DNA Strands Level Scrambling Based Color Image Encryption Scheme

In the past, many image encryption schemes have been developed through the swapping operations at the different levels of granularity. These levels span bits, Deoxyribonucleic acid (DNA) molecules, pixels, blocks of pixels. In this study, a new scheme for the encryption of color images based on the DNA strands level scrambling (DNASLS) and chaotic system has been proposed. After a color image is input, it is decomposed into the red, green and blue components. After it, these components are merged to form a big single image. Intertwining logistic map (ILM) has been used for the random data which generates three streams of random numbers. These streams have been further manipulated in such a way that nine streams are spawned out of them. One stream out of these nine streams has been used for the generation of a key image. Two streams have been used to DNA-encode the big single image and the key image. Afterwards, the strands of DNA-encoded single image are swapped with each other. Four streams determine the addresses of two DNA encoded pixels for the selection. A yet another stream is being used to select a particular strand from the DNA strands. To create the diffusion effects, an XOR operation has been done between the DNA encoded image after the swapping of strands and the DNA encoded key image. Finally, the last and ninth stream has been used to decode the DNA-encoded pixels into the decimal form. Purely random numbers with no inter-dependence have been employed in the entire encryption process. The effects of plaintext sensitivity have been achieved through the incorporation of Secure Hash Algorithm-256 or SHA-256 hash codes. In the end, the experiment and the security analysis have been performed. The results of the validation metrics like information entropy(7.9973), average key sensitivity(99.61%) and mean absolute error(84.7158) demonstrate the security, defiance to the number of attacks and a potential for real world application of the proposed image cipher.

Hence, measures must be taken to avoid any such untoward situation. Classically, the security of data has been ensured through the ciphers like Rivest, Shamir, and Adleman (RSA), Data Encryption Standard(DES), Advanced Encryption Standard(AES), International Data Encryption Algorithm(IDEA) etc. But in the context of images, unluckily, these ciphers can not be used because they were designed to encrypt textual data [1], [2]. Diametrically opposite to text, images have different characteristics like high inter-pixel relationship, high volume and redundancy. Chaotic maps/systems have proved very handy in generating the random and chaotic data for the images encryption technology. These maps have excellent qualities like extreme dependence upon the initial values and the systems parameters, mixing, ergodicity, aperiodicity etc. Dozens of image cryptosystems have been produced in the past using these maps [3], [3]- [26]. Although, chaotic maps have excellent properties as described above, even then many image ciphers were broken due to having different weaknesses and vulnerabilities in their design principles [27]- [29]. So more cautious and corrective measures need to be taken to avert these attacks.
Two types of chaotic maps exist, i.e., low-dimensional and high-dimensional. Both have their pros and cons. In particular, the low-dimensional maps [37]- [39], due to their simple structure, are easy in their implementation in some programming setup but they are plagued with low chaoticity and randomness, small key space and hence poor security [40], [41] which is not suitable for the secured cryptosystems. For instance, Xiao et al [42] cracked an image cryptosystem [43] by chosen plaintext attack. In contrast to them, highdimensional maps [10], [24], [30] render more random and chaotic data which is in line with the security demands of the ciphers, but they are hard for implementation. So, a proper balance is required to strike between these two competing needs.
DNA computing has been successfully incorporated in the realm of images cryptography due to its excellent characteristics of extra-ordinary information density, ultra-low energy consumption and massive parallelism [38], [44]. Researchers have produced a lot of image ciphers by combining the chaotic systems and DNA computing. But some image ciphers contain different defects in their design. Som et al. [45] wrote an RGB image cryptosystem using chaotic map and DNA encoding, for instance. In this particular image cipher, to permute the pixels'positions, an Arnold cat map was used. This map has a defect of limited number of iterations [46]. Further, the plain image must be square for the Arnold cat map which is not suitable for the rectangular images. So, a suitable map addressing both the square and rectangular images should be used. Moreover, few encryption schemes have low plaintext sensitivity in their design which led to their breakage due to the launch of chosen-plaintext and known-plaintext attacks upon them. For instance, the cipher [47] was cryptanalyzed through the launch of a chosenplaintext attack [48]. The reason was that the chaotic data generated were not dependent upon the input plain image. To put this in other words, this algorithm suffered from the poor plaintext sensitivity which ultimately could not endure the chosen-plaintext attack. So, new ciphers with rich plaintext sensitivity are required.
Recently, an image cryptosystem through the usage of DNA computing and coupled map lattices was written by Wang et al. [49]. They used SHA-256 hash algorithm to create the plaintext sensitivity. In a yet another study conducted recently by [50], a color image cipher was developed through the usage of DNA operations and spatiotemporal chaotic system. In this particular scheme, the color planes were DNA encoded according to the random DNA encoding rules. These color planes were combined to make a new matrix and a DNA level scrambling was performed with the help of the matrix generated through the mixed nonlinear coupled map lattices system. By considering the above discussion, a better level of granularity has been tried to introduce in the current study, i.e., DNA strands (A, T, C, G) for the basic building block of permutation and swapping. Whatsoever ciphers we happen to explore from the literature, the DNA level confusion/scrambling/swapping was realized by making the DNA encoded pixel as the basic building block. The given cipher has more sophistication and randomization as far as the operations of confusion and diffusion are concerned since the effects of both the operations have been realized through a single action of swapping the DNA strands. Moreover, the selection of DNA encoded pixels and the DNA strands come directly from the streams of chaotic data. These streams depend upon the given plaintext image. So the proposed cipher has the high plaintext sensitivity to defy any potential differential attack which is also sometimes called as known plaintext/chosen plaintext attack.
Following lines describe the remaining portion of the paper. Section 2 discusses the basic principles upon which the current study rests, i.e., the theory of chaotic system and the DNA computing. Section 3 deals with the generation of the random data and the algorithm for encryption which have been developed for the proposed cipher. Section 4 is for the experimentation of the potential encryption scheme. Security analysis has been performed in the section 5. The paper has been wrapped up in the last section 6 along with the necessary remarks of conclusion.

II. BASIC PRINCIPLES
In this section, the basic principles for the proposed image cipher will discussed a little bit.

A. CHAOTIC SYSTEM
Theory of chaos probes into the conduct of dynamical systems that are too much sensitive to the chaotic system's initial states and system parameters. On the surface, this behavior seems random, but there is a strict deterministic pattern generated by this system. According to this theory, a very minute change in either the initial states or the system parameters cause a very marked change in the output. Strictly complying with this philosophy, a plethora of chaotic systems/maps have been designed. These systems are the mathematical functions giving the stream of random numbers. We have used intertwining logistic map for this purpose [51]. (1) In the above equation, 0 < µ ≤ 3.999, |k 1 | > 33.5, |k 2 | > 37.9, |k 3 | > 35.7. When this map is compared to its predecessor logistic map, it has better behavior of chaoticity. Apart from that, it has much even distribution and contains no blank windows [52].

B. DNA COMPUTING
In DNA theory, each DNA molecule comprises of four bases/strands A(Adenine), C(Cytosine), G(Guanine) and T(Thymine). There exists a complementary relationship with each other pair-wise for these bases. Specifically, if '00' is attached to C then '11' will be attached to G. In the same way, if '10' is attached to A then '01' will be attached to T. Since 4!=24, there come out a total of 24 kinds of encoding. After checking all these 24 encodings, there exist 8 such encodings which comply with the Watson-Crick complementary rules (Table 1). Apart from that, according to the research conducted in [53], some binary operations like addition, subtraction and XOR have been reported. Of these operations, this research has only used the XOR operation ( Table 2). In order to incorporate DNA computing in the proposed image cipher, two conversion functions, i.e., DNA_Encoding and DNA_Decoding have been used in the algorithm. The first function will convert the given 8-bit pixel intensity value and some rule number to its DNA molecule analogue of length four and the second one will do the reverse process of the first one. In each conversion, some specific rule taken from the Table 1

III. PROPOSED IMAGE ENCRYPTION SCHEME
This scheme encrypts an RGB image img with arbitrary size say m × n × 3 by using the DNA strands level scrambling. The flowchart diagram characterizing the algorithm's flow has been depicted in the Figure 1.
After the color/RGB image is input, it is broken into its three color components each of size m × n. They are joined together for making a single grayscale image with size m×3n. This act of merging/concatenation bears more randomization as the DNA strands made from the pixels will be inter-blended freely facing no watertight compartments of the specific components thus boosting the security effects. SHA-256 hash codes for each given input color image has been utilized to embed the plaintext sensitivity in the proposed image cryptosystem. Each input image will have unique hash codes which will counter any potential known and chosen plaintext attack. A single pixel's change in the input image would generate a categorically different encrypted image. The hash codes generated through the SHA-256 hash function will update the variables of the chaotic map being used in the cipher's development.
The three streams of random numbers, i.e., u, v and w have been generated by iterating the ILM. Through these three streams, nine keystreams have been developed due to the peculiar requirement of the algorithm. These nine streams are row1, column1, row2, column2, selector, key − image, rule1, rule2 and rule3. To start the encryption process, first of all, the input image img has been DNA-encoded by using the keystream rule1 to get the image img1. Further, keystream rule2 is used to DNA-encode key image key − image for getting key image key−image1. The DNA-encoded image img1 along with the streams row1, column1, row2, column2 and selector are fed into the DNA strands level scrambler (DNASLS). DNASLS randomly selects two pixels of the image img1 at the addresses (row1, column1) and (row2, column2). The keystream selector selects two particular strands from these two pixels and swaps them. It is to be noted that (row1, column1) and (row2, column2) will select entirely two different pixels from the DNA encoded pixels. They have no relation with each other. DNASLS will iterate this process for 3mn times and will yield the DNA strands based scrambled image img2. Next, to produce the diffusion effects, img2 and DNA encoded key image key − image1 have been XORed as described earlier to get the image img3.
After it, DNA encoded image img3 has been translated into the decimal form by using the keystream rule3 to get the img4. In the next stage, This image is broken into the three components, merged together to obtain the cryptic image img5. The size of img5 will be m × n × 3 which is same as of the original input image.

A. KEY STREAM GENERATION PROCEDURE
Plaintext sensitivity has been embedded in the potential image cipher. For this purpose, through the hashing of SHA-256 function of given plaintext image, a 256-bit secret key is obtained. In this way, for each input plain image, a different 256-bit secret key will be obtained. Through this act, a strong nexus is built between the input image and the corresponding 256-bit secret key which boosts the security effects of the potential image cipher. The slightest tempering in any of the bit of the input image will cause to produce completely different hash codes. 8-bit blocks k 1 , k 2 , . . . , k 32 have been created out of the 256-bit secret key K .
Step 1: Through the following equations (2) -(8), the secret key has been tempered as follows: In the above equations, ⊕ refers to the XOR operation. Further, x 0 , y 0 , z 0 , µ 0 , k 1 , k 2 , x 3 are the variables of the chaotic map before the sensitivity and x 0 , y 0 , z 0 , µ 0 , k 1 , k 2 , x 3 are the variables of the chaotic map after the sensitivity.
Step 2: Through the iteration of the chaotic map 1 a number of times, i.e., (n 0 +3mn), we have got these streams of random numbers u = [u 1 : The value of n 0 is 500 here. The first n 0 values are ignored and the remaining values have been used to avoid any kind of transient effects of the chaotic system.
Step 3: The step 2 yields chaotic sequences u, v and w which are in ''raw'' form. To make them useful, they are normally refined so that they may be used in the algorithm. These sequences along with the dimension of the input image (m, n) have been sent to the Algorithm 1 to generate the nine keystreams of random numbers, i.e., row1, column1, row2, column2, key − image, selector, rule1, rule2 and rule3. Of course, these streams will be used in the algorithmic logic we have written for this image cipher.

B. IMAGE ENCRYPTION PROCEDURE
Assume the size of the input color/RGB image say img is m×n×3. The following steps explain the potential encryption procedure in detail.
Step 1:(Breaking RGB image and concatenating components) Break this color image img into its constituent color channels, i.e., red, green and blue and concatenate these components to obtain the single grayscale image img1. The size of this grayscale image is m × 3n.
Step 2:(DNA encoding of pixels and key image) Reshape the pixel data img1 and chaotic streams key − image, rule1 and rule2 to m × 3n. Convert img1 and key − image into the DNA strands according to the keystreams rule1
Step 3:(DNA strands level scrambling) An algorithm called DNA strands scrambler has been called to randomly scramble the DNA strands as shown in the Algorithm 2. As can be seen from this algorithm, The strands img1(row1(i), column1(i))(selector(i)) and img1(row2(i), column2(i))(selector(i)) have been swapped by using the variable temp for i = 1, 2, 3, . . . , 3mn. Lastly, the line 6 assigns the value of img1 to img2 and returns it.
Step 4:(DNA level diffusion) Carry out an XOR operation between the img2 and key − image1 to get the img3 as follows. Step 5:(Conversion of DNA strands into decimal) Reshape the keystream rule3 to m × 3n and convert the DNA strands into the decimal form to get img4 as below.
Step 6:(Breaking and merging the image into the color image) Finally, break the img4 image into individual components. Further, they are joined with each other to get the cipher color image img5 whose size is m × n × 3.
Because the potential cryptosystem for the images has been built upon the principle of private key, so the decryption algorithm will be an exact inverse of the steps of the encryption algorithm.

V. SECURITY AND THE PERFORMANCE ANALYSES
This section is concerned with a comprehensive security and performance analyses of this new proposed image cryptosystem.

A. KEY SPACE
In the literature, many attacks exist to reach to the original data. Brute-force attack is one of them. In this attack, hackers try to exhaust all the possible keys so that the relevant one may be discovered. This attack can be countered by enlarging the set of possible keys called key space. In principle, all the ciphers can be broken through this attack. But the key space is usually kept so large that, all the possible keys can not be checked in a practical time. The minimum threshold for the key space proposed by the scientists is 2 100 [3]. x 0 , y 0 , z 0 and µ, k 1 , k 2 , k 3 constitute the secret key of the potential image cryptosystem. The total key space gets calculated to be 10 105 ≈ 2 348 if 10 −15 is assumed to be the computer precision of the platform in which the research work was carried out. We have taken these latest researches [3], [10], [26], [49], [55] on the image cryptography using the chaotic systems and DNA computing for the sake of comparison. Table 3 conducts a comparative analysis of the potential encryption algorithm with the researches we just mentioned. One can see that the proposed algorithm beats [3], [10], [55] regarding the key space.

B. KEY SENSITIVITY
Any good cryptosystem is assumed to have an extreme sensitivity to the key it has. Extreme sensitivity to a key refers to the fact that upon doing a very faint tempering in one of the parameters of the key, the output should have a huge change. There are two modes of a cryptosystem, i.e., encryption and decryption. This sensitivity is checked through both the modes. In the first mode, a very minute change is made in one of the parameters of the key. Then two outputs, i.e., the output without making a change in the key and the output with making a change in the key are analyzed. These two outputs should be drastically different with each other for a good cryptosystem. In the decryption mode, a very small tempering is made in the secret key and the output produced should again be very different from the one which was obtained without making any change in the key.   . For the sake of demonstrating the key sensitivity, a microscopic tempering of 10 −14 say ( ) is done in just one parameter x 0 (x 0 = x 0 + ) of the key Key 0 . Let the new key set {x 0 , y 0 , z 0 , µ, k 1 , k 2 , k 3 } formed is Key 1 . Through the usage of this key Key 1 , the new encrypted image has been shown in the Figure 5c. Apart from the outputs of the crytosystems with minutely changed keys, Figure 5d draws the differential picture got by the two encrypted images of Figures 5b and 5c. Besides, with just a minute change of 10 −14 in one of the parameters of the keys, there is 99.5855% difference in the pixels of these two images of Figure 5b and Figure 5c. The impact of changing the remaining parameters in the key upon the output has been shown in the Table 4. Entire results have been obtained by using the two keys, i.e., Key 0 and Key t (t = 1, 2, . . . 14). The table depicts that 99.5778% is the least rate of difference between any two cipher images which is better than [2], [56], [57]. Apart from that, the average key sensitivity is 99.61 which is equal to the [58] and better than [56], [57]. These statistics depict that the potential image cipher has better security effects.
The key sensitivity for the decryption mode has been demonstrated through the cipher images in the Figures 5b and 5c. An attempt is made to decrypt these ciphered images in the Figures 5e-5h. These figures along with their description clearly indicate that the cipher image is obtained by employing only the correct key. So, these illustrations say that the potential scheme for the image encryption enjoys a high sensitivity of the key for its encryption and decryption machineries.

C. STATISTICAL ANALYSIS 1) HISTOGRAM
Histogram of an image gives a pictorial representation of the pixels' intensity values. Histogram of any natural image has slanting/curved bar over it. This bar is replete with the information. The hacker can exploit this bar to fulfill his/her malicious intentions. So, this is the job of the cipher to refashion the pixel intensity values in such a way that the resulting histogram may have a uniform bar over it. This uniformity of the bar of a histogram is a great deterrent to any kind of leakage of the information contained by the image. Further, It is very daunting to the hackers and make their histogram attack unsuccessful. Figures 6 and 7 depict the histograms of the plain and cipher images of Lena. It can be seen from the figures that histograms have a slating bar in case image is plain, whereas they have a uniform bar for the cipher/cryptic images.   Scientists have introduced a metric called variance to compute the uniformity of the histograms. Its formula is In the above equation, X = {x 0 , x 1 , x 2 , . . . , x 255 } refers to the vector of the histogram values. Besides, x a and x b are the numbers of pixels whose gray values are equal to a and b respectively. N represents the number of gray levels. The ciphers producing images with a low variance values of the histograms are better [59], [60].  [26]. Whereas the variance for the histogram of the plain Lena image is 59,640.

2) CORRELATION ANALYSIS
This analysis is normally done for the second statistical attack. In normal images, the pixels are highly interrelated with each other. This is the reason that these normal images are sensible to the human eye. One of the main tasks of any image cryptosystem is to disturb this inter-pixel relationship so that the resultant image may lose this sense. Upto what extent, the objective has been achieved after the cipher algorithm get applied to the normal image is checked through this metric. The following mathematical formula is utilized to find the correlation coefficient among the pixels(CC) [30]: This equation contains some variables. Here we will describe them. r and s are the color values of two consecutive/adjacent pixels and Z represents the pixels' numbers in the given image. Besides, the consecutive pixels form a correlation distribution in the three directions. These distributions have been demonstrated through the Figure 8. These directions include the horizontal, vertical and diagonal for both the original/input image and the cryptic Lena image. The correlation coefficients between two adjacent/ consecutive pixels for the plain Lena image and its corresponding ciphered version are shown in the Table 6. The 6 shows that the value of CC for the plain image is near to 1, while this value is near to 0 in case of the cipher image. Further Table 6 and Figure 8 jointly depict that the potential relationing between the adjacent/pixel positions become marginalized showing the success of the proposed cipher. Besides, a comparison has also been done between the proposed cipher and other related ciphers in the Table 7.

D. INFORMATION ENTROPY ANALYSIS
Information entropy mathematically characterizes the randomness and unpredictability of some signal. Its formula was   developed by an information theorist Shannon [61] in 1949.
where IE is the information entropy. The above equation calculates the information entropy when q is given as an information source. Further, p(q b ) gives the probability of q b . The maximum value of the entropy for the given 256 gray levels comes out to be 8. So this serves as an ideal value for the information entropy. The more close the value of information entropy to 8 is, it is always better. Table 8 gives the entropies' values for the pictures of the potential scheme. One can see that the average value is very near to 8, which is an ideal value in this context. Therefore, the proposed scheme is robust against the entropy attack. A comparison has been drawn in the Table 8. One can see that the proposed cryptosystem does better than [3], [10], [26], [49], [55] as far as entropy is considered for the Lena image.

E. DIFFERENTIAL ATTACK
Hackers have a lot of schemes in their ''ammunition'' to crack the image cipher. Differential attack is one of them. In this particular attack, two samples of cipher images are obtained. The first one through a straightforward way whereas the second one by changing a intensity value for some randomly selected pixel in the given input image. Through an ingenious manipulation, the potential relationship between the plain and ciphered images can be figured out which ultimately lead to the revelation of the key. To combat this attack, two measures are normally used by the research community. The first measure is called number of pixels change rate (NPCR), while the second measure is usually called as unified average changing intensity(UACI). These two measures are calculated on the plain input image and the cipher output image. VOLUME 8, 2020  Their mathematical formulas are where M and N represent the width and height of the image respectively. S(p, q) can be defined by: E and E are respectively the cryptic/output images before and after one pixel of the plain image is changed. Both the NPCR and UACI values of the chosen eight images have been shown in Table 9. The averages of NPCR and UACI for the selected images are 99.6027% and 33.4908% respectively which expressly prove that the potential encryption scheme is sufficiently potent to withstand the attacks of NPCR and UACI which are differential in character. Further Table 10 draws a comparison of the metrics of the proposed scheme for the Lena image with some other algorithms [3], [10], [26], [49], [55]. Clearly, the proposed method has the better values of NPCR and UACI than [49] and [3], [49], [55] respectively.

F. PEAK SIGNAL-TO-NOISE RATIO ANALYSIS
A lot of metrics exist to gauge the efficiency and performance of the ciphers. Peak signal-to-noise ratio is one of them.  It aims at measuring the difference/discrepancy between the original plain image and the encrypted output image. Mathematically it is defined as N q=1 (P 0 (p, q) − P 1 (p, q)) 2 (18) where (M , N ) is the dimensions of the test image. P 0 (p, q) and P 1 (p, q) are the pixel values of the plain/original and encrypted images respectively. Further, MSE is the mean squared error between the original image and the encrypted image. The larger value of MSE is always desirable. Since MSE and PSNR are reciprocally interrelated, so the larger value of MSE will lead to the smaller value of PSNR. Table 11 shows the PSNR value obtained by the proposed cipher and some of the chosen ones. One can see the infinite (∞) value in the first row of the table. This infinite value signals that there is not a difference of single pixel intensity value between the two images. These two images are plain image and the decrypted image. This caused due to the value of zero for MSE lying in the denominator for the formula of PSNR. These phenomena also refer that the proposed image cryptosystem is lossless. The PSNR value for the image of Lena given by the proposed algorithm is better than [62]- [64] as given by the Table 11.

G. MEAN ABSOLUTE ERROR (MAE)
Creating a maximum discrepancy between the plain input image and the ciphered output image is one of the recurrent themes of any image cryptosystem. To measure it, a test metric called Mean absolute error (MAE) is utilized in this regard. Its mathematical formulation is: In the above equation, P is the plain image and C is the cipher image. (M, N) is the dimension of the image. The relatively larger value of MAE is desirable for the security effects. Table 12 depicts the results of this metricMAE given by the proposed algorithm. Besides, this table also compares our result with some other researches. The proposed cipher performed better than [10], [63], [65].

H. NOISE AND DATA CROP ATTACKS
Things are not as straightforward as they sound. Sometimes, either during storage or during transmission, the encrypted image may subject to noise attack due to which it is corrupted. Now the decryption algorithm should be robust enough to restore the original image in a way that it may be easily recognized. Further, occasionally, some portion of the ciphered image may be damaged due to the crop/data loss attack on it. Again, the decryption algorithm should decode the image in such a way that the original input image may be recognized. Obviously, the restored images can be easily discerned. Given these results, we are justified to say that the proposed scheme is robust enough to withstand the noise and data loss attacks and bears promise for some real world setting.

I. CONTRAST AND ENERGY ANALYSIS
Generally speaking, contrast analysis renders a measure of local intensity variations existing in an image. Put in other words, through this metric, heterogeneity of the pixels of an image is gauged. The relatively higher values of the contrast mirror that the image has abundantly different gray levels which is a good security effect. Contrast of an image is defined as [66] In the above equation, p(a, b) is the number of gray-level co-occurrence matrices (GLCM). Contrast of both the plain image and the cipher image has been calculated and the corresponding results have been displayed in the Table 13. The value of the contrast for the Lena image is 10.5112(average of red, green and blue channels) which is better than 10.4511 [67] and 8.4156 [66]. These signs indicate the relatively better security effects of the proposed cipher as compared to the existing ones. Apart from that, energy of an image gives the sum of the squared elements in the gray level co-occurrence matrix given as [66] where p(a, b) is the number of gray-level co-occurrence matrices. Table 14 portrays the energy analyses results for both the plain and cipher images. One can see that the results VOLUME 8, 2020     of the plaintext images are relatively higher than their ciphertext counterparts. Besides the average energy value for the three components for all the images is 0.0156 which is better than 0.0176 [66].

J. SPEED AND COMPLEXITY ANALYSIS
The proposed algorithms of encryption and decryption have been written and compiled under the Intel(R) Core(TM) i5-4210U CPU @ 1.70 GHz 2.40 GHz, 8 GB memory. Besides, the platform selected for this work is Windows 10 and MATLAB R2016a. Complexity analysis refers to the computational time an algorithm takes. Normally two types of analyses exist, i.e., the empirical analysis and the theoretical analysis. The former analysis directly measures the time taken by the algorithm through some gadget like stopwatch. Table 15 gives the time taken for encryption by the different images. The time taken by the Lena image and the average for all the eight images is 5.9328 sec and 5.7754 sec respectively which is better than the [68] and [69].
As far as the theoretical analysis is concerned, a number of factors like input, compiler, software, hardware etc. eclipse its universality. The latter analysis forgoes these limitations and carries us to such a setting which renders a pure computational performance of the given algorithm. Inspired by this fact, we have resorted to theoretical analysis only. Asymptotics [72] -a mathematical theory, is normally employed to carry out this analysis. The complexity for iterating the ILM is (9MN ) where (M , N ) is the dimension of the input image. The complexity of DNA encoding for the pixel data and the key image is (3MN ) each. The complexity for the swapping operations for the DNA strands is (3MN ). Morever (3MN ) is the complexity for the DNA diffusion. Lastly, the complexity for DNA to decimal conversion is (3MN ). The total complexity comes out to be (24MN ) which is equal to [10], [26] and better than O(64N 2 ) [73].

VI. CONCLUSION
By treating the single DNA strand as a basic unit for scrambling, a novel image encryption scheme has been developed in this study. Plethora of image ciphers exist based on the theories of chaos and DNA computing. The novelty of the proposed scheme lies in the fact that a greater degree of sophistication and randomness has been thrown in the proposed image cipher by lowering the level of granularity to the DNA strand. In the previous ciphers, the basic unit of scrambling has been a whole DNA molecule which is relatively bigger than a DNA strand. Apart from that, SHA-256 hash codes have been used to embed the plaintext sensitivity in the cipher. Four dedicated and independent streams of random numbers are for the selection of two DNA encoded molecules. The fifth independent stream of random number is for the selection of a particular DNA strand which is to swapped between these two selected DNA molecules. This act of swapping served both the purposes of confusion and diffusion. Besides, only a single round of XOR operation between the pixel data after the swapping of the strands and the DNA encoded key image has been carried out. Both the experimentation and the security analyses of the proposed cipher gave very promising results which indicate the robustness, good security effects, defiance to the different threats and a potential for a real world application of the proposed scheme.
NADEEM IQBAL received the M.Phil. degree in computational science and engineering from the NUST, Islamabad, Pakistan. He is currently working as an Assistant Professor with the School of Computing and Information Sciences, Imperial College of Business Studies (ICBS), Lahore, Pakistan. Prior to joining the ICBS, he worked in various academic institutions and has guided numerous undergrad and masters students. His research interests span images cryptography, computer graphics and philosophy of mathematics.
MUHAMMAD HANIF received the B.S. degree in information technology from the University of Malakand, Pakistan, and the M.S. degree in information technology from SEECS, NUST, Islamabad, Pakistan. He is currently pursuing the Ph.D. degree in computer science with NCBA&E Lahore, Pakistan. He is currently working as an Assistant Professor with the Department of Computer Science, Bahria University, Lahore Campus, Pakistan. He was with various academic institutions, and has supervised numerous bachelor's and master's students from past eight years. His current research interests include images cryptography, computer graphics, networking, cloud computing, and the Internet of Things.
SAGHEER ABBAS received the M.Phil. degree in computer science and the Ph.D. degree from the School of Computer Science, NCBA&E, Lahore, Pakistan. He has been teaching graduate and undergraduate students in computer science and engineering for the past eight years. He is currently an Assistant Professor with the School of Computer Science, NCBA&E. He has published about 60 research articles in international journals and reputed international conferences. His current research interests include cloud computing, the IoT, intelligent agents, image processing, and cognitive machines with various publications in international journals and conferences.
MUHAMMAD ADNAN KHAN received the B.S. and M.Phil. degrees from the International Islamic University, Islamabad, Pakistan, by obtaining scholarship award from the Punjab Information and Technology Board, Govt of Punjab, Pakistan, and the Ph.D. degree from ISRA University, Pakistan, by obtaining a scholarship award from the Higher Education Commission, Islamabad, Pakistan. He is currently working as an Assistant Professor with the Department of Computer Science, Lahore Garrison University, Lahore, Pakistan. Before joining the Lahore Garrison University, he has worked in various academic and industrial roles in Pakistan. He has been teaching graduate and undergraduate students in computer science and engineering for the past 12 years. He is currently guiding four Ph.D. scholars and six M.Phil. Scholars. He has published more than 150 research articles in International Journals as well as reputed International Conferences. His research interests primarily include machine learning, MUD, image processing and medical diagnosis, channel estimation in multi-carrier communication systems using soft computing with various publications in journals and conferences of international repute. VOLUME 8, 2020 SULTAN H. ALMOTIRI received the B.Sc. degree (Hons.) in computer science from King Abdulaziz University, Saudi Arabia, in 2003, and the M.Sc. degree in internet, computer, and system security and the Ph.D. degree in wireless security from Bradford University, U.K., in 2006. He was the Chairman of the Computer Science Department, Umm AlQura University, Saudi Arabia, and the Vice Dean of eLearning and distance Education with Umm AlQura University, Saudi Arabia. He is currently an Assistance Professor with the Computer Science Department, Faculty of Computer and Information Systems, Umm AlQura University. His research interests including cyber security, cryptography, AI, machine learning, eHealth, eLearning, IoT, RFID and wireless sensors, and image processing.
MOHAMMED A. AL GHAMDI (Associate Member, IEEE) received the B.Sc. degree (Hons.) in computer science from King Abdulaziz University, Saudi Arabia, in 2004, the master's degree in internet software systems from the University of Birmingham, in 2007, and the Ph.D. degree in computer science from the University of Warwick, U.K, in 2012. He is currently an Associate Professor with the Computer Science Department, Umm Al-Qura University, Saudi Arabia. He has published a number of good quality journal papers in data analysis, AI, cloud computer, cyber security and machine learning.