## Menglong Wu* , Yan Li and Wenkai Liu## |

0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | |
---|---|---|---|---|---|---|---|---|

00 | A | A | C | G | C | G | T | T |

01 | C | G | A | A | T | T | C | G |

10 | G | C | T | T | A | A | C | G |

11 | T | T | G | C | G | C | A | A |

DNA complementary and algebraic operations are the core processes of DNA-based encryption algorithms. Since DNA complementary operation abides by the single mapping principle, the DNA complementary rules must satisfy the formulas defined in Eq. (3), where [TeX:] $$B\left(x_{i}\right)$$ is a base pair of [TeX:] $$x_{i}$$ and they are complementary.

Based on Eq. (3), there are 6 available DNA complementary rules, as shown below:

DNA algebraic operation is based on traditional binary algebraic operations, such as, addition, subtraction, XOR and XNOR. According to DNA encoding rule 1, the definitions of DNA addition, subtraction, XOR and XNOR operations based on two DNA codes are given in Table 2.

In this paper, a hierarchical bilateral-diffusion architecture is proposed for color image encryption, utilizing the hyperchaotic system and DNA operation. The concrete design of the proposed mechanism consists of three main parts: (1) cipher matrixes generation, (2) pixel-permutation and pixel-diffusion algorithm, and (3) bilateral block-diffusion algorithm based on DNA sequence operation, which will be further discussed as follows.

In all cryptosystems, to overcome exhaustive attacks, the cipher keys are required to be long and sensitive enough. In this paper, since ten cipher matrixes are required for image encryption and decryption, two 4D hyperchaotic systems, the hyper-chaotic Lorenz system and Chen’s hyper-chaotic system, are utilized to satisfy the requirements of high randomicity and sensitivity. The design concept of the cipher matrixes generation is shown in Fig. 1, which can work by iterating the chaotic sequences with two hyperchaotic systems and integrating the intermediate variables into cipher matrixes through a specific generation algorithm. Suppose the plain image is in size of [TeX:] $$M \times N$$ and the number of DNA blocks is t, the whole ten cipher matrixes can be generated by the following steps.

Step 1: Take four initial values [TeX:] $$x_{0}, y_{0}, z_{0}, w_{0}$$ as inputs of hyper-chaotic Lorenz system with control parameters [TeX:] $$r_{1}, r_{2}$$ and iterate for [TeX:] $$r_{1}+r_{2}$$ times to gain four chaotic values, denoted as [TeX:] $$x^{\prime}, y^{\prime}, z^{\prime}, w^{\prime}.$$

Step 2: Plus four initial values [TeX:] $$m_{0}, n_{0}, p_{0}, k_{0}$$ with chaotic values [TeX:] $$x^{\prime}, y^{\prime}, z^{\prime}, w^{\prime}$$ and take them as inputs of Chen’s hyper-chaotic system with control parameters [TeX:] $$t_{1}, t_{2}, t_{3}.$$ Then, iterate them for [TeX:] $$t_{1}+t_{2}+t_{3}$$ times.

Step 3: Continually put the obtained chaotic values into hyper-chaotic Lorenz system and Chen’s hyper-chaotic system in sequence, where the intermediate sequences of hyper-chaotic Lorenz system is denoted as [TeX:] $$x_{\mathrm{i}}, y_{\mathrm{i}}, z_{\mathrm{i}}, w_{\mathrm{i}}$$ and the intermediate sequences of Chen’s hyper-chaotic system is denoted as [TeX:] $$m_{\mathrm{i}}, n_{\mathrm{i}}, p_{\mathrm{i}}, k_{\mathrm{i}}.$$

Step 4: Iterate the chaotic sequences for 500+8MN times and generate four cipher matrixes in size of [TeX:] $$M \times 4 N$$ under the definitions in Eqs. (5)–(8).

Step 5: Divide [TeX:] $$A_{M \times 4 N}$$ into four pixel-permutation cipher matrixes, [TeX:] $$X_{M \times N}, Y_{M \times N}, Z_{M \times N}, H_{M \times N};$$ and then Reshape [TeX:] $$B_{M \times 4 N} \text { and } C_{M \times 4 N}$$ into two pixel-diffusion cipher matrixes with the size of [TeX:] $$2 M \times 2 N,$$ denoted as [TeX:] $$U_{2 M \times 2 N} \text { and } V_{2 M \times 2 N} ; \text { Divide } D_{M \times 4 N}$$ into DNA encoding cipher matrix [TeX:] $$E_{1 \times t},$$ DNA decoding cipher matrix [TeX:] $$F_{1 \times \mathrm{t}},$$ DNA complementary cipher matrix [TeX:] $$S_{1 \times \mathrm{t}}$$ and DNA algebraic cipher matrix [TeX:] $$T_{1 \times t}.$$

Step 6: Execute modulus operation to [TeX:] $$S_{1 \times \mathrm{t}} \text { and } T_{1 \times \mathrm{t}} \text {, where } S_{1 \times \mathrm{t}}$$ is set in the range of [0,5] and [TeX:] $$T_{1 \times t}$$ is set in the range of [0,3].

Permutation and diffusion are two vital operations in the image encryption algorithm. In the designed system, a pixel-permutation algorithm is used to confuse the order of pixels in the plain image, and the pixel-diffusion algorithm is used to alter the subsequent pixels values of the image matrix, which will be further combined with DNA based block-diffusion algorithm for an impressive performance on statistical attack and differential attack.

The designed pixel-permutation algorithm acts as the primal confusing method to the plain image, which exchanges pixels in coordinate (i,j) and (m,n) through cipher matrixes [TeX:] $$X_{M \times N}, Y_{M \times N}, Z_{M \times N},H_{M \times N}.$$ The exchanging rules of the two pixels are defined in Eqs. (9) and (10). There, all the pixel values will be entirely scrambled by repetitively executing the algorithm from coordinate (1,1) to (M,N).

On the other hand, pixel-diffusion algorithms are considered the vital role of image encryption against differential attack, since even single-pixel can greatly influence others. Therefore, two pixel-diffusion algorithms are introduced to the system for better performance, pixel-diffusion I and pixel-diffusion II, which scan the image matrix in the opposite direction. Specifically, the pixel-diffusion I algorithm is a forward-diffusion algorithm that starts from the first element and alters the remaining pixels value in the sequence. Suppose the input image matrix is [TeX:] $$P_{M \times N},$$ the obtained image matrix after pixel-diffusion I algorithm can be calculated by Eq. (11), denoted as [TeX:] $$I_{M \times N} \text {, where } U_{2 M \times 2 N}$$ is the cipher matrix and a,b are two cipher keys. The diffusion operation is accomplished by executing the algorithm from coordinate (1,1) to (M,N).

On the contrary, the pixel-diffusion II algorithm is a backward-diffusion algorithm that starts from the last element and alters the remaining pixels value in the negative direction. Similarly, suppose the input image matrix is [TeX:] $$P_{M \times N},$$ and the obtained image matrix [TeX:] $$I_{M \times N}$$ can be calculated by Eq. (12), where [TeX:] $$V_{2 M \times 2 N}$$ is the cipher matrix and c,d are two cipher keys. The diffusion operation is accomplished by executing the algorithm from coordinate (M,N) to (1,1).

As a matter of fact, confusing the original image with only XOR-based diffusion algorithm is seen as a deficient method when encountering strongly differential attacks. Therefore, this paper presents a bilateral block-diffusion algorithm for better sensitivity, utilizing DNA encoding, DNA decoding, DNA complementary operation and DNA algebraic operation. Under the peculiar diffusion structure of forward pixel-diffusion, DNA based bilateral block-diffusion and backward pixel-diffusion, the image encryption mechanism shows an impressive ability to overcome statistical attacks and differential attacks.

The proposed block-diffusion algorithm is constituted by forward DNA diffusion algorithm and backward DNA diffusion algorithm. It diffuses the image by two bilateral directions, where the forward diffusion starts from block 1 to block t and backward diffusion starts from block t to block 1. DNA complementary operation and DNA algebraic operation are the core operations of DNA diffusion, which acts on each current DNA block with the previous DNA block. For instance, if the current block is block i, then the previous block of forward DNA diffusion is block i-1, and the previous block of backward DNA diffusion is block i+1.

The adopted DNA complementary operation is a substitution operation with iteration, and the results are determined by the DNA complementary rules in Eq. (4). Suppose the current DNA block is denoted as K, the previous DNA block is denoted as J, and the block after DNA complementary operation is denoted as R. Then, the calculation principle of an intact DNA complementary process can be illustrated as follow:

where [TeX:] $$K_{i, j}, J_{i, j}, R_{i, j}$$ are the elements in block K,J,R respectively, and [TeX:] $$B\left(K_{i, j}\right)$$ represents a one-time complementary operation to [TeX:] $$K_{i, j}.$$ In the designed algorithm, cipher matrix [TeX:] $$S_{1 \times \mathrm{t}}$$ is required to select the complementary rule, and the elements in block J are used to decide the iterations of complementary substitution.

On the other hand, the adopted DNA algebraic operation is a subsequent process to DNA complementary operation, which alters the elements in block R with block J. The DNA algebraic rule is decided by the elements in the cipher matrix [TeX:] $$T_{1 \times \mathrm{t}}, \text { where } T_{i, j}=0$$ represents addition operation, [TeX:] $$T_{i, j}=1$$ represents subtraction operation, [TeX:] $$T_{i, j}=2$$ represents XOR operation and [TeX:] $$T_{i, j}=3$$ represents XNOR operation.

The proposed encryption mechanism for a color image is described in Fig. 2, involving one pixel-permutation algorithm, two pixel-diffusion algorithms and the DNA based bilateral block-diffusion algorithm. The complete image encryption steps are illustrated as follows.

Step 1: Input cipher keys [TeX:] $$x_{0}, y_{0}, z_{0}, w_{0}, m_{0}, n_{0}, p_{0}, k_{0}, r_{1}, r_{2}, t_{1}, t_{2}, t_{3}$$ to gain ten cipher matrixes.

Step 2: Separate the plain image into R, G, B channel matrixes in the size of [TeX:] $$M \times N.$$

Step 3: Execute pixel-permutation algorithm to the image matrix from coordinate (1,1) to (M,N), through cipher matrixes [TeX:] $$X_{M \times N}, Y_{M \times N}, Z_{M \times N}, H_{M \times N};$$ Then, run pixel-diffusion I algorithm to the obtained matrix from coordinate (1,1) to (M,N), through cipher matrix [TeX:] $$U_{2 M \times 2 N}$$ and cipher keys a,b.

Step 4: Proceed the DNA based forward block-diffusion algorithm as follows: partition the image matrix into t blocks and convert into DNA blocks under the encoding rules defined in matrix E_(1×t); keep the first DNA block unchanged; For each of the remaining t-1 blocks, make DNA complementary operation and DNA algebraic operation with the previous block sequentially, based on cipher matrixes [TeX:] $$S_{1 \times \mathrm{t}} \text { and } T_{1 \times \mathrm{t}};$$ then, convert all the DNA blocks into a decimal matrix with the decoding rules defined in matrix [TeX:] $$\mathrm{F}_{1 \times \mathrm{t}}.$$

Step 5: Similarly, proceed the DNA based backward block-diffusion algorithm as follows: partition and convert the matrix into t DNA blocks with matrix [TeX:] $$\mathrm{E}_{1 \times \mathrm{t}},$$ and remain block t unchanged; from block t-1 to block 1, execute DNA complementary operation and DNA algebraic operation based on cipher matrixes [TeX:] $$S_{1 \times \mathrm{t}} \text { and } T_{1 \times \mathrm{t}};$$ convert the DNA blocks into a decimal matrix with matrix [TeX:] $$\mathrm{F}_{1 \times \mathrm{t}}.$$

Step 6: From coordinate (M,N) to (1,1), convert the matrix with pixel-diffusion II algorithm through cipher matrix [TeX:] $$V_{2 M \times 2 N}$$ and cipher keys c,d in sequence.

Step 7: For each component matrix of R, G, B channel, loop execute the transformation from step 3 to step 6. Then, merge the three-channel matrixes into one final cipher image.

The experimental of the proposed image encryption mechanism is tested in this part. Four color images are utilized to test the encryption and decryption performance, named “Lena” in the size of [TeX:] $$512 \times 512 \times 3,$$ “street” in the size of [TeX:] $$1280 \times 720 \times 3,$$ “waterfall” in the size of [TeX:] $$800 \times 600 \times 3,$$ and “mountain” in the size of [TeX:] $$1024 \times 680 \times 3,$$ as shown in Fig. 3(a)–3(d), respectively. Meanwhile the experiments are implemented using MATLAB R2018b on a computer with Intel Core i5 processor and 8 GB RAM in Windows 10 operating system.

The initial value and other control parameters are described in Table 3, where [TeX:] $$x_{0}, y_{0}, z_{0}, w_{0}$$ are four initial value of hyper-chaotic Lorenz system, [TeX:] $$m_{0}, n_{0}, p_{0}, k_{0}$$ are four initial value of Chen’s hyper-chaotic system, [TeX:] $$r_{1}, r_{2}, t_{1}, t_{2}, t_{3}$$ are the control parameters of the two chaotic systems and a,b,c,d are the parameters of two pixel-diffusion algorithms. The encryption for the four plain images is shown in Fig. 3. It can be seen from the experimental results that the cipher images are unrecognizable and shown no correlation to the plain images. Besides, the cipher images are all decrypted successfully. Hence, the feasibility of the proposed image encryption algorithm has been verified.

Table 3.

Item | Value |
---|---|

Chaotic systems | [TeX:] $$\begin{gathered} x_{0}=26.7837, y_{0}=-8.9013, z_{0}=59.4985, w_{0}=-247.3752, \\ m_{0}=37.5082, n_{0}=-16.3594, p_{0}=69.4987, k_{0}=137.4891, \\ r_{1}=58, r_{2}=231, t_{1}=48, t_{2}=9, t_{3}=168 \end{gathered}$$ |

Pixel-diffusion algorithms | a=78,b=215,c=97,d=38 |

The computational complexity can influence the computational speed greatly for both encryption and decryption processes. Therefore, to verify whether the proposed encryption mechanism is suitable enough for color image encryption, this section gives the time complexity of the encryption process for theoretical support and analysis, as follows. Firstly, the input color image with the size of [TeX:] $$M \times N$$ is separated into three pixel-matrixes, so the time complexity is [TeX:] $$O(3 \times M \times N).$$ The pixel-permutation process exchanges the pixel value in each pixel-matrix of three channels, so the time complexity is also [TeX:] $$O(3 \times M \times N).$$ The pixel-diffusion process alters the pixel value in the three pixel-matrixes, so the time complexity for pixel-diffusion I and pixel-diffusion II algorithm are both [TeX:] $$O(3 \times M \times N).$$ For DNA based block-diffusion process, the time complexity for DNA encode/decode is [TeX:] $$O(12 \times M \times N),$$ since 4 DNA codes are needed to represent one pixel value. Similarly, the time complexity for DNA complementary and algebraic operation is also [TeX:] $$O(12 \times M \times N),$$ since the operations are all based on the DNA codes after DNA encodes. Thus, the overall time complexity of the proposed image encryption mechanism is [TeX:] $$O(12 \times M \times N).$$

Computational time is a significant indicator in the image encryption area. For a well-designed image encryption algorithm, the computational time is required to be as low as possible when guaranteeing system security. In this part, the image encryption algorithm is executed 100 times to gain the average encryption time of 3.30 seconds, with an image size of [TeX:] $$512 \times 512 \times 3.$$ Since the bilateral-diffusion architecture only involves low computational operations such as addition, subtraction, XOR, and XNOR operation, the proposed algorithm has shown an excellent speed performance of image encryption. Besides, the design of DNA-based block diffusion also saved plenty of computing time and achieved better encryption efficiency. Table 4 gives the experimental results and compares them with other algorithms [2,4,13,22] in computational times, which indicates that the proposed algorithm has achieved better computational speed performance.

The image histogram can directly reveal the distribution of the pixel values. The histograms of plain image and cipher image in R, G, B channels are given in Fig. 4. It can be noticed that the histograms of plain images are tended to some specific shapes, and the pixel values are concentrated to several fixed intervals, while the histograms of cipher images show their excellent uniformity. Hence, it is exceedingly difficult to extract the related information and recover the plain image. Therefore, the proposed algorithm can overcome the statistical attacks from histogram analysis.

Correlation analysis is another statistical attack, which intends to search the relation of adjacent pixels in the cipher images and recover the plain images. Since the correlations of adjacent pixels in plain images are usually very large in horizontal, vertical, and diagonal directions, reducing the correlation of adjacent pixels in the image encryption algorithm is vital. In this part, 10000 pairs of adjacent pixels are selected randomly to evaluate the correlations between plain and cipher images. Fig. 5 gives the distribution diagrams of adjacent pixels in plain image and cipher image. It shows that the correlations of the adjacent pixels in the plain image are very strong, which the distribution is very close to a straight line. Meanwhile, the distribution diagrams of the cipher image are tended to be very disordered, which indicates that the correlation of cipher image is very little.

Further, the correlation coefficient acts as a vital measurement criterion to quantify the correlation of images. Eqs. (14)–(17) given the formulas of the correlation coefficient, where x,y are adjacent pixel values and N is the sample size.

The experimental results of the correlation coefficient in plain image and cipher image are shown in Table 5. The correlation coefficients are supposed to be very close to theoretical value zero, and our test results are satisfied with the demands. Table 5 also lists the comparison with other image encryption algorithms [5,13,14,20]. All the experimental results are very close to zero, which shows that the proposed algorithm has a great ability to against statistical attacks.

Table 5.

Correlation coefficient | Horizontal | Vertical | Diagonal |
---|---|---|---|

Lena | 0.9900 | 0.9807 | 0.9719 |

Proposed method | 0.0036 | 0.0068 | -0.0029 |

Wu et al. [5] | -0.0080 | 0.0098 | -0.0058 |

Rehman et al. [13] | -0.0238 | -0.0013 | 0.0006 |

Liu et al. [14] | 0.0011 | -0.0013 | -0.0019 |

Chai et al. [20] | -0.0027 | 0.0033 | -0.0035 |

The information entropy can measure the uncertainty of an information source, which can be calculated by Eq. (18).

Hence, the uncertainty of the cipher image can be evaluated by calculating the image information entropy. The comparison with other algorithms is given in Table 6 [1,2,14,21]. It can be noticed that all the experimental results are very close to theoretical value 8 in each channel component, which indicates that the cipher image is of great randomness to resist entropy attack.

Table 6.

Information entropy | R channel | G channel | B channel |
---|---|---|---|

Lena | 7.2600 | 7.5949 | 6.9660 |

Proposed method | 7.9993 | 7.9992 | 7.9993 |

Arpaci et al. [1] | 7.9949 | 7.9945 | 7.9941 |

Kang and Guo [2] | 7.9980 | 7.9979 | 7.9978 |

Liu et al. [14] | 7.9992 | 7.9993 | 7.9994 |

Li et al. [21] | 7.9991 | 7.9973 | 7.9967 |

The differential attack is a strong attack in which the attackers may change the pixel values in plain images and seek the difference between the cipher images to crack the cipher keys. The number of pixel change rate (NPCR) and UACI are two test indexes to evaluate whether the encryption algorithm can resist differential attacks. They are defined in Eqs. (19)–(21), where P(i,j) and C(i,j) are the pixel values of two cipher images in the size of [TeX:] $$M \times N.$$

In this part, two plain images with one-pixel value difference are selected for the differential attack test, and the experimental results are given in Table 7. The theoretical value of NPCR and UACI are 99.6094% and 33.4635%, respectively. The comparisons with other algorithms are also given in Table 7 [2,14,21]. It can be noticed that our algorithm has the best performance in both NPCR and UACI tests compared to other image encryption algorithms. Therefore, our algorithm has a strong ability to resist the differential attack.

Table 7.

Algorithm | R channel | G channel | B channel | |||
---|---|---|---|---|---|---|

NPCR | UACI | NPCR | UACI | NPCR | UACI | |

Proposed method | 99.61 | 33.49 | 99.62 | 33.43 | 99.60 | 33.47 |

Kang and Guo [2] | 99.65 | 33.46 | 99.65 | 33.47 | 99.65 | 33.44 |

Liu et al. [14] | 99.60 | 33.06 | 99.59 | 30.59 | 99.64 | 27.60 |

Li et al. [21] | 99.60 | 33.25 | 99.62 | 33.50 | 99.61 | 33.39 |

As a well-designed image encryption algorithm, the key space should be larger than [TeX:] $$2^{100}$$ to resist brute-force attacks. The cipher key of the proposed system is constituted by four initial values of hyper-chaotic Lorenz system, [TeX:] $$x_{0}, y_{0}, z_{0}, w_{0},$$ four initial values of Chen’s hyper-chaotic system, [TeX:] $$m_{0}, n_{0}, p_{0}, k_{0},$$ five control parameters in the chaotic systems, [TeX:] $$r_{1}, r_{2}, t_{1}, t_{2}, t_{3}$$ and four parameters of pixel-diffusion algorithms, a,b,c,d. The initial values [TeX:] $$x_{0}, y_{0}, m_{0}, n_{0}$$ are in the range of (-40,40), [TeX:] $$z_{0}, p_{0}$$ are in the range of (1,81), [TeX:] $$w_{0}, k_{0}$$ are in the range of −250,250. All the initial values are floating numbers with the accuracy of [TeX:] $$10^{-14}.$$ The control parameters [TeX:] $$r_{1}, r_{2}, t_{1}, t_{2}, t_{3} \text { and } a, b, c, d$$ are integers in the range of [0,255]. Hence, the key space of the proposed algorithm can be calculated by Eq. (22).

The comparisons with other existing algorithms [1,5,21,23,24] are as shown in Table 8. It is noticed that only the key space in [21] is larger than ours and the key space in our scheme is much larger than the theoretical value [TeX:] $$2^{100}.$$ Hence, it indicates that our algorithm has a strong ability to against the brute-force attacks.

Table 8.

Algorithm | Key space | Theoretical value |
---|---|---|

Proposed method | [TeX:] $$2^{500} \approx 10^{150}$$ | [TeX:] $$>2^{100}$$ |

Arpaci et al. [1] | [TeX:] $$2^{232}$$ | [TeX:] $$>2^{100}$$ |

Wu et al. [5] | [TeX:] $$2^{349}$$ | [TeX:] $$>2^{100}$$ |

Li al. [21] | [TeX:] $$2^{576}$$ | [TeX:] $$>2^{100}$$ |

Hraoui et al. [23] | [TeX:] $$>2^{100}$$ | [TeX:] $$>2^{100}$$ |

Wu et al. [24] | [TeX:] $$10^{117}$$ | [TeX:] $$>2^{100}$$ |

As a well-designed cryptosystem, the cipher key is supposed to be very sensitive for a slight altering. In this part, the key sensitivity is tested by changing the parameters slightly when decryption to seek the difference between the correctly decrypted image and the parameters changed decrypted images. The experimental results are as shown in Fig. 6, where Fig. 6(a) is a decrypted image with correct cipher key, while Fig. 6(b)–6(e) are decrypted images with slightly changed cipher keys. It can be noticed from Fig. 6 that all the changed cipher keys are failed in image recovery and show no correlation with the plain image. Therefore, the proposed system has a high key sensitivity against blind decryption.

This paper proposes a hierarchical bilateral diffusion architecture for color image encryption based on the hyperchaotic system and DNA sequence operation. To against exhaustive attacks, hyper-chaotic Lorenz system and Chen’s hyper-chaotic system are compounded and weighted to generate cipher matrixes, which results in highly key sensitive with a key space of [TeX:] $$2^{500}.$$ On the other hand, to guarantee system security without sacrificing too much computational time, this paper innovated the encryption mechanism with hierarchical bilateral diffusion architecture to resist various potential attacks. Under the specific diffusion architecture of forward pixel-diffusion, DNA based block-diffusion, and backward pixel-diffusion, the plain image shows excellent ability against statistical attacks and differential attacks. Specifically, our scheme reduces the correlation coefficient of plain image from 0.9809 to 0.0044 and increases the information entropy of plain image from 7.2736 to 7.9993 to overcome statistical attacks. Also, the experimental results of differential attacks indicate that the NPCR and UACI can reach 99.61% and 33.46% on average, which is very close to the theoretical value 99.6094% and 33.4635%. Meanwhile, the computational time consumption under the proposed image encryption scheme is relatively lower than some current image encryption algorithms, costing only 3.30 seconds to encrypt one image. All the experimental results demonstrate that the proposed mechanism is highly efficient in encrypting images with prominent characteristics, such as large key space, stronger key sensitivity, low time consumption, and superior ability to resist varieties of typical attacks. Thus, the proposed diffusion architecture provides an effective method for color image encryption, with expansive application prospects including wireless communication, network data transmission, and big data storage. In the future, this work may achieve even better performance and broader application scenarios under the combination of various image processing techniques, such as image steganography and image compression.

He graduated from the Institute of Semiconductors, Chinese Academy of Sciences as a Ph.D. candidate in 2002. He is currently a professor of Information Science and Technology at the North China University of Technology. He mainly engaged in optical communication, photonic devices and photonic integration.

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