Nonlinear Parameter Modulation for Low-Cost Enhancement of Chaotic Entropy

In this paper, we have proposed non-linear parameter modulation as a low-cost technique to widen the chaotic region of analog one-dimensional (1-D) discrete-time chaotic maps, referred to as seed maps. The non-linear modulation circuits are designed with low transistor-count topologies. The design scheme generally applies to a wide range of 1-D discrete-time analog seed maps. The chaotic performance improvement after adding the non-linear modulation is examined with bifurcation plots and three chaotic entropy metrics namely, correlation coefficient, Lyapunov exponent, and correlation dimension. Along with the traditional design of a chaotic oscillator, two novel oscillator topologies are presented to demonstrate the versatile applicability of the proposed non-linear modulation scheme for designing chaotic systems with elevated performance. This hardware-efficient design with promising chaotic behavior shows the potential to be employed in many hardware-constrained chaos-based security applications for integrated circuits including robust random number generators, reconfigurable logic, physically unclonable function-based authentication, and so on.