Computational Intelligence and Neuroscience

Volume 2017, Article ID 6919675, 11 pages

https://doi.org/10.1155/2017/6919675

## Chaotic Image Encryption Algorithm Based on Bit Permutation and Dynamic DNA Encoding

School of Electrics and Information Engineering, Zhengzhou University of Light Industry, Zhengzhou 450002, China

Correspondence should be addressed to Ying Niu; nc.ude.iluzz@gniyuin

Received 19 May 2017; Revised 10 July 2017; Accepted 16 July 2017; Published 22 August 2017

Academic Editor: Amparo Alonso-Betanzos

Copyright © 2017 Xuncai Zhang 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

With the help of the fact that chaos is sensitive to initial conditions and pseudorandomness, combined with the spatial configurations in the DNA molecule’s inherent and unique information processing ability, a novel image encryption algorithm based on bit permutation and dynamic DNA encoding is proposed here. The algorithm first uses Keccak to calculate the hash value for a given DNA sequence as the initial value of a chaotic map; second, it uses a chaotic sequence to scramble the image pixel locations, and the butterfly network is used to implement the bit permutation. Then, the image is coded into a DNA matrix dynamic, and an algebraic operation is performed with the DNA sequence to realize the substitution of the pixels, which further improves the security of the encryption. Finally, the confusion and diffusion properties of the algorithm are further enhanced by the operation of the DNA sequence and the ciphertext feedback. The results of the experiment and security analysis show that the algorithm not only has a large key space and strong sensitivity to the key but can also effectively resist attack operations such as statistical analysis and exhaustive analysis.

#### 1. Introduction

With the rapid development of multimedia technology and network technology, digital image processing has been widely applied to all aspects of human life, such as remote sensing, industrial inspection, medical field, meteorology, communications, reconnaissance, and intelligent robots. As a result, increasing attention has been paid to image information. Additionally, it is more important to protect the security of image data, especially in military, commercial, and medical fields. Image encryption technology has become an effective way to protect the transmission of digital images [1]. Image data has the characteristics of large amounts of data, strong correlations, and high redundancy. The existing classical encryption methods cannot meet the needs of image encryption because of its low efficiency and security.

As a type of complex nonlinear system, chaotic systems have initial value sensitivity, pseudorandomness, and nonperiodicity, which are consistent with the characteristics required for cryptography. A chaotic sequence can be used as a random key, which can achieve the same encryption effect as the first time, and it is not capable of being broken, in theory. Thus, chaotic encryption technology has been widely used in the field of information security, especially in the field of image encryption [2, 3].

At present, most of the confusion and diffusion structure of image encryption algorithms is based on chaotic systems for the use of chaotic sequences, and it is restricted by the computer word length, which can cause degradation in the chaotic dynamics, especially for a low-dimensional chaotic system [4]. This limitation seriously affects the security of the chaotic encryption. Therefore, many scholars use hyperchaos systems to ensure the complexity of the chaotic sequence, to improve the security of the algorithm. However, there is no denying that an encryption algorithm that is composed of a single chaotic map cannot guarantee the security of the encrypted image [5].

DNA is an important carrier of the biological genetic information that is stored in the body, and genetic metabolism plays an important role in the organism. It has a very large scale of parallelism, ultrahigh storage density, and low energy consumption as well as a unique molecular structure and molecular recognition mechanism, which determines its outstanding information storage and information processing ability [6]. DNA has great potential in the field of information security, information hiding, and authentication, which provides a new way for the development of modern cryptography [7–9]. Boneh et al. cracked 56 keys in four months in 1995, which is the first time that DNA was used to crack the traditional encryption standard DES [10]. Subsequently, the development of DNA cryptography research has become a hot topic. In 1999, Gehani and others used DNA as an information carrier, using biochemical technology in the DNA molecule and achieved one of the traditional encryption algorithms [11]. In 2013, Le Goff et al. achieved a 3D-particle array encryption model, and they combined DNA particle technology and thermal shrinkage sheets with DNA polymers fixed on a polyethylene heat-shrinkable film; in this way, they successfully formed a three-dimensional DNA hydrogel particle array size within 100 *μ*m [12]. These DNA encryption algorithms are used to encrypt text information, and it is quite difficult for image information to be directly encrypted.

In recent years, combined with the dual advantage of the DNA molecule and chaotic systems, an image encryption algorithm based on DNA molecules and chaotic systems is presented. In 2012, Liu et al. proposed an image encryption algorithm based on DNA encoding and chaotic map [13]. In 2014, [14] Liu et al. proposed a RGB image encryption algorithm based on DNA encoding and chaos map. In 2015, Wang et al. presented an image encryption technique based on 2D logistic mapping and DNA operations [15]. In 2017, Chai et al. presented an image encryption algorithm that is based on chaos combined with DNA operations [16]. In the same year, we proposed a type of digital image encryption technology based on hyperchaos mapping and DNA sequence library arithmetic to realize a scrambling position transformation of image pixels and the spread of the pixel values [17]. These algorithms displace only the positions of the image pixels and change the gray value. However, the bit’s position changes are smaller, and it is not able to achieve the purpose of true diffusion [18]. In the replacement phase, the advantage of the bit replacement is obviously better than pixel permutation, because it not only changes the position but also changes the sizes of the pixels [19].

Therefore, in this paper, a new image encryption algorithm based on chaotic systems and dynamic DNA encoding is proposed. The algorithm uses Keccak to compute the hash value of the given DNA sequence as the initial value of the chaotic map, generating a chaotic index of the image position that performs scrambling, which is coupled with a butterfly network to achieve a level of scrambling. Finally, through the study of the dynamic DNA encoding of images and the operations of a given DNA sequence, the additional use of ciphertext feedback can help to achieve the replacement and diffusion of the pixels, which has further improved the security of the encryption.

#### 2. Fundamental Theory

##### 2.1. Hyperchaos System

As a type of special nonlinear phenomenon, chaos has good pseudorandomness and unpredictability of the orbit and has extreme sensitivity to initial conditions and structure parameters; in addition, it is iterative and not repetitive and has a series of excellent features, which are widely used toward the secrecy of communication. Compared with a low-dimensional chaotic system, high-dimensional chaotic systems have a more positive Lyapunov exponent and are more complex, and it is more difficult to predict the dynamic characteristics, which can effectively solve the degradation problem of the low-dimensional chaotic system with dynamics characteristics. It also has strong confidentiality, a simple algorithm, and large key space characteristics. In 2005, Lee and others constructed a hyperchaos Chen system via state feedback control, and its equation iswhere , , , and are the system state variables and , , , , and are the control parameters of the system. When = 35, = 3, = 12, = 7, and , the system’s performance is hyperchaos.

##### 2.2. Keccak Algorithm

Keccak is a standard one-way hash function algorithm. The hash functions are designed to take a string of any length as input and produce a fixed-length hash value. When the hash value is attached to the message or stored with the message, the message can be prevented from being modified in the process of storage for transmission. Messages are different; the resulting hash value is also different, and even if there is only one bit of change in the message, the hash value will be completely useless. By using this feature, we can change the pixel value of the image by selecting the appropriate message and using the hash value generated by the Keccak hash function and the operation of the image. At the same time, the hash value is modified to set the initial value and system parameters of the chaotic system, to further improve the security of the encryption. Keccak has no length limit on the upper limit of the input data length, and it can generate arbitrary hash values.

##### 2.3. DNA Encoding Algebraic Operations

The DNA molecule is composed of four DNA nucleotides, which are adenine (A), cytosine (C), guanine (G), and thymine (T). For two single-stranded DNA molecules, a stable DNA molecule can be formed by hydrogen bonds between nucleotides. The chemical structure of the base determines the principle of complementary base pairing, and it is also known as the Watson-Crick base pairing principle. In other words, A and T are paired by two hydrogen bonds, and G and C are paired by three hydrogen bonds. The natural combination is quaternary, similar to the binary semiconductor formed by on and off [20]. Therefore, the information can be stored and calculated by using the permutations and combinations of bases.

*(1) DNA Encoding Rule*. If we act according to the encoding rules, A→00, C→01, G→10, T→11, then the complementary number matching is 01*↔*10 and 00*↔*11, and the complementary base pair matching is A*↔*T and C*↔*G. In this case, there are eight encoding combinations that satisfy the complementary pairing rules, as shown in Table 1.