through a suitably chosen chaotic map. We compare the uncoded probability of error (Pr(/spl epsiv/)) attainable by intended receivers that know the initial condition to the associated Pr(/spl epsiv/) of unintended receivers that know the modulation scheme but not the initial condition. The sensitive dependence of chaotic sequences on initial conditions, together with the presence of channel noise, can be exploited to provide substantially lower Pr(/spl epsiv/) to intended than to unintended receivers. We develop computationally efficient methods for obtaining tight bounds on the best P r(/spl epsiv/) performance of intended and unintended receivers. In the process, we identify chaotic map attributes that affect the relative Pr(/spl epsiv/) advantages provided to intended receivers and develop methods for designing maps that achieve a target gap between the intended and unintended receiver Pr(/spl epsiv/).

[1]  Haralabos C. Papadopoulos,et al.  Maximum-likelihood estimation of a class of chaotic signals , 1995, IEEE Trans. Inf. Theory.

[2]  G. Mazzini,et al.  Statistical modeling of discrete-time chaotic processes-basic finite-dimensional tools and applications , 2002, The IEEE International Symposium on Circuits and Systems, 2003. Tutorial Guide: ISCAS 2003..

[3]  Thomas L. Carroll,et al.  Spread-spectrum sequences from unstable periodic orbits , 2000 .

[4]  Ezio Biglieri,et al.  Design of spread-spectrum sequences using chaotic dynamical systems and ergodic theory , 2001 .

[5]  Gianluca Mazzini,et al.  Interference bounds for DS-CDMA systems based on chaotic piecewise-affine Markov maps , 2000 .

[6]  Jovan Dj. Golic,et al.  A Comparison of Cryptanalytic Principles Based on Iterative Error-Correction , 1991, EUROCRYPT.

[7]  Gregory W. Wornell,et al.  Statistical analysis and spectral estimation techniques for one-dimensional chaotic signals , 1997, IEEE Trans. Signal Process..

[8]  Tambe,et al.  Driving systems with chaotic signals. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[9]  S. Wicker.  Error Control Systems for Digital Communication and Storage , 1994 .

[10]  Michael W. Hoffman,et al.  Fully programmable, scalable chaos-based PN sequence generation , 2000 .

[11]  E. Ott.  Chaos in Dynamical Systems: Contents , 2002 .

[12]  Jovan Dj. Golic,et al.  Convergence of a Bayesian Iterative Error-Correction Procedure on a Noisy Shift register Sequence , 1992, EUROCRYPT.

[13]  Michael C. Mackey,et al.  Chaos, Fractals, and Noise , 1994 .

[14]  Clare D. McGillem,et al.  A chaotic direct-sequence spread-spectrum communication system , 1994, IEEE Trans. Commun..

[15]  G. Mazzini,et al.  Corrections to "Chaotic Complex Spreading Sequences for Asynchronous DS-CDMA—Part I: System Modeling and Results" 1 , 1998 .

[16]  Mw Hirsch,et al.  Chaos In Dynamical Systems , 2016 .

[17]  Riccardo Rovatti,et al.  Chaotic complex spreading sequences for asynchronous DS-CDMA. I. System modeling and results , 1997 .

[18]  R. Rovatti,et al.  Chaotic complex spreading sequences for asynchronous DS-CDMA. Part II. Some theoretical performance bounds , 1998 .

[19]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[20]  Grebogi,et al.  Roundoff-induced periodicity and the correlation dimension of chaotic attractors. , 1988, Physical review. A, General physics.

[21]  Carroll,et al.  Driving systems with chaotic signals. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[22]  Neri Merhav,et al.  On the threshold effect in the estimation of chaotic sequences , 2003, IEEE Transactions on Information Theory.

[23]  Tohru Kohda.  Information sources using chaotic dynamics , 2001 .

[24]  Alan V. Oppenheim,et al.  Synchronization of Lorenz-based chaotic circuits with applications to communications , 1993 .

[25]  Edward Ott,et al.  Chaos in Dynamical Systems - 2nd Edition , 2002 .