A GRU and chaos-based novel image encryption approach for transport images

An Intelligent Transport System (ITS) uses smart devices to capture the traffic data in the form of images. However, the adversary can steal and misuse this traffic information. Hence, it becomes essential to have an efficient encryption strategy to save data from various types of attacks. This paper proposes a novel encryption algorithm that uses the Gated Recurrent Unit (GRU) and Sine-Cosine chaotic map to encrypt transport images. The encryption scheme is divided into three phases. In the first phase, two intermediate keys and the seed value required for creating chaotic sequence are generated using unique combinations of 128-bit share key and 128-bit initial vector. In the second phase, permutation is performed using one of the intermediate keys and the chaotic sequence generated by the novel Sine-Cosine chaotic map. The final phase performs the diffusion process using the other intermediate key and GRU approach that uses the chaotic sequence generated by the Sine-Cosine map. The performance of the proposed encryption approach is analyzed using various standard encryption metrics, attacks and decryption parameters. The obtained results and comparative results with existing approaches reveal that the proposed method is suitable for implementing secure and efficient transport image cryptosystems.

smart devices to perform real-time traffic management, public data collection, and vehicles speed checking [48]. These smart devices record a large amount of data in the form of images to perform such functions. The data is communicated to the server via a public channel, due to which the intruders gets a chance to steal the recorded information during the communication. Hence, an efficient and robust encryption algorithm is required to save such information from the security attacks.
In image cryptography, a digital image is converted into a noise like image [25]. Chaos-based techniques have become very popular for developing image cryptosystems in the last two decades. Researchers have proposed various chaos-based algorithms to secure images from different types of attacks. There are two basic stages in the chaos-based image encryption process, i.e., permutation and diffusion. The permutation phase consists of changing the position of the image pixels from their original position, whereas the diffusion phase comprises of modifying the pixel values. However, the efficiency of both phases depends on the choice of a good chaotic map, i.e. a good chaotic map is essential for an encryption strategy to provide optimal security.
The dynamic system is chaotic, if it has the following three properties: initial condition sensitivity, topological transitivity, and dense periodic orbit. A chaotic map provides randomness, and makes the encryption algorithm sensitive towards the initial conditions. The researchers use various parameters such as the bifurcation diagram, Lyapunov Exponent, and Shannon Entropy to analyze the chaos function. The chaos maps are mainly divided into two categories single dimension chaotic maps [16]- [65] and multi-dimensional chaotic maps [22]- [19]. This single-dimensional chaotic system is simple to implement, but it is lesser secure than the multi-dimensional chaotic system. Logistic map (LM) is the traditionally used single-dimensional chaotic map. However, the LM suffers from issues like small keyspace, blank windows, and stable windows. Hence, to address issues, the researchers have proposed many hybrid chaos maps [16], transformed chaos maps [13], and multi-dimensional chaotic maps such as two-dimensional [57], three-dimensional chaos maps [54], and even fivedimensional chaos maps [26]. Along with chaos maps, many researchers have focused on permutation and diffusion mechanisms to improve the efficiency of the image encryption process. Two-level Scrambling [44], S-box [6], High efficient Scrambling [21], Pseudorandom with Fisher algorithm [39], Bit-level permutation [43], DNA-level self-adaptive confusion [56], Bit manipulation confusion [19], and Chaotic Magic Transform (CMT) [20] are some of the approaches that have been used by the researchers for improving permutation phase, recently. Also, researchers combined various mechanisms such as Genetic algorithms [15], DNA approach [56], Cellular Automata [53], for improving the diffusion process. The proposed work also contributes in this direction, which proposes a Sine-Cosine chaos map used to generate random sequences for permutation and GRU-based diffusion phases. The objective of work is to develop an efficient encryption scheme for securing transport images that resists against various security attacks.

Related work
In the last few years, various chaos-based encryption strategies, for securing image data, have been proposed [12,23,28,30,33,34,41,58,60,61,63]. In these encryption strategies, the researchers have used the different types of chaos maps. Some of the security approaches used the same secret key for encrypting different images. Hence, the known or chosen plaintext attacks can be performed on these encryption schemes [9,11,36,45,66]. The researchers have also suggested many other security mechanisms that use the self-adaptive techniques [37], orbit variation [8], variable control parameters [35] etc. to resist from chosen/known plaintext attack.
In 2018, three different one dimensional cosine transformed hybrid chaos functions were proposed [21]. The authors named these chaotic functions as Tent-Logistic cosine map (TLC), Sine-Tent cosine map (STC), and Logistic-Sine cosine (LSC) map. These chaotic maps are designed using combinations of the Logistic map, Sine map, and Tent map. The authors proved the proposed LSC map to be more secure and efficient than the other proposed two maps. Also, the authors proved robustness of their proposed chaotic maps in terms of bifurcation diagram, lyapunov exponent, and sample entropy. However, the range of control parameter of these chaotic maps lies between 0 to 1, only, i.e., there is still a scope to improve this range.
In 2019, a medical image encryption scheme based on four-dimensional chaotic system was proposed [38]. The author used four control parameters x, y, z, u, whose values lie between −0.33 to 0.33, −0.33 to 0.33, −0.46 to 0.46, and − 1.28 to 1.28, respectively. The authors used two different chaotic sequences for the confusion and diffusion process. The performance of the chaotic map is examined using the Lyapunov Exponent. However, the small chaotic range of control parameter, and complexity of implementing multidimensional chaos map are the two issues that can still be worked upon. The work in [24] also suggested a medical image encryption scheme that uses the double humped Logistic Map. The authors claimed that the generalized parameter that is added to the chaotic map, gives control over the chaotic range. The proposed chaotic map is analysed using the lyapunov exponent and bifurcation Diagram. The proposed chaos map has wider chaotic range, however it suffers from issue of blank window within this range.
The researchers have also proposed image encryption schemes using chaos system and DNA encoding [4]. The authors used the one dimensional Logistic Chebyshev map and the Sine-Chebyshev map for the image encryption. The control parameter of the chaotic map lies between 0 to 4. The secret key for the chaotic system is develop using the hash function and the initial key. The authors used DNA encoding to provide the ultra-low power and huge storage for their proposed cryptography scheme [1,4]. However, their work focused mainly on the analysis of grey scale images and encryption parameters only. The work in [16] proposed medical image encryption scheme based on chaotic hybrid map and DNA sequence. The hybrid map is formed using the three different maps i.e., Logistic map, Sine map and Tent map. The range of control parameter lies between 1.4 to 4. The authors claimed that the sample entropy is close to 10 during the entire value of the control parameter. The approach provides the larger key space, high key sensitivity, resistance from statistical and exhaustive attacks. However, no decryption analysis was performed by the authors. The authors in [46] proposed DNA based encryption strategy for the multiple images using Duffing map, and in [32], proposed encryption and compression strategy for encrypting image data.
In 2021, the authors of [27] implemented an image encryption approach using one of the one dimensional hybrid chaotic maps proposed in the work of [21], and a novel pseudorandom key mechanism. The authors used the 384-bit secret key for the encryption process. However, the main focus of their work was to handle brute force attacks, only. The work in [44], also proposed an encryption scheme for medical images. The authors used the two-level Scrambling and Tangent over Cosine Cosine (ToCC) map for the encryption process. The scheme is divided into three different parts. The first part consists of the padding of the image. Then, it creates two different chaotic maps in the second phase. The last phase consists of modified High Efficient Scrambling (mHES). The authors used the padding to improve the security. However, padding results in increase of the cipher image size during data transfer.
The researchers of [17] proposed encryption strategies using the Two Dimensional Coupled Map Lattice (2DCML) fractional-order chaotic map, and deep learning approach Once Forward Long Short Term Memory (OF-LSTM). The authors claimed that the combination of chaotic system and deep learning approach performs better than the traditional chaotic system. However, 2DCML chaos map also suffers from the issue of lower chaotic range of control parameter. The authors of [48] proposed encryption algorithm for the transportation system using the controlled Neural Network. The encryption algorithm uses the Lorenz chaotic system and key control finite field neural network. The authors claimed that the encryption algorithm provides the substantial mixing properties along with the 5% increase of the information entropy than another scheme.
The review of the literature reveals that only a few works have applied machine or deep learning methods for building their chaos based cryptosystems, and used transportation images for analyzing their encryption schemes. The issues discussed above, and the challenge of securing transportation image data motivated us to propose a new image encryption scheme. Hence, the objective of the proposed work is to use a novel combination of one dimensional Sine-Cosine chaos map and GRU operation for building secure and efficient image cryptosystem. The scheme is divided into three phases. In the first phase, two intermediate keys and the seed value required are generated using unique combinations of 128-bit share key and 128bit initial vector. In the second phase, permutation is performed using one of the intermediate keys and the chaotic sequence generated by the novel Sine-Cosine chaotic map. The final phase performs the diffusion process using the other intermediate key and GRU approach that uses the chaotic sequence generated by the Sine-Cosine map. The performance of the proposed encryption approach is analyzed using various standard encryption metrics such as Correlation Coefficient (CC), Entropy, Number of Change Pixel Rate (NPCR) and Unified Averaged Changed Intensity (UACI), Brute Force attack, Histogram Analysis, and Chosen Plaintext attack. The decryption efficiency of the proposed approach has been tested by using Bit Corrected Ratio (BCR), Mean Square Error (MSE), Signal to Distortion Ratio (SDR), Peak signal to noise ratio (PSNR), and Root Mean Square Error (RMSE) metrics. This paper is divided into six sections. The Section 2 presented above discussed the related work, and Section 3 describes the techniques that are used to implement the proposed algorithm. Section 4 discusses the proposed image encryption scheme in detail. The analysis of the proposed encryption algorithm is presented in Section 5, and Section 6 discusses the conclusion and future work.

Preliminaries
This section introduces the proposed Sine-Chaos map and discusses its evaluation in terms of different parameters. Also, fundamentals of GRU are presented in this section.

Sine-cosine Chaos map
The Sine-Cosine Chaos Map is defined in eq. (1). This map uses the combination of sine and cosine functions. The chaotic map makes use of control parameter r, and its value lies between 2.2 to 8, i.e., r ϵ [2. 2,8].
To evaluate the said map, the proposed work uses three parameters such as bifurcation diagram, lyapunov Exponent, and shannon Entropy. It can be observed from Fig. 1 that the proposed one dimensional hybrid Sine-Cosine chaos map has uniform bifurcation diagram over a wider range of values, more positive Lyapunov Exponent and maximum Shannon entropy value than Logistic map and Sine map, which makes it suitable for building a secure image cryptosystem.

Gated recurrent unit
In last two decades, researchers have proposed a number of machine and deep learning algorithms for developing various image processing applications [2,3,[29][30][31]52]. One of such technique is Gated Recurrent Units that are used for storing the past information. Gated Recurrent Units were first introduced by the Kyunghyun Cho et al. [10] in 2014. It is similar to the Long Short Term Memory (LSTM) [18], with only difference GRU uses lesser parameters than LSTM for computation. The GRU provides better performance on smaller and less frequent datasets. It consists of two types of gates, i.e., update gate, reset gate. The purpose of the update gate is to hold the previous information. The reset gate is used to decide how much previous information to forget. The mathematical expressions for GRU are given as: where z t , r t , b h t , h t , x t define as the update gate vector, reset gate, candidate activation, output, input, respectively. The GRU approach uses sigmoid activation function (σ g ), and hyperbolic tangent activation function (∅ h ). Figures 2 and 3 show the detailed architecture of the GRU approach and integration of the chaotic map with gated recurrent unit, respectively. For performing encryption, the input x t is passed as the value produced by the chaotic map, which then generates x t + 1 and h t . According to the eq. (4), when the value of the reset gate (r t ) is set equal to zero, then the previous value of the hidden state i.e., h t − 1 , is discarded, and the value of b h t depends upon the chaotic map (x t ). Hence, the probability of discarding the previous hidden state (h t − 1 ) is controlled by the reset gate. Similarly, if the value of the z t is close to 1 in eq. (2), then the b h t is controlled by the h t . Therefore, the probability of the hidden state h t is decided by the update gate. The benefit of combining GRU with chaotic map is that the GRU contains the previous values of the chaotic sequence. Hence, it becomes difficult for the attacker to decrypt the encrypted image, even if it gets some kind of information leaks regarding the secret keys. Figure 4 shows the details of proposed encryption scheme using the Sine-Cosine chaotic function and the GRU approach. This section discusses the proposed image encryption scheme by dividing it into four parts. Firstly, in the initialization phase initial values i.e. seed and key values, that are required for different operations of the encryption scheme, are generated. Also, the original image is split into three color components Red 'R', Green 'G' and 'Blue'.

Proposed encryption scheme
In the second part, sequence generation using the proposed Sine-Cosine chaos map, and subsequently, permutation operation is carried out. In the third part, diffusion using GRU and cipher image creation are performed. In the final part, decryption strategy is described. These

Initialization
The proposed encryption scheme uses 128-bit share key and 128-bit initial vector. The share key and the initial vector are further divided into four different parts S1, S2, S3, S4 and I1, I2,  6) and eq. (7) describes the mathematical formula for generating Key 1 and Key 2 , respectively, which are used for the permutation and diffusion process, respectively. The seed value for the proposed Sine-Cosine chaotic map is generated using eq. (8). Seed

Chaotic sequence generation and permutation
Firstly, the matrix of random sequence is generated using the chaotic map and the Key 1 . Algorithm 1 shows the process for generating the sequence matrix. Then, the given input image is shuffled according to the random sequence of matrix as shown in Algorithm 2. The permutation operation is performed using the following steps: Step 1: Generate the random sequence using the following steps: (c) Eq. (9) generates the 64 different random values using the chaotic sequence and shared key. The random value is stored in the tmp variable. Algorithm 1 shows the overall procedure of generating the random sequence to shuffle the color image.  Step 2: Take the color image and transform the image transform into 64, size/64, 3, where size is the total number of pixels in the color image i.e., size = rows * cols.
Step 3: Then, the pixel of the image is shuffled using the eq. (10). Algorithm 2 shows the procedure of the permutation process for the image.

Diffusion and cipher image creation
The proposed scheme uses the GRU approach for the diffusion operation. The GRU approach uses Secret key, h0 and sequence of the Sine-Cosine map. Following are the various steps of diffusion process: Step 1: Generate the sequence from the Sine-Cosine map using the eq. (1).
Step 2: Apply GRU to the chaotic sequence. The GRU approach takes h0 and chaotic sequences as the input variables and generate the output variable GRUVal as well as updated h0. The h0 defines as the weight matrix for the GRU approach.
Step 3: The output of the GRU approach is converted into the 8-bit unsigned integer value using the eq. (11). Step 4: The cipher image is formed using the bitwise XOR operation applying in the permutated image and the output image using eq. (12). The Algorithm 3 represents the overall procedure of the encryption strategy. Figures 7 and 8 shows the example of the diffusion process and flow diagram of the encryption scheme, respectively.
Algorithm 3: Encryption Figure 9 and Algorithm 4 present the overall decryption strategy for the chaos-based encryption scheme. The decryption of the cipher image is reverse of encryption process. The various steps followed to perform the decryption are as follows:

Decryption strategy
Step 1: The chaotic sequence is formed using the Sine-Cosine Chaotic map.
Step 2: Apply the GRU approach on the chaotic sequence. It generates the IntermediateImage image according to the eq. (13) and eq. (14).
Step 3: Generate the decrypted image by applying the reverse permutation to the intermediate image using eq. (15).

Experimental setup and results
The proposed encryption scheme has been implemented on 11th generation Intel Core i7 processor having 512 GB SSD drive and 16 GB RAM, by using Windows 10 operating system and the Python Language. The Python packages like torch, numpy, matplotlib, pillow, skimage, scipy have been applied to perform the experiments. The proposed encryption scheme is analyzed using the various standard encryption parameters, decryption parameters and attack scenarios. The set of transport images that have been used for performing the said analysis are shown in Table 1. Each

Statistical attack
In statistical attacks, the adversary breaks the encryption scheme according to the statistical analysis of the encryption algorithm. The two parameters used to check resistance of the cryptosystem against statistical attack are Correlation Coefficient (CC) and Entropy. The CC is defined as the relationship between the neighboring pixels of the image. The value of the CC should be equal to zero to resist statistical attack. It is mathematically defined using eq. (16) to (19).
where, L is defined as the size of the image. The second parameter Information Entropy measures the unpredictability and the randomness in an image. The entropy value is calculated using the multiplication of the probability of an event (Si) and the logarithm of (1/Si). Then, the summation of the resulted value is used to compute the Information Entropy, as shown in eq. (20).    Table 2 shows the Information Entropy values of Red 'R', Green 'G', Blue 'B' components of cipher image, obtained using the proposed image encryption algorithm. Column 1 of Table 2 shows the original image and corresponding encrypted image. For instance, of Img1, the encrypted image is shown as Img1_c. It can clearly be observed that the values are close to the ideal value eight, which makes the proposed scheme suitable against statistical attacks.

Differential attack
The attacker can perform the differential attack by taking the two cipher images. The first cipher image is generated from the original image, and it is denoted by C 1 . The second cipher image (C 2 ) is created using the trivial change of the original image. Then, the attacker compares these cipher images to observe a predefined pattern. Two metrics are used to test resistance of an encryption scheme against the differential attack, i.e., NPCR and UACI. NPCR is computed using the total number of the pixels that are changed in cipher image C 1 and cipher image C 2 , and is mathematically computed using eq. (21) and (22).
The value of the NPCR should be high for a good encryption scheme. The UACI is calculated as the average of the intensity of the two cipher images as represented in eq. (23). The value of the UACI should also be higher for a good image cryptosystem.
The NPCR and UACI value are represented in Table 2 corresponding to the Red, Blue, Green, RGB components of the cipher image. The high values for both the parameters prove the capability of the proposed method against differential attacks. The encryption metrics like NPCR, UACI, Entropy, Information Gain, Correlation Coefficient Horizontal (CCH), Correlation Coefficient Vertical (CCV), Correlation Coefficient Diagonal (CCD) are also computed for different size of the images, as shown in Table 3 [47]. The information gain has been computed by subtracting the input image entropy from the cipher image entropy. It can be observed for the results that the proposed scheme works equally good for variable size input image data.

Brute force attack
In brute force attack, the attacker applies exhaustive search that consists of all the possible combinations to decrypt the cipher image. The proposed approach uses 128-bit shared key and 128-bit Initial vector. Hence, the adversary requires 2 128 total combination for guessing the secret key, which is more than enough to resist brute force attack.

Histogram analysis
A histogram represents the distribution of pixels of the image as per values of the pixel. The histogram distribution should be uniform for the cipher image, such that it becomes impossible for an attacker to make idea about the original image. Table 4 shows the histograms of all three components of the original images that are shown in Table 1, and corresponding all three components of their cipher images. All odd numbered rows of the Table 3 show original image histograms, and even numbered rows show cipher image histogram. For instance, the image Img1_O_red in row 1 shows the histogram for the red component of original Imag1 shown in Table 1, and the corresponding cipher image histogram for that red component image is shown by the image Img1_C_red in row 2. It can be observed from results that all cipher image histograms look uniform, hence the proposed scheme passes the histogram requirement of good image cryptosystem.

Chosen plaintext attack
In the chosen plaintext attack, the attacker computes the cipher image from the original image using the encryption algorithm. The goal of the adversary is to get some part or fully shared key of the encryption process using the combination of the different images. In the proposed encryption scheme, the combination of share key and random number is used. Hence, it generates the different Key1, and Key2, as well as Seed values for many different images. Thus, the encryption scheme provides the resistance of the chosen plaintext attack.

Decryption metrics evaluation
There are various metrics like Bit Correct Ratio (BCR), Mean Square Error (MSE), Peak Signal to Noise Ratio (PSNR), which are used by the researchers for analyzing the decrypted image according to the different types of noise ('Salt & Pepper', 'Gaussian noise'). Salt and pepper noise is a type of impulse noise that occur due to the sharp and sudden distribution of the image signal. The salt and pepper noise degrade the image quality, and it contains a few of the pixels are very noisy. Due to the noisy pixels, the image looks like a sprinkling black and white dot in the image. Gaussian Noise is a statistical noise, and its Probability Density Function (PDF) is equivalent to the normal distribution.
To perform these metrics, firstly original image is converted into cipher image using the Initial,and ShareKey. Then, 'Salt & Pepper' and 'Gaussian noise' are added to the cipher image at different level, and the resultant image is named as "modified cipher image". After that, the "modified cipher image" is decrypted using the same Initial, and ShareKey, and is named as "modified decrypted Image". The subsections describe the analysis of the BCR, MSE, PSNR value of the "modified decrypted Image" with the original image.

Bit correct ratio (BCR)
The BCR is computed as the amount of bit errors present in the original image and the decrypted image. Mathematically, BCR is represented as: where I (x, y) and D(x, y) represent the pixel value at position x and y of original image, and received image to the receiver i.e., "modified decrypted image". The overall value of Bit Correct Ratio belongs to [0, 1]. Ideally, the value of BCR is 1. Table 5 shows the values obtained for BCR using the proposed approach. It can be observed from the results that the value of the BCR is close to the ideal value, whenever small amount of noise added to the input image.

Mean square error (MSE)
Mean Square Error (MSE) is estimated as the error present in the original image I(x, y) and the received image D(x, y). The value of the MSE should be smaller. Mathematical, it is defined as: Table 5 shows the MSE values obtained using the proposed approach. It can be observed from the results that the after adding small amount of noise, the value of the MSE close to 0, which makes proposed approach suitable for building image cryptosystem.

Signal to distortion ratio
The Signal to Distortion Ratio (SDR) calculates the value of the distortion of the pixel values of the plain image and decrypted image. The range of the signal to distortion ratio lies between the 0 to infinity i.e., SDR = [0, ∞) and the distortion between the pixel values should be minimum. Mathematically, it is defined as: Table 5 shows the SDR values obtained using the proposed approach. The results show that the value of the signal to distortion ratio is higher, whenever small amount of salt and paper noise is added.

PSNR
Peak signal to noise ratio (PSNR) defines as the ratio of the maximum size of input image and the noise of the image. PSNR calculates using the eq. (27).
PSNR ¼ 10*log 10 255*255 ffiffiffiffiffiffiffiffiffi ffi MSE p ð27Þ Where MSE defines as the mean square error. Ideally, the value of the Peak signal to noise ratio should be larger for providing the better quality. Table 5 shows the PSNR values obtained using the proposed approach. The obtained result shows that the value of the PSNR become high, even if small amount of noise is added.

Root mean square error
Root Mean Square Error (RMSE) represents as the square root of the mean square error. The range of the Root Mean Square Error lies between the 0 to infinity i.e., [0, ∞).   Table 5 shows the RMSE values obtained using the proposed approach. The value of the RMSE obtained using proposed approach is close to the ideal value, whenever small amount of noise added to the decrypted image. The decryption metrics like BCR, MSE, RMSE, SDR, and PSNR are also computed for different size of the images, as shown in Table 6. It can be observed for the obtained values that the proposed scheme works well for different size of images, as well.

Time analysis
The proposed algorithm takes an average of 5.6 seconds for performing encryption and decryption of an input image of size 512 * 512 by using the system with specifications described earlier in the start of this section. The time has been calculated using time () function from python time library.

Comparison of proposed scheme with existing schemes
This section gives describes comparison of the proposed scheme with various existing image encryption schemes in terms of different encryption and decryption parameters. The make the comparison uniform, the proposed scheme uses Lena image of size 512 * 512 for obtaining values of all the parameters. To perform the comparison, two statistical tests i.e. Wilcoxon sign rank test [14] and Friedman ranking analysis [44], are performed. The results of the Wilcoxon sign rank test for the p value are shown in Table 7. Figure 10 shows the comparison on the basis of Friedman ranking analysis of proposed scheme with the existing scheme. Table 8 shows the values obtained for the different encryption and decryption parameters using the proposed scheme, and the values given for those parameters in the published works    of other schemes. It can be observed from the comparative analysis that the proposed approach performs well against both encryption and decryption tests.

Conclusion and future work
This paper discussed the novel Sine-Cosine chaotic map and GRU based image encryption strategy for secure transport images. The encryption scheme generated two intermediate keys and the seed value using unique combinations of 128-bit share key and 128-bit initial vector, in its first phase. It performed permutation, in its second phase, by using one of the intermediate keys, and the chaotic sequence generated by the novel Sine-Cosine chaotic map. Finally, it performed diffusion by using the other intermediate key and GRU approach. The GRU approach also uses the chaotic sequence generated by the Sine-Cosine map. The testing of the proposed encryption scheme against various encryption parameters like NPCR, UACI, CC, noise attack, brute force attack, and, against different decryption parameters BCR, PSNR, MSE showed that the proposed image cryptosystem is robust and efficient against different security attacks. The work can further be extended by using the proposed scheme in different areas of research such as IoT, medical, military communication etc., and for other encrypting other forms multimedia data such as audio and video. Visual Cryptography can also be used for enhancing the security of the proposed encryption scheme.
Funding This study did not receive any funding from any of the resource.

Declarations
Ethics approval This article does not contain any studies with human participants or animals performed by any of the authors.
Conflict of interest All the authors and the submitted manuscript do not have any conflict of interest.