A Dynamic Image Encryption Scheme Based on Quantum Walk and Chaos-Induced DNA

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Introduction
With the rapid development of Internet communication, as the carrier of information, color images are widely used in personal information exchange, medical pathological images, trade secrets, military satellite images, and other felds.At the same time, image privacy information disclosure and vulnerability to illegal attacks or tampering by unsafe third parties in transmission are also becoming more and more prominent.Traditional encryption algorithms such as AES and RSA cannot satisfy the strong correlation of image pixels.Some novel encryption schemes, such as the DNA base rule has become a common image encryption method.Compressed sensing technology is also more and more integrated into the process of image encryption.Te reversible data hidden in the encrypted image are also a manifestation of encryption which have been proposed by researchers [1][2][3][4].With the development of quantum computing [5] and quantum communication [6], researchers urgently need to fnd an encryption scheme that can adapt to the characteristics of color images and generate efective and reliable keys.Te advantages of the proposed scheme are refected in the use of the quantum walk algorithm and dynamic DNA coding to improve the security performance of image encryption.
Quantum walk has the behavior similar to that of the chaotic system, which can produce a reliable pseudorandom number sequence as the key of image encryption.In quantum computing, quantum walk is exponentially faster than classical walk because of its parallel processing of quantum superposition states and the interference between qubits.Tis concept has been widely used since it was proposed by Aharonov et al. [7].In 2011, Di Franco et al. [8] proposed to use the two-dimensional coin state to control the walker's quantum walk on the twodimensional plane.In theory, the infnite key space makes it impossible to crack the key.In 2020, Abd El-Latif et al. [9] proposed application of controlled alternating quantum walk as the pseudo-random number generator in quantum color image encryption shows good security and efciency.Ten in 2021, Abd-El-Atty et al. [10] proposed a new image encryption scheme based on quantum walk and double random phase coding, which achieved good results in correlation, histogram, sensitivity, and other simulation experiments.In the same year, Wang et al. [11] combined the random probability distribution matrix generated by quantum random walk with the DNA coding of the image, which proved that the color image encryption is efective and feasible.
Due to the advantages of a sensitive initial value, large key space, and unpredictability, high level chaos is more common.Yousif et al. [12] proposed a fusion of highdimensional chaotic systems and DNA sequence coding operations.Te techniques used will make cryptographic systems more robust to attacks.Te chaotic system plays an important role in image encryption and often appears together with other encryption technologies, which reduces the correlation between adjacent pixels when encrypting color images and improves the security of encryption by modifying pixel values [13][14][15][16][17].In 2016, Tang and Jiang [18] used high-dimensional chaotic maps to encrypt images, which can efectively improve the key space of the encryption algorithm.In 2020, Hanif et al. [19] proposed an encryption system based on chaotic system, cyclic shift operation, and SHA-384 hash function, which increases the required key space and plaintext sensitivity.At the same time, the efectiveness, robustness, and practical applicability of the proposed RGB image cryptosystem are proved.In 2023, Zhang et al. [20] used a one-dimensional chaotic system to generate a series of new two-dimensional chaotic graphs with excellent chaotic performance, respectively, called 1D-NLSCM and 2D-NCTCM, and designed an adaptive image encryption algorithm to overcome the shortcomings of some existing encryption algorithms that are independent of the target image.Wu et al. [21] used the improved one-dimensional chaotic system to generate keys, and the key and the ordinary image were randomly transformed into the DNA matrix to strengthen the security of the encryption scheme.
DNA sequence [22] operation has the merit of ultralarge-scale parallelism and high-density data storage to achieve fast encryption and decryption applications.Te encrypted image algorithm which combines image hashing and chaotic sequence control DNA coding has increasingly become the future research trend [23,24].In 2021, Dong et al. [25] proposed a color image DNA encryption system based on multioptical chaos and pseudo-random substitution of pixel values.Te author claims that this scheme is expected to be used in color image encryption applications in optical communication.In 2022, Huang and Zhou [26] generated the initial conditions of the chaotic system by calculating the SHA-512 hash function value of the plaintext image and the external key, compressing the original image, reencrypting the difused DNA image by bit-level replacement, and improving global dynamic difusion, which improved the encryption speed and reduced the transmission burden.
Based on the quantum walk algorithm and image watermarking algorithm, the encryption scheme proposed in this paper can ensure the secure transmission of image information [27][28][29][30].Te main process of the encryption scheme in this paper is as follows: (1) reorder the random matrix of three-channel pixels of color images according to quantum walking as a means of image scrambling; (2) input the image hash value into the high-dimensional chaotic system to realize the correlation between plaintext and ciphertext; (3) set the key sequence to dynamically select eight DNA coding rules and replace pixel values to realize encryption.Tis process mainly involves diferent times of XOR operations, which increases the encryption complexity.Finally, the watermark information is introduced into the encryption link as a monitoring means to improve the security of image information.
Te organizational structure of this paper is as follows: the frst section is the introduction, the second section introduces the related work, the third section implements the specifc encryption algorithm, the fourth section analyzes and compares the simulation results, and the fnal section draws a conclusion.

Related Work
2.1.Quantum Walk.Te quantum walk uses a quantum state with phase instead of classical bits.Te walker divides the whole quantum system into H p position space and H c coin space in Hilbert space H � H p ⊗ H c , in which the coin state can be expressed as follows: where |↑〉 indicates that the coin throwing result is upward, |↓〉 indicates that the coin throwing result is downward, and Each walker performs two unitary operations.First, the coin fip operator is acted on the initial state |ψ 0 〉 of the coin state to fip the coin.A commonly used coin tossing operator is the Hadamard operator: Its function is to obtain a superposition state: Te walking direction is determined according to the diferent coin throwing results, and the walking is realized by the ofset operator S.

2
Quantum Engineering Ten, under the action of the ofset operator, the walkers in diferent initial states move to the next adjacent point along the direction after coin tossing: Te process of quantum walk is from the initial state |ψ 0 〉 to the fnal state |ψ T 〉 � (U c ) T |ψ 0 〉 after the T step.Tis evolution process iterates U c � S • (C ⊗ I) constantly and maintains the superposition, which can be obtained by measuring the fnal state.Te probability distribution similar to the classical walk in each position is as follows: 2.2.Chaotic System.Tis paper adopts a high-dimensional Chen chaotic system in reference [31].Its mathematical model is as follows, and it has high requirements on the initial value and control parameters and is sensitive to generate four chaotic sequences for encryption.
When the control parameter i � 36, j � 3, k � 28, h � 16, and − 0.7 ≤ l ≤ 0.7 of the system is selected, the system has a chaotic attractor, and the chaotic system enters a chaotic state.Compared with low-dimensional chaos, the nonlinear behavior of high-dimensional chaos is more difcult to predict, which ameliorates the security performance of the image encryption algorithm.

DNA Sequence.
Te main function of the DNA sequence in image encryption technology is to encode and decode image pixels into specifc DNA bases and carry out XOR operation to replace the original pixel values.For example, a color digital image with pixel values between 0 and 255.Te 8-bit binary pixel value is represented as 4 DNA bases.For example, one pixel value is 77, and its binary value is "01 00 11 01."Te DNA encoding of changing this value depends on choosing a diferent encoding rule when encrypting the image.For example, if you choose rule 8, it will become "CTAC."Using the same DNA rule 8, "CTAC" is converted to a digital format to get the same pixel value of 77.But if you choose another DNA rule to decode, such as rule 1, then "CTAC" will be"10 11 00 10," and the pixel value will be 178.Te eight DNA codes are as follows (Table 1).In addition, DNA base XOR operations are introduced in Table 2. XOR operation is used for encryption in this paper.

Algorithm
In this paper, the algorithm frstly uses quantum walk to generate a random sequence to scramble the image, then uses classical high-dimensional chaos to generate a random sequence, controls and selects diferent DNA coding rules and XOR rules, and fnally realizes the process of dynamic coding, which improves the coding randomness of image encryption pixel values and achieves high security encryption efect.However, based on the above encryption algorithm, the security of the image can only be guaranteed at the transmission source, and it is unable to detect whether the image information is attacked or whether the image information's copyright is protected in the transmission process.Terefore, the sender embeds the imperceptible watermark information in the encrypted image, and the receiver recognizes the watermark information to know whether the encrypted image is from the other party and whether it is attacked.

Initial Scrambling.
Te image was separated by RGB three channels to obtain three N × N matrices, and the pixel values were extracted by row and synthesized into a onedimensional array Img[] of 3 × N × N. Next, the twodimensional quantum walk was adopted.Tat is, |↑〉 coin state is used to determine the left of the walker along the xaxis (up the y-axis), that is, |↓〉 coin state is used to determine the right of the walker along the x-axis (down the y-axis).Te initial state is selected as follows: where |0 x 〉 indicates the walker's position on the x-axis, |0 y 〉 indicates the walker's position on the y-axis, and the state after performing a unitary operation U c after one step is as follows:

Quantum Engineering
After walking N steps: 〉, the probability distribution of the quantum walker in each position is calculated, the probability distribution value is multiplied by 10 12 to get a large enough integer, and then the modulus of 255 is taken to get a series of random remainder sequence N ′ with a size of 3 × M × N.
As shown in Figure 1, this sequence is used as the index of the abovementioned one-dimensional array Img[], N ′ is arranged in ascending order while array Img[] is also rearranged, and then divided into three arrays and restored to the original pixel matrix position by row, thus achieving the initial scrambling efect of the image.

DNA Encryption.
On the basis of Section 3.1, the SHA-256 algorithm is used to generate a series of fxed hash values for the scrambled image, which is represented as a hexadecimal message digest of 64 in length.Any slight change to the pixel of an image will produce diferent hash values.Te message digest is divided into four m j blocks; each block contains 16 hexadecimal numbers, which are converted to foating-point values as input of new initial values of the chaotic system, where j � 1, 2, 3, 4.
Te plaintext image is associated with the generated chaotic sequence, which ensures that the encryption key depends on the image, resists the chosen-plaintext attack, and improves the security.
Te chaotic system generates four chaotic sequences X, Y, Z, and W with a length of t + 3 × N × N. In order to avoid the transient efect, the frst t elements were taken out, the pixel values of the three channels of the image were converted into binary, and diferent DNA coding and decoding methods were independently selected for diferent ranges of random number values in the X sequence.Ten, for the encoded DNA base, the XOR operation is carried out by randomly repeating a certain random number of chaotic sequences, and the Y and Z sequences are modifed to get the following equation: Te new sequence elements are randomly arranged in integers of 0-7.Te DNA sequence at the starting position of XOR operation is selected through sequence Y ′ , and the number of XOR operations is determined through sequence Z ′ .Te sequence of DNA XOR rules is fexible.Diferent output chaotic sequence values dynamically select diferent DNA rules.Tis way of randomly and dynamically selecting rules determines the complexity of XOR operation.Compared with fxed selection, DNA coding encryption is more complex, which improves the difculty of cracking.
Eight DNA XOR rules are put into an array with a length of 8 according to the custom order: D [8] � [ACGT, CTAG, TGCA, GATC, CATG, GTAC, TCGA, AGCT].For example, a point with a pixel value of 77 is coded as CTAC by the x-sequence selection coding rule 8.If the values of the chaotic sequence at this time are Y ′ [2] and Z ′ [5], the process of each operation is as follows: CTAC starts with the value TGCA at the position of D [2], and then XOR operation is performed in the order of D [2], D [3], D [4], D [5], i.e.TGCA, GATC, CATG, and GTAC.Te result of each iteration is as follows: Te fnal output is TGCT.According to the chaotic sequence W according to the above rules, another decoding rule is selected to replace the pixel value and converted to decimal pixels.Te image matrix is output, and the encryption is completed at this time.Te image encryption process is shown in Figure 2.

Watermark Embedding.
Immediately after the completion of Section 3.2 encryption, the watermarking algorithm based on DWT (discrete wavelet transform) and SVD (singular value decomposition) is used to embed and extract the watermark of the encrypted image.Te whole process is shown in Figure 3. First, the image is transformed by DWT transform, and the DWT of the image f(i, j) with the size of M × N is defned as follows: Table 1: Eight DNA coding rules.Quantum Engineering Usually, let t 0 � 0, where t � 1, 2, . . ., t − 1 and M � N � 2 t .One scale function φ(i, j) and three twodimensional wavelet functions ψ H (i, j), ψ V (i, j), ψ D (i, j) represent the changes of column direction, row direction, and diagonal direction, respectively.Haar wavelet is selected as wavelet basis function.Te change of measurement function corresponds to the gray change of the image:  Quantum Engineering where l � H, V, D { }, and the expression of f(i, j) is obtained by inverse discrete wavelet transform.
Te imperceptibility and robustness of the watermark are considered to be contradictory.Generally, the lowfrequency part concentrates most of the energy of the image.Although the robustness efect of embedding is good, it is easy to cause image distortion, and the high-frequency part is vulnerable to attack.Terefore, this paper comprehensively selects HL subband to embed the watermark information.Ten, the HL subband is divided into 8 * 8 blocks, and each block is SVD decomposed B i � U i  i V T i .Ten, the watermark information is superimposed on the frst singular value σ i (maximum singular value) of  i according to the embedding factor, according to the following rules, Z � σ i mod q when W (i,j) ′ � 0 where q is the watermark embedding intensity factor, W(i, j) is the scrambled watermark information, and the embedded block is Finally, the synthetic image embedded with watermark is obtained by IDWT transform.

Watermark Extraction.
Te receiver receives the image sent by the sender, which is composed of a watermark image embedded in an encrypted image.In this paper, the watermark is extracted by blind extraction, that is, DWT transformation is carried out on the synthetic image without the participation of the original image, and 8 * 8 block processing is also carried out and decomposed according to SVD.
Perform the next analysis based on the extracted watermark information.When the encrypted image is attacked, the change of the watermark information is the same as the image.Terefore, the identity information of the sender can be verifed according to the integrity of the extracted watermark information and the content of the watermark information, and the receiver can know whether the image transmitted by the other party has been attacked by a third party.If there is no change in the information, the image is decrypted.Te whole process is shown in Figure 3.

Reverse Decryption.
In this paper, the process of image decryption is the inverse process of image encryption.Te main process is as follows: the receiver of the image information frstly performs DWT and SVD transformation on the image.(1) If the completely efective and correct watermark information is extracted, the random sequence X, Y, Z, and W is used in encryption provided by the sender and the self-defned XOR rule D [8].At this time, the decryption is carried out according to the following procedure: Te DNA coding of the pixel value is calculated with the W sequence to obtain De img[], the application rule is reversed through Y ′ [i] to obtain the initial pixel coding De img[], Time() represents the number of Z ′ [i] XOR operations, and fnally the uncoded pixel value of the scrambled image img ′ [] is obtained according to X Te initial state and walking steps of the quantum walk provided by the sender are calculated to obtain the sequence, which is divided into key 1 key 2 key 3 and arranged with the three channel pixels (2) If the extracted watermark information is damaged, it will be deemed that the transmission is invalid and the sender will resend the encrypted information.

Encryption Efect and Security Analysis
4.2.1.Key Sensitivity Analysis.Te change of any bit of the key used in the ideal image encryption scheme will cause a completely diferent encryption and decryption result.Te key sensitivity of the chaotic system is related to the initial value and control parameters.When the value w 0 � 0.1345875401 of one of the decryption keys is changed by w 0 ′ � w 0 ± 10 − 12 , the original plaintext image cannot be recovered, which proves that the encryption system is very sensitive to the key change.After changing the encryption key w 1 by one bit, w 2 is obtained.Te same image is encrypted with w 1 and w 2 , respectively.Comparing the pixel change rate after two encryptions, the key is only diferent by one bit.By comparing the diference between the two ciphertext images, the number of pixel change rate (NPCR in Section 4.3.1) is 99.5941%, and it shows that the key sensitivity is very high.Te test of plaintext sensitivity is explained in the diferential attack.

Time Complexity Analysis.
In the process of replacing image pixels with random sequences generated by quantum walk, three channel images are processed separately, with a time complexity of O(N * N).In the process of encrypting image pixels with DNA base coding pixels, a total of four chaotic sequences are involved, with a time complexity of O(4 * 3 * N * N) (N is the image size).Te key generation time is 0.447 s, and the encryption and decryption time of DNA encoded pixels is shown in Table 3.

Histogram Analysis.
Te histogram shows the statistical information of the image through the distribution of the gray values of the pixels in the color image.Te more uniform the histogram distribution of the encrypted image is, the more difcult it is for the attacker to decipher the transformation relationship between the plaintext and ciphertext image through statistical analysis.Te efect of image histogram before and after encryption is shown in Figures 4 and 5.
Te experimental results show that the histogram efect distribution of the encryption algorithm is very uniform and can "hide" the pixel distribution characteristics of the original image, that is, the attacker cannot analyze the rules of ciphertext and plaintext, so it can resist statistical attacks.Figures 4 and 5, respectively, show the histogram distribution of the 4.1.07.tif image before and after encryption and the 3D visual histogram efect.Figure 6, respectively, shows the histogram efect of the 4.1.08.tif image before and after encryption.
According to reference [32], the same plaintext image is encrypted with diferent keys (key1 and key2) by changing one bit parameter in the encryption key, and the variance Quantum Engineering value of the histogram of the encrypted image is calculated.Te variance value is around 5400, which indicates that the average gray value of each pixel fuctuates around 73. Te closer the variance value of the two encryption results, the higher the uniformity of the encrypted image and the better the encryption performance when the key changes.Te experimental results are shown in Table 4.
In addition, the similarity of the two histograms is judged by the Chi-Square experiment and calculating the Bhattacharyya distance of the histogram.For the image, the greater the chi-square value is, the lower the image similarity is; otherwise, the higher the similarity is, the maximum value has no upper bound and the minimum value is 0.
Bhattacharyya distance is used to measure the similarity of two probability distributions.In fact, in image recognition, it is to judge the distribution of diferent pixels between them.Te higher the Pap distance is, the lower the similarity is, the maximum value is 1, and the minimum value is 0. Te experimental results are shown in Table 5.

Correlation Analysis.
It is a necessary standard for the encryption algorithm to abate the correlation between adjacent pixels in the encrypted image.Te correlation coefcient of adjacent pixels is calculated in each channel of the plaintext image and the ciphertext image, and adjacent pixels Te experimental results in Figures 7 and 8 show that the pixels of each channel of the plaintext image are concentrated in the diagonal, while the pixels of the ciphertext image are uniformly distributed.Te experimental results are shown in Table 6, which indicate that the correlation coefcient is lower than that of the plaintext image, indicating that the adjacent pixels are irrelevant and have a strong ability to resist statistical analysis.

Information Entropy Analysis.
Image information entropy mainly measures the uncertainty or randomness of pixel information.For an image with completely random pixels, if its distribution is uniform enough, the ideal value of information entropy is 8. Te calculation formula is as follows: where x i is the gray value and P(x i ) is the probability of the grayscale x i .Te experimental results are shown in Table 7, which show that the information entropy of the encrypted image reaches more than 7.99, which shows excellent performance, and indicate that the probability distribution of each gray value in the image is uniform, which can efectively resist statistical information attacks.

Randomness of Sequences.
According to the requirements of the NIST SP 800-22 standard, this paper detects the randomness of the set of random numbers and encrypted image pixel values generated by the chaotic system.After several tests, it is found that the P value of the test result is greater than 0.01, and it has passed 15 tests.Te experimental results show that the Chaotic sequence as the key and the ciphertext image have good randomness, as shown in Table 8.

Gray Diference Analysis.
Gray value diference (GVD) is a measure of randomness between the original image and the encrypted image.By comparing the information diference between the two images, if the two images are exactly the same, it is 0; otherwise, it is 1.Quantum Engineering where G(x, y) represents the gray value at position (x, y).Te average neighborhood gray diference of the image is calculated, which can be calculated with the following formula: VN and VN ′ represent the average neighborhood gray value.
Te experimental results (Table 9) show that the gray diference of the encrypted image is very close to the ideal value 1, which is quite diferent from the original image.It is difcult to analyze the relationship between the two through M and N are the width and height of two random images, which are defned as follows: UACI can be used to measure the average value of color component contrast intensity.Te calculation formula is as follows: Te experimental results (Table 10) show that the NPCR value of each channel pretty approaches its ideal value of 99.6094%, and the UACI value approaches its ideal value of 33.4635%.
Four classical attacks are mentioned in reference [33]: ciphertext-only attack, known plaintext attack, plaintext selected attack, and ciphertext selected attack.If a cryptographic system can withstand selective plaintext attacks, it can withstand other types of attacks.Te encryption scheme in this paper has the ability to resist statistical analysis attack, and the large key space cannot be used to brute force crack the plaintext image when only the ciphertext is known.At the same time, diferential attack is a selective plaintext attack, and experimental results show that the encryption scheme can efectively resist this type of attack.

Noise Attack Analysis.
Te mean square error (MSE) and the peak signal to noise ratio (PSNR) are important indicators to measure image robustness.It is defned as follows: the smaller the mean square error, the higher the PSNR, which means that the distortion between the two images is smaller.Salt and pepper noise is achieved by randomly changing the original image pixels to black or white pixels.Te proportion of added noise to the number of image pixels varies, and the number of noise also varies.In this chapter's experiment, the proportion added is 5%, 10%, and 50%.Gaussian noise refers to the addition of noise that follows a Gaussian distribution.Te level of added noise can be controlled by adjusting the size of Quantum Engineering 11 the Gaussian distribution standard deviation.Te intensity added in this chapter's experiment is 0.002, 0.05, and 0.3, as shown in Figure 9. Te comparison with other reference is shown in Table 11.
Te experimental results show that although the PSNR of the encrypted image against the attack decreases after decryption, the original image can still be seen visually after decryption, indicating that the encryption algorithm has good security and certain robustness to noise attack.

Analysis of Occlusion Attack.
Te pixels of 1/16, 1/8, and 1/4 area of the whole image in the encrypted image are randomly removed or covered, and then its PSNR is decrypted and analyzed, as shown in Table 12.
Te experimental results (Figure 10) show that the decrypted image can still restore the image to a certain extent, indicating that the encryption algorithm has strong robustness.Te experimental results show that according to the above simulation attack, the watermark information changes greatly intuitively, and the information in the twodimensional code cannot be recognized.Tis paper does not aim at the robustness of the watermark but uses the change of the watermark information as a means of detecting the attack in the transmission process of the 5% s&p noise 10% s&p noise 50% s&p noise Quantum Engineering encrypted image so that the receiver can be keenly aware of the malicious attack and tampering in the transmission process according to the change of the watermark information and inform the sender to retransmit.

Conclusion
In this paper, the dynamic encryption algorithm based on quantum walking and chaos-induced DNA limits the access of image information at the source of transmission.In the classical chaotic control DNA image encryption algorithm based on improved encryption code complexity, the experimental results show that the randomness of the encrypted image information, key sensitivity, and information entropy efect are good.It can efectively resist statistical analysis attack and diferential attack.In addition, the watermarking algorithm based on DWT and SVD detects whether the image is tampered or forged in the transmission process.Te combination of the whole process establishes the secure transmission scheme of the image in the open network channel, which provides a new idea for the image encryption scheme.Of  Quantum Engineering 13 course, the time efciency of the scheme still needs to be further optimized.

Figure 3 :
Figure 3: Te fow chart of image transmission.

4. 4 .
Watermark Attack Detection and Analysis 4.4.1.Imperceptibility Evaluation of Watermark.Taking the r-channel image in the RGB component of the encrypted test image as an example, this paper embeds a 64 * 64 binary watermark QR code image.Te experimental results (Figure11) show that the embedded watermark image is almost the same as the encrypted image visually.Te PSNR of the encrypted image is 41.24 db.Te higher the PSNR value, the better the invisibility of the watermark.

4. 4 . 2 .
Watermark Attack Detection.By simulating the addition of salt and pepper noise attack with a density of 0.005 (Figure12(a)), Gaussian noise attack with a variance of 0.002 (Figure12(b)), 1/8 clipping attack (Figure12(c)), and 90degree rotation attack (Figure12(d)) to the encrypted image embedded with watermark, the watermark image is extracted as follows:

Figure 9 :
Figure 9: Salt and pepper noise attacks and decrypt images.
Tis paper uses plaintext images from the standard test diagram in the USC-SIPI database, where 4.1.07.tif (256 * 256) and 4.1.08.tif (256 * 256) are free to use.Te simulation environment is Win10 operating system and 2.5 GHz CPU.Pycharm software and tool libraries such as Qiskit, Numpy, and Scipy are used to program and run Python code and show the results.

Table 3 :
Time cost of encrypting and decrypting images (time (s)).

Table 4 :
Histogram variance values of diferent images.

Table 5 :
Te Chi-square value and Bhattacharyya distance of diferent images.

Table 6 :
Image correlation analysis and comparison.

Table 7 :
Information entropy of diferent images.

Table 8 :
Chaos sequence and randomness of encrypted images.

Table 10 :
NPCR and UACI results of images.

Table 12 :
Te PSRN value of occlusion attack analysis.