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Image multi‐encryption architecture based on hybrid keystream sequence interspersed with Haar discrete wavelet transform

2020; Institution of Engineering and Technology; Volume: 14; Issue: 10 Linguagem: Inglês

10.1049/iet-ipr.2019.0991

1751-9667

Edwin A. Umoh, Ogechukwu N. Iloanusi, Uche A. Nnolim,

Image and Video Stabilization

IET Image ProcessingVolume 14, Issue 10 p. 2081-2091 Research ArticleFree Access Image multi-encryption architecture based on hybrid keystream sequence interspersed with Haar discrete wavelet transform Edwin A. Umoh, Corresponding Author Edwin A. Umoh edwin.umoh.pg76768@unn.edu.ng orcid.org/0000-0002-7772-3659 Department of Electronic Engineering, University of Nigeria, Nsukka, NigeriaSearch for more papers by this authorOgechukwu N. Iloanusi, Ogechukwu N. Iloanusi orcid.org/0000-0002-6306-9713 Department of Electronic Engineering, University of Nigeria, Nsukka, NigeriaSearch for more papers by this authorUche A. Nnolim, Uche A. Nnolim Department of Electronic Engineering, University of Nigeria, Nsukka, NigeriaSearch for more papers by this author Edwin A. Umoh, Corresponding Author Edwin A. Umoh edwin.umoh.pg76768@unn.edu.ng orcid.org/0000-0002-7772-3659 Department of Electronic Engineering, University of Nigeria, Nsukka, NigeriaSearch for more papers by this authorOgechukwu N. Iloanusi, Ogechukwu N. Iloanusi orcid.org/0000-0002-6306-9713 Department of Electronic Engineering, University of Nigeria, Nsukka, NigeriaSearch for more papers by this authorUche A. Nnolim, Uche A. Nnolim Department of Electronic Engineering, University of Nigeria, Nsukka, NigeriaSearch for more papers by this author First published: 24 June 2020 https://doi.org/10.1049/iet-ipr.2019.0991Citations: 7AboutSectionsPDF 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 A novel image multi-encryption architecture based on hybrid keystream sequence generated by a single hyperchaotic system and Haar discrete wavelet transform (HDWT) is proposed. The architecture consists of a pre-cipher stage, first encryption operation, Haar discrete wavelet decomposition stage and a second encryption operation. In the pre-cipher stage, the algorithm applies two-level pixel position permutation of the image. The first encryption operation is accomplished by diffusing the pixel's numbers with keystream sequence generated by a sequence generator SG-1. The resulting cipher image is decomposed using two-dimensional HDWT decomposition technique. The decomposed image is further encrypted through operation between keystream sequence generated by sequence generator SG-2 and bytes of the decomposed image which are selected with the aid of a novel pseudo – 4 bit Boolean truth table-based byte selection mechanism. SG-1 and SG-2 are special cases of the hyperchaotic system and are evolved online by separately nullifying selected parameters of the hyperchaotic system. The novelty of the proposed architecture lies in the possibility of increasing the number of sequence generators, which can result in exponentially huge key space and fast encryption speed. A comprehensive complexity analysis of performance, security and robustness to attacks, confirmed the feasibility of the architecture. 1 Introduction Multimedia information is part of social entertainments and companionship, educational development, biometrics, forensic and online transactions; hence the need to secure them from malicious interferences, theft, hacking attempts and unauthorised retrieval cannot be overemphasised. One way of protecting multimedia data over transmission channels is through encryption, which is a process of protecting information from unauthorised access, theft or manipulation. Chaos is a feature of non-linear deterministic dynamic systems which have pronounced sensitivity to disturbances in their parameters and initial conditions [1]. By integrating the characteristics of chaos such as extreme sensitivity to initial conditions and control parameters, ergodicity and aperiodic noise-like dynamics into the modelling and design of encryption schemes, a new class of encryption schemes commonly known as chaos-based encryption schemes are produced, and some of the limitations of non-chaos-based cryptosystems such as small key space and low complexity of confusion and diffusion mechanisms are overcome. The basic information about an image can be extracted from its pixels. Thus, two techniques known as confusion and diffusion are generally applied to obscure high redundancy and strong correlation among image pixels, first, by subjecting image pixels to permutation at the confusion stage and second, by modifying the pixel values at the diffusion stage such that a slight change in one pixel will disorient as many pixels as possible. These confusion and diffusion processes encryption operations are enhanced by the use of discrete chaotic sequence generated by chaotic maps and flows. The application of wavelets in image encryption schemes has become popular due to their multiresolution properties and good localisation characteristics in the time and frequency domains. Commonly used wavelets are Haar, Morlet, Mexican hat and Daubechies wavelets [2]. Haar wavelet is the most flexible and has been applied to enhance the security of chaos-based cryptosystems [3] In Haar discrete wavelet transform (HDWT), the number of steps has a minimal effect on the decomposition of an image because the merged data of all the decompositions is usually the same as the size of the input image. Some detailed preliminaries on wavelets and Haar wavelet transform can be found in [4]. Architectures of image encryption schemes are crucial to their security and performance because they contribute to complexity in terms of performance, throughput and structural elegance. An image encryption scheme based on hyperchaotic Rabinovich and exponential chaos maps was proposed in [5], in which chaotic sequences generated from the Rabinovich system were combined with sequences produced by chaotic maps to produce security keys. In [6], pixels and bit-level permutation techniques were used to enhance the security layers of a chaos-based encryption scheme, which encrypts an image in the spatial and frequency domains. A fast-selective image encryption scheme which applied discrete wavelet transform and chaos synchronisation was proposed in [7]. In the paper, DWT was applied to decompose an image into subsets of data, while a chaotic matrix was constructed from a master hyperchaotic system (HS) and applied to encrypt the data. In [8], a frequency domain method was proposed, where Daubechies wavelets were used to decompose an image, while the low-pass sub-bands were encrypted using the discrete-time chaotic system. In [9], a symmetric image encryption scheme in time and wavelet domains was proposed. The scheme applied integer wavelet transform to decompose an image, while the diffusion was accomplished via keys generated with spatiotemporal chaos. In [10, 11], image encryption schemes based on the use of HSs and look-up table were proposed. The algorithms effectively encrypted images. Other encryption methods that have been proposed include the use of Fisher–Yates shuffling method in conjunction with chaotic economic map [12], parallel computing system [13], finite-precision error [14], compound homogenous HS [15], bit level Brownian motion [16], Josephus traversing and mixed chaotic map [17], chaos mixing [18], TRN keys from environmental noise [19] and substitution box and chaotic system [20]. However, in spite of their elegant structures and intrinsic characteristics such as large positive Lyapunov exponents and sensitivity to perturbations and ergodicity, several HSs including those used in the aforementioned reviews suffer from relatively small key space and poor bifurcation properties. These properties are usually depicted by bifurcation diagrams that are riddled intermittently with periodic windows. The periodic windows are regions of the bifurcation maps that are not chaotic and can, therefore, leak information which can lead to inefficient encryption and design failure. In this paper, a novel multi-encryption architecture which uses hybrid keystream sequence separately generated by a single HS, in conjunction with HDWT to produce a complex image pixel diffusion process that exponentially enlarges the key space and improves encryption efficiency, is presented. The novelty of the scheme lies in the possibility of increasing the number of sequence generators and XOR operations in the second stage, with resultant multiplication of encryption operation on an image (only two sequence generators are used in the paper), byte permutation strategy adopted to mix image pixels based on a pseudo-4-bit Boolean truth table, method of interspersing HDWT between the two encryption stages and the cipher recombination method which effectively resists chosen plaintext attack (CPA). Multi-encryption based on the proposed architecture has not received attention in the literature and differs from other reported works on 'double hyperchaotic encryption', 'double domain encryption', 'double image encryption' or 'triple image encryption' [21–23]. For example, the algorithm proposed in [21], encrypted two images simultaneously without using hyperchaotic dynamics. In [22], two HSs are utilised to generate two distinct chaotic sequences which were used to encrypt images. In [23], an image is encrypted in both spatial and frequency domains using a single HS to generate a chaotic sequence for each round of encryption. The topology applied required three chaotic sequences for two-stage cipher operations. However, in our proposed architecture, multiple keystream sequence can be generated online from a single HS (only two are generated in this paper). Generating multiple keystream sequence from a single HS reduces computational complexity and implementation cost when compared to encryption systems which utilised more than one HS for sequence generation. Other multiple image encryption schemes in the literature can be found in [24–27]. The rest of the paper is organised as follows: Section 2 gives the background information on the chaotic map and HS used in the study. Section 3 gives a detailed description of the proposed architecture. Section 4 presents the numerical simulation results and comparative analysis of performance and security metrics of the proposed architecture with selected works in the literature, while the conclusion is given in Section 5. 2 Overview of logistic map (L-map) and HS In this section, an overview of the chaotic map and HS, used in the proposed encryption scheme is provided. 2.1 Logistic map The L-map is commonly used to generate the discrete sequence for image pixel mapping and confusion operations, and is defined mathematically as (1)where . represents the initial population, a is a positive number and n is the number of iterations. L-map has four dynamic regions, namely periodic, stable, oscillating and chaotic region. It is periodic () when , stable () when , oscillatory () when and chaotic () when . In this study, a was selected in the region in order to avoid periodic windows that may result in encryption inefficiency. Equation (1) generates a number of chaotic sequences in the range to 255 (for an 8 bit greyscale image), with an initial condition and . The chaotic sequences are subsequently converted into unsigned integers in the range of 0–255 by multiplying the sequence elements with 255. The resulting sequences are mapped to the image pixel values and row- and column-shuffled according to Algorithm 1 (see Fig. 1). Fig. 1Open in figure viewerPowerPoint Algorithm 1: Pixel_Shuffle 2.2 Hyperchaotic system – HS The choice of the HS [28] is justified, based on its rich dynamics, large positive Lyapunov exponent, huge parameter space and parametrically optimised bifurcation properties, which collectively overcome the problems of small key space and periodic window-riddled bifurcation diagrams associated with many HSs. The HS is described by the following four-coupled ordinary differential equations (2)where are system parameters and are state variables. By exploiting the parameter space of HS to nullify appropriate system parameters, two topologically equivalent sequence generators, designated SG-1 and SG-2 are evolved as follows: when and the following parameters are set: , , , , , SG-1 is evolved. Similarly, when and , , , , SG-2 is evolved. f and s denote first and second stage, respectively. Algebraically, SG-1 and SG-2 are special cases of HS, which are described by the following equations [29, 30] (3) (4) 3 Proposed architecture of the multi-encryption scheme The architecture of the proposed multi-encryption scheme is shown in Fig. 2. Fig. 2Open in figure viewerPowerPoint Architecture of the image multi-encryption scheme Fig. 2 consists of a pre-cipher stage in which the pixel values of the input image are mapped to the sequence produced by the L-map and shuffled in row and column directions, based on Algorithm 1, first encryption stage in which the sequence generated by SG-1 is used to diffuse image pixel values based on Algorithm 3 (see Fig. 3), two-dimensional HDWT stage in which the ciphered image from the first encryption stage is further decomposed based on Algorithm 4 (see Fig. 4), and finally, a second encryption stage in which the HDWT-decomposed image undergoes further encryption using the sequence generated by SG-2 based on Algorithm 5 (see Fig. 5). The result is a final encrypted image. The two hybrid sequence generators SG-1 and SG-2 are evolved from the HS-based on Algorithm 2 (see Fig. 6). Detailed steps involved in the algorithms are given under the following subsections. Fig. 3Open in figure viewerPowerPoint Algorithm 3: FSE Fig. 4Open in figure viewerPowerPoint Algorithm 4: Haar DWT (steps, 'Haar', M, N, ) Fig. 5Open in figure viewerPowerPoint Algorithm 5: SSE Fig. 6Open in figure viewerPowerPoint Algorithm 2: HS 3.1 Pre-cipher stage The input to the pre-cipher stage is an sized 8 bit pre-processed colour image , where M denotes row of size 256 pixels and N denote column of size 256 pixels. The three components of are denoted as and , where and . is converted to a plain 8 bit greyscale image for use as a plain image in the experiment. The L-map described under Section 2.1 was iterated for rounds until a new discrete sequence was obtained. This sequence was used to shuffle image pixels , row-wise and column-wise, as described in Algorithm 1, resulting in and . The IEEE Standard for floating point number [31] was satisfied in the exponential multiplications. A new bidirectionally shuffled image was subsequently created, where 'R' and 'C' denotes row and column respectively. The shuffled image was subsequently converted to a 1D vectored image denoted by . The shuffling procedure is described by Algorithm 1. 3.2 Hyperchaotic keystream sequence generators Two separate keystream sequence is generated by a single HS, in this order: when , HS←SG-1, provided that the initial conditions (5) Similarly, when and , HS←SG-2, provided that the initial conditions (6) The procedure for evolving sequence generators is given by Algorithm 2. 3.3 First stage encryption (FSE) Setting original security keys, and , activates sequence generator SG-1, and iterating SG-1 for times using the fourth-order Runge Kutta algorithm with step size , produces four keystream sequence based on the operation: (7)A novel byte permutation mechanism based on a pseudo-4-bit Boolean truth table is used to select matching groups of three true bits (1's) of for diffusion with keystream sequence SG-1. Table 1 depicts the pseudo-4-bit Boolean truth table, where are Boolean minterms which represent the number of permutable strings of state variables that can be derived from Table 1. Table 1. Pseudo-4-bit Boolean truth table T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T The symbol '*' denotes a null variable. Minterms containing three true bits (T's): , , and are selected, and each byte is symbolically reassigned to a state variable in the following order: (8) (9) (10) (11)For ease of transformation, are replaced with a new group of variables , and the three true bytes of each minterm are assigned to the new group of variables in the following order: (12)Furthermore, the three true bytes of each group in (12) are labelled as 'most significant byte (MSB)', 'intermediate byte (ITB)' and 'least significant byte (LSB)' respectively. The MSB is cyclically interchanged with the ITB in (12) in order to form a new group of modified variables, given by (13) and corresponds to three of four state variables selected from (7). The three state variables are denoted as and . FSE is performed by double XOR operations between and and every three bytes of , denoted by . The encryption operation is given by (14)where are the output encrypted images, are the three bytes of the final shuffled image and are recombined cipher images obtained during operation on the shuffled image, while f denotes the first stage. The FSE image which results from (14) is labelled . The procedure for encrypting an image during the FSE is given by Algorithm 3. The Haar wavelet-based discrete wavelet transform (HDWT) was performed on , based on the procedure described by Algorithm 4. 3.4 Second stage encryption (SSE) In the SSE, the new image is reshaped. Security keys are selected and the procedure applied in FSE is repeated. However, unlike the FSE where , the two significant bytes of MSB, ITB and LSB are not cyclically interchanged in SSE, i.e. This differentiation increases the complexity of differential attacks. Moreover, in SSE, the diffused pixel values of results in an arbitrary selection of bytes for mixing with the sequence of SG-2. are recombined cipher images of each operation on The procedures of final encryption of in SSE are described by Algorithm 5. 4 Numerical simulation results and comparative analysis In order to verify the feasibility, efficiency and robustness of the proposed algorithm, a series of computer simulations in the MATLAB computing environment was carried out, using Windows 7 operating system with 64-bit OS, Intel (R) CORE ™ i7-3540M central processing unit (CPU) @ 3.0 GHz and an 8.0 GB RAM. Five widely used images of size pixels namely, Mandrill, Lena, Peppers, Boat and Cameraman, respectively, were selected and pre-processed to 8-bit greyscale plain images. The histograms of the plain and encrypted images, key space, global Shannon entropy, correlation coefficients of adjacent pixels of the plain, encrypted and decrypted images, structural contents, mutual information, plaintext and key sensitivity to cryptographic attacks, time complexity and robustness to noise degradation were analysed. In all the analysis performed, only works that featured the aforementioned images with the same resolution as those in this study were selected for comparative analysis. The five plain 8-bit greyscale input images are shown in Fig. 7, while their encrypted counterparts are shown in Fig. 8. Fig. 7Open in figure viewerPowerPoint Plain images (a) Mandrill, (b) Lena, (c) Peppers, (d) Boat, (e) Cameraman Fig. 8Open in figure viewerPowerPoint Encrypted images (a) Mandrill, (b) Lena, (c) Peppers, (d) Boat, (e) Cameraman The perception of distortion of the encrypted images with respect to the plain image, known as perceptual security, were measured using peak signal-to-noise ratio (PSNR) metric. The computed values of PSNR of the encrypted images obtained for the first stage and SSE are as follows: Mandrill (14.5530, 14.5836), Lena (13.9509, 13.9705), Peppers (13.6964, 13.6966), Boat (14.1000, 14.0648) and Cameraman (13.1340, 13.1429), respectively. The computed PSNR indicates the absence of the relationship between the plain and encrypted images. 4.1 Key space analysis In the proposed algorithm, the global set of original security keys is a multi-parameter set which is represented by , where and are initial conditions of SG-1 and SG-2; subscripts 'e' and 'd' denotes encryption and decryption operations, respectively; while all other subscripts and variables are as defined in previous sections. The original global key set is given by All the numbers are double precision numbers. In order to compare with related works, we adopted the commonly used precision number . Thus, the key space is a combination of . This is huge when compared with the minimum key bits permutation considered to be computationally infeasible with conventional digital computing technique. Some recent works that featured similar images with the same resolutions reported the following key space sizes: [32], [33], [34], [35], [6], [36] and [37]. A comparative analysis of the key space size obtained with the proposed algorithm and those in the aforementioned works shows that the proposed algorithm possesses a huge key space than them, and therefore robust against brute force attacks. 4.2 Structural content and mutual information Structural content (SSC) measures the degree of similarity between the plain and decrypted images, and is expressed by the relationship (15)where and represent the plain image and decrypted images, respectively. Mutual information () gives a measure of image matching which can be used to evaluate the similarity between cipher images obtained during the two encryption operations. is given by the relationship: (16)where is the joint probability mass function (PMF) of random variables X and Y, and are the marginal PMF of X and Y. X and Y represent the cipher images of the first and SSE. implies dissimilarity, while implies similarity. Generally, for two identical images, is approximately the joint entropy of the images, which is basically close to their global Shannon entropy. The computed SSC are as follows: Mandrill (0.9966), Lena (0.9969), Peppers (0.9977), Boat (0.9889) and cameraman (0.9782), respectively. It is observable that the SSC≃1 of the plain and decrypted images are relatively high (SSC≃1), which implies the decryption performance is high. Similarly, the of the encrypted images are as follows: Mandrill (0.8227), Lena (0.8343), Peppers (0.8229), Boat (0.8220) and Cameraman (0.8205). The computed are high because the pixels of the encrypted images of the first encryption stage were diffused prior to the SSE operation. The confirmed the efficiency of the diffusion process of the encryption scheme. 4.3 Statistical attacks analysis 4.3.1 Histogram analysis Generally, histograms of the distribution of pixel intensities of an encrypted image appear uniform in the spatial dimension of the image. In order to evaluate the uniformity of the distribution beyond the visual inspection, and measure their closeness to the histogram of an ideal random image, a uniformity assessment is essential. In this work, the histograms of the encrypted image were uniformly distributed and indistinguishable from those obtained in other works. Consequently, the Euclidean distance between the histograms of the encrypted images and random image is computed in the next subsection. 4.3.2 Encrypted image histogram uniformity assessment The Euclidean distance between the histogram of an ideal random image and those of the encrypted images is computed using the relationship: (17)where and are histograms of the random and encrypted images, respectively, and n is the number of pixels. The computed Euclidean distances of the images are given as follows: Mandrill (0.0021), Lena (0.0019), Peppers (0.0018), Boat (0.0028) and Cameraman (0.002). The computed DH of the images is close to . Generally, the Euclidean distance between two ideal random images is 0, which implies similarity. Hence, we can infer that there is a similarity between and . Consequently, the pixel intensities are random and uniformly distributed. 4.3.3 Correlation analysis of adjacent pixels of plain and encrypted images The correlation maps of adjacent pixels obtained illustrated the diffusion of redundancy and correlation among adjacent pixels in the horizontal (H), vertical (V) and diagonal (D) directions. The correlation coefficients of the adjacent pixels of the plain and encrypted images were computed based on the relationship: (18)where (19) (20) (21)x and y are greyscale values of two adjacent pixels in an image. N is the total number of duplets obtained from the images. , are pairs of adjacent pixels, randomly selected from the plain and encrypted images. The computed of the plain images are given as follows: Mandrill (0.8955(H), 0.8764(V), 0.8272(D)), Lena (0.9554(H), 0.9775(V), 0.9326(D)), Peppers (0.9636(H), 0.9742(V), 0.9399(D)), Boat (0.8812(H), 0.9209(V), 0.8349(D), Cameraman (0.9133(H), 0.9431(V), 0.9098(D)). implies the correlation of adjacent pixels in the plain image. The computed of the encrypted images and their comparative analysis with those in selected works are tabulated in Table 2. It can be seen that the of all encrypted images are close to zero. This implies that there are no mutual relationships between adjacent pixels of the images in the horizontal, vertical and diagonal directions. Thus, no information can be extracted from the pixel intensities of the encrypted images. The comparative analysis presented in Table 2 shows that the computed of the five images compares favourably with those obtained for similar images in the selected works. The variations in the computed obtained using the proposed algorithm and those of selected works are due to differences in the formats and quality of images used in experiments, and their effects on the performance of the encryption algorithms. Consequently, some values are closer to zero in some directions than in others. The computed generally confirms that the encryption algorithm can withstand statistical attacks. Table 2. Comparative analysis of Reference work Direction Mandrill Lena Pepper Boat Cameraman proposed algorithm horizontal −0.00018 0.009188 0.01418 0.00616 0.01418 vertical 0.005203 0.006364 0.00836 0.00201 0.00836 diagonal 0.001768 0.002898 0.00433 0.00458 0.00433 [37] horizontal −0.0070 0.00030 0.00760 NA 0.00960 vertical 0.0059 −0.0030 −0.0074 NA −0.0130 diagonal −0.0090 −0.0028 0.0128 NA −0.0132 [38] horizontal 0.0059 0.0032 0.0037 0.0073 0.0198 vertical 0.0041 0.0019 0.00258 0.0109 0.0132 diagonal 0.0028 0.0011 0.0079 0.0016 0.0032 [39] horizontal 0.0026 0.0056 0.0016 0.0001 0.0024 vertical 0.0009 0.0037 0.0059 0.0031 0.0013 diagonal 0.0052 0.0032 0.0034 0.0015 0.0098 [40] horizontal 0.0060 0.0061 0.0049 0.0085 0.0053 vertical 0.0058 0.0116 0.0031 0.0092 0.00126 diagonal 0.0016 0.0018 0.0079 0.0024 0.0005 [41] horizontal 0.0055 0.0041 0.0021 0.0073 0.0145 vertical 0.0015 0.0021 0.0218 0.0216 0.0084 diagonal 0.0041 0.0009 0.0096 0.0035 0.0026 4.3.4 Correlation coefficient of plain and decrypted images Correlation coefficient of the plain and decrypted images quantifies their closeness. It is computed by the relationship: (22)where and . represents the plain image and is the encrypted image. Ideally, the value of the correlation coefficient ranges from to , where implies that the two images are identical, while indicates the exact opposite. The computed of the images are given as follows: Mandrill , Lena , Peppers , Boat and Cameraman , respectively. Compared to the of Lena and Cameraman presented in [42], the computed are relatively high, which indicates a better decryption performance. 4.4 Differential attacks analysis 4.4.1 Key sensitivity analysis A secure encryption scheme is extremely sensitive to its security keys. Consequently, a slight change to even a single bit in the key structure will result in different ciphers. The number of pixels changing rate (NPCR) and unified average changing intensity (UACI) are metrics that gauge the sensitivity of a scheme's security keys. NPCR examines the percentage of different pixel numbers before and after a slight change, while UACI measures the difference in pixel intensity among the two images. NPCR and UACI are expressed mathematically as follows: (23) (24) (25) where is a bipolar array, are row and column indices of the images. M and N are the length and width of the image, respectively. Given as defined in Section 4.1, then the influence of the slight change in key bit results in a new set of global keys represented by the following variables: (26)In order to test for key sensitivity, a slight change is made to any of the initial conditions quartet and . A key bit was slightly changed to , and the key sensitivity was evaluated. The decryption performance of the images based on the slightly different security keys is shown in Fig. 9. Fig. 9Open in figure viewerPowerPoint Set of decrypted images with slightly changed security keys (a) Mandrill, (b) Lena, (c) Peppers, (d) Boat, (e) Cameraman The influence of the slight change to keys was evaluated using mean square error (MSE) and PSNR. The results obtained are as follows: Mandrill (MSE_6782.1, PSNR_9.8172), Lena (MSE_7808.6, PSNR_9.205), Peppers (MSE_8318.8, PSNR_8.9302), Boat (MSE_7641, PSNR_9.2991) and Cameraman (MSE_9455.9