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(ε)) attainable by intended receivers that know the initial condition to the associated Pr(ε) 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(ε) to intended than to unintended receivers. We develop computationally efficient methods for obtaining tight bounds on the best P r(ε) performance of intended and unintended receivers. In the process, we identify chaotic map attributes that affect the relative Pr(ε) advantages provided to intended receivers and develop methods for designing maps that achieve a target gap between the intended and unintended receiver Pr(ε).