Communicating with hyperchaos: The dynamics of a DNLF emitter and recovery of transmitted information

V S Udaltsov,J P Goedgebuer,L Larger,J B Cuenot,P Levy,W T Rhodes

doi:10.1134/1.1595224

Abstract

It is reported that signal encoding with high-dimensional chaos produced by delayed feedback systems with strong nonlinearity can be broken. The procedure is described and the method is illustrated with chaotic waveforms obtained from a strongly nonlinear optical system used by the authors previously to demonstrate signal encryption and decryption with wavelength chaos. The method can be extended to any systems ruled by nonlinear time-delayed differential equations.

Highlights

The security of these systems is still open for discussion, chaotic communications based on simpler encryption schemes have been shown to be susceptible to cracking mainly in two cases, as follows: (i) it was shown that information transmitted by a DNLF system with a weak nonlinearity introduced by an erbium optical amplifier in the feedback loop [9] could be successfully unmasked by considering the chaotic waveform as a convolution of the original laser pulses with an “echo” function associated with the delayed feedback loop [10]; (ii) a second type of attacks was proposed for the system with only one extremum Mackey–Glass nonlinear function [11] from time-series analysis [12, 13]
We report on our investigation of the security features of systems of this type that exhibit a strong nonlinearity and, a more complex encryption scheme
The extremes of results obtained in our experiments have shown that the mismatch of τ in the transmitter and the receiver can reach a value of 4–5% without incurring dramatic problems in recovery of the message signal in the receiver, so the value of τ can be known with an accuracy of the order of a few percent

Summary

Introduction

The proper delay time TR = T, response time τR = τ, bifurcation parameter βR = β, and nonlinear function FR = F allow recovery of the message by subtracting y(t) from x(t), yielding a difference signal The output transmitter signal obtained and that we used in our simulations is shown, was approximately 1 ms in duration, and was sampled at 86-ns intervals to yield N = 12000 points.

Results

Conclusion