Physical-layer secrecy with DS/SS from piecewise linear chaotic Markov maps: analysis and design

We study a class of pseudo-chaotic spread spectrum systems for secure communication over additive white Gaussian noise channels, whereby a symbol stream is linearly modulated on a sequence generated by iterating an initial condition through a suitably chosen chaotic map. We compare the optimal 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 Pr(ε) benefits to intended receivers. We develop bounds on the best Pr(ε)performance of intended and unintended receivers. In the process, we identify properties of the chaotic maps that affect the secrecy benefits and develop methods for designing maps that meet a required level of secrecy.