Advanced framework for highly secure and cloud‐based storage of colour images

IET Image ProcessingVolume 14, Issue 13 p. 3143-3153 Research ArticleFree Access Advanced framework for highly secure and cloud-based storage of colour images Nithya Chidambaram, Nithya Chidambaram ECE Department, School of EEE, SASTRA Deemed University, Thanjavur, 613401 IndiaSearch for more papers by this authorPethuru Raj, Pethuru Raj Chief Architect SRE Division, Reliance Jio Info Comm. Ltd. (RJIL), Bangalore, 560025 IndiaSearch for more papers by this authorKarruppuswamy Thenmozhi, Karruppuswamy Thenmozhi ECE Department, School of EEE, SASTRA Deemed University, Thanjavur, 613401 IndiaSearch for more papers by this authorRengarajan Amirtharajan, Corresponding Author Rengarajan Amirtharajan amir@ece.sastra.edu ECE Department, School of EEE, SASTRA Deemed University, Thanjavur, 613401 IndiaSearch for more papers by this author Nithya Chidambaram, Nithya Chidambaram ECE Department, School of EEE, SASTRA Deemed University, Thanjavur, 613401 IndiaSearch for more papers by this authorPethuru Raj, Pethuru Raj Chief Architect SRE Division, Reliance Jio Info Comm. Ltd. (RJIL), Bangalore, 560025 IndiaSearch for more papers by this authorKarruppuswamy Thenmozhi, Karruppuswamy Thenmozhi ECE Department, School of EEE, SASTRA Deemed University, Thanjavur, 613401 IndiaSearch for more papers by this authorRengarajan Amirtharajan, Corresponding Author Rengarajan Amirtharajan amir@ece.sastra.edu ECE Department, School of EEE, SASTRA Deemed University, Thanjavur, 613401 IndiaSearch for more papers by this author First published: 02 October 2020 https://doi.org/10.1049/iet-ipr.2018.5654Citations: 33AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract The evergrowing virtualised information technology infrastructure is powered by cloud-centric technology around the world. Cloud-based multimedia storage has become an essential aspect for users and business behemoths. However, as per a survey of Norton, around 3800 breaches have been publicly disclosed with 4.1 billion numbers of records exposed in 2019, which is a 54% rise when compared to 2018. So the data security is a widely quoted barrier for cloud storage. Ciphering the confidential images before transmission and subsequent storage in cloud database needs critical attention for techno-specific applications. In image encryption, chaos-based keys can do better confusion, but the diffusion process using XOR is vulnerable to chosen plain text attack. The proposed colour image encryption scheme innately uses Deoxyribo Nucleic Acid coding that blends well with chaotic cryptosystem for an efficient statistical shift. The ciphered images are stored in authenticated and authorised cloud storage facilities. The experimentation is carried out with the help of Amazon Web Services storage instances. The proposed image encryption scheme offers a strong resistance towards the brute force, occlusion, statistical and differential attacks and yields near-zero correlation and good entropy. 1 Introduction The evergrowing nature of modern gadgets has paved the way for the swift transaction of multimedia contents in social networks. However, the security of communication is the biggest concern looking at the nature of attacks and their impact on personal and social life [1]. With the broader acceptance and adoption of scores of pioneering cloud-assisted technologies and tools, cloud environments (public, private and hybrid) have emerged as the most optimised and organised information technology (IT) infrastructures for hosting and delivering an increasing array of the enterprise-scale business solutions [2]. Noticeably, cloud storage solutions and services have become a widely claimed choice for organisations across the globe to stock all kinds of business, social, personal, and professional data [3]. The prime advantage of cloud is the simplification to access data at high speed by any network, any media and any device [4]. However, data security is a huge concern due to the severe vulnerability and hitch in cloud storage [5, 6]. Security algorithms are designed towards improvisation of confidentiality, authentication, integrity and non-repudiation [7]. Images are one of the most utilised forms of multimedia objects for a variety of applications. Image security in a cloud platform is a significant problem to be addressed. Images are encrypted either in spatial or transform domain based on different requirements and parameters to enhance confidentiality [8, 9]. Due to the correlation dependency of image pixels, conventional cryptographic approaches alone cannot fit for ciphering the image [10, 11]. Image encryption algorithms employ chaos as an excellent solution for improving confusion and diffusion owing to its characteristics such as large keyspace, periodicity and sensitivity to initial conditions [12, 13]. A two-layer RGB image encryption algorithm was proposed by Kumar et al. [14] wherein the pixel diffusion was accomplished using Deoxyribo Nucleic Acid (DNA) complementary rule and Elliptic curve public key. In another scheme, the colour image was encrypted using phase retrieval in transform domain [15]. Annaby et al. [16] suggested that chaotic based confusion and diffusion processes for RGB image ciphering. There are various one-dimensional (1D) and 2D chaotic maps available which are applied to generate the permutation and diffusion matrices [17]. The fractional logistic map reduces neighbourhood relation of pixels in the ciphered image with confusion process alone [18, 19]. A two-point diffusion process using 2D Henon map has been suggested by Ping et al. [20] to resist chosen-plaintext attack. To enhance the strength of encryption, DNA and chaotic maps and attractors are employed together to improve confusion – diffusion process in colour images [21]. In the work proposed by Wu et al. [22] the key generation was carried out using the logistic map and the image diffusion was performed by DNA XORing operation. New RGB encryption was suggested to increase the key space with Lorenz-Rossler chaotic attractors along with DNA addition and XOR operations [23]. To resist the known-plaintext attack, a two-level permutation process has been proposed in which the coupled lattice map and extended hamming distance have been utilised in addition to DNA operations [24]. Wu et al. [25] suggested a DNA-based encryption approach based on the key generation using the plain image and 2D logistic adjusted sine map. Chai et al. [26] experimented inter–intra confusion and the DNA based diffusion image encryptio. Ur Rehman et al. [27] developed a hash-based initial seed selection for chaos to generate random keys as a part of image encryption. DNA blended with multidimensional chaotic maps and attractors are suggested by various literature for colour as well for medical images [28–30]. With the quintessence extracted from the existing literature, chaotic maps with lower dimension are proven for secure image encryption but not strange encryption due to the limitations like a bounded range of unpredictability and keyspace [13]. By increasing the dimensions of chaotic maps, the loopholes of 1D chaos are resolved, but equally, the complexity overhead will be increased. In this proposed work, the above-stated issues are addressed here, instead of increasing the dimension of maps, hybrid maps have been proposed by the confluence of two different 1D maps to enhance randomness of encrypted image and enlarged keyspace. Fully homomorphic encryption approach has been suggested in the cloud storage image security where the complexity overhead is high for small scale images [31]. The proposed algorithm has employed a novel approach for image encryption using DNA operation blended chaos interfaced with secure cloud storage and access. The significant contribution of the proposed work is as follows: Proposal of RGB image security solution for cloud storage applications. The utility of DNA and chaotic maps for lightweight but effective confusion and diffusion of pixels. Image encryption with large keyspace to withstand brute force attack. Performance of various attack analyses to justify the effectiveness of encryption. The notable novelty involved in the suggested work is: Interfacing authenticated Amazon cloud storage with image encryption process using LabVIEW platform. Demonstration of authenticated access to the encrypted RGB images in cloud environment through proper credential verification. The structure of the paper is framed as follows: Section 2 deals with prerequisites for the encryption. Section 3 explains the methodology followed by experimental results and performance analysis in Section 4. The paper is concluded in Section 5. 2 Prerequisites 2.1 Chaotic system The chaotic system always preferred by image encryption because of its properties. The proposed work used the 1D logistic map and coupled two 1D chaotic maps where more randomness and distribution of key with larger key space are achievable [11]. The range of initial control parameters is 3.57 ≤ α ≤ 4 and 0 ≤ X(0) ≤ 1 for a 1D logistic map and the initial control parameters of coupled logistic sine (CLS) map range from 0 ≤ µ ≤ 4 and 0 ≤ Y(0) ≤ 1. The chaotic functions for a 1D logistic map and CLS map are expressed through the following equations: (1) (2)The sensitivity to initial conditions in a chaotic sequence can be depicted through the bifurcation diagrams. Figs. 1a and b show the relation of control parameters of the 1D logistic map in 100 and 5000 iterations, respectively. Figs. 1c and d show the bifurcation diagram of CLS map for 100 and 5000 iterations, respectively. Fig. 1Open in figure viewerPowerPoint Bifurcation diagram (a) 1D logistic map of 100 iterations, (b) 1D logistic map of 5000 iterations, (c) CLS map of 100 iterations, (d) CLS map of 5000 iterations 2.2 DNA approach A DNA sequence contains nucleic acid bases A (adenine), C (cytosine), G (guanine) and T (thymine) which enable binarisation of bases into two-bit binary numbers. DNA blended image encryption approach gives better efficiency and time complexity. DNA acid bases represented in pair of binary bits 00, 01, 10 and 11. Based on Watson and Crick's complementary rule, A and T are complementary and G and C are inverted pairs. Among the 24 rules, only eight rules are suitable for image encryption, as shown in Table 1. Table 1. DNA encoding complementary rules Binary stream DNA encoded rules 1 2 3 4 5 6 7 8 00 A A T T C C G G 01 C G G C A T A T 10 G C C G T A T A 11 T T A A G G C C To achieve the diffusion process, DNA coding support operations such as addition, subtraction and XORing. DNA addition and subtraction are performed using modulo four operations which are presented in Tables 2 and 3. Similarly, for every rule set, there will be a DNA addition and subtraction result set. Table 2. DNA addition + A C G T A A C G T C C G T A G G T A C T T A C G Table 3. DNA subtraction − A C G T A A T G C C C A T G G G C A T T T G C A 3 Proposed approach Secure image communication between the end-user and cloud storage units is proposed. Fig. 2 shows the proposed security framework. The approach consists of confusion trailed by DNA-based diffusion stage. Final ciphered image is coupled to public cloud service for storage, and it can be regained as the original plain image only with the secret key(s) employed. The following sections explore the details of image encryption and decryption. Fig. 2Open in figure viewerPowerPoint Structure of proposed model 3.1 Image encryption process Input plain colour image is of size M × N = m is divided into three colour channels and encrypted using DNA coupled chaotic maps. Initial permutation stage is shuffling of the plain image pixels depends on 14-digit matchless sequences of the 1D logistic map. DNA encoding and its operation are performed in a diffusion stage together with CLS map. 3.1.1 Key generation Algorithm – 1D logistic chaos generation as key.Input: Initial control parameters α, X1(0) and image size (m)Output: Arrays are LN is the non-decreasing order sequence of L and LI-the respective index of LN sequenceSet l1←(α × X1(0)) × (1 − X1(0))Initialise L = { }Set j←2LoopSet lj←(α × lj−1) × (1−lj−1)Set A←mod (lj × 1014, m); Set j←j + 1if element ‘A’ not in array ‘L’, then add A to Lelse continue loop until size of L < m[LI, LN] = sort (L)Return (LI, LN) Algorithm – Coupled logistic sine (CLS) sequence generation as key.Input: Initial control parameters are μ, Y1(0), pixel bit depth (n) and image size (m)Output: Random sequence D = (D1, D2, D3, …, Dm)for j←1 to m doif j = 1 thenset dj←mod(μ × Y1(0) × (1 − Y1(0)) + (4 − μ) × sin (Π × Y1(0)/4), 1)elseset dj←mod((μ × dj−1 × (1 − dj−1) + (4 − μ) × sin (Π × dj−1)/4), 1)endfor j←1 to m doset Dj = mod (dj × 1014, n)Return (D) 3.1.2 Confusion stage Alter the positions of the pixel of three colour planes based on the 1D logistic key. The pseudo-code for the confusion process is given below. Algorithm – Image Scrambling Process.Input: Plain colour image P and scrambler key LIOutput: Scrambled colour planes of the plain image SR, SG, SBFor i←1 to m doSet SR(i)←PR(LI(i)); Set SG(i)←PG(LI(i));Set SB(i)←PB(LI(i))Return (SR, SG, SB) 3.1.3 DNA diffusion stage Cipher Block Chaining (CBC) operation is the core part of the diffusion process where pixels are ciphered in chronological. The pseudo-code for the CBC process is given below. Algorithm – Cipher Block Chaining Process.Input: Scrambled colour planes SR, SG and SB, 8-bit private key (K1) and DNA rule setOutput: Ciphered image, EFor all scrambled colour planes (Sx←SR, SG and SB) doFor i←1 to m doif i = 1 then set Sx1(i) = xor (Sx(i), K1)else set Sx1(i) = xor (Sx(i), E(i − 1))Set P(i)←DNA encode based on rule (Sx1(i))Set Q(i)←DNA encode based on rule (D(i))endFor i←1 to m doCompute DNA addition to get ciphered image ESet Ex(i)[7:6]←mod ((P(i)[7:6] + Q(i)[7:6]), 4)Set Ex(i)[5:4]←mod ((P(i)[5:4] + Q(i)[5:4]), 4)Set Ex(i)[3:2]←mod ((P(i)[3:2] + Q(i)[3:2]), 4)Set Ex(i)[1:0]←mod ((P(i)[1:0] + Q(i)[1:0]), 4)EndReturn (E) where x specifies the red, green and blue colour planes. Store the encrypted image E in storage area allotted for the user in Amazon public cloud after verifying the login details of the user. 3.2 Image decryption process Only the legitimate user with login certificate can retrieve the ciphered image from the cloud using private keys, the original image is recovered from the ciphered image. 3.2.1 DNA diffusion stage Algorithm – Cipher Block Chaining Process.Input: Ciphered image colour planes ER, EG and EB,The 8-bit private key (K1) and DNA rule setOutput: Plane-wise confused image SR, SG, SBFor all colour planes (Ex←ER/EG/EB) doFor i←1 to m doSet P(i)←DNA encode based on rule (Ex(i))Set Q(i)←DNA encode based on rule (D(i))Compute DNA subtraction to get Sx1if P(i)[x:y] < Q(i)[x:y] thenSet Sx1(i)[x:y]←4 + (P(i)[x:y]−Q(i)[x:y])else Set Sx1(i)[x:y]←P(i)[x:y]−Q(i)[x:y]endFor i←1 to m doif i = 1 then set Sx(i) = xor (Sx1(i), K1)else set Sx(i) = xor (Sx1(i), Ex(i − 1))endReturn (SR, SG, SB) 3.2.2 Confusion stage Reassemble the positions of the pixel of RGB planes using a 1D logistic key. The pseudo-code for the confusion process is given below. Algorithm – Image Reassembling Process.Input: Plane-wise confused image SR, SG, SB and scrambler key LIOutput: Plane-wise plain image PR, PG, PB[RI, RN] = sort (LI)For i←1 to m doSet PR(i)←SR(RI(i)); Set PG(i)←SG(RI(i));Set PB(i)←SB(RI(i));Return (PR, PG, PB) 3.3 Cloud storage connectivity with security framework Amazon public cloud offers the Simple Storage Service (S3) where the ciphered images are stored. Users should register and availed with the login credentials to get services from the Amazon Web Services (AWS) cloud, which is a level 1 authentication. Further to get S3 service from AWS, there is a need to have the access and secret key pairs as the second level of authentication. If the user credentials are valid then the captcha is generated and expected to enter the captcha as the third level of authentication, then S3 storage area is accessed after verifying the originality of the access control entities. Legitimate users across the three levels of authentication, only can put or get an encrypted image to or from the S3. Block diagram of image uploading after access granted is shown in Fig. 3a. If the user credentials are valid, then the captcha is validated, as shown in Fig. 3b. Fig. 4 illustrates the AWS S3 storage area with uploaded ciphered images. Fig. 3Open in figure viewerPowerPoint Block diagram of AWS (S3) interface with the framework (a) Uploading encrypted image into AWS S3 bucket, (b) Download the encrypted image after authentication via captcha Fig. 4Open in figure viewerPowerPoint Cloud storage of the encrypted image in AWS S3 Bucket 4 Results and discussions The proposed security framework was implemented on LabVIEW platform in Intel Core i5, 2.5 GHz CPU, 4 GB of RAM and 500 GB as the system configuration for the colour images of USC – SIPI database (http://sipi.usc.edu/database/). Fig. 5 shows the snapshot of the front panel for image encryption. Robustness of the proposed approach against statistical, differential, cropping attack and encryption quality has been investigated to justify the confidential storage of an image in the cloud. Ciphered images and one-bit change in the image are stored in the Amazon public cloud service for storage called S3, which is shown in Fig. 6. Fig. 5Open in figure viewerPowerPoint Front panel of the proposed image encryption algorithm Fig. 6Open in figure viewerPowerPoint Amazon public cloud storage environment 4.1 Brute force attack analysis 4.1.1 Key space and sensitivity analysis In this approach, one private key K1 whose size is 8-bits and four control parameters of size 14-digits for chaotic sequence generation are used. So, K1 has space of 28 (≃102). The total keyspace is 102 × 1014 × 1014 × 1014 × 1014 ≃ 1058. The strength of the algorithm resides in the key if one bit of key is varied, then there is a drastic change in the ciphered image compared to the one which is arrived during the original key used. Fig. 7a shows the cipher image of plain using the original key with one-bit change (C1). Difference between the encrypted image with original key and a bit changed key is shown in Fig. 7b. Similarly, during decryption, the ciphered image is decrypted using the original key and original key with one-bit change revealed in Fig. 7c. Difference between two decrypted images using a valid and invalid key is shown in Fig. 7d. Fig. 7Open in figure viewerPowerPoint Key sensitivity analysis (a) Cipher image using an original key with one-bit change (C1), (b) Difference image between cipher image with original key C and C1, (c) Decrypted image using an original key with the one-bit change, (d) Difference image between decrypted images using a valid and invalid key 4.2 Statistical attack analysis Too poor visual quality is expected for an encrypted image to resist the statistical attack. The capability of the algorithm is studied using metrics such as correlation, histogram, and information entropy. 4.2.1 Histogram analysis Pixel intensity must be equally distributed after encryption to state that the image is impulsiveness. Distribution of pixel intensities close to ideal means the response is flat, offers better anti-attack behaviour. Fig. 8 shows the plane wise histogram of house plain image. Fig. 9 represents the plane wise cipher image of the house, which is entirely deviated from the plain image, and the response is extremely flat. So the statistical attack is hard enough. Fig. 8Open in figure viewerPowerPoint Planewise histogram of house plain image Fig. 9Open in figure viewerPowerPoint Planewise histogram of house cipher image 4.2.2 Correlation analysis Neighbourhood relation of the pixel in the original image must be close to one, whereas, in the ciphered image, it must be close to zero means extremely uncorrelated [32]. The strength of the algorithm measured using this metric and anti-statistical attack ability is justified. Neighbourhood relation of the pixel is expressed by the following equation (3)where Ix and Iy are greyscale values of two adjacent pixels of the encrypted image, σIx is the standard deviation of the image and E(I) is the mean of the image. Fig. 10 shows the neighbourhood pixel relation of the original image in horizontal, vertical and diagonal directions of red plane. Fig. 11 depicts the correlation among the neighbourhood pixels of the ciphered image in all three directions. From Fig. 11 it is clear that in ciphered image correlation among the co-located pixels are close to zero. Coefficient values for three different planes in all three directions are tabulated in Table 4. Fig. 10Open in figure viewerPowerPoint Neighbourhood pixel representation in horizontal, vertical and diagonal directions of plain image Fig. 11Open in figure viewerPowerPoint Neighbourhood pixel representation in horizontal, vertical and diagonal directions of cipher image Table 4. Correlation coefficients of original and cipher images Image Correlation Plain Ciphered R G B R G B Couple HC 0.948713 0.930282 0.917206 −0.00056159 −0.00450608 0.00604782 VC 0.955689 0.952825 0.943545 −0.00155151 −0.00208045 −0.00242335 DC 0.915807 0.89628 0.886365 −0.00574273 −0.0064167 −0.00156299 Lena HC 0.933561 0.905638 0.859151 −0.00020268 −0.00153669 −0.00343206 VC 0.9638 0.946469 0.905638 −0.00014400 0.00405293 −0.00555131 DC 0.935289 0.907703 0.860089 −0.00309766 −0.000400902 −0.00026181 Girl HC 0.97262 0.971511 0.95793 0.00421451 −0.00541716 −0.00447635 VC 0.961912 0.964409 0.951516 −0.00298838 0.000436208 0.00090498 DC 0.943594 0.947105 0.933754 0.00371998 −5.72708E-5 −0.00208579 House HC 0.966486 0.980323 0.981817 0.0015934 −0.000678746 −0.00075502 VC 0.934693 0.947409 0.974798 0.00378232 0.0079032 −0.00024953 DC 0.912111 0.931562 0.962788 −0.00216451 −0.00279887 0.00197161 Jelly beans HC 0.973029 0.970555 0.977571 0.00562362 0.00827226 0.00723267 VC 0.973745 0.97388 0.979018 −0.00056594 0.000200256 −0.00046717 DC 0.953654 0.952096 0.967184 0.00605552 −0.000232526 −0.00218401 HC – Horizontal Correlation; VC – Vertical Correlation; DC – Diagonal Correlation. 4.2.3 Information entropy The randomness of the ciphered image is analysed through Shannon entropy. Global Shannon Entropy (GSE) is estimated by the following equation: (4)where P(Ij) is the probability rate Ij, b is the bit depth of a pixel in the image which has always 2b as its maximum intensity. Range of entropy should subsist between 0 and b. Entropy measured for every colour plane in original and encrypted is tabulated and shown in Table 5. Obtained entropy for the ciphered image is closer to ‘8’, and it shows that the proposed algorithm has higher randomness. Table 5. Global Shannon Entropy for plain and encrypted images Image RGB plane Plain GSE Cipher GSE Local shannon entropy (LSE) measure No. of blocks = 30 (Block size = 44 × 44) critical LSE hl = 7.9019 hl = 7.9017 hl = 7.9015 hr = 7.9030 hr = 7.9032 hr = 7.9034 α = 0.05 α = 0.01 α = 0.001 Couple R 6.24988 7.9974 7.9023 pass pass pass G 5.96415 7.99759 7.9019 pass pass pass B 5.93092 7.99746 7.9030 pass pass pass Lena R 5.70058 7.99752 7.9027 pass pass pass G 6.05009 7.99719 7.9031 pass pass pass B 5.40721 7.99686 7.9014 pass pass pass Girl R 6.42005 7.9965 7.9026 pass pass pass G 6.44568 7.99715 7.9010 pass pass pass B 6.38071 7.99732 7.9024 pass pass pass House R 6.43105 7.99753 7.9018 pass pass pass G 6.53893 7.99744 7.9029 pass pass pass B 6.23204 7.99748 7.9010 pass pass pass Jelly beans R 5.79199 7.99745 7.9013 pass pass pass G 6.21951 7.99714 7.9011 pass pass pass B 6.79864 7.99677 7.9023 pass pass pass Wu et al. [33] have originated the local entropy measure, here non-overlapping blocks of size 44 × 44 from the ciphered image are chosen to prove real randomness. The given Table 5 shows local entropy values and is close to the required bit depth (≃8). The entropy justifies the degree of unpredictability, and the proposed algorithm will resist statistical attack. 4.3 Encryption quality analysis 4.3.1 Chi-square test The measure of pixel distribution over the encrypted image is called a Chi-square test. This test varied from histogram analysis in which the graphical view of pixel intensity distribution obtained. It is estimated using the following expression: (5)where ‘i’ is the intensity level of the image pixels. Value of ideal must be 2b, where b is the pixel bit depth. If b = 8 then the ideal value is 256. Chi-square probability distribution test is made with 1 and 5% as significance level with 255 as the degree of freedom to get the significant values which are 310.457 and 293.2478, respectively. Based on the theory of the null hypothesis, the significant value should be higher than the chi-square value. Table 6 revealed that the pixel distribution is uniform for the encrypted image. Table 6. Pixel distribution analysis using Chi-square test Test metrics Couple Lena House R χ2-value 235.383 224.75 223.344 H0 test accept accept accept G χ2-value 218.219 255.859 231.914 H0 test accept accept accept B χ2-value 231.453 285.555 228.172 H0 test accept accept accept 4.3.2 Maximum histogram deviation To justify the encryption quality of the proposed algorithm, the deviation of the ciphered image from the plain image must be identified [32]. Maximum deviation revealed that ciphered image pixels are uniformly distributed, and the algorithm has good quality. Histogram deviation is calculated by the following equation: (6)where HISTMD is the Histogram Maximum Deviation, b is the pixel bit depth, and diff(i) is the difference of ith index histogram value in the plain and ciphered image. 4.3.3 Irregular deviation This analysis gives a defined change of pixels values between plain and cipher image [32]. The looseness histogram deviation with uniform distribution is measured using irregular deviation analysis. It computed by finding the histogram ‘H’ of difference between plain and its ciphered image. By using the following (7) irregular deviation is computed further (7)where b is the pixel bit depth, hj is histogram value at index ‘j’ and MH – an average of the histogram (for b = 8) is obtained (8) 4.3.4 Deviation from ideality It is a measure of how much the cipher image histogram deviates from the ideally expected encrypted image histogram. The encryption algorithm should be capable of distributing the pixel intensity uniformly, which raises the difficulty of statistical attack. For an ideally encrypted image histogram is Deviation from ideality is estimated through the following equation: (9)where m × n is the total size and H(i) is the histogram of cipher image. Deviation from ideality must be close to zero. Table 7 shows the analysis of histogram deviation, irregular deviation and deviation from ideality for encryption quality and the proposed algorithm meet out the required values for accepting it as a good quality algorithm. Table 7. Deviation analysis for encryption quality test Cipher image Deviation from ideality Irregular deviation Histogram deviation R G B R G B R G B Couple 0.04776 0.04641 0.04788 21,174 15,234 14,474 86,292 89,516.5 90,601 Girl 0.05532 0.05044 0.04876 34,878 25,500 23,184 80,694 81,936.5 84,171.5 House 0.04522 0.04776 0.04663 48,638 39,782 36,186 73,684.5 70,719 79,228.5 Jelly beans 0.04797 0.05068 0.05374 35,408 33,144 45,132 84,607.5 79,152 66,527 Lena 0.04852 0.04739 0.05227 32,102 33,453 38,159 83,912 81,294.5 87,629.5 4.4 Differential attack analysis To prove the ability of algorithm against differential attack, Number of Changing Pixel Rate (NPCR) and Unified Averaged Changed Intensity (UACI) parameters are measured. NPCR and UACI are the measures of the difference in a match between two different cipher images. They are calculated using (10) and (11) respectively (10)where m × n is the image size, and diff is the count of mismatched pixels between two different images c1 and c2. Cipher of plain image (c1) and cipher of the plain image with one-pixel change (c2) are compared. diff(i) = 0; if c1(i) = c2(i) else diff(i) = 1 (11)Table 8 shows the differential attack ability of the test images for the proposed encryption approach. Table 8. Differential attack ability test parameters Test parameters Couple Lena Girl House Jelly beans NPCR, % R 99.6704 99.6124 99.6368 99.6368 99.6307 G 99.5865 99.6140 99.6048 99.6033 99.5987 B 99.5605 99.6201 99.6368 99.6078 99.6307 UACI R 33.4308 33.4235 33.4345 33.3655 33.4931 G 33.4197 33.4838 33.5365 33.4412 33.4155 B 33.5429 33.5983 33.3035 33.4146 33.2925 4.5 Adversary model