Security and Communication Networks

Volume 2018 (2018), Article ID 2708532, 13 pages

https://doi.org/10.1155/2018/2708532

## A New Chaos-Based Color Image Encryption Scheme with an Efficient Substitution Keystream Generation Strategy

School of Computer Science and Engineering, Northeastern University, Shenyang 110004, China

Correspondence should be addressed to Chong Fu

Received 10 August 2017; Accepted 3 January 2018; Published 20 February 2018

Academic Editor: Leo Y. Zhang

Copyright © 2018 Chong Fu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper suggests a new chaos-based color image cipher with an efficient substitution keystream generation strategy. The hyperchaotic Lü system and logistic map are employed to generate the permutation and substitution keystream sequences for image data scrambling and mixing. In the permutation stage, the positions of colored subpixels in the input image are scrambled using a pixel-swapping mechanism, which avoids two main problems encountered when using the discretized version of area-preserving chaotic maps. In the substitution stage, we introduce an efficient keystream generation method that can extract three keystream elements from the current state of the iterative logistic map. Compared with conventional method, the total number of iterations is reduced by 3 times. To ensure the robustness of the proposed scheme against chosen-plaintext attack, the current state of the logistic map is perturbed during each iteration and the disturbance value is determined by plain-pixel values. The mechanism of associating the keystream sequence with plain-image also helps accelerate the diffusion process and increase the degree of randomness of the keystream sequence. Experimental results demonstrate that the proposed scheme has a satisfactory level of security and outperforms the conventional schemes in terms of computational efficiency.

#### 1. Introduction

Nowadays, digital image information has been widely communicated over the Internet and wireless networks owing to the rapid advancements in the multimedia and communication technology. Meanwhile, the protection of digital image information against illegal usage has become an important issue. A direct and obvious way to protect image data from unauthorized eavesdropping is to employ an encryption algorithm. Unfortunately, the renowned block ciphers, such as Triple-DES, AES, and IDEA, are not suitable for practical image encryption. This is because the security of these algorithms is mainly ensured by their high computational cost, making them hard to meet the demand for online communications when dealing with digital images characterized by bulk data capacity. To meet this challenge, many different encryption technologies have been proposed. Among them, the chaos-based algorithms provide an optimal trade-off between security and efficiency. The first chaos-based image encryption scheme was suggested by Fridrich in 1998 [1]. The permutation-substitution network, introduced by Claude Shannon in his classic 1949 paper, Communication Theory of Secrecy Systems, and now a guiding principle for the design of a secure cipher, is adopted in her approach. In each round of the cipher, the pixel positions are firstly scrambled in a secret way, which leads to a great reduction in the correlation among neighboring pixels. Then, the pixel values are altered sequentially and the influence of each pixel is diffused to all its succeeding ones during the modification process. With such a structure, a minor change in one pixel of the plain-image may result in a totally different cipher-image with several overall rounds of encryption.

Conventionally, three area-preserving invertible chaotic maps, that is, the cat map, the baker map, and the standard map, are widely used for image scrambling. Unfortunately, this kind of permutation strategy suffers from two main disadvantages, that is, the periodicity of discretized version of chaotic maps and applicability to only square images [2–4]. To address these two drawbacks, Fu et al. [5] suggested an image scrambling scheme using a chaotic sequence sorting mechanism. Unfortunately, this method takes a whole row/column of an image as the scrambling unit and results in weaker confusion effect compared with many of the existing schemes working on individual pixels. In [6], inspired by the natural ripple-like phenomenon that distorts a reflection on a water surface, Wu et al. suggested a novel scrambling algorithm that shuffle images in an dimensional ( D) space using wave perturbations. In [7], the original pixel level matrix is considered as a natural 3D bit matrix, and a new 3D bit-level permutation algorithm is proposed. During the permutation stage, the original and target bit locations are both randomly selected to further enhance the permutation effect.

In the substitution stage, various discrete chaotic maps and continuous chaotic systems can be employed to generate keystream sequences with desired statistical properties, including the most commonly used ones like the logistic map [2], the Lorenz system [8], the Chen system [9], and varieties of high dimensional chaotic systems [10]. Obviously, low dimensional chaotic maps, especially the logistic map, have the advantages of simplicity and high efficiency but suffer from small key space; in contrast, high dimensional chaotic systems, especially the hyperchaotic systems, provide sufficiently large key space but at the expense of computations. Recently, it has been reported that many existing image encryption schemes have been successfully broken by using known/chosen-plaintext attacks [11–14]. This is due to the fact that the substitution keystream sequences used in these schemes are solely determined by the secret key. That is, the same keystream sequence is used to encrypt different plain-images unless a different secret key is used. Consequently, the keystream sequence may be determined by encrypting some specially created images (e.g., an image with all pixels having the same value) and then comparing them with their corresponding outputs. Obviously, if a keystream sequence depends on both the secret key and the plaintext, then such analysis may become impractical. For instance, in [15], the keystream elements are extracted from multiple-time iteration of the logistic map, and the iteration times are determined by plain-pixel values. Unfortunately, the redundant iteration operations downgrade the efficiency of the cryptosystem to some extent. In [16], the value of each keystream element is dynamically altered according to the plain-pixel values during the substitution process.

To better meet the challenge of online secure image communications, much research has been done on improving the efficiency of chaos-based image ciphers. For instance, in [17], Xiang et al. investigated the feasibility of selective image encryption on a bit-plane. It is concluded that only selectively encrypting the higher four bit-planes of an image can achieve an acceptable level of security. As only 50% of the whole image data are encrypted, the execution time is reduced. In [18], Wong et al. proposed a more efficient diffusion mechanism using simple table lookup and swapping techniques as a light-weight replacement of the 1D chaotic map iteration. Following this work, Chen et al. [19] presented an efficient image encryption scheme with confusion and diffusion operations being both performed based on a lookup table. The other advantage of their approach is that it can effectively tolerate the channel errors, which may lead to the corruption of cipher data. It has been demonstrated that images recovered from the damaged cipher data have satisfactory visual perception. In [20], Fu et al. introduced a novel bidirectional diffusion strategy to minimize the number of encryption rounds needed to spread the influence of each individual pixel over the entire cipher-image. Experimental results have demonstrated that their scheme takes one round of permutation and two rounds of substitution to obtain a satisfactory diffusion effect. In [16, 21–23], chaos-based image ciphers using a bit-level permutation were suggested. Owing to the substitution effect introduced in the permutation stage, the number of iteration rounds required by the time-consuming substitution procedure is reduced, and hence a shorter encryption time is needed. In [8], Fu et al. suggested a fast chaos-based image cipher with the permutation key determined by the hash value of the original image. Owing to the avalanche property of hash function, completely different shuffled images will be produced even if there is a tiny difference between the original ones, thereby accelerating the diffusion process. In [24], Chen et al. presented a novel image encryption scheme using a Gray-code-based permutation. Taking full advantage of (, , )-Gray-code achievements, the new permutation strategy provides superior computational efficiency. In [25], Hua et al. introduced an image encryption algorithm based on a new two-dimensional sine logistic modulation map (2D-SLMM). Compared with corresponding seed maps, the new map has wider chaotic range, more parameters, and complex chaotic properties while remaining of relatively low implementation cost. Accordingly, the algorithm provides a good trade-off between security and efficiency.

Conventionally, in the substitution stage, one keystream element is obtained from the current value of a state variable of an iterative chaotic system. That is, to generate a keystream sequence of length* m*, a -dimensional chaotic system should be iterated (*m/n*) times. In the present paper, we introduce an efficient logistic map-based keystream generation strategy that can simultaneously extract three keystream elements from the current state of the map. As a result, the total number of iterations is reduced by 3 times and the encryption time is shortened. In the permutation stage, the positions of subpixel in each color channel of the plain-image are scrambled across the entire color space using a pixel-swapping strategy under the control of a keystream sequence generated from the hyperchaotic Lü system. To ensure the robustness of the proposed scheme against chosen-plaintext attack, the current state of the logistic map is perturbed during each iteration and the disturbance value is determined by plain-pixel values. The mechanism of associating the keystream sequence with plain-image also helps accelerate the diffusion process and increase the degree of randomness of the keystream sequence. Experimental results demonstrate that the proposed scheme has a satisfactory level of security and outperforms the conventional schemes in terms of computational efficiency.

The rest of this paper is organized as follows. The proposed permutation and substitution algorithms are thoroughly described in Sections 2 and 3, respectively. In Section 4, the degree of randomness of the substitution keystream sequences generated using our proposed method is evaluated by using NIST test suite. In Section 5, the confusion and diffusion performance of the proposed cryptosystem are analyzed. The security and efficiency of the cryptosystem are analyzed in Sections 6 and 7, respectively. Finally, Section 8 concludes the paper.

#### 2. Color Image Permutation Using a Pixel-Swapping Strategy

The hyperchaotic Lü system [26], which is employed in our scheme to generate the permutation keystream sequence, is described bywhere , , are the constants of Lü system [27] and is a control parameter. When , , , and , the system exhibits a hyperchaotic behavior, and the projections of its phase portrait are shown in Figure 1. Evidently, the initial conditions of the system are the immediate candidate for the secret key for permutation, as they uniquely determine a chaotic trajectory from which the permutation keystream is extracted.