Chaotic-Pulse-Position Modulation: A third party intrusion scheme using Kalman Filter

In this paper, we focus on the security issue of a chaotic digital communication scheme called chaotic-pulse- position modulation. We design a third party intrusion scheme to test to see if CPPM is as secure as is claimed. Experiments are conducted with various chaotic maps, where CPPM is used to modulate the message at the transmitter and a Kalman filter fed with a polynomial approximation is used at the receive. It is, shown that we can recover the original message without knowing the initial state or the chaotic map used at the transmitter. The bit error rate performances under different signal to noise ratios are evaluated to show the feasibility of this task. Furthermore, we use a bank of Kalman filters, each having polynomial models of various degrees, to estimate the degree of the chaotic map used at the transmitter. Successful results are reported.