VOLTERRA FUNCTIONAL SECURE COMMUNICATION SYSTEMS

Abstract

Two methods, based on nonlinear dynamics, are described for broad- and narrow-band communication systems. The first approach employs hyperchaotic discrete time series carrier sequences generated with mixed linear–nonlinear coupled differential equations [Irving & Dewson, 1997]. In this first approach it is assumed that the solution of the coupled ordinary differential equations can be represented as a multichannel Volterra functional expansion. Identification, synchronization and the potential unmasking of hyperchaotic communications systems, are achieved by generating a tractable hierarchy of ascending order time series moment equations by operating on a suitably truncated Volterra functional expansion. The estimated moment hierarchy facilitates the calculation of the coefficients of the coupled differential equations that generate the multichannel carrier that is to be modulated by the message. Due to its ability to easily and accurately estimate the coefficients of the governing differential equations the method is applied to the multichannel carrier sequences of data generated by a set of hyperchaotic equations. The inherent problem of resynchronization in chaotic communication systems cannot be avoided in general because of the evolutionary, time dependent, nature of the time series carriers used. This time dependence problem that results in repeated resynchronization can be avoided by considering an alternative and innovative approach that employs time series carrier sequences generated by an input–output multichannel Volterra kernel expansion [Dewson & Irving, 1996]. In this second method, mixed order multichannel Volterra kernel functions are used to generate the carrier sequence that is then modulated by the message. The Volterra kernel function values used to generate the carrier can be identified with the moment hierarchy method [Dewson & Irving, 1996] enabling the message to be deconvolved from the transmitted signal. The modulated nonlinear multichannel signal is transmitted to the receiver. The effect of transmission is to distort and corrupt the signal. In this work it is assumed that the distortions to the transmitted signal remain small, with the case where they become significant being treated elsewhere. First, the case where the signal is received free from both noise and distortion, for example the decryption of an encrypted e-mail, is first considered. Then signal reception in the presence of additive noise is considered. Each of the two proposed methods has been investigated to determine their accuracy and robustness in the presence of additive noise.