A Novel Privacy Approach of Digital Aerial Images Based on Mersenne Twister Method with DNA Genetic Encoding and Chaos

: Aerial photography involves capturing images from aircraft and other ﬂying objects, including Unmanned Aerial Vehicles (UAV). Aerial images are used in many ﬁelds and can contain sensitive information that requires secure processing. We proposed an innovative new cryptosystem for the processing of aerial images utilizing a chaos-based private key block cipher method so that the images are secure even on untrusted cloud servers. The proposed cryptosystem is based on a hybrid technique combining the Mersenne Twister (MT), Deoxyribonucleic Acid (DNA), and Chaotic Dynamical Rossler System (MT-DNA-Chaos) methods. The combination of MT with the four nucleotides and chaos sequencing creates an enhanced level of security for the proposed algorithm. The system is tested at three separate phases. The combined effects of the three levels improve the overall efﬁciency of the randomness of data. The proposed method is computationally agile, and offered more security than existing cryptosystems. To assess, this new system is examined against different statistical tests such as adjacent pixels correlation analysis, histogram consistency analyses and its variance, visual strength analysis, information randomness and uncertainty analysis, pixel inconsistency analysis, pixels similitude analyses, average difference, and maximum difference. These tests conﬁrmed its validity for real-time communication purposes.


Introduction
Aerial photography, or the process of capturing images from aircraft or other flying objects is one of the most widely used methods of remote sensing. The images captured using this method are used in a wide variety of applications ranging from urban planning, real-estate management, disaster evaluation, traffic congestion management, to road network detection, vehicle detection, common in encrypting images, Zhang et al. [33] have successfully combined both AES and Piece-Wise Linear Chaotic Map (PWLCM) to create an effective new means for the secure transmission of remote sensing images and achieved fast encryption. Recently, Liu et al. [34] proposed an encryption system that combines both DNA bases probability with two-dimensional logistic map in order to process remote sensing images. Here, the pixel rearrangement (or confusion) was accomplished by having the logistic map generate sequences, while the DNA sequence operation helped the process achieve diffusion. The proposed cryptosystem demonstrated an acceptable running speed. As the data represented by a remote sensing image is of having inevitable relevance and of national importance, specific encryption mechanisms for their secure transmission are necessary. The basic schematic chart of our proposed image encryption system is demonstrated by Figure 1. This cryptosystem works in three distinct phases, that is, Mersenne Twister (MT) method phase, DNA phase, and Rossler Dynamical chaotic map phase. Figure 2 shows the encrypted output of the two aerial images.

Contribution
The main contributions of this research article are summarized as follows: • Developing an efficient cryptosystem based on multiple phases using a substitution permutation process. This will generate high randomness sequencing and exhibit low correlation among the pixels of aerial images, ensuring secure transmission.
• Investigating numerous existing algorithms and conducting randomness test for existing cryptosystems that used coloured images.

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Comparing results of the proposed cryptosystem with Younas et al. [35] results according to MSE, PSNR, NCC, SC, and NAE.

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Developing a modernized version of the chaos-based diffusion algorithm, which provides a higher value of MSE and entropy-based randomness than existing algorithms. The higher value demonstrate that the cryptosystem proposed here is capable of generating highly protected encrypted images.
The remainder of our work is organized in the following order. The three methods (e.g., Mersenne Twister, DNA encoding/decoding process, and CDRS) that constitute the phases of the proposed cryptosystem are detailed in Section 3. Section 4 discusses the dataset and detailed steps of the proposed image encryption scheme. In Section 5, many statistical tests are applied to the proposed scheme to authenticate it. Finally, concluding remarks and thoughts on directions for future works are presented in Section 6.

Background
This section discusses the MT method, DNA encoding/decoding and CDRS.

Mersenne Twister
The Mersenne Twister (MT) method was initially proposed by Makoto Matsumoto in 1997 as a means of building high-quality pseudo-random numbers for image encryption schemes [36][37][38]. The system based on the MT method generates random sub-sequences (periods), known as Mersenne primes, in an efficient process that exhibits high computational speed and reliability as well. Diverse variants of MT provides high computational speed and strong levels of security. The two most highly utilized MT are SIMD-oriented Fast MT (SFMT) and CryptMT. Makoto Matsumoto introduced SFMT, system is based on a Linear Feedback Shift Register (LFSR) that generates 128 bits long integers, in 2006. CryptMT is a streaming cipher that generates prime numbers (random sub-sub-sequences) in a modified form of Twisted Generalized Feedback Shift Register (TGFSR) that takes an incomplete array to realize the periods. This system is based on the inversive decimation method often used for primitivity testing regarding the characteristic polynomial of a linear recurrence with its computational complexity of operation OP 2 , where 'P' denotes the degree of the polynomial. It should be noted that MT generates a very long period, that is 2 (19937−1) that includes 263 dimensions of equidistribution and has a limit of 32 bit of accuracy, as it generates random numbers that are free from correlation. This system offers high-speed computations.

MT Theories
The system is based on a uniform pseudo-random sequence that generates word of vectors [39]. The uniform integers have a limit between 0 and 2 w − 1. The w is a row vector over the binary finite field F 2 . The equation is based on a recurring process, and is defined in Equation (1): whereas in Equation (1), A is constant while w × w is the chosen matrix that is shown in Equation (3): whereas, n denotes the degree of recurrence and m denotes the integer with a range as shown in Equation (2): · · · · · · · · · a w−1 a w−2 · · · · · · · · · a 0 .
The value of K = 0,1,2,3, · · · . X n is the row vector for the word size w that is generated when K = 0. The initial seeds for the aforementioned system is X 0 , X 1 , X 2 , · · · , X n−1 .

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x l k+1 shows the lower rightmost r bits from x k+1 . • x u k shows the upper leftmost w-r bits from x k . • ⊕ is used to bit-wise XOR operation between the original pixels and random numbers generated through a proposed step using an MT generator. • | is the concatenating operation.
• x u k |x l k+1 is known as concatenation vector, generated when concatenating the upper leftmost w-r bits from x u k and the lower rightmost r bits from x l k+1 orderly.

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Finally vector A, as shown above is multiplied with right-side of this vector.

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Lastly, bit-wise ⊕ is employed for the purpose of addition of x k+m to give rise to another vector that is, x k+n . The simple bit shift operation is further utilized for the process of multiplication of The system is further elaborated in Equation (4): whereas, the value of x = (x w−1 , x w−2 , . . . , x 0 ) and a indicates a vector that has been formed at the bottom (row) of A. " " signifies bit-wise right shift. Thus the recurrence (1) calculation takes bit-shift, bit-wise XOR, or bit-wise AND operation. It is to be noted that MT has a total (n−1) dimensional distribution; that is the reason it exhibits excellent characteristics of PRNG k distribution tests, and it is assumed to be the best way to gauge the randomness of PRNG. Improving the k-distribution to v-bit accuracy within the raw sequence generated from recurrence (1) is known as tempering and this process produces final pseudo-random numbers. Each generated word is multiplied to w × w invertable matrix T from right, which yields the result of tempering matrix x into z := x × T. The matrix T is to chosen in such a way that the binary operation is possible, which is shown in Equation (5): whereas, the preceding equation asserts that u, s, t, and l are known as tempering bit shifts while b and c are tempering bit-masks. Here, the bit-wise left shift is signified by " ". MT works on two parts, that is, recurring, and tempering. The process of recurring is similar to LFSR in that both entail that each bit is state deriving from the recursion, while each individual bit occurring at the output end satisfies the recurring of the bits forming the states.

DNA Encoding/Decoding
Deoxyribonucleic Acid (DNA) is comprised of four distinct varieties of nucleotides whose sequences forms the whole DNA molecule. The four nucleotides are adenine (A), cytosine (C), guanine (G), and thymine (T) and combination of these four types can be used to encode binary numbers: 00, 01, 10, and 11. Out of the 24 possible encoding rules in DNA only eight types meet Watson-Crick (W-C) complementary rule [40] as demonstrated in Table 1. Because an image pixel is represented with 8 bits, four DNA bases are needed in order to encode it. Different encoding rules produce different DNA sequences for a single pixel. If the pixel value of an image is 81, then the value in its corresponding binary form can be represented as [01000111]. Depending on the rule being used, we get different DNA base combinations. If we draw on Rule 1 for DNA encoding, then the encoded binary results in [CACT].
By contrast, the sequence will be [GTGA] after adopting rule 8. The reverse method of encoding is the decoding rule. Thus, the same DNA sequence will be decoded differently depending upon the rule referenced in encoding it. As an example, the DNA sequence [ATCG] could be decoded to show a binary sequence [01100011] when using Rule 3 or to the binary sequence [10011100] if using Rule 6. Table 1 demonstrates all possible encoding rules. A 00 00 01 01 10 10 11 11 T 11 11 10 10 01 01 00 00 C 01 10 00 11 00 11 01 10 G 10 01 11 00 11 00 10 01

Chaotic Dynamical Rossler System
CDRS was initially investigated in 1976 by Otto Rossler in his work on chemical kinetics study [41]. This system is based on three traditional differential equations, all non-linear dynamical systems. The system operates as a continuous-time differential equation. It has better chaotic characteristics and exhibits fractals behavior as well. The map attractor resembles the Lorenz chaotic system. The chaotic map has many applications in various fields. It is defined in Equation (6): whereas, in the above equation, a, b, and c are control parameters. The values are adjusted as: a = 0.2, b = 0.2, and c = 5.7. The value of c is in the range of 1 ≤ c ≤ 6. It is important to note that we can find finite iteration from CDRS that exhibits infinite iterations. The attractor is generated using a Rossler system is shown in Figure 3. The plotting of random sequences generated at three phases (MT, DNA, and CDRS) is shown in Figure 4.

Dataset Description and the Proposed Scheme
In our work, we used Dataset for Object Detection in Aerial images (DOTA) which is a large-scale public database of aerial images taken from various sensors and plate-forms such as Google Earth, satellite JL-1, and satellite GF-2 [42]. Before their inclusion in DOTA, The collected images are scanned and annotated by experts to verify their nature. The contents of DOTA includes images of Airplanes, ships, sports venues and vehicles of various sizes, colours, and natures. In this paper, we have used different images with different colors schemes so that the proposed scheme could be verified on a number of images. The sensitive images such as buses and airplanes are encrypted in this paper. However, one can also encrypt natural scene images via the proposed scheme. The encryption steps can verify that the proposed scheme has the ability to encrypt any image. The encryption steps are outlined as: Let us consider an image I with the dimension M × N × 3. I is resized to 512 × 512 × 3. step 2: The resized image I is then divided into three respective layers, that is, R = red, G = green, and B = blue, where R, G, and B measure 512 × 512. step 3: Twister Seed Function (TSF) is initiated and used to generate uniformly distributed random numbers from MT. step 4: MT is iterated for N = 270,000 times, and the first 7858 values thus generated are discarded in order to overwhelm the transient effect, Random values are stored in α. step 5: The value of α is multiplied with a higher number of 10 14 to get β. step 6: Absolute and round function are applied on β, and the value is stored in γ. step 7: Modulus 256 operation is applied on γ to get a row matrix ζ. step 8: ζ is XOR with R, G and B to get encrypted channels, R 1 , G 1 and B 1 . step 9: In this step the output of the DNA code random sequencing is XOR with R 1 , G 1 and B 1 (previous step) to get new encrypted layers R 2 , G 2 and B 2 . step 10: CDRS is added as an additional layer of security and R 2 , G 2 and B 2 pixels are permuted using CDRS random sequence which is stored in R 3 , G 3 and B 3 . step 11: All layers, that is, red, green, and blue, are encrypted,

Statistical Analysis
This section is based on several statistical tests that have been performed on various aerial images with different views procured through DOTA. We have taken five aerial images to analyse with the proposed scheme. Various tests were carried out to check the resistance level of the hybrid-based cryptosystem. The security analysis includes Histogram Analysis (HA), Adjacent Correlation Analysis

Histogram Consistency Analyses and Its Variance
The test is applied in order to examine the distribution of pixels within each channels of the colour image. The regularity of the pixels depends on the randomness (random numbers) that have been produced through the presented scheme. In contrast, the non-uniformity of the pixels indicate that the system is not performing well with the generated random numbers. Maximum randomness is achieved when the pixels are distorted at MT level, and are further inserted to DNA genetic encoding and CDRS. The uniformity has been assessed by the distribution of the pixel's value with χ 2 and the variance of the histogram analysis. The variance with its 256 grey level is defined in Equation (7) var whereas in Equation (7), as mentioned earlier the value of Z = {z 0 , z 1 , · · · , z 255 } is the vector representing histogram values. Both Z i as well as Z j indicate the total number of pixels whose grey level value is equivalent to i and j. Visually histograms for channels wise and full-coloured images with a 3D surface is investigated. In Figure 9, the colored image based on yellow buses is divided into three respective grey layers. The grey layers are initially treated by the MT process in phase 1.
The encrypted layers are shown in Figure 10. The highly encrypted grey layers are obtained after XOR and the permutation process in phases 2, and 3 (DNA, CDRS) respectively as shown in Figure 11. In Figures 12-14 are the plain and encrypted histogram layers (R, G, and B) where R = red, G = green, and B = blue using MT method. The randomness of the pixels is increased by executing additional layers of DNA and CDRS, as shown in Figures 15 and 16. The final encrypted image with its respective histogram is shown in Figure 17. The layers are further examined using a three-dimensional surface process. The pixels of the final three encrypted images are depicted in Figures 18-20. The uniformity of the pixels in encrypted layers implies that the proposed scheme generates maximum random values.

Visual Strength Analysis
Visual Strength Analysis (VSA) intends to investigate the visual quality of an image using a Gray Level Co-occurrence Matrix (GLCM). The necessary tests that are included in VSA are the homogeneity level, energy level and contrast level test. Homogeneity level examines the pixels diagonally. The energy level can be examined by an aggregate squared method. The texture of an object is recognized by contrast analysis. The tests are elaborated as follows:

Homogeneity Level
The closeness of distribution in GLCM is used to find the homogeneity level. Mathematically the statistical parameter is defined in Equation (8): In each case, the value under evaluation must be properly sized in order to validate our proposed method. The average homogeneity test result values for colored images of 512 × 512 × 3 dimensions are tabulated in Table 2 while layer-wise homogeneity result for 5 types of aerial images are shown in Tables 3-7. The calculated values are less than 0.4, which indicates the higher levels of security achieved by the proposed scheme.

Energy Level
Energy test monitors the actual information content. The test is based upon mean squared values as demonstrated in Equation (9): The test has been conducted using GLCM. The valid range of energy lies in [0, 1]. It is essential to have a smaller value for an encrypted image in order to validate the presented scheme. The value of 0.156 is obtained for all the colored and channel-wise aerial images, which is shown in Tables 2-7. The results validated the proposed scheme.

Contrast Level
Contrast experiment is used to explore the texture of an image. The analysis is suitable to find the intensity level of the pixels. The test is defined in Equation (10): It is essential to attain a large value to validate the proposed scheme, that is to show its robustness and statistically better resistance against external attacks. The results are shown for five distinct coloured aerial images, and the test is implemented on three grey layers as well. The values of contrast analysis are shown in Tables 2-7. The assessed values are greater than '10' which depicts that the calculated results are valid and ensures the potential robustness of the presented scheme. The cryptosystem proposed can be executed in order to secure real-time communication.

Adjacent Pixels Correlation Analysis
The plain images are transformed in such a way that they become visually meaningless as every pixel is distorted through our encryption procedures. The presented scheme must avoid any statistical attack by reducing the correlation among the pixels. The correlation among pixels is reduced to conceal the actual image data. We have selected certain large aerial images. The test is defined in Equations (11)-(13): The expectation of the variable x can be calculated by E(x) and the variance by D(x). The total number of pixels are denoted by N which is equal to 512 × 512. The calculated values are shown in Table 8. The extreme values of the correlation analysis are 0 and 1. The value that converges to 1 indicates that the adjacent pixels are decidedly correlated, while 0 demonstrates that these pixels are highly dissimilar and dispersed in actual range from 0 to 255. All the values in the table for an encrypted image are less than 0, as shown in Table 8. The resulting images are depicted in Figures 21-23.

Information Randomness and Uncertainty Analysis
The most appropriate test to find the security level of the proposed system is the entropy test, which measures the degree of randomness present in the source of information. Here entropy, H(mm i ),is defined in Equation (14): In the equation above, the P(m i ) is the probability occurrence of message signal m i . The test is applied to certain aerial images captured through UAV. Entropy has a theoretical value of 8 and by converging here, the value indicates that the pixel values from 0 and 255 are randomly distributed in the cipher images, thereby making the actual image data concealed in a better way. The attacker must not be able to crack any image data from the encrypted form. The results of this test are recorded in Table 9 for each of the five aerial view images. The channel-wise results are shown in Table 10 and then compared with several other current processes, as outlined in both Tables 10 and 11.

Mean Square Analysis
This security test is utilized in order to assess the reliability of our suggested scheme. MSE can be calculated between the original plain image P(i, j) and the ciphered image C(i, j). Mathematically, MSE is defined as outlined in Equation (15): where M × N denotes the total image size. It is desirable to have high value for MSE, and it signifies high-level of security. The MSE values for several UAV-based aerial images are shown in Table 12.
The value we proposed is now compared with the work conducted by Younas et al. Table 13.
The estimated values indicate that robust security is achieved using three-phase encryption process. Three plain images are considered for its counterpart encrypted images to show the MSE level, which is shown in Figures 24 and 25. The encrypted part of each colored image is shown in Figure 26.

Peak to Signal Noise Ratio
This metric is utilized in order to evaluate the quality of an encryption. The statistical test is described in Equation (16): In Equation (16) above, it is shown that the increase in MSE value also results in a decrease in PSNR. The two crucial security parameters are contrary to each other, that is, increasing one quantity decreases another. For better image encryption process, the value of PSNR should be high. We have calculated PSNR value in decibels as shown in Table 12, and the result is compared with one of the existing schemes, as demonstrated in Table 13. The results have validated the proposed scheme.

Average Difference
This criterion is utilized in order to identify the average difference of pixels between the original plain image and its encrypted counterpart. This test has applications in various fields such as image processing techniques, image quality, object detection and recognition systems. The value for AD must be high which implies that there must be large difference between plain image and encrypted counterparts. The equation for AD is shown in Equation (17): In the above equation, x(i, j) are plain images and y(i, j) are cipher images. M indicates image width and N indicates image height and overall measure is 512 × 512 × 3. The test results of AD are shown in Table 14 and these results validated the cryptosystem we have proposed.

Maximum Difference
Maximum Difference (MD) is extensively used to differentiate two images. With this process, we find out the actual difference between the pixels of both the original and the encrypted images. Here, the higher value of MD implies the existence of a large difference between the source image and its encrypted counterpart. By contrast, the low value of MD implies that the intimated scheme is weak; thus, the robustness of the scheme towards statistical attack is small making it more susceptible to other attacks as well. Mathematically the test is defined in Equation (18): whereas in the aforementioned Equation (18), x(i, j) and y(i, j) are two images for which we are calculating MD. The x(i, j) denotes the plain image while y(i, j) denotes encrypted image. The test is applied to numerous channels of different aerial images. The estimated values are shown in Table 14.
As indicated in Table 14, differences between pixels of these two images are high. The results in Table 14 has validated the requirement of a secure cryptosystem.

Pixels Similitude Analyses
The subsection is divided into three types of tests, that is, NCC, SC, and NAE. The criteria are explained in subsequent subsections.

Normalized Cross Correlation
The test is conducted to determine the levels of similarity, if any between two images through cross correlation analysis. This is expressed in Equation (19): Here we compare the plain image and cipher counterpart. In Equation (19) above, x(i, j) indicates the plain image while y(i, j) indicate the cipher counterpart. M denotes the width of the image and N denotes the height. The range of NCC lies in [−1, 1] where values approaching 1 indicates that the correlation among pixels is weak and value of -1 indicate high correlation. We applied NCC on various aerial photography to see the normalized correlation of plain and encrypted image to authenticate the proposed scheme. The results as depicted by Table 15 make clear that relation of pixels in the encryption case is not strong. This measure intends to identify any structural relationship between aggregate weight of two images. The plain and encrypted images must have no close relationship with each other. SC is defined in Equation (20): As above M × N denotes the image size through its height and width. Similarly x(i, j) and y(i, j) denote the two test images (plain and cipher).
The value nearest unity demonstrate that there is strong relationship between the structural content of both plain and encrypted image. The calculated list of values is not close to unity, as shown in Table 15, which implies the relationship is weak for the suggested scheme. The average value of 0.5, intimates that high confusion, diffusion, and noise is added to the source images to obtain highly secure cryptosystem.

Normalized Absolute Error
The NAE is one of the popular security metrics to determine the encryption quality of an image. The metric determines the absolute error to differentiate the plain and encrypted image. The test is defined in Equation (21): In the above Equation (21), x(m, n) is the plain image that has m rows and n columns. x ∧ (m, n) is the cipher image. The Equation (21) calculate the absolute error between plain and encrypted image. The larger estimated value of NAE, for example, approaching unity, indicates the good nature of the scrambled image. The values of NAE are calculated for various aerial images that are depicted in Table 15. The average value here is greater than 0.7, which indicates that a higher level of security has been achieved. A comparison between our results and the NCC, SC,and NAE values obtained by Younas et al. [35] is made in Table 16. Here the improved result of our works are demonstrated. The level of efficiency of any cryptographic algorithm can be judged by its computational/time complexity which is also known as execution time for an encryption scheme. The execution time is calculated for each channel at three different phases and results are shown in Table 17. From Table 18, we can note that the proposed system is computationally agile comparing to existing cryptosystems. The execution time is calculated using Windows 10 pro, Matlab 2017 (a) version, with a CPU core TM i3 3227U, 1.9 GHZ, and 4 GB RAM.

Concludings Remarks and Future Projections
In this study, we presented a novel encryption algorithm designed to guarantee secure transmission of aerial images. The system has appropriated numerous phases of aerial photography encryption process using random sequencing of DNA and MT. XORed operation is applied on all channels of an aerial image. Furthermore, the permutation process is employed using CDRS to strengthen the security of the proposed solution. The proposed algorithm is further subjected to multiple experiments conducted to confirm the robustness and security analyses. Finally, the algorithm and its results are compared to several other existing methods in the literature. It is evident from all security measures that the proposed scheme is secure against many attacks including entropy and correlation, and so forth. In future, we will investigate the proposed encryption method for securing remote sensing big data [52][53][54][55]. Moreover, our future goal is to compare the security level of the proposed scheme with other traditional cryptosystems such as AES and DES. Another challenging topic to be explored is the feasibility of the proposed scheme for real-time videos and audios. In fact, the proposed scheme provides high computational efficiency and chaos-based sensitivity, which can be beneficial in the case of real-time audio and video encryption.