Research Article  Open Access
Bin Wang, Yingjie Xie, Shihua Zhou, Changjun Zhou, Xuedong Zheng, "Reversible Data Hiding Based on DNA Computing", Computational Intelligence and Neuroscience, vol. 2017, Article ID 7276084, 9 pages, 2017. https://doi.org/10.1155/2017/7276084
Reversible Data Hiding Based on DNA Computing
Abstract
Biocomputing, especially DNA, computing has got great development. It is widely used in information security. In this paper, a novel algorithm of reversible data hiding based on DNA computing is proposed. Inspired by the algorithm of histogram modification, which is a classical algorithm for reversible data hiding, we combine it with DNA computing to realize this algorithm based on biological technology. Compared with previous results, our experimental results have significantly improved the ER (Embedding Rate). Furthermore, some PSNR (peak signaltonoise ratios) of test images are also improved. Experimental results show that it is suitable for protecting the copyright of cover image in DNAbased information security.
1. Introduction
With wide usage of multimedia technologies and excessive spread of Internet, protecting copyright of digital image is attracting a great deal of attention. Data hiding or watermarking technique, which is a major means of protecting copyright, is widely used in digital image and is quite efficient method. Because of their features of parallelism, highcapacity storage, and low energy consumption, DNA computing is used into many fields, such as image encryption, information security, and other applications [1–9].
Reversible data hiding or watermarking and irreversible data hiding are two main technologies for protecting copyright. Reversible data hiding embeds information bits by modifying the host signal but enables the exact (lossless) restoration of the original host signal after extracting the embedded information. Irreversible data hiding cannot enable the exact (lossless) restoration of the original host signal after extracting the embedded information. The former is widely used in the medical image, military information, and other applications with high security requirement. Fridrich et al. proposed a reversible image watermarking algorithm [10]. They formulated two general methodologies for lossless embedding that could be applied to images as well as any other digital objects. Xuan et al. proposed a novel distortionless image data hiding algorithm based on integer wavelet transform [11]. The proposed algorithm could invert the stegoimage into the original image without any distortion after the hidden data were extracted. Tian presented a novel reversible dataembedding method for digital images [12]. The method explored the redundancy in digital images to achieve very high embedding capacity and keep low distortion. The histogram modification method was used into reversible data hiding by Ni et al. [13]. This algorithm utilized the zero or the minimum points of the histogram of an image and slightly modifies the pixel grayscale values to embed data into the image. It was proved analytically and shown experimentally that the peak signaltonoise ratio (PSNR) of the marked image generated by this method versus the original image was guaranteed to be above 48 dB. According to the above four main methods, a number of works based on reversible data hiding are recently proposed [14–18].
A DNA sequence consists of four different bases, namely, A (adenine), C (cytosine), G (guanine), and T (thymine). Base pairs, which form between specific nucleobases (also termed nitrogenous bases), are the building blocks of the DNA double helix and contribute to the folded structure of both DNA and RNA, namely, A with T and C with G [19]. Adleman used molecular biology to solve an instance of the directed Hamiltonian path problem [1]. There was a stirring of interest in DNA computing after his research. Lipton employed DNA computing to solve the famous “SAT” problem of computer science [2]. Ouyang et al. solved the maximal clique problem by DNA computing [3]. Braich et al. proposed a solution of a 20variable 3SAT problem on a DNA computer [4]. Qian et al. used DNA strand displacement to simulate four points of neural network computation [5]. Chang et al. employed DNA computing to achieve factoring integers and break RSA public encryption algorithm [6]. Shoshani et al. proposed a molecular cryptosystem for images by DNA computing [7]. Babaei proposed a reliable data encryption algorithm, OneTimePad algorithm (OTP), which is theoretically unbreakable [8]. Liu et al. addressed a RGB color image encryption method based on logistic chaotic sequence and DNA computation [9]. Recently, Chang et al. proposed the new applications of DNA computing, quadratic congruence, and factoring integers. In [20], the authors used an adapted multiobjective version of the differential evolution metaheuristics to design reliable DNA libraries. Jiao et al. proposed an unsupervised spectral matching classifier to perform the task of clustering different ground objects in specific spectral DNA feature encoding subspaces [21]. Zhou et al. designed a new tile selfassembly model to solve the maximum matching problem. In [22], the author proposed a generic delay gate that could be interfaced with virtually any DNA system and presented a theoretical proof of concept of its applicability.
In this paper, we propose a novel algorithm of reversible data hiding based on DNA computing. The algorithm of histogram modification proposed by Ni et al. that is a classical algorithm for reversible data hiding [13]. Inspired by this algorithm, DNA computing is used to realize this algorithm. Compared with previous results, our experimental results have significantly improved the ER (Embedding Rate). Furthermore, some PSNR (peak signaltonoise ratio) of test images are also improved. Experimental results show that it is suitable for protecting the copyright of cover image in DNAbased information security.
The paper is organized as follows. In the next section, the related works are described in detail. In Section 3, the proposed algorithm is described in detail, and performance analyses and simulation results are reported. Finally, conclusions are drawn in Section 4.
2. Related Works
2.1. Histogram Modification
The histogram modification was proposed in Ni et al.’s paper [13]. In his method, a zero point (zp for short) and a peak point (pp for short) of the histogram are firstly found. In order to shift the histogram, the grayscale value of pixels between zp and pp is incremented by “1.” It could leave one grayscale value empty and embed watermarking in the pp. For the process of extracting watermarking, bit “1” is extracted from the pixel with the value , and bit “0” is extracted from the pixel with the value pp. For others histogram, , the pixel value is subtracted by 1. Completing the reverse process, the original image can be recovered without any distortion.
2.2. DNA Coding
DNA coding is the key step for DNA computing [23–25]. For the binary bit, 0 with 1 is complementary. So 00 with 11 are complementary, and 01 with 10 are also complementary. In this paper, we consider A = 00, T = 11, C = 01, and G = 10 to encode binary message to DNA sequences. There are eight DNA coding methods to convert binary message to DNA sequences that are stated in Table 1. Here, we use the first DNA coding method.

Mao et al. reported a onedimensional algorithmic selfassembly of DNA triplecrossover molecules that could be used to execute four steps of a logical (cumulative XOR) operation on a string of binary bits [26]. Rothemund et al. reported a molecular realization, using twodimensional selfassembly of DNA tiles, of a cellular automaton whose updated rule computes the binary function XOR [27]. Frezza et al. reported the design and functional characterization of a complete set of modular DNAbased Boolean logic gates (AND, OR, and ANDNOT) and further demonstrated their wiring into a threelevel circuit that exhibited Boolean XOR (exclusive OR) function [28]. Recently, Shi et al. constructed DNA molecular systems based on DNA strand displacement performing computation of logic gates, including AND, OR, and XOR logic gates [29]. These works show that DNA computing can be used to realize the XOR operation. In this paper, we define the XOR results from two DNA bases. The results are listed in Table 2.

3. The Algorithm of Reversible Data Hiding Based on DNA Computing
3.1. Embedding Watermarking
In this paper, some standard test images are used to test the effect of proposed algorithm. The cover image firstly is encoded into DNA sequences based on the first row in Table 1. In Ni’s algorithm, we should find a zero point and a peak point. In our algorithm, each pixel of cover image is encoded into four bases. Summing up the number of last base for each DNA sequence, the base with max number is found out. According to the max number, the length of watermarking is determined. The pseudocode of Ni’s algorithm is briefly stated as follows [14]:(1)Generate its histogram .(2)In the histogram , find the peak point and zero point .(3)If the zero point , recode the coordinate of those pixels and the pixel grayscale value as overhead bookkeeping information. Then set .(4)Without loss of generality, assume . Move the whole part of the histogram with to the right by 1 unit. This means that all the pixel grayscale values are added by 1.(5)Scan the image, when meeting the pixel, check the tobeembedded hit. If the tobeembedded bit is “1,” the pixel grayscale value is changed to . If the bit is “0,” the pixel value remains .
Using the same rule, we encode the watermarking into DNA sequence. Then embedding watermarking combines the max base with the watermarking base by using XOR operation from Table 2. The max bases of cove image are replaced with the results of XOR operation. The detailed of embedding watermarking is illustrated in Figure 1.
Note that the proposed algorithm should reserve one max base and the location of all bases in the cover image. They are corresponding to the pp and zp for the histogram modification and used to recover original image without any restoration. The proposed algorithm does not increase the size of image, so the space complexity is . The proposed algorithm mainly includes five steps, and their time complexity is (encoding cover image), (finding the max bases), (determining the length of watermarking), (implementing XOR operation), and (replacing the max bases). So the time complexity of proposed algorithm is .
3.2. Extracting Watermarking
The extracting watermarking process is similar to that of embedding procedure in the reversed order. It can be briefly stated as follows.
Step 1. Obtain the max base and the location and encode the watermarked image.
Step 2. According to Table 2, extract watermarking by using XOR operation.
Step 3. Replace the last bases of the watermarked image with the XOR results of Step 2.
Step 4. Decode the watermarking and the image after extracting watermarking.
Step 5. Output the watermarking and image.
3.3. Performance Analyses and Simulation
In this chapter, performance analyses and simulation of proposed algorithm are described in detail.
3.3.1. PSNR and ER
The PSNR (peak signaltonoise ratio) and ER (Embedding Rate) can be used to evaluate the effect of algorithm for image watermarking. The PSNR is defined as where ; and are image width and length, respectively; and and are pixel value of the original image and watermarked image, respectively. For the histogram modification algorithm, the difference between and is equal to 1 in the worst case; namely, all the pixels are changed. So , and PSNR = 48.13 dB. The ER is the Bits Per Pixel and defined aswhere denotes the number of embedding watermarking and denotes the number of pixels of cover image. For the histogram modification algorithm, all the pixels of cover image embedded onebit watermarking in the best case, so the maximum of ER is equal to 1 bpp.
3.3.2. Simulation and Experiment
In this section, four different standard images with size are used to test the effect of proposed algorithm, respectively, Lena, Airplane, Baboon, Boat, House, and Tiffany.
Figure 2 shows the effect of proposed algorithm. Figure 2(a) is the original cover image, Figure 2(b) is the watermarked image, Figure 2(c) is the recovered imager after extracting watermarking, and Figure 2(d) is the difference image between Figures 2(a) and 2(b). Figure 2(d) is an allblack figure, so the test image can be reversibly recovered by our algorithm. Figure 3 shows the changes of histogram of Lena. Figure 3(a) is the histogram of cover image, and Figure 3(b) is the histogram of watermarked image.
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(b)
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(d)
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Figures 4–8 are other test cover images, Airplane, Baboon, Boat, House, and Tiffany, respectively. Each subimage (a) is a cover image. Each subimage (b) is the watermarked image. Each subimage (c) is the histogram of (a) and (d) is the histogram of (b).
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(b)
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(d)
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(b)
(c)
(d)
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(d)
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(d)
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Table 3 reports the results of Ni’s algorithm [13]. Table 4 lists the results of our algorithm. Compared with these results, our algorithm significantly improves the number of watermarking bits and ER. Some PSNR of test images are also improved, except for Baboon and Boat. But small differences do not influence greatly the quality of watermarked image. In Ni’s algorithm, the watermarking is embedded in peak point, which is a pixel of cover image. Its value is from range of 0 to 255. In proposed algorithm, we make the max base as the peak point, which is from range of A to T, namely, A, C, G, and T. So the proposed algorithm could increase the number of peak points and ER.


4. Conclusions
In this work, we combine image watermarking with DNA computing that proposes a novel algorithm for reversible data hiding. We firstly introduce the method of histogram modification, which is a famous algorithm and proposed by Ni et al. [13], and the background of DNA computing. Combined with the merits of DNA computing, we realize reversible data hiding based on biological technology. Compared with previous results, our experimental results have significantly improved the ER. Furthermore, some PSNR of test images are also improved. Experimental results show that it is suitable for protecting the copyright of cover image in DNAbased information security. In the future work, we will attempt to use DNA computing and quantum computing to hide watermarking.
Competing Interests
The authors declare that there are no competing interests regarding the publication of this paper.
Acknowledgments
This work is supported by the National Natural Science Foundation of China (nos. 61402066, 61370005, 61572093, 61402067, 61425002, 61672121, 61672051, and 31370778), Program for Changjiang Scholars and Innovative Research Team in University (no. IRT_15R07), the Program for Liaoning Innovative Research Team in University (no. LT2015002), the Basic Research Program of the Key Lab in Liaoning Province Educational Department (nos. LZ2014049 and LZ2015004), Scientific Research Fund of Liaoning Provincial Education (nos. L2015015, and L2014499), and the Program for Liaoning Key Lab of Intelligent Information Processing and Network Technology in University.
References
 L. M. Adleman, “Molecular computation of solutions to combinatorial problems,” Science, vol. 266, no. 5187, pp. 1021–1024, 1994. View at: Publisher Site  Google Scholar
 R. J. Lipton, “DNA solution of hard computational problems,” Science, vol. 268, no. 5210, pp. 542–545, 1995. View at: Publisher Site  Google Scholar
 Q. Ouyang, P. D. Kaplan, S. Liu, and A. Libchaber, “DNA solution of the maximal clique problem,” Science, vol. 278, no. 5337, pp. 446–449, 1997. View at: Publisher Site  Google Scholar
 R. S. Braich, N. Chelyapov, C. Johnson, P. W. K. Rothemund, and L. Adleman, “Solution of a 20variable 3SAT problem on a DNA computer,” Science, vol. 296, no. 5567, pp. 499–502, 2002. View at: Publisher Site  Google Scholar
 L. Qian, E. Winfree, and J. Bruck, “Neural network computation with DNA strand displacement cascades,” Nature, vol. 475, no. 7356, pp. 368–372, 2011. View at: Publisher Site  Google Scholar
 W.L. Chang, M. Guo, and M. S.H. Ho, “Fast parallel molecular algorithms for DNAbased computation: factoring integers,” IEEE Transactions on Nanobioscience, vol. 4, no. 2, pp. 149–163, 2005. View at: Publisher Site  Google Scholar
 S. Shoshani, R. Piran, Y. Arava, and E. Keinan, “A molecular cryptosystem for images by DNA computing,” Angewandte Chemie  International Edition, vol. 51, no. 12, pp. 2883–2887, 2012. View at: Publisher Site  Google Scholar
 M. Babaei, “A novel text and image encryption method based on chaos theory and DNA computing,” Natural Computing, vol. 12, no. 1, pp. 101–107, 2013. View at: Publisher Site  Google Scholar  MathSciNet
 L. Liu, Q. Zhang, and X. Wei, “A RGB image encryption algorithm based on DNA encoding and chaos map,” Computers and Electrical Engineering, vol. 38, no. 5, pp. 1240–1248, 2012. View at: Publisher Site  Google Scholar
 J. Fridrich, M. Goljan, and R. Du, “Lossless data embedding for all image formats,” in Proceedings of the Security and Watermarking of Multimedia Contents IV, pp. 572–583, San Jose, CA, USA, January 2002. View at: Publisher Site  Google Scholar
 G. Xuan, J. Zhu, J. Chen, Y. Q. Shi, Z. Ni, and W. Su, “Distortionless data hiding based on integer wavelet transform,” Electronics Letters, vol. 38, no. 25, pp. 1646–1648, 2002. View at: Publisher Site  Google Scholar
 J. Tian, “Reversible data embedding using a difference expansion,” IEEE Transactions on Circuits and Systems for Video Technology, vol. 13, no. 8, pp. 890–896, 2003. View at: Publisher Site  Google Scholar
 Z. Ni, Y.Q. Shi, N. Ansari, and W. Su, “Reversible data hiding,” IEEE Transactions on Circuits and Systems for Video Technology, vol. 16, no. 3, pp. 354–362, 2006. View at: Publisher Site  Google Scholar
 K.L. Chung, W.J. Yang, and W.N. Yang, “Reversible data hiding for depth maps using the depth nosynthesiserror model,” Information Sciences, vol. 269, pp. 159–175, 2014. View at: Publisher Site  Google Scholar  MathSciNet
 B. Ou, X. Li, Y. Zhao, R. Ni, and Y.Q. Shi, “Pairwise predictionerror expansion for efficient reversible data hiding,” IEEE Transactions on Image Processing, vol. 22, no. 12, pp. 5010–5021, 2013. View at: Publisher Site  Google Scholar  MathSciNet
 Z. Qian, X. Zhang, and S. Wang, “Reversible data hiding in encrypted JPEG bitstream,” IEEE Transactions on Multimedia, vol. 16, no. 5, pp. 1486–1491, 2014. View at: Publisher Site  Google Scholar
 H. J. Shiu, S. Y. Tang, C. H. Huang, R. C. T. Lee, and C. L. Lei, “A reversible acoustic data hiding method based on analog modulation,” Information Sciences, vol. 273, pp. 233–246, 2014. View at: Publisher Site  Google Scholar
 H.T. Wu, J.L. Dugelay, and Y.Q. Shi, “Reversible image data hiding with contrast enhancement,” IEEE Signal Processing Letters, vol. 22, no. 1, pp. 81–85, 2015. View at: Publisher Site  Google Scholar
 J. D. Watson and F. H. C. Crick, “Molecular structure of nucleic acids: a structure for deoxyribose nucleic acid,” Nature, vol. 171, no. 4356, pp. 737–738, 1953. View at: Publisher Site  Google Scholar
 J. M. ChavesGonzález and M. A. VegaRodríguez, “DNA strand generation for DNA computing by using a multiobjective differential evolution algorithm,” BioSystems, vol. 116, no. 1, pp. 49–64, 2014. View at: Publisher Site  Google Scholar
 H. Jiao, Y. Zhong, and L. Zhang, “An unsupervised spectral matching classifier based on artificial dna computing for hyperspectral remote sensing imagery,” IEEE Transactions on Geoscience and Remote Sensing, vol. 52, no. 8, pp. 4524–4538, 2014. View at: Publisher Site  Google Scholar
 N. Aubert, Y. Rondelez, T. Fujii, and M. Hagiya, “Enforcing logical delays in DNA computing systems,” Natural Computing, vol. 13, no. 4, pp. 559–572, 2014. View at: Publisher Site  Google Scholar  MathSciNet
 Q. Zhang, B. Wang, X. Wei, and C. Zhou, “A novel constraint for thermodynamically designing DNA sequences,” PLoS ONE, vol. 8, no. 8, Article ID e72180, 2013. View at: Publisher Site  Google Scholar
 Q. Zhang, B. Wang, X. Wei, X. Fang, and C. Zhou, “DNA word set design based on minimum free energy,” IEEE Transactions on Nanobioscience, vol. 9, no. 4, pp. 273–277, 2010. View at: Publisher Site  Google Scholar
 H. Liu, D. Lin, and A. Kadir, “A novel data hiding method based on deoxyribonucleic acid coding,” Computers & Electrical Engineering, vol. 39, no. 4, pp. 1164–1173, 2013. View at: Publisher Site  Google Scholar
 C. Mao, T. H. LaBean, J. H. Reif, and N. C. Seeman, “Logical computation using algorithmic selfassembly of DNA triplecrossover molecules,” Nature, vol. 407, no. 6803, pp. 493–496, 2000. View at: Publisher Site  Google Scholar
 P. W. K. Rothemund, N. Papadakis, and E. Winfree, “Algorithmic selfassembly of DNA Sierpinski triangles,” PLoS Biology, vol. 2, no. 12, 2004. View at: Publisher Site  Google Scholar
 B. M. Frezza, S. L. Cockroft, and M. R. Ghadiri, “Modular multilevel circuits from immobilized DNAbased logic gates,” Journal of the American Chemical Society, vol. 129, no. 48, pp. 14875–14879, 2007. View at: Publisher Site  Google Scholar
 X. Shi, Z. Wang, C. Deng, T. Song, L. Pan, and Z. Chen, “A novel biosensor based on DNA strand displacement,” PLoS ONE, vol. 9, no. 10, Article ID e108856, 2014. View at: Publisher Site  Google Scholar
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Copyright © 2017 Bin Wang 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.