## 1 Introduction  
Since the high-speed growth and wide application in the field of the multimedia information and internet technology, the security demands for data communication and image information confidentiality have continually increased [1]. Recently, because of the good advantages of chaotic signals, such as the broadband random responses, and sensitivity to the system's initial conditions (butterfly effect), many studies have applied these properties to solve and enhance information security and image encryption and decryption issues [2, 3, 4, 5, 6, 7, 8, 9]. In the literature [2], a new algorithm that integrated a chaotic system was proposed in order to construct a new transforming-scrambling-diffusion model for color image encryption. In [3], logistic and rectangular chaotic maps were used to implement the image encryption. However, the approaches introduced in the proposed algorithms were simple processes and could not generate uniform distribution for resisting statistical attacks [2]. In [4], the hyper-chaotic system and DNA plane were utilized to propose an image encryption approach. In [5], a new image encryption algorithm was proposed based on complex number chaotic maps. A hybrid approach combined with a fast chaotic algorithm and advanced encryption standard (AES) image encryption was proposed in the literature [6]. Then, Cramer's rule was used to decompose both encrypted images, and the images could be decrypted using chaos and AES decryption algorithms, respectively. In [7], the logistic map was introduced to construct a chaos cryptosystem, and it was concluded that the logistic map algorithm for image encryption exhibits a good encryption speed. The Arnold chaos system was used to design a round key generator in AES and to combine the chaos random numbers with modified AES in order to propose an algorithm for image encryption in the literature [8]. The advantages of chaotic systems, such as ergodicity and randomness, were also introduced in the literature [9] to ensure a good S-Box for encrypting the plaintext blocks with different S-Box. However, no synchronization procedures were considered in the above reports [2; 3; 4; 5; 6; 7; 8; 9]. Therefore, for the chaos-based cryptosystems proposed in these works [2; 3; 4; 5; 6; 7; 8; 9], because of the butterfly effect of chaos systems, the transmitter and receiver must have the same initial conditions in order to generate the same chaos random states and complete the correct encryption and decryption. Although the above methods have proposed many analyses and comparisons to prove the security and feasibility of their encryption algorithms, it is under the assumption condition that an unauthorized user does not know the parameters and initial values of their chaotic systems. In other words, the initial conditions play the role of secure keys, and their encryption algorithms are quite secure if the assumption is valid. However, this also implies that when performing encryption and decryption, the above-mentioned parameter information, as well as the initial conditions of the chaotic systems, must be exchanged through a public channel, thereby increasing the possibility of being cracked. Therefore, in this paper, a synchronization technology will be investigated to solve this problem. Such a synchronization design will allow information, such as the parameters and initial conditions of the chaotic system, not be transmitted through a public channel. Through the synchronization technique, only some mixed information, that is not related to system parameters and initial values, needs to be transmitted to the receiving end, and a synchronization controller can be constructed so that the transmitting and receiving ends can simultaneously generate the same chaotic random sequence. In this way, it could be applied to design a new encryption system with high security. In [10], a simple synchronization controller subjected to uncertain chaotic parameters was proposed, and then extended the chaos synchronization to construct secure communication systems.