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This study used the complex dynamic characteristics of chaotic systems and Bluetooth to explore the topic of wireless chaotic communication secrecy and develop a communication security system. The PID controller for chaos synchronization control was applied, and the optimum parameters of this PID controller were obtained using a Particle Swarm Optimization (PSO) algorithm. Bluetooth was used to realize wireless transmissions, and a chaotic wireless communication security system was developed in the design concept of a chaotic communication security system. The experimental results show that this scheme can be used successfully in image encryption.

The chaos phenomenon was first proposed by Lorenz using the simulation equation of the atmosphere, but it did not attract much attention from scientists until Feigenbaum proposed the general theory of chaos phenomenon. Chaos is a phenomenon that seems disorderly but contains rules. It is a complex dynamic non-periodic and nonlinear system that cannot be explained by single data, and should be analyzed using overall continuous data. It has a very extensive Fourier spectrum, and has a fractal in the phase plane. The key in its state response is the initial value of the system. If a system has different initial values, the response varies largely; this phenomenon is called the butterfly effect [

At present, many scientists have applied the chaotic system concept to image encryption. This work can be briefly introduced as follows: Gao

The chaotic synchronization system generally consists of a master chaotic system, a slave chaotic system, and a controller synchronizing the master and slave systems. The controller processes the signals of the master chaotic system, and transmits them to the slave chaotic system, so as to synchronize the trajectories of the two systems [_{p}, K_{i}_{d}

In order to observe the procedure of chaotic synchronization, the Master/Slave system of a single input single output (SISO) is used. The differential equations [

Master System:

Slave System:

Among which, _{m}(t)_{m1},x_{m2},x_{m3}^{n}_{s}(t)_{s1},x_{s2},x_{s3}^{n}^{n}^{n}_{m}(t)_{s}(t)^{n×1} and C∈R^{1×n},

Since the initial value conditions of the master system and slave system are different, the synchronous controller is added, and the slave system is driven by the signals of the synchronous controller. Thus, the master system and the slave system have coincident response, that is synchronization. The state error of master and slave systems is defined as follows:

The primary objective of this system is to propose a simple and effective PID controller, using a PSO algorithm to obtain the optimum PID parameter values to synchronize two identical chaotic systems with different initial conditions. The _{e}_{m}_{s}_{e}(t)_{p}_{i}_{d}

As the PID controller is realized in digital control, the continuous PID controller is converted into a discrete PID.

In general cases, the adjustment of PID controller involves selecting proper parameters _{p}, K_{i}, K_{d}

This paper uses IAE as the objective function (OF), so

According to PSO algorithm, an ideal gain parameter adjustment method for PID controller is determined to minimize the objective function.

As the PSO algorithm has memory and distributed search features [

In _{m}_{s}_{p}, K_{i}, K_{d}

The PSO algorithm is used to solve the parametric optimization as mentioned in the previous section. First, ^{3}_{i}_{max},z_{max}_{max}_{p}_{i}_{d}

According to “PSO in Electromagnetics” [

The velocity update equation is shown below

_{i}

W: Inertia Weight

_{1}, _{2}: Learning constant

_{and}

_{best}

_{best}

_{i}

Position update equation of each particle point in particle swarm:

This study used the Sprott chaotic synchronization system and cryptology concept to design a wireless communication secrecy system, and employed LabVIEW software to transmit images in wireless mode. The data were encrypted and decrypted by computer to computer. Bluetooth, which is a wireless personal LAN, was used for wireless transmission. The transmission frequency of Bluetooth was 2.45 GHz. Besides digital data transmission, sound transmission was also available. The transmission speed of Bluetooth was 2∼3 Mb per second, and encryption protection could be set. The frequency changed 1,600 times per min, so it was unlikely to be intercepted and was free from interference from electromagnetic waves. Each Bluetooth-based connecting device had a 48-bit address according to the IEEE 802 standard. It could connect one or many devices, and the maximum transmission range was about 100 m. This study used a D401 mini-Bluetooth receiver V2.0 EDR, with a transmission distance of 20 m, and a transmission speed of 2.1 Mb per second.

In the image encryption and decryption, the user has to enter a key, and this value is mixed with the chaotic signal. A password is then generated randomly as the chaotic signal changes, and is mixed with the pixels of the original image. The chaotic signal is used to select 16 different data ordering modes. The RGB values of pixels are combined by staggered arrangement for encryption and decryption. The initial value of this chaotic system is generated randomly. In synchronous signal transmission, another chaotic system is used for encryption and decryption, and the initial value of this chaotic signal is obtained from the key entered by the user. The system structure is shown in

This study used LabVIEW to design the PID controller, applied a PSO algorithm to obtain the optimum parameter values and perform synchronization control for the Sprott [

Master:

Slave:
_{m}, x_{s}_{m}, ẋ_{s}_{m1}(0),x_{m2}(0),x_{m3}(0)_{s1}(0),x_{s2}(0),x_{s3}(0)_{p},k_{i},k_{d}_{p}_{i}_{d}

This study produced two images for encryption and decryption. One was a picture of an airplane, and the experimental results are shown in

This study successfully used PSO to obtain the optimum parameter values of a chaotic synchronization PID controller, and applied it in chaotic communication secrecy. A traditional PID controller can only be used in fixed systems, and must be redesigned if it is to be used in different systems, which consumes a high hardware setting time and cost. This study used LabVIEW, instead of the traditional PID controller, so that when it is applied in other systems, only the parameters of the PID controller need to be changed, so the time and cost can be reduced. Bluetooth was used to realize wireless transmissions. In the application of wireless communications, future studies can focus on the encryption and decryption of images in order to improve the security of wireless transmission.

The financial support of this research by the National Science Council of the R.O.C., under Grant No. NSC 100-2628-E-167-002-MY3 is greatly appreciated.

Block diagram of PID controlled chaotic synchronization system of the PSO algorithm.

PSO algorithm process block diagram.

Structure diagram of Image encryption and decryption of chaotic synchronous cryptographic system.

Transmission interface.

Reception control interface.

IAE convergence curve.

IAE convergence curve by PSO and EP with the initial conditions [xm1(0), xm2(0), xm3(0)] = [0.1, 0.1, 0.1] and [xs1(0), xs2(0), xs3(0)] = [−1, −1, −1].

_{p}

_{i}

_{d}

_{m1}_{s1}

_{m2}_{s2}

_{m3}_{s3}

Original picture of an airplane.

Post-encryption effect.

Decryption effect when the key entered is incorrect.

Statistical chart of R value distribution of the original image.

Statistical chart of G value distribution of the original image.

Statistical chart of B value distribution of the original image.

Statistical chart of R value distribution after encryption.

Statistical chart of G value distribution after encryption.

Statistical chart of B value distribution after encryption.

Original scenery picture.

Post-encryption effect.

Decryption effect when the key entered is incorrect.

Statistical chart of R value distribution of the original image.

Statistical chart of G value distribution of the original image.

Statistical chart of B value distribution of the original image.

Statistical chart of R value distribution after encryption.

Statistical chart of G value distribution after encryption.

Statistical chart of B value distribution after encryption.

The convergence situation of PSO

170 | 0.7592 | |

53 | 0.6697 |

The convergence situation of PSO

80 | 0.6726 | |

26 | 0.4132 |