Study on an efficient hyper-chaos-based image encryption scheme using global bit permutation

1.Introduction

With the increasing popularity of network and information technology, the information transfer via Internet is increasingly common. As a greatly efficient approach of privacy and security protection, image encryption has drawn considerable attention and plenty of algorithms utilizing various techniques have been explored in the past decades. Due to the fact that images are inherently bulk data with a high correlation among pixels and significant data redundancy, existing encryption methods cannot figure out real-time image encryption tasks well. Thus, amounts of chaos-based encryption methods achieved inspiring results in amounts of real tasks [1].

The fundamental structure of chaos-based approaches consists of two procedures: permutation and diffusion phases. In recent years, pixel-level based permutation methods have achieved significant results in many image encryption tasks [2, 3, 4]. Liu et al. [5] utilized one-time keys and two reliable chaotic maps, and combined MD5 algorithm with existing cycle encryption. Wang et al. [6] proposed an encryption method which associated a 4D Lorenz hyper-chaotic system with gene recombination.

To deal with the drawback inherently existing in approaches utilizing pixel-level permutation, various approaches utilizing bit-level permutation have been proposed. Zhu et al. [7] developed an algorithm that uses a logistic map and an Arnold map separately for diffusion and permutation. Li et al. [8] reported a five-dimensional multi-wing hyper-chaotic system and the permutation process divided the image into blocks, and each block is multiplied by a constant matrix. Moreover, DNA sequence has been used for image encryption [9, 10]. Unfortunately, this kind of algorithm has the same weakness as the ones using pixel-level permutation.

In order to solve the above-described problems, this study presents an efficient real-time encryption algorithm on the basis of hyper-chaos and a global bit cycle shift (HC-GBCS). Theoretical and numerical analyses indicate that the proposed method resists different attacks and owns low time complexity. In addition, the encryption test on finger-vein images shows that the proposed method has a significant performance in practical application.

The remainder of our study is summarized as follows. The basic theory of the 4D hyper-chaotic system is introduced in Section 2. In Section 3, the proposed approach is introduced in detail. Experimental results and performance analysis are presented in Section 4, and conclusions are drawn in Section 5.

2.Hyper-chaotic system

Although traditional low-dimensional chaotic systems are highly efficient, they suffer from inadequate key spaces and low security. On the contrary, high-dimensional hyper-chaotic systems own more positive Lyapunov exponents, more complicated and unpredictable dynamic characteristics, and higher randomness [11]. The 4D hyper-chaotic system adopted in our study can be given as follows [12]:

where x1-x4 are state variables and a-k are constant values. When a=8,b=40,c=2,d=14,g=5,h=0.2 and k=0.05, the above system is hyper-chaotic.

3.Proposed image encryption system

This paper presents a novel real-time image encryption algorithm based on hyper-chaos and a global bit cycle shift (HC-GBCS). First, the plain image is used to generate a 256-bit external secret key K through the SHA-256 secure hash algorithm. Then a 4D hyper-chaos system which is initialized by using secret key K is introduced to generate the chaotic sequence. Then the image is shuffled by a pixel-level permutation and decomposed into eight binary bitplane images. Finally, global bit permutation and diffusion operations are conducted to change the image intensity distribution and further enhance the security.

4.Experimental results and security analyses

Various experiments are conducted to analyze and verify the effectiveness of the presented method. In the experiments, except the natural images with size 256×256, finger-vein images are extra led in to demonstrate that our proposed algorithm has unique advantages in the security field of the real world. In addition, Wangs algorithm (GR-HC) [6], Zhus algorithm (BLP) [7], Lis algorithm (PL-BL) [8], Tengs algorithm (CML) [14], Chens algorithm (LUT) [15] and another Chens algorithm (DSVSM) [16] are compared with our proposed algorithm.

4.2Key sensitivity

An efficient encryption method should be sensitive to the secret key for resisting different attacks. The plain image could not be recovered even if the key has a slight difference. The Lena image with size 256×256 is utilized to verify the sensitivity of the presented encryption method. From Fig. 1b and d, we can see that the cipher-image is totally different when the key a1 is increased by only 10-16. Furthermore, as shown in Fig. 1e and f, the cipher-image is decrypted incorrectly when it adopts a secret key which is subtly different from the initial key. We can conclude that even a subtle difference in the decryption key will cause the encrypted image to be unrecoverable. Hence, the presented encryption method is greatly sensitive to the key.

Figure 1.

Analysis of key sensitivity: (a) Lena image, (b) Encrypted image (a1 = 0.2), (c) Encrypted image (a1 = 0.200000000000001), (d) Difference between (b) and (c), (e) Decryption of image (b) with a1 = 0.200000000000001, (f) Decryption of image (b) with a1 = 0.2.

5.Conclusions

This study presented a hyper-chaos-based image encryption scheme utilizing global bit cycle shift. The algorithm utilizes a 4D hyper-chaotic system whose preliminary parameters are produced by SHA-256 secure hash algorithm, and adopts global bit permutation to enhance the security of the encryption system.

The system can deal with the problems inherently existing in encryption methods utilizing low-dimensional chaotic map. Furthermore, global bit permutation can transform the pixel distribution of plain images and enhance the cryptosystem security. The amount of experiments and corresponding analysis, including key space analysis, key sensitivity analysis, correlation analysis, and packet loss and packet error analysis, validate that the presented approach is secure and reliable for image encryption. In addition, the encryption test on finger-vein images show that the proposed method has a significant performance in practical application.