wilamowski-b-m-irwin-j-d-industrial-communication-systems-2011

23-8 Industrial Communication Systems
23.2.4 Practical Impulsive Synchronization of Chaotic Systems
with Parametric Uncertainty and Mismatch
The above schemes are applicable to situations that the parameters of chaotic systems are time invariant
and these parameters should be identical for both chaotic systems, in order to ensure perfect synchronization.
In practical situations, these requirements are difficult to be met because the designed
chaotic systems cannot be perfectly implemented and the chaotic systems are inevitably exposed to an
environment that may cause their parameters varying within a small range. Recently, a new scheme
to design a secure communication system with parametric uncertainties and mismatches is proposed
in [JWL08], based on the results in [WJL07].
In the proposed scheme, designers are allowed to specify certain tolerance bounds for parametric
uncertainties and mismatches. These bounds, together with a prespecified synchronization error
bound, will be used to select impulsive intervals. With the designed system and impulsive intervals, the
message recovering error is shown to be within a bound depending on the prespecified synchronization
error bound, and transmitted signals can be decoded accurately even in the presence of uncertainties
and mismatches. Readers are advised to refer to [JWL08] and [WJL07] for details.
23.3 Secure Communication Using Chaos Synchronization
Continuous chaotic synchronization is adopted in the first three generations of chaos-based secure
communications. Over the past decade, techniques using impulsive chaotic synchronization have
been developed and this has started the fourth generation [COS93,WC93,YWC97,ZL97,T99]. Since
in impulsive synchronization information on states of the driving system is transmitted only at the
impulsive instants, the fourth generation has the following features: ensuring more effective transmission
efficiency while enhancing security and being less sensitive to channel noise. For example,
less than 94.Hz of bandwidth is needed to transmit synchronization control signals with a third-order
chaotic transmitter in the fourth generation, but 30.kHz bandwidth required in the other three generations
[T99].
In this section, a digital secure communication system based on impulsive synchronization will be
presented.
23.3.1 Secure Communication Schema
The secure communication block diagram is shown in Figure 23.1 [LLWS03]. The secure communication
schema uses a magnifying glass to enlarge the effect of parameter mismatch and an impulsive control
strategy [LWSX01] for the synchronization of chaotic circuits. The proposed scheme is essentially a onetime
pad [S96] with the random signals replaced by chaotic signals generated from a chaotic system. In
this schema, Chua’s chaotic circuit is adopted to implement the chaotic system with three state variables.
The schema has two major parts: encrypter and decrypter. The input can be of all types of signals that
can be digitized by existing technology, like texture, audio, video, image, speech, and so on, which can
be first compressed. If the input signal is analog, it is digitized by a corresponding technology. Since
chaos is very sensitive to initial condition, the quantization error is required to be less than certain values
to ensure the synchronization of the encrypter and the decrypter [HLYS00].
The compressed and digitized signal acts as the plaintext p(t) in the encryption process. The ciphertext
and the synchronization impulse are then modulated and transmitted to the decrypter via a network.
After demodulating and decrypting, the received plaintext is decompressed and the original message
is recovered.
The encrypter consists of a chaotic system and a classical encryption function e(·). The decrypter
is composed of an impulsive differential system, a corresponding decryption function d(·), and an
© 2011 by Taylor and Francis Group, LLC