Mathematical Problems in Engineering

Volume 2014, Article ID 917147, 10 pages

http://dx.doi.org/10.1155/2014/917147

## Image Encryption Algorithm Based on DNA Encoding and Chaotic Maps

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

Received 6 November 2014; Accepted 9 December 2014; Published 31 December 2014

Academic Editor: Miguel A. F. Sanjuan

Copyright © 2014 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

We propose a new image encryption algorithm based on DNA sequences combined with chaotic maps. This algorithm has two innovations: (1) it diffuses the pixels by transforming the nucleotides into corresponding base pairs a random number of times and (2) it confuses the pixels by a chaotic index based on a chaotic map. For any size of the original grayscale image, the rows and columns are fist exchanged by the arrays generated by a logistic chaotic map. Secondly, each pixel that has been confused is encoded into four nucleotides according to the DNA coding. Thirdly, each nucleotide is transformed into the corresponding base pair a random number of time(s) by a series of iterative computations based on Chebyshev’s chaotic map. Experimental results indicate that the key account of this algorithm is 1.536 × 10127, the correlation coefficient of a 256 × 256 Lena image between, before, and after the encryption processes was 0.0028, and the information entropy of the encrypted image was 7.9854. These simulation results and security analysis show that the proposed algorithm not only has good encryption effect, but also has the ability to repel exhaustive, statistical, differential, and noise attacks.

#### 1. Introduction

With the development of science, technology, and society, the computer industry, in which a small branch of digital images applications has become increasingly pervasive, has come to occupy a dominant position worldwide. Digital images have become one of the most popular media types and are now used extensively in various fields such as politics, economics, defense, and education [1]. However, because of the open nature of networks, image transmission security is subject to potential threats. In some fields, such as military affairs, commerce, and medical treatment, digital images also need to meet the highest requirements of confidentiality [2]. Consequently, image encryption technology has become an effective way to protect images being transmitted.

Various common image encryption algorithms are available, including text encryption technology, SCAN language-based encryption technology, quadtree image encryption technology, vector quantization encryption technology (VQ), encryption technology based on pseudorandom sequences, encryption technology based on the “key image” chaotic encryption technology, and image encryption technology based on DNA computing [3–10]. Recently, chaotic encryption technology has been attracting increasing attention. Chaos is an inner-class random process of nonlinear systems performance and is very sensitive to initial values, thus resulting in unpredictable results. The benefits of chaotic encryption technology include simple implementation, robustness, fast encryption, and high security [11]. However, although chaotic encryption technology has many advantages, it also has a number of deficiencies. For example, at present, most chaotic encryption algorithms confuse the single image pixel value or location, but the utilization of only one of the two strategies does not ensure high security for the image [12], and thus it is easy for attackers to crack an encrypted image by simply using the pixel comparison method.

In 1994, Adleman first introduced DNA computing into the encryption field, which created a new stage of information processing. DNA encryption is a new frontier and is presently at the forefront of international cryptography research [13, 14]. DNA molecules harness massive parallelism and have low energy consumption and high storage density [15, 16]. Therefore, image encryption algorithms based on DNA computing possess unique advantages that the traditional cryptographic algorithms do not have. However, using only DNA encoding to encrypt images is not secure. Therefore, we combine chaos encryption technology and image encryption based on DNA computing to solve the hidden insecurity problems existing when images are confused using the chaotic encryption technology. First, we confuse the digital image pixels using the chaotic encryption technology. We then diffuse the confused pixels using DNA encoding. The diffusion process is also applied to the chaotic encryption technology and, finally, we obtain the encryption result.

In summary, our study successfully combines chaotic encryption technology and DNA coding techniques in a method that has been verified via a large number of experiments and security analyses to prove the security and rationality of the algorithm.

#### 2. DNA Encoding and Chaotic Maps

##### 2.1. DNA Encoding and Complementary Rule

DNA sequencing is the process used to map the nucleotide sequence forming a strand of DNA. Four bases, adenine (A), thymine (T), guanine (G), and cytosine (C) form the building blocks of genetic code. “A” binds with “T” and “G” binds with “C” [17]. We know that every digital image pixel can be expressed by 8-bit binary numbers [18]. Because the binary numbers “0” and “1” are complementary, “00” and “11” and “01” and “10” are also complementary. If we use the four deoxynucleotides “A,” “T,” “G,” and “C” to represent the binary numbers “00,” “11,” “01,” and “10,” respectively, then each pixel can be encoded into a string of nucleotides. For example, the gray value of a digital image pixel is 228, and the binary corresponding to this value is “11100100.” According to the above rules, the string of nucleotides that corresponds to this binary is “TCGA.” There are 24 types of combinations for the four nucleotides. However, only eight coding combinations are suitable for the principle of complementarity. These rules are summarized in Table 1.