Radial basis function networks as chaotic generators for secure communication system

This paper improves upon a new class of discrete chaotic systems (i.e. chao tic maps) recently introduced for effective information encryption. The non linearity and adaptability of these systems are achieved by designing prope r radial basis function networks. The potential for automatic synchronizati on, the lack of periodicity and the extremely large parameter spaces of the se chaotic maps offer robust transmission security. The Radial Basis Functi on (RBF) networks offer a large number of parameters (i.e. the centers and spreads of the RBF kernels and the weights of the linear layer) while at th e same time as universal approximators they have the flexibility to impleme nt any function. The RBF networks can learn the dynamics of chaotic systems (maps or flows) and mimic them accurately by using many more parameters th an the original dynamical recurrence. Since the parameter space size increa ses exponentially with respect to the number of parameters, the RBF based s ystems greatly outperform previous designs in terms of encryption security. Moreover, the learning of the dynamics from data generated by chaotic syst ems guarantees the chaoticity of the dynamics of the RBF networks and offer s a convenient method of implementing any desirable chaotic dynamics. Since each sequence of training data gives rise to a distinct RBF configuration, theoretically there exists an infinity of possible configurations.