## 1 Introduction  
With the popularity of smart phones, digital images are becoming one of the most important data formats in our daily life, and it is easier to get than in the old days. However, security issues arise when these images need to be transferred over the internet or stored on the cloud, especially some of them contain privacy. Moreover, digital images are also used in many sensitive areas such as medical, national defense and legal affairs. Therefore, the security of digital images is becoming an eye-catching issue for many researchers [1; 2; 3]. As we all know, encryption is the most easy way to protect information security, and there are many excellent algorithms for encrypting text structure data which play important roles for protecting data security in network communication, e.g., DES, AES, RSA, etc. Unfortunately, those algorithms weakly adapt to the image data characteristics, such as high redundancy, strong correlation between pixels, etc. As a result, text structure encryption algorithms are not good at image encryption, and may cause some problems such as low efficiency, contour information leakage, etc. [4; 5]. Chaos systems which were first proposed by [PERSON] [6] have many good characteristics, e.g., sensitivity of initial values and parameters, etc., are very suitable for designing an image cryptosystem. The first chaotic cryptosystem is proposed by [PERSON] [7] who is a British scientist. After that, the chaotic system was beginning to be used to design image encryption systems. Usually, chaotic image encryption schemes use chaotic systems to generate key stream or some scrambling control sequences or nonlinear components, and then do permutation and diffusion to plain image to generate cipher image. In recent years, there are many image encryption schemes based on chaotic systems proposed to the public [8; 9; 10; 11; 12; 13]. DNA computing was first proposed by [PERSON] [14] in 1994. After then, DNA computing had found some good characteristics such as ultra-high information density, great parallelism and ultra-low energy consumption. [PERSON] et al. [15] was first proposed the DNA computing in designing image cryptosystem. After [PERSON], many image encryption schemes based on DNA computing appeared in public [16; 17; 18; 19; 20; 21]. [PERSON] et al. [22] found that if the algorithm adopts binary coding, the coding efficiency is low, and it would be easy cracked when cryptosystem is not related to plain image. [PERSON] et al. [23] found that an image encryption system based on DNA computing must contain diffusion part, if only scramble processing would not be security. [PERSON] et al. [24] cracked an DNA computing based encryption system, and found that image cryptosystem must be able to resist differential attack, otherwise can reconstruct the equivalent key by part of known plaintext attack. Recently, some interesting works on image encryption by using DNA computing. [PERSON] et al. [16] proposed an image encryption scheme based on coupled map lattices and DNA encoding. In this scheme, rows and columns cyclic shift operation is used to scramble the image DNA matrix. The diffusion performance is good, however, the sensitivity of plaintext seems a little weak. [PERSON] [20] proposed an image encryption scheme using DNA computing and hash function. This scheme related plaintext by hash function to make image cryptosystem has enough sensitivity to resist differential attack. However, the hash value of plain image also needs to transfer to the decryption part, it is harmful for key management. [PERSON] et al. [21] proposed a DNA computing based image encryption scheme using cellular automata. This scheme is cleverly designed but real security key only the initial value of logistic map, that it is hard to resist brute force attack. To overcome the shortage mentioned above, we proposed a novel chaos-based image encryption scheme by using randomly DNA encode and plaintext related permutation.