Mathematical Problems in Engineering

Volume 2016 (2016), Article ID 6408741, 11 pages

http://dx.doi.org/10.1155/2016/6408741

## Image Encryption Algorithm Based on Dynamic DNA Coding and Chen’s Hyperchaotic System

College of Information and Computer Engineering, Northeast Forestry University, Harbin 150040, China

Received 30 April 2016; Accepted 25 August 2016

Academic Editor: Nazrul Islam

Copyright © 2016 Jian 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 development of national information processes, specific image information from secret departments or individuals is often required to be confidentially transmitted. Numerous image encryption methods exist, especially since the initial value sensitivity and other characteristics of chaos theory and chaos theory-based encryption have become increasingly important in recent years. At present, DNA coding constitutes a new research direction of image encryption that uses the four base pairs of DNA code and image pixel values to establish a special correspondence, in order to achieve pixel diffusion. There are eight DNA encoding rules, and current methods of selecting the DNA encoding rules are largely fixed. Thus, the security of encoded data is not high. In this paper, we use the Lorenz chaotic system, Chen’s hyperchaotic system, and the DNA encoding combination and present a new image encryption algorithm that can dynamically select eight types of DNA encoding rules and eight types of DNA addition and subtraction rules, with significant improvements in security. Through simulation experiments and histograms, correlations, and NPCR analyses, we have determined that the algorithm possesses numerous desirable features, including good encryption effects and antishear and antinoise performances.

#### 1. Introduction

With the development of national information processes, people have paid increasing attention to secure transmission of image information. The traditional classical encryption algorithms primarily include the DES, IDEA, and RSA algorithms [1–3]. However, compared to text files, image files contain a larger amount of data, so the traditional encryption algorithms are not suitable for image encryption. While some image encryption techniques have emerged, based on mathematical transformations, nevertheless, their security is inadequate.

Chaotic encryption technology has been used as the mainstream of encryption technology in recent years [4], but the use of chaotic technology only is not safe enough [5–7]. In recent years, image encryption technology based on DNA computing has been extensively used by scholars, but work is still at the initial stages of research. At present, most of the image encryption algorithms that are based on DNA coding adopt relatively fixed coding methods, and security is not high. In this paper, DNA coding and chaotic encryption technology are combined, and a dynamic DNA coding image encryption algorithm is proposed that can improve the security of the encryption process. Based on simulation experiments, the algorithm has been shown to exhibit good encryption effects and can effectively resist statistical, shear, and other attacks.

#### 2. Dynamic DNA Coding and Chaotic Mapping

##### 2.1. DNA Coding

A DNA sequence consists of four different basic nucleotides, namely, A, T, C, and G [8], whereby pairing is allowed only between A and T and C and G. Additionally, each pixel point in a grayscale image can be represented by an 8-bit binary number, taking the values of 0 and 1. The binary value pair also constitutes a complementary relationship pair. Since 00 and 11 and 01 and 10 are also complementary, the DNA bases A, C, G, and T can be encoded using the digit pairs 00, 01, 10, and 11. Thus, 24 types of this coding scheme can be obtained, but the program must satisfy the pairing rules, in that A bases must be paired with T and C must be paired with G, so only eight types of programs are effective. These are shown in Table 1. For example, if the grayscale value of a pixel in an image is equal to 147, it can be converted to the binary value “10010011.” If the first rule in Table 1 is selected, the 8-bit binary number can be expressed as “GCAT.” Furthermore, if the fourth rule is chosen, then the 8-bit of the binary number can be expressed as “ATCG.”