A Symmetric Key Multiple Color Image Cipher Based on Cellular Automata, Chaos Theory and Image Mixing

The transmission of sensitive and secret images over a public network demands effective techniques to safe-guard and conceal the data. In this paper, a symmetric multiple color image encryption technique is proposed by adopting a dual permutation and dual substitution framework. Initially, the input images are combined into a large image and then segmented into pure-image elements. These pure-image elements are


Introduction
High speed networks and communication infrastructure in the modern digital facilitate easy and rapid online communication. Online, real-time communication is put to good use in telemedicine, weather monitoring, defense surveillance, and social media, to name a few. In these fields, images area primary source of information and, further, a massive quantum of visual content is transmitted using public networks and stored in the cloud. Given that such digital images may contain secret and sensitive information of a personal, financial or national nature, it is imperative to ensure their safety in order to stop in formation leaks. Image encryption is a great way to protect digital images, especially during their transmission. Image encryption renders meaningful images unrecognizable. Classical encryption techniques that work well on textual data do not do so on images, owing to their high correlation and colossal dimensions. Therefore, digital image enciphering has emerged as a key area of study. Over the last few years, experts have proposed image ciphers based on the chaos theory and cellular automata. Cellular automata exhibit fascinating properties like complex behavior and unpredictability in terms of simple rules, while chaotic maps possess excellent sensitivity and ergodicity. Hence, the union of cellular automata (CA) and chaos theory-based image encryption design offers a superior solution for image security issues.

Related Work
Wolfram introduced the notion of using cellular automata to produce secret keys [34], and since then much work has been carried out on CA-based ciphers. Jin proposed a fast image cipher using a cellular automata-generated attractor as the encryption function [12]. In this technique, the state attractor based key streams contain at most eight states only. Zhang et al. [41], proposed a two-dimensional cellular automata-based image cryptosystem, in which balanced CA are used for permutation. The experiments proved that this technique powerful enough to withstand sta-tistical attacks. Chai et al. proposed an image encryption and compression technique by employing CA and compressive sampling [5]. Their algorithm uses the cellular automata rule to achieve confusion. But the entropy values of the encrypted images are low. Jeyaram [11] et al. proposed a new cellular automata-based image cipher that uses a radius-2, class-III CA to scramble pixels. A cellular automata and DNA computing-based image encryption method was presented by Zhou et al. [45]. Their scheme introduces the Thymine DNA cellular automata and T-DNA-CA for encryption. This algorithm has high computational overhead. Mondal et al. proposed a cellular automata-based image cryptosystem [19], where CA are adopted to produce a pseudo-random sequence that confronts noise attacks efficiently. Hanis [9] et al. presented a dual-image encryption-compression technique that employs cellular automata and a modified convolution technique. Their scheme utilized a set of CA rules to scramble pixel locations. Perales [21] proposed a cellular automata-based color image cipher, with the elementary CA Rule-45 used for key generation. Asadollahi et al. [2], proposed an image enciphering method based on cellular automata and the Arnold map, wherein cellular automata are used to change pixel values. The above schemes are designed only for single-image encryption.
Matthews [18] pointed to the application of chaos in encryption algorithms, and since then a slew of chaos theory-based image ciphers have been presented. An image encryption fusion and compression approach, based on chaos and compressive sampling, was put forward [17], with a 1D logistic map used to build a sensing matrix. Ramasamy [22] et al. introduced an image cipher using enhanced logistic-tend map. This scheme achieved both confusion and diffusion properties of an ideal cipher. A novel image cryptosystem that uses a 1D logistic map and random sampling was introduced by Zhu et al. [46]. The hardware and software design of 1D map-based schemes are simple, but 57 Information Technology and Control 2021/1/50 the smaller key space makes the technique susceptible to brute force attacks. The RGB image cipher, using chaos and the Chinese remainder theorem, was introduced by Guo et al. [8]. Their technique uses a chaotic quantum map to shuffle the RGB image. Patro [20] et al. proposed a chaos theory-based multi-image cryptosystem whereas cross-coupled map is used for executing diffusion and permutation operations, with the results indicating that their algorithm confronts known plain-image and chosen plain-image attacks. Sui et al. [25], presented a dual image enciphering scheme using a logistic map and the discrete fractional transform. The logistic map in this technique relocates and modifies image pixel values, and the method demonstrates a significant resistance to conventional cipher image-only attacks. Sui et al. again presented a dual-image cipher using a fractional angular transform and coupled logistic map [26], wherein the fractional computation takes a much longer encryption time. Liu [16] et al. proposed a chaotic system-based dual-image cryptosystem employing S-boxes and a chaotic sequence for dual-image diffusion, with a large key space being the strength of the algorithm. Zhang [40] et al. presented a chaotic map and a permutation model-based multiple-image cipher technique. Li et al. [14], proposed a dual-image enciphering scheme by adopting the chaos theory and gyrator transform, in which a standard map is utilized to generate the position of the pixel scrambling area. A cycle shift and chaos theory-based image cipher was proposed by Wang et al. [33], where pixel substitution is realized by the circular shift which greatly increases security. Zhou et al. designed a 1D logistic map and cosparse representation-based dual-image encryption scheme [44], utilizing the chaotic map to construct a measurement matrix. This method showed poor resistance against statistical attacks. Tutueva [29] et al. introduced a method using adaptive chaotic map to construct chaos-based cipher. This scheme achieved larger key space. Tutueva [30] et al. again utilized adaptive chatic maps to create hash function. This novel approach effectively counters birthday attack.
Sawlikar [24] et al. reported a dual-image encryption and compression scheme that undertakes two stages of encryption for enhanced security strength. Alfalou et al. [1], introduced a many-image simultaneous encryption, fusion and compression scheme in which encryption is executed by utilizing biometric infor-mation. A multiple-image cipher to protect medical images was proposed [3]. Zhong [42] et al. presented a dual-image cryptosystem by adopting random-phase encoding. Zhang [37] et al. designed a many-image cipher scheme utilizing the orthogonal basis matrix and double random-phase encoding, where images are encrypted in parallel. Their algorithm strongly resists occlusion attacks, though the computation cost is higher. Xiong [36], proposed a vector decomposition-based many-image cryptosystem that uses private keys, in addition, for enhanced security. Chen [6] et al. presented a multiple-image asymmetric cipher based on compressive sampling and feature fusion. In reference [43], Nanrun et al. developed a dual-image enciphering technique using the discrete fractional random transform and discrete wavelet transform. Zhang [39] et al. introduced a novel many-image encryption scheme based on the mixed-image elements obtained from the many images used. Xiaoqiang et al. [38], again designed a multi-image cipher using chaos and mixed-image content. Karawia [13] et al. developed a many-image cryptosystem based on an economic map and mixed-image elements. Most of the dual-and multi-image ciphers presented above are indented only for grayscale image encryption.

Motivation and Justification
An array of internet-based applications, such as telemedicine, cloud computing, and social media, transmit large volumes of secret images over public networks. The security of these sensitive images is a major concern, with image encryption working best for image data protection. Cellular automata are very simple rules that generate highly complex random patterns that have been applied successfully in cryptographic algorithms. Chaos is a phenomenon that occurs in greatly sensitive, deterministic nonlinear dynamical systems. It is extremely difficult to predict chaos behavior, and chaos theory has been a good candidate for image encryption techniques. Circular shift operations can be used to perform value substitution operations effectively and with little computation, while zigzag order scanning can be used for satisfactory permutation operations. Reconstructing an original image from very small-sized, mixed-image elements is impossible without keys. All of the above has motivated the development of a symmetric color image encryption scheme using cellular automata, zigzag scanning, circular

Paper Organization
The rest of this paper is arranged as follows. Section 2 describes the mixed-image elements, cellular automata, zigzag pattern, circular shift and 2D logistic map. Section 3 presents the proposed multiple color image enciphering and deciphering procedures. Section 4 outlines the experimental setup. Section 5 lists and analyzes, Matrix algebra makes it possible to segme matrix into sub-matrices and, conversely, matrices can be combined to form a si matrix. Images are treated as matrices w processing so they can be divided and me [38][39]. For instance, the input image1, show Figure 1.a, can be segmented into 64 small images, as shown in Figure 1.b, and the images joined easily. Cons that P mxn 1 P mxn 2 ,…., P mxn h are h original p images divided into the sub-image sets, S 1 ={ S 2 ={s i 2 },…,S h ={s i h }. Each member of the se S is called a pure-image element. A new m set, X = {{s i 1 } ∪ { s i 2 } ∪…∪ {s i h }}, can created from mixing the pure elements. E member of the set, xi∈ X, is termed a mi image element Flowers Image ,…., performed by adopting a dual permutation and dual substitution framework that effectively dissipate the statistical structure of plaintext and enhances confusion property; b) Key Selection: The initial configurations for cellular automata, the starting position for zigzag scanning, the starting seeds for the logistic map, and the 512bit hash are the keys of this system which offers larger key space and withstand plaintext-based threats.

Paper Organization
The rest of this paper is arranged as follows. Section 2 describes the mixed-image elements, cellular automata, zigzag pattern, circular shift and 2D logistic map. Section 3 presents the proposed multiple color image enciphering and deciphering procedures. Section 4 outlines the experimental setup. Section 5 lists and analyzes,

Mixed Image Elements
Matrix algebra makes it possible to segment a matrix into sub-matrices and, conversely, submatrices can be combined to form a single matrix. Images are treated as matrices while processing so they can be divided and merged [38][39]. For instance, the input image1, shown in Figure 1.a, can be segmented into 64 small subimages, as shown in Figure 1

Flowers Image
are h original plain images divided into the sub-image sets, S 1 ={ ge encryption is l permutation and that effectively e of plaintext and b) Key Selection: cellular automata, ag scanning, the ap, and the 512stem which offers d plaintext-based n anged as follows.
-image elements, ern, circular shift n 3 presents the e enciphering and on 4 outlines the lists and analyzes,

A Basic Background 2.1. Mixed Image Elements
Matrix algebra makes it possible to segment a matrix into sub-matrices and, conversely, submatrices can be combined to form a single matrix. Images are treated as matrices while processing so they can be divided and merged [38][39]. For instance, the input image1, shown in Figure 1.a, can be segmented into 64 small subimages, as shown in Figure 1 }, S 2 ={ dual substitution framework that effectively dissipate the statistical structure of plaintext and enhances confusion property; b) Key Selection: The initial configurations for cellular automata, the starting position for zigzag scanning, the starting seeds for the logistic map, and the 512bit hash are the keys of this system which offers larger key space and withstand plaintext-based threats.

Paper Organization
The rest of this paper is arranged as follows. Section 2 describes the mixed-image elements, cellular automata, zigzag pattern, circular shift and 2D logistic map. Section 3 presents the proposed multiple color image enciphering and deciphering procedures. Section 4 outlines the experimental setup. Section 5 lists and analyzes,

Mixed Image Elements
Matrix algebra makes it possible to segment a matrix into sub-matrices and, conversely, submatrices can be combined to form a single matrix. Images are treated as matrices while processing so they can be divided and merged [38][39]. For instance, the input image1, shown in Figure 1.a, can be segmented into 64 small subimages, as shown in Figure 1

Flowers Image
},…, S h ={ substitution framework: image encryption is performed by adopting a dual permutation and dual substitution framework that effectively dissipate the statistical structure of plaintext and enhances confusion property; b) Key Selection: The initial configurations for cellular automata, the starting position for zigzag scanning, the starting seeds for the logistic map, and the 512bit hash are the keys of this system which offers larger key space and withstand plaintext-based threats.

Paper Organization
The rest of this paper is arranged as follows. Section 2 describes the mixed-image elements, cellular automata, zigzag pattern, circular shift and 2D logistic map. Section 3 presents the proposed multiple color image enciphering and deciphering procedures. Section 4 outlines the experimental setup. Section 5 lists and analyzes,

A Basic Background 2.1. Mixed Image Elements
Matrix algebra makes it possible to segment a matrix into sub-matrices and, conversely, submatrices can be combined to form a single matrix. Images are treated as matrices while processing so they can be divided and merged [38][39]. For instance, the input image1, shown in Figure 1.a, can be segmented into 64 small subimages, as shown in Figure 1

Flowers Image
}. Each member of the set s i ∈ S is called a pure-image element. A new mixed set,

Paper Organization
The rest of this paper is arranged as follows. Section 2 describes the mixed-image elements, cellular automata, zigzag pattern, circular shift and 2D logistic map. Section 3 presents the proposed multiple color image enciphering and deciphering procedures. Section 4 outlines the experimental setup. Section 5 lists and analyzes, that P mxn 1 P mxn 2 ,…., P mxn h images divided into the s S 2 ={s i 2 },…,S h ={s i h }. Eac S is called a pure-image set, X = {{ s i 1 } ∪ { s i 2 } created from mixing th member of the set, x i ∈ image element

Cellular Automata
Conventional science uses mathematical models to describe phenomena in the natural world. The underlying principle of cellular automata (CA) is the use of simple rules, in the form of programs, to create models that describe the world [34]. What is remarkable about cellular automata is that very simple rules produce extremely Where −1 , and +1 represent the state of j at time t-1, t and t+1, respectively, and g is function that represents the rule. The rule use this scheme is Rule-30 from the ECA, w states that every cell must be looked at in rela to the cell at its right. If the color of both c was white in the previous step, the new colo the cell must be the same as the previous colo the cell to its left -or else, the new color mus 59 Information Technology and Control 2021/1/50 X = {{ [38][39]. For instance, the input image1, shown in Figure 1.a, can be segmented into 64 small subimages, as shown in Figure 1.  [38][39]. For instance, the input image1, shown in Figure 1.a, can be segmented into 64 small subimages, as shown in Figure 1.b, and the subimages joined easily. } ∪…∪ { processing so they can be divided and merged [38][39]. For instance, the input image1, shown in Figure 1.a, can be segmented into 64 small subimages, as shown in Figure 1.b, and the subimages joined easily.

Cellular Automata
Conventional science uses mathematical models to describe phenomena in the natural world. The underlying principle of cellular automata (CA) is the use of simple rules, in the form of programs, to create models that describe the world [34]. What is remarkable about cellular automata is that very simple rules produce extremely intricate random patterns as they evolve over time. More generally, CA is an array of discrete cells, wherein every cell is colored either black (1) or white (0). The content (color) of every cell it contains is updated parallelly at each step in its evolution, based on simple definite rules. The CA rule sets produce four classes of patterns: nesting, randomness, repetition and complex [33]. We are motivated to use the random class pattern in the design of our cipher. Elementary cellular automata (ECA) are a basic form of cellular automata in which the state of each cell depends on only three cells. The new state of a cell is defined by Equation (1),

Cellular Automata
Conventional science uses mathematical models to describe phenomena in the natural world. The underlying principle of cellular automata (CA) is the use of simple rules, in the form of programs, to create models that describe the world [34]. What is remarkable about cellular automata is that very simple rules produce extremely intricate random patterns as they evolve over time. More generally, CA is an array of discrete cells, wherein every cell is colored either black (1) or white (0). The content (color) of every cell it contains is updated parallelly at each step in its evolution, based on simple definite rules. The CA rule sets produce four classes of patterns: nesting, randomness, repetition and complex [33]. We are motivated to use the random class pattern in the design of our cipher. Elementary cellular automata (ECA) are a basic form of cellular automata in which the state of each cell depends on only three cells. The new state of a cell is defined by Equation (1), Where −1 , and +1 represent the state of cell j at time t-1, t and t+1, respectively, and g is the function that represents the rule. The rule used in this scheme is Rule-30 from the ECA, which states that every cell must be looked at in relation to the cell at its right. If the color of both cells was white in the previous step, the new color of the cell must be the same as the previous color of the cell to its left -or else, the new color must be the opposite [34]. Figure 2.a shows Rule-30 and Figure 2.b how differently Rule-30 behaves from its random initial state (condition). The finite cellular automaton is employed in the proposed scheme, in which cells are arranged in a ring structure where the right neighbor of the rightmost cell is the leftmost cell, and the left neighbor of the leftmost cell is the rightmost cell [12].

Zigzag Patterns
The zigzag pattern used in this work carries out second-level pixel permutation to enhance the strength of the cipher. This is done by scanning the matrix in the zigzag manner shown in Figure  3.a, while transforming the matrix representation of the image into a one-dimensional vector. In a (1) Where Where −1 , and +1 represent the state of cell j at time t-1, t and t+1, respectively, and g is the function that represents the rule. The rule used in this scheme is Rule-30 from the ECA, which states that every cell must be looked at in relation to the cell at its right. If the color of both cells was white in the previous step, the new color of the cell must be the same as the previous color of the cell to its left -or else, the new color must be the opposite [34]. Figure 2.a shows Rule-30 and Figure 2.b how differently Rule-30 behaves from its random initial state (condition). The finite cellular automaton is employed in the proposed scheme, in which cells are arranged in a ring structure where the right neighbor of the rightmost cell is the leftmost cell, and the left neighbor of the leftmost cell is the rightmost cell [12].

Zigzag Patterns
The zigzag pattern used in this work carries out second-level pixel permutation to enhance the strength of the cipher. This is done by scanning the matrix in the zigzag manner shown in Figure  3.a, while transforming the matrix representation of the image into a one-dimensional vector. In a and Where −1 , and +1 represent the state of cell j at time t-1, t and t+1, respectively, and g is the function that represents the rule. The rule used in this scheme is Rule-30 from the ECA, which states that every cell must be looked at in relation to the cell at its right. If the color of both cells was white in the previous step, the new color of the cell must be the same as the previous color of the cell to its left -or else, the new color must be the opposite [34]. Figure 2.a shows Rule-30 and Figure 2.b how differently Rule-30 behaves from its random initial state (condition). The finite cellular automaton is employed in the proposed scheme, in which cells are arranged in a ring structure where the right neighbor of the rightmost cell is the leftmost cell, and the left neighbor of the leftmost cell is the rightmost cell [12].

Zigzag Patterns
The zigzag pattern used in this work carries out second-level pixel permutation to enhance the strength of the cipher. This is done by scanning the matrix in the zigzag manner shown in Figure  3.a, while transforming the matrix representation of the image into a one-dimensional vector. In a represent the state of cell j at time t-1, t and t+1, respectively, and g is the function that represents the rule. The rule used in this scheme is Rule-30 from the ECA, which states that every cell must be looked at in relation to the cell at its right. If the color of both cells was white in the previous step, the new color of the cell must be the same as the previous color of the cell to its left -or else, the new color must be the opposite [34]. Figure 2.a shows Rule-30 and Figure 2.b how differently Rule-30 behaves from its random initial state (condition). The finite cellular automaton is employed in the proposed scheme, in which cells are arranged in a ring structure where the right neighbor of the rightmost cell is the leftmost cell, and the left neighbor of the leftmost cell is the rightmost cell [12].

Zigzag Patterns
The zigzag pattern used in this work carries out second-level pixel permutation to enhance the strength of the cipher. This is done by scanning the matrix in the zigzag manner shown in Figure 3.a, while transforming the matrix representation of the image into a one-dimensional vector. In a zigzag scanning pattern, the starting point is salient, since different starting points produce different permutation orders. For instance, the matrix shown in Figure 3.b is scanned from two different starting points and the results shown in Figure 3.c and Figure 3.d. The starting point of the zigzag scanning pattern is obtained from the zigzag scanning pattern, the starting point is salient, since different starting points produce different permutation orders. For instance, the matrix shown in Figure 3.b is scanned from two different starting points and the results shown in Figure 3.c and Figure 3.d. The starting point of the zigzag scanning pattern is obtained from the input images so that every new input image has a different zigzag pattern. This input dependency of the algorithm resists chosen plaintext-based attacks.

Circular Shift Operations
Circular shift operations, which are reversible, change pixel values simply and efficiently [33]. There are two types of circular shift operations, left and right. In a k-bit left circular shift, each bit is shifted a k binary digit to the left, circularly. Consider an n-bit binary sequence, Bn = {b0,b1 …bn-2, bn-1, where 0≤ n ≤ n-1}. The 1-bit left circular shift operation changes the binary sequence as follows:{b1, b2… bn-1, b0}. For instance, if a four-bit sequence (1000)2 is circularly shifted 1-bit left, the result is (0001)2, that is, the decimal (8)10 is changed to the decimal (1)10. The k-bit left circular shift is employed in the proposed system to perform the first-level pixel value substitution.

Circular Shift Operations
Circular shift operations, which are reversible, change pixel values simply and efficiently [33]. There are two types of circular shift operations, left and right. In a k-bit left circular shift, each bit is shifted a k binary digit to the left, circularly. Consider an n-bit binary sequence, B n = {b 0 ,b 1 …b n-2 , b n-1 , where 0≤ n ≤ n-1}. The 1-bit left circular shift operation changes the binary sequence as follows:{b 1 , b 2 … b n-1 , b 0 }. For instance, if a four-bit sequence (1000) 2 is circularly shifted 1-bit left, the result is (0001) 2, that is, the decimal (8) 10 is changed to the decimal (1) 10 . The k-bit left circular shift is employed in the proposed system to perform the first-level pixel value substitution.

The Two-Dimensional Logistic Chaotic Map
Chaos is a complex behavior, arising from a deterministic nonlinear dynamical system that exhibits the two special properties of unpredictability and sensitivity.

Figure 3
Example of Zigzag Scanning

The Two-Dimensional Logistic Chaotic Map
Chaos is a complex behavior, arising from a deterministic nonlinear dynamical system that exhibits the two special properties of unpredictability and sensitivity. It is hard to predict chaos behavior, and a system like this one is highly sensitive to the starting seeds. These two properties make the chaos theory most suited to developing ciphers. The 2D logistic map [32] used in the proposed system is defined in Equation (2). It has a best distribution than provided by previously proposed logistic maps.  Figure 4.

Bifurcation Diagram:
Bifurcation phenomenon displays the change in dynamic behavior when the control parameters change to a critical point [28,31]. Bifurcation diagrams of the Equation (2) are shown in Figure 5. The fixed point and period-doubling are observed from the bifurcation diagram. It is clear from the Figure 5 that Equation (2) turns into chaos through double periodic bifurcation.

Lyapunov Exponent
Lyapunov exponent is a standard way to measure the degree of sensitive dependence on initial seeds of dynamical systems [27]. The Largest Lyapunov Exponent is nonnegative in the chaotic region [9]. The Lyapunov exponents for the Equation (2) is calculated [23] for the time series and the initial seeds of the Equation (2) as: (x1 = 0.898 and y1 = 0.954). It can be observed form the Figure 6 that the positive Lyapunov exponent contribute to the support of hyper chaotic. It is hard to predict chaos behavior, and a system like this one is highly sensitive to the starting seeds. These two properties make the chaos theory most suited to developing ciphers. The 2D logistic map [32] used in the proposed system is defined in Equation (2). It has a best distribution than provided by previously proposed logistic maps.

Cellular Automata
Conventional science uses mathematical models to describe phenomena in the natural world. The underlying principle of cellular automata (CA) is the use of simple rules, in the form of programs, to create models that describe the world [34].
What is remarkable about cellular automata is that very simple rules produce extremely intricate random patterns as they evolve over time. More generally, CA is an array of discrete cells, wherein every cell is colored either black (1) or white (0). The content (color) of every cell it contains is updated parallelly at each step in its evolution, based on simple definite rules. The CA rule sets produce four classes of patterns: nesting, randomness, repetition and complex [33]. We are motivated to use the random class pattern in the design of our cipher. Elementary cellular automata (ECA) are a basic form of cellular automata in which the state of each cell depends on only three cells. The new state of a cell is defined by Equation (1),

2.3
Th sec str the 3.a of (2) where p 1 , p 2 , q 1 and q 2 are parameters. The 2D logistic map behaves chaotically when the value of the parameters ranges between 2.  Figure 4.

Bifurcation Diagram
Bifurcation phenomenon displays the change in dynamic behavior when the control parameters change to a critical point [28,31]. Bifurcation diagrams of the Equation (2) are shown in Figure 5. The fixed point and period-doubling are observed from the bifurcation di- agram. It is clear from the Figure 5 that Equation (2) turns into chaos through double periodic bifurcation.

Lyapunov Exponent
Lyapunov exponent is a standard way to measure the degree of sensitive dependence on initial seeds of dynamical systems [27]. The Largest Lyapunov Exponent is nonnegative in the chaotic region [9]. The Lyapunov exponents for the Equation (2) is calculated [23] for the time series and the initial seeds of the Equation (2) as: (x 1 = 0.898 and y 1 = 0.954). It can be observed form the Figure 6 that the positive Lyapunov exponent contribute to the support of hyper chaotic.

Figure 4
Trajectory of the 2-D logistic map

Figure 4
Trajectory of the 2-D logistic map

Figure 6
Largest Lyapunov Exponent

Figure 4
Trajectory of the 2-D logistic map

Figure 6
Largest Lyapunov Exponent

Figure 6
Largest Lyapunov Exponent

The Proposed Algorithm
The framework of the new system is shown in Figure 7.
The two prime and inevitable cipher design principles of confusion and diffusion are realized in this approach through the inclusion of substitution and permutation operations. The key generation, enciphering and deciphering processes are explained here.

Key Generation
The initial configurations for cellular automata, the starting position for zigzag scanning, the starting values for the logistic map, and the 512-bit hash are the keys of this system. To withstand plaintext-based threats, the keys are computed from the input images and obtained as follows: Step 1: Obtain the 512-bit hash by applying the SHA-512algorithm on the input images.
Step 2: Compute the initial configuration.
The two initial configuration vectors,

The Proposed Algorithm
The framework of the new system is shown in Figure 7. The two prime and inevitable cipher design principles of confusion and diffusion are realized in this approach through the inclusion of substitution and permutation operations. The key generation, enciphering and deciphering processes are explained here.

Key Generation
The initial configurations for cellular automata, the starting position for zigzag scanning, the starting values for the logistic map, and the 512bit hash are the keys of this system. To withstand plaintext-based threats, the keys are computed from the input images and obtained as follows: Step 1: Obtain the 512-bit hash by applying the SHA-512algorithm on the input images.
Step 2: Compute the initial configuration. The two initial configuration vectors,{R 0 P and C 0 P }, for Rule-30 are calculated from the 512-bit hash as follows. Case 1: If the length of configuration (L) is 1≤ L ≤512, select L bits from the rear end of the 512-bit hash in reverse order. Case 2: If the length of configuration (L) is ≤1024, select the first 512 bits from the rear end of the 512-bit hash in reverse order and the remaining bits from the front end in the forward order.
Step 3: Find the starting position of the zigzag scanning pattern.
The 512-bit hash of the input image is grouped into 8-bit segments and transformed to 64-decimal numbers, d1, d2, d3, …., d64. The starting position (p0, q0) of the zigzag scanning pattern is computed using Equation (3), where w is the dimension of the image.
Step 4: Compute the starting values of the 2D logistic map.
In the 2D logistic map, the two initial values (x1, y1) used are computed using Equation (4), where (xs, ys) are the starting seeds.

The Proposed Algorithm
The framework of the new system is shown in Figure 7. The two prime and inevitable cipher design principles of confusion and diffusion are realized in this approach through the inclusion of substitution and permutation operations. The key generation, enciphering and deciphering processes are explained here.

Key Generation
The initial configurations for cellular automata, the starting position for zigzag scanning, the starting values for the logistic map, and the 512bit hash are the keys of this system. To withstand plaintext-based threats, the keys are computed from the input images and obtained as follows: Step 1: Obtain the 512-bit hash by applying the SHA-512algorithm on the input images.
Step 2: Compute the initial configuration. The two initial configuration vectors,{R 0 P and C 0 P }, for Rule-30 are calculated from the 512-bit hash as follows. Case 1: If the length of configuration (L) is 1≤ L ≤512, select L bits from the rear end of the 512-bit hash in reverse order. Case 2: If the length of configuration (L) is ≤1024, select the first 512 bits from the rear end of the 512-bit hash in reverse order and the remaining bits from the front end in the forward order.
Step 3: Find the starting position of the zigzag scanning pattern.
The 512-bit hash of the input image is grouped into 8-bit segments and transformed to 64-decimal numbers, d1, d2, d3, …., d64. The starting position (p0, q0) of the zigzag scanning pattern is computed using Equation (3), where w is the dimension of the image.
Step 4: Compute the starting values of the 2D logistic map.
In the 2D logistic map, the two initial values (x1, y1) used are computed using Equation (4), where (xs, ys) are the starting seeds.

Case 2:
If the length of configuration (L) is ≤1024, select the first 512 bits from the rear end of the 512-bit hash in reverse order and the remaining bits from the front end in the forward order.
Step 3: Find the starting position of the zigzag scanning pattern.
The 512-bit hash of the input image is grouped into 8-bit segments and transformed to 64-decimal numbers, d 1 , d 2 , d 3 , …., d 64 . The starting position (p 0, q 0 ) of the zigzag scanning pattern is computed using Equation (3),

The Proposed Algorithm
The framework of the new system is shown in Figure 7. The two prime and inevitable cipher design principles of confusion and diffusion are realized in this approach through the inclusion of substitution and permutation operations. The key generation, enciphering and deciphering processes are explained here.

Key Generation
The initial configurations for cellular automata, the starting position for zigzag scanning, the starting values for the logistic map, and the 512bit hash are the keys of this system. To withstand plaintext-based threats, the keys are computed from the input images and obtained as follows: Step 1: Obtain the 512-bit hash by applying the SHA-512algorithm on the input images.
Step 2: Compute the initial configuration. The two initial configuration vectors,{R 0 P and C 0 P }, for Rule-30 are calculated from the 512-bit hash as follows. Case 1: If the length of configuration (L) is 1≤ L ≤512, select L bits from the rear end of the 512-bit hash in reverse order. Case 2: If the length of configuration (L) is ≤1024, select the first 512 bits from the rear end of the 512-bit hash in reverse order and the remaining bits from the front end in the forward order.
Step 3: Find the starting position of the zigzag scanning pattern.
The 512-bit hash of the input image is grouped where w is the dimension of the image.
Step 4: Compute the starting values of the 2D logistic map.
In the 2D logistic map, the two initial values (x 1 , y 1 ) used are computed using Equation (4),

The Proposed Algorithm
The framework of the new system is shown in Figure 7. The two prime and inevitable cipher design principles of confusion and diffusion are realized in this approach through the inclusion of substitution and permutation operations. The key generation, enciphering and deciphering processes are explained here.

Key Generation
The initial configurations for cellular automata, the starting position for zigzag scanning, the starting values for the logistic map, and the 512bit hash are the keys of this system. To withstand plaintext-based threats, the keys are computed from the input images and obtained as follows: Step 1: Obtain the 512-bit hash by applying the SHA-512algorithm on the input images.
Step 2: Compute the initial configuration. The two initial configuration vectors,{R 0 P and C 0 P }, for Rule-30 are calculated from the 512-bit hash as follows. Case 1: If the length of configuration (L) is 1≤ L ≤512, select L bits from the rear end of the 512-bit hash in reverse order. Case 2: If the length of configuration (L) is ≤1024, select the first 512 bits from the rear end of the 512-bit hash in reverse order and the remaining bits from the front end in the forward order.
Step 3: Find the starting position of the zigzag scanning pattern.
The 512-bit hash of the input image is grouped . (4) where (x s , y s ) are the starting seeds. Figure 8 shows the flowchart of the proposed multiple color image encryption process. The process of transforming h plain images into h encrypted images consists of the following steps.

Encryption Algorithm
Step 1: Combine all the h input images to create one large image (I).
Step 2: Create pure-image elements by segmenting the large image.
Step 3: Generate the mixed-image elements. A per-

Figure7
Block diagram of the proposed technique

The Proposed Algorithm
The framework of the new system is shown in Figure 7. The two prime and inevitable cipher design principles of confusion and diffusion are realized in this approach through the inclusion of substitution and permutation operations. The key hash in reverse order. Case 2: If the length of configuration (L) is ≤1024, select the first 512 bits from the rear end of the 512-bit hash in reverse order and the remaining bits from the front end in the forward order.
Step Generation al configurations for cellular automata, ing position for zigzag scanning, the alues for the logistic map, and the 512re the keys of this system. To withstand based threats, the keys are computed input images and obtained as follows: Obtain the 512-bit hash by applying the algorithm on the input images. ompute the initial configuration. initial configuration vectors,{R 0 P and C 0 P }, 30 are calculated from the 512-bit hash s. If the length of configuration (L) is 1≤ L ect L bits from the rear end of the 512-bit hash in reverse order. Case 2: If the length of configuration (L) is ≤1024, select the first 512 bits from the rear end of the 512-bit hash in reverse order and the remaining bits from the front end in the forward order.
Step 3: Find the starting position of the zigzag scanning pattern.
The 512-bit hash of the input image is grouped into 8-bit segments and transformed to 64-decimal numbers, d1, d2, d3, …., d64. The starting position (p0, q0) of the zigzag scanning pattern is computed using Equation (3), where w is the dimension of the image.
Step 4: Compute the starting values of the 2D logistic map.
In the 2D logistic map, the two initial values (x1, y1) used are computed using Equation (4), where (xs, ys) are the starting seeds. Generation l configurations for cellular automata, ng position for zigzag scanning, the alues for the logistic map, and the 512re the keys of this system. To withstand ased threats, the keys are computed nput images and obtained as follows: Obtain the 512-bit hash by applying the algorithm on the input images. ompute the initial configuration. nitial configuration vectors,{R 0 P and C 0 P }, 0 are calculated from the 512-bit hash . f the length of configuration (L) is 1≤ L ct L bits from the rear end of the 512-bit hash in reverse order. Case 2: If the length of configuration (L) is ≤1024, select the first 512 bits from the rear end of the 512-bit hash in reverse order and the remaining bits from the front end in the forward order.
Step 3: Find the starting position of the zigzag scanning pattern.
The 512-bit hash of the input image is grouped into 8-bit segments and transformed to 64-decimal numbers, d1, d2, d3, …., d64. The starting position (p0, q0) of the zigzag scanning pattern is computed using Equation (3), where w is the dimension of the image.
Step 4: Compute the starting values of the 2D logistic map.
In the 2D logistic map, the two initial values (x1, y1) used are computed using Equation (4), where (xs, ys) are the starting seeds. eneration configurations for cellular automata, g position for zigzag scanning, the lues for the logistic map, and the 512e the keys of this system. To withstand ased threats, the keys are computed put images and obtained as follows: btain the 512-bit hash by applying the lgorithm on the input images. mpute the initial configuration. itial configuration vectors,{R 0 P and C 0 P }, 0 are calculated from the 512-bit hash the length of configuration (L) is 1≤ L t L bits from the rear end of the 512-bit hash in reverse order. Case 2: If the length of configuration (L) is ≤1024, select the first 512 bits from the rear end of the 512-bit hash in reverse order and the remaining bits from the front end in the forward order.
Step 3: Find the starting position of the zigzag scanning pattern.
The 512-bit hash of the input image is grouped into 8-bit segments and transformed to 64-decimal numbers, d1, d2, d3, …., d64. The starting position (p0, q0) of the zigzag scanning pattern is computed using Equation (3), where w is the dimension of the image.
Step 4: Compute the starting values of the 2D logistic map.
In the 2D logistic map, the two initial values (x1, y1) used are computed using Equation (4), where (xs, ys) are the starting seeds. eneration configurations for cellular automata, g position for zigzag scanning, the lues for the logistic map, and the 512e the keys of this system. To withstand ased threats, the keys are computed put images and obtained as follows: btain the 512-bit hash by applying the lgorithm on the input images. mpute the initial configuration. itial configuration vectors,{R 0 P and C 0 P }, 0 are calculated from the 512-bit hash the length of configuration (L) is 1≤ L t L bits from the rear end of the 512-bit hash in reverse order. Case 2: If the length of configuration (L) is ≤1024, select the first 512 bits from the rear end of the 512-bit hash in reverse order and the remaining bits from the front end in the forward order.
Step 3: Find the starting position of the zigzag scanning pattern.
The 512-bit hash of the input image is grouped into 8-bit segments and transformed to 64-decimal numbers, d1, d2, d3, …., d64. The starting position (p0, q0) of the zigzag scanning pattern is computed using Equation (3), where w is the dimension of the image.
Step 4: Compute the starting values of the 2D logistic map.
In the 2D logistic map, the two initial values (x1, y1) used are computed using Equation (4), where (xs, ys) are the starting seeds. Step 1: Combine all the h input images to create one large image (I).
Step 2: Create pure-image elements by segmenting the large image.
Step 3: Generate the mixed-image elements. A permutation operation is employed on the pureimage elements to create mixed-image elements. In this work, a two-stage permutation operation is performed. The first stage of the permutation operation, based on Rule-30 of the elementary cellular automata, is as follows. The permutation is performed on both rows and columns. The two different initial configuration vectors {R 0 P and C 0 P } of the circular boundary ECA are obtained as presented in the key generation phase. In accordance with Rule-30, the initial configuration vectors , R 0 P and C 0, P may selfevolve and can acquire two evolved configurations, R i P = { R 0 P , R 1 P , .. R e P … , R m P } and C i P = { C 0 P , C 1 P , .. C e P … , C n P }, where e is the e th round configuration, and m and n denote the dimensions of the big-image matrix,(I).The R P sequence is used for row permutation and the C P sequence for column permutation. Figure 9 gives an example. (6

Row
Step 4: Transform the big image matrix into a one-dimensional vector with zigzag scanning.
Step 5: Perform the k-bit left circular shif operation on each pixel value.
Step 6: Do the bitwise exclusive-or operation. A pixel-level substitution based on the logistic map is performed in the proposed method, in which a new value is set for each pixel, a follows. The 2D logistic map (1) is iterated to obtain random sequences that are preprocessed in Equation (7) before being used. The simple exclusive-or operation is used in the pixe substitution process, as defined in Equation (8), Where I = 1, 2, ..., L (L is sequence length) Where (R, G& B) are color components.

= {
Step 1: Combine all the h input images to create one large image (I).
Step 2: Create pure-image elements by segmenting the large image.
Step 3: Generate the mixed-image elements. A permutation operation is employed on the pureimage elements to create mixed-image elements.
In this work, a two-stage permutation operation is performed. The first stage of the permutation operation, based on Rule-30 of the elementary cellular automata, is as follows. The permutation is performed on both rows and columns. The two different initial configuration vectors {R 0 P and C 0 P } of the circular boundary ECA are obtained as presented in the key generation phase. In accordance with Rule-30, the initial configuration vectors , R 0 P and C 0, P may selfevolve and can acquire two evolved configurations, R i P = { R 0 P , R 1 P , .. R e P … , R m P } and C i P = { C 0 P , C 1 P , .. C e P … , C n P }, where e is the e th round configuration, and m and n denote the dimensions of the big-image matrix,(I).The R P sequence is used for row permutation and the C P sequence for column permutation. Figure 9 gives an example.
Row Permutation (RP): Case 1: If R e P (i)== R e−1 P (i), every value of the i th row of the image matrix Ie-1 is left, circularly shifted s1 times.
value of the j th column of the image matrix Ie-1 is upward, circularly shifted s5 times. Case 3: If C e P (j)== 1 and C e−1 P (j) == 0, every value of the j th column of the image matrix Ie-1 is downward, circularly shifted s3 times.
Step 5: Perform the k-bit left circular shift operation on each pixel value.
Step 6: Do the bitwise exclusive-or operation. A pixel-level substitution based on the logistic map is performed in the proposed method, in which a new value is set for each pixel, as follows. The 2D logistic map (1) is iterated to obtain random sequences that are preprocessed in Equation (7) before being used. The simple exclusive-or operation is used in the pixel substitution process, as defined in Equation (8), Where I = 1, 2, ..., L (L is sequence length) Where (R, G& B) are color components.
Step 1: Combine all the h input images to create one large image (I).
Step 2: Create pure-image elements by segmenting the large image.
Step 3: Generate the mixed-image elements. A permutation operation is employed on the pureimage elements to create mixed-image elements.
In this work, a two-stage permutation operation is performed. The first stage of the permutation operation, based on Rule-30 of the elementary cellular automata, is as follows. The permutation is performed on both rows and columns. The two different initial configuration vectors {R 0 P and C 0 P } of the circular boundary ECA are obtained as presented in the key generation phase. In accordance with Rule-30, the initial configuration vectors , R 0 P and C 0, P may selfevolve and can acquire two evolved configurations, R i P = { R 0 P , R 1 P , .. R e P … , R m P } and C i P = { C 0 P , C 1 P , .. C e P … , C n P }, where e is the e th round configuration, and m and n denote the dimensions of the big-image matrix,(I).The R P sequence is used for row permutation and the C P sequence for column permutation. Figure 9 gives an example.

Row
Step 4: Transform the big image matrix into a one-dimensional vector with zigzag scanning.
Step 5: Perform the k-bit left circular shift operation on each pixel value.
Step 6: Do the bitwise exclusive-or operation. A pixel-level substitution based on the logistic map is performed in the proposed method, in which a new value is set for each pixel, as follows. The 2D logistic map (1) is iterated to obtain random sequences that are preprocessed in Equation (7) before being used. The simple exclusive-or operation is used in the pixel substitution process, as defined in Equation (8), Where I = 1, 2, ..., L (L is sequence length) Where (R, G& B) are color components.
Step 7: Segment the big image into h encrypted … , Step 1: Combine all the h input images to create one large image (I).
Step 2: Create pure-image elements by segmenting the large image.
Step 3: Generate the mixed-image elements. A permutation operation is employed on the pureimage elements to create mixed-image elements. In this work, a two-stage permutation operation is performed. The first stage of the permutation operation, based on Rule-30 of the elementary cellular automata, is as follows. The permutation is performed on both rows and columns. The two different initial configuration vectors {R 0 P and C 0 P } of the circular boundary ECA are obtained as presented in the key generation phase. In accordance with Rule-30, the initial configuration vectors , R 0 P and C 0, P may selfevolve and can acquire two evolved configurations, R i P = { R 0 P , R 1 P , .. R e P … , R m P } and C i P = { C 0 P , C 1 P , .. C e P … , C n P }, where e is the e th round configuration, and m and n denote the dimensions of the big-image matrix,(I).The R P sequence is used for row permutation and the C P sequence for column permutation. Figure 9 gives an example.

Row
Step 4: Transform the big image matrix into a one-dimensional vector with zigzag scanning.
Step 5: Perform the k-bit left circular shift operation on each pixel value.
Step 6: Do the bitwise exclusive-or operation. A pixel-level substitution based on the logistic map is performed in the proposed method, in which a new value is set for each pixel, as follows. The 2D logistic map (1) is iterated to obtain random sequences that are preprocessed in Equation (7) before being used. The simple exclusive-or operation is used in the pixel substitution process, as defined in Equation (8), � X s = x i × 10 14 mod 256 Y s = y i × 10 14 mod 256 . Z s = X s ⊕ Y s Where I = 1, 2, ..., L (L is sequence length) Where (R, G& B) are color components.

} and
Step 1: Combine all the h input images to create one large image (I).
Step 2: Create pure-image elements by segmenting the large image.
Step 3: Generate the mixed-image elements. A permutation operation is employed on the pureimage elements to create mixed-image elements. In this work, a two-stage permutation operation is performed. The first stage of the permutation operation, based on Rule-30 of the elementary cellular automata, is as follows. The permutation is performed on both rows and columns. The two different initial configuration vectors {R 0 P and C 0 P } of the circular boundary ECA are obtained as presented in the key generation phase. In accordance with Rule-30, the initial configuration vectors , R 0 P and C 0, P may selfevolve and can acquire two evolved configurations, R i P = { R 0 P , R 1 P , .. R e P … , R m P } and C i P = { C 0 P , C 1 P , .. C e P … , C n P }, where e is the e th round configuration, and m and n denote the dimensions of the big-image matrix,(I).The R P sequence is used for row permutation and the C P sequence for column permutation. Figure 9 gives an example.

Row Permutation (RP):
Case 1: If R e P (i)== R e−1 P (i), every value of the i th row of the image matrix Ie-1 is left, circularly shifted s1 times.
value of the j th column of the image matrix Ie-1 is upward, circularly shifted s5 times. Case 3: If C e P (j)== 1 and C e−1 P (j) == 0, every value of the j th column of the image matrix Ie-1 is downward, circularly shifted s3 times.
Step 5: Perform the k-bit left circular shift operation on each pixel value.
Step 6: Do the bitwise exclusive-or operation. A pixel-level substitution based on the logistic map is performed in the proposed method, in which a new value is set for each pixel, as follows. The 2D logistic map (1) is iterated to obtain random sequences that are preprocessed in Equation (7) before being used. The simple exclusive-or operation is used in the pixel substitution process, as defined in Equation (8), � X s = x i × 10 14 mod 256 Y s = y i × 10 14 mod 256 . Z s = X s ⊕ Y s Where I = 1, 2, ..., L (L is sequence length) Where (R, G& B) are color components.

= {
Step 1: Combine all the h input images to create one large image (I).
Step 2: Create pure-image elements by segmenting the large image.
Step 3: Generate the mixed-image elements. A permutation operation is employed on the pureimage elements to create mixed-image elements. In this work, a two-stage permutation operation is performed. The first stage of the permutation operation, based on Rule-30 of the elementary cellular automata, is as follows. The permutation is performed on both rows and columns. The two different initial configuration vectors {R 0 P and C 0 P } of the circular boundary ECA are obtained as presented in the key generation phase. In accordance with Rule-30, the initial configuration vectors , R 0 P and C 0, P may selfevolve and can acquire two evolved configurations, R i P = { R 0 P , R 1 P , .. R e P … , R m P } and C i P = { C 0 P , C 1 P , .. C e P … , C n P }, where e is the e th round configuration, and m and n denote the dimensions of the big-image matrix,(I).The R P sequence is used for row permutation and the C P sequence for column permutation. Figure 9 gives an example. (6)

Row
Step 4: Transform the big image matrix into a one-dimensional vector with zigzag scanning.
Step 5: Perform the k-bit left circular shift operation on each pixel value.
Step 6: Do the bitwise exclusive-or operation. A pixel-level substitution based on the logistic map is performed in the proposed method, in which a new value is set for each pixel, as follows. The 2D logistic map (1) is iterated to obtain random sequences that are preprocessed in Equation (7) before being used. The simple exclusive-or operation is used in the pixel substitution process, as defined in Equation (8), � X s = x i × 10 14 mod 256 Y s = y i × 10 14 mod 256 . Z s = X s ⊕ Y s Where I = 1, 2, ..., L (L is sequence length) Where (R, G& B) are color components.
Step 1: Combine all the h input images to create one large image (I).
Step 2: Create pure-image elements by segmenting the large image.
Step 3: Generate the mixed-image elements. A permutation operation is employed on the pureimage elements to create mixed-image elements. In this work, a two-stage permutation operation is performed. The first stage of the permutation operation, based on Rule-30 of the elementary cellular automata, is as follows. The permutation is performed on both rows and columns. The two different initial configuration vectors {R 0 P and C 0 P } of the circular boundary ECA are obtained as presented in the key generation phase. In accordance with Rule-30, the initial configuration vectors , R 0 P and C 0, P may selfevolve and can acquire two evolved configurations, R i P = { R 0 P , R 1 P , .. R e P … , R m P } and C i P = { C 0 P , C 1 P , .. C e P … , C n P }, where e is the e th round configuration, and m and n denote the dimensions of the big-image matrix,(I).The R P sequence is used for row permutation and the C P sequence for column permutation. Figure 9 gives an example. (6)

Row
Step 4: Transform the big image matrix into a one-dimensional vector with zigzag scanning.
Step 5: Perform the k-bit left circular shift operation on each pixel value.
Step 6: Do the bitwise exclusive-or operation. A pixel-level substitution based on the logistic map is performed in the proposed method, in which a new value is set for each pixel, as follows. The 2D logistic map (1) is iterated to obtain random sequences that are preprocessed in Equation (7) before being used. The simple exclusive-or operation is used in the pixel substitution process, as defined in Equation (8), � X s = x i × 10 14 mod 256 Y s = y i × 10 14 mod 256 . Z s = X s ⊕ Y s Where I = 1, 2, ..., L (L is sequence length) Where (R, G& B) are color components.

… ,
Step 1: Combine all the h input images to create one large image (I).
Step 2: Create pure-image elements by segmenting the large image.
Step 3: Generate the mixed-image elements. A permutation operation is employed on the pureimage elements to create mixed-image elements. In this work, a two-stage permutation operation is performed. The first stage of the permutation operation, based on Rule-30 of the elementary cellular automata, is as follows. The permutation is performed on both rows and columns. The two different initial configuration vectors {R 0 P and C 0 P } of the circular boundary ECA are obtained as presented in the key generation phase. In accordance with Rule-30, the initial configuration vectors , R 0 P and C 0, P may selfevolve and can acquire two evolved configurations, R i P = { R 0 P , R 1 P , .. R e P … , R m P } and C i P = { C 0 P , C 1 P , .. C e P … , C n P }, where e is the e th round configuration, and m and n denote the dimensions of the big-image matrix,(I).The R P sequence is used for row permutation and the C P sequence for column permutation. Figure 9 gives an example. (6)

Row
Step 4: Transform the big image matrix into a one-dimensional vector with zigzag scanning.
Step 5: Perform the k-bit left circular shift operation on each pixel value.
Step 6: Do the bitwise exclusive-or operation. A pixel-level substitution based on the logistic map is performed in the proposed method, in which a new value is set for each pixel, as follows. The 2D logistic map (1) is iterated to obtain random sequences that are preprocessed in Equation (7) before being used. The simple exclusive-or operation is used in the pixel substitution process, as defined in Equation (8), � X s = x i × 10 14 mod 256 Y s = y i × 10 14 mod 256 . Z s = X s ⊕ Y s Where I = 1, 2, ..., L (L is sequence length) Where (R, G& B) are color components.
}, where e is the e th round configuration, and m and n denote the dimensions of the big-image matrix,(I).The R P sequence is used for row permutation and the C P sequence for column permutation. Figure 9 gives an example.

Row Permutation (RP):
Case 1: If and C i P = { C 0 P , C 1 P , .. C e P … , C n P }, where e is the e th round configuration, and m and n denote the dimensions of the big-image matrix,(I).The R P sequence is used for row permutation and the C P sequence for column permutation. Figure 9 gives an example.

Row Permutation (RP): Case 1:
If R e P (i)== R e−1 P (i), every value of the i th row of the image matrix Ie-1 is left, circularly shifted s1 times. Case 2: If R e P (i)== 0 and R e−1 P (i) == 1, every value of the i th row of the image matrix Ie-1 is left, circularly shifted s2 times. Case 3: If R e P (i)== 1 and R e−1 P (i) == 0, every value of the i th row of the image matrix Ie-1 is right, circularly shifted s3 times. s1, s2 and s3 are calculated using Equation (5): Step 7: images.

De
Multip multipl images which using t right c restore locatio zigzag using segmen

Figure 9
Permutation process based on CA == and C i P = { C 0 P , C 1 P , .. C e P … , C n P }, where e is the e th round configuration, and m and n denote the dimensions of the big-image matrix,(I).The R P sequence is used for row permutation and the C P sequence for column permutation. Figure 9 gives an example.

Row Permutation (RP): Case 1:
If R e P (i)== R e−1 P (i), every value of the i th row of the image matrix Ie-1 is left, circularly shifted s1 times. Case 2: If R e P (i)== 0 and R e−1 P (i) == 1, every value of the i th row of the image matrix Ie-1 is left, circularly shifted s2 times. Case 3: If R e P (i)== 1 and R e−1 P (i) == 0, every value of the i th row of the image matrix Ie-1 is right, circularly shifted s3 times. s1, s2 and s3 are calculated using Equation (5): Step 7: Se images.

Decry
Multiplemultiple-i images a which in using the right circ restore t location zigzag sc using CA segmente

Figure 9
Permutation process based on CA (i), every value of the i th row of the image matrix I e-1 is left, circularly shifted s 1 times.

Case 2:
If evolve and can acquire two evolved configurations, R i P = { R 0 P , R 1 P , .. R e P … , R m P } and C i P = { C 0 P , C 1 P , .. C e P … , C n P }, where e is the e th round configuration, and m and n denote the dimensions of the big-image matrix,(I).The R P sequence is used for row permutation and the C P sequence for column permutation. Figure 9 gives an example.

Row Permutation (RP):
Case 1: If R e P (i)== R e−1 P (i), every value of the i th row of the image matrix Ie-1 is left, circularly shifted s1 times. Case 2: If R e P (i)== 0 and R e−1 P (i) == 1, every value of the i th row of the image matrix Ie-1 is left, circularly shifted s2 times. Case 3: If R e P (i)== 1 and R e−1 P (i) == 0, every value of the i th row of the image matrix Ie-1 is right, circularly shifted s3 times. s1, s2 and s3 are calculated using Equation (5) Step 7: images.

De
Multip multip images which using t right c restore locatio zigzag using segmen

Figure 9
Permutation process based on CA == 0 and configuration vectors , R 0 and C 0, may selfevolve and can acquire two evolved configurations, R i P = { R 0 P , R 1 P , .. R e P … , R m P } and C i P = { C 0 P , C 1 P , .. C e P … , C n P }, where e is the e th round configuration, and m and n denote the dimensions of the big-image matrix,(I).The R P sequence is used for row permutation and the C P sequence for column permutation. Figure 9 gives an example.

Row Permutation (RP):
Case 1: If R e P (i)== R e−1 P (i), every value of the i th row of the image matrix Ie-1 is left, circularly shifted s1 times. Case 2: If R e P (i)== 0 and R e−1 P (i) == 1, every value of the i th row of the image matrix Ie-1 is left, circularly shifted s2 times. Case 3: If R e P (i)== 1 and R e−1 P (i) == 0, every value of the i th row of the image matrix Ie-1 is right, circularly shifted s3 times. s1, s2 and s3 are calculated using Equation (5) Step imag

3.3
Mu mu ima wh usi righ res loc zig usi seg

Figure 9
Permutation process based on CA (i) == 1, every value of the i th row of the image matrix I e-1 is left, circularly shifted s 2 times.

Case 3: If
phase. In accordance with Rule-30, the initial configuration vectors , R 0 P and C 0, P may selfevolve and can acquire two evolved configurations, R i P = { R 0 P , R 1 P , .. R e P … , R m P } and C i P = { C 0 P , C 1 P , .. C e P … , C n P }, where e is the e th round configuration, and m and n denote the dimensions of the big-image matrix,(I).The R P sequence is used for row permutation and the C P sequence for column permutation. Figure 9 gives an example.

Row
Step image

D
Mult mult imag whic using right resto locat zigza using segm obtained as presented in the key generation phase.
In accordance with Rule-30, the initial configuration vectors , R 0 P and C 0, P may selfevolve and can acquire two evolved configurations, R i P = { R 0 P , R 1 P , .. R e P … , R m P } and C i P = { C 0 P , C 1 P , .. C e P … , C n P }, where e is the e th round configuration, and m and n denote the dimensions of the big-image matrix,(I).The R P sequence is used for row permutation and the C P sequence for column permutation. Figure 9 gives an example. evolve and can acquire two evolved configurations, R i P = { R 0 P , R 1 P , .. R e P … , R m P } and C i P = { C 0 P , C 1 P , .. C e P … , C n P }, where e is the e th round configuration, and m and n denote the dimensions of the big-image matrix,(I).The R P sequence is used for row permutation and the C P sequence for column permutation. Figure 9 gives an example.

Row Permutation (RP): Case 1:
If R e P (i)== R e−1 P (i), every value of the i th row of the image matrix Ie-1 is left, circularly shifted s1 times. Case 2: If R e P (i)== 0 and R e−1 P (i) == 1, every value of the i th row of the image matrix Ie-1 is left, circularly shifted s2 times. Case 3: If R e P (i)== 1 and R e−1 P (i) == 0, every value of the i th row of the image matrix Ie-1 is right, circularly shifted s3 times. s1, s2 and s3 are calculated using Equation (5): Step 7: Seg images.

Decryp
Multiple-im multiple-im images ar which inv using the 2 right circu restore th location i zigzag sca using CA segmented . C e P … , C n P }, where e is the e th round configuration, and m and n denote the dimensions of the big-image matrix,(I).The R P sequence is used for row permutation and the C P sequence for column permutation. Figure 9 gives an example.

Row Permutation (RP): Case 1:
If R e P (i)== R e−1 P (i), every value of the i th row of the image matrix Ie-1 is left, circularly shifted s1 times. Case 2: If R e P (i)== 0 and R e−1 P (i) == 1, every value of the i th row of the image matrix Ie-1 is left, circularly shifted s2 times. Case 3: If R e P (i)== 1 and R e−1 P (i) == 0, every value of the i th row of the image matrix Ie-1 is right, circularly shifted s3 times. s1, s2 and s3 are calculated using Equation (5): Column Permutation (RP): Case 1: If C e P (j)== C e−1 P (j), every value of the j th column of the image matrix Ie-1 is upward, circularly shifted s4 times. Case 2: If C e P (j)== 0 and C e−1 P (j) == 1, every

De
Multip multip images which using right c restore locatio zigzag using segme

Figure 9
Permutation process based on CA == and C i P = { C 0 P , C 1 P , .. C e P … , C n P }, where e is the e th round configuration, and m and n denote the dimensions of the big-image matrix,(I).The R P sequence is used for row permutation and the C P sequence for column permutation. Figure 9 gives an example.

Row Permutation (RP): Case 1:
If R e P (i)== R e−1 P (i), every value of the i th row of the image matrix Ie-1 is left, circularly shifted s1 times. Case 2: If R e P (i)== 0 and R e−1 P (i) == 1, every value of the i th row of the image matrix Ie-1 is left, circularly shifted s2 times. Case 3: If R e P (i)== 1 and R e−1 P (i) == 0, every value of the i th row of the image matrix Ie-1 is right, circularly shifted s3 times. s1, s2 and s3 are calculated using Equation (5): Column Permutation (RP): Case 1: If C e P (j)== C e−1 P (j), every value of the j th column of the image matrix Ie-1 is upward, circularly shifted s4 times. Case 2: If C e P (j)== 0 and C e−1 P (j) == 1, every

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Figure 9
Permutation process based on CA ( j), every value of the j th column of the image matrix I e-1 is upward, circularly shifted s 4 times.

Case 2:
If configuration vectors , R 0 P and C 0, P may selfevolve and can acquire two evolved configurations, R i P = { R 0 P , R 1 P , .. R e P … , R m P } and C i P = { C 0 P , C 1 P , .. C e P … , C n P }, where e is the e th round configuration, and m and n denote the dimensions of the big-image matrix,(I).The R P sequence is used for row permutation and the C P sequence for column permutation. Figure 9 gives an example.

Row Permutation (RP):
Case 1: If R e P (i)== R e−1 P (i), every value of the i th row of the image matrix Ie-1 is left, circularly shifted s1 times. Case 2: If R e P (i)== 0 and R e−1 P (i) == 1, every value of the i th row of the image matrix Ie-1 is left, circularly shifted s2 times. Case 3: If R e P (i)== 1 and R e−1 P (i) == 0, every value of the i th row of the image matrix Ie-1 is right, circularly shifted s3 times. s1, s2 and s3 are calculated using Equation (5): (5) Column Permutation (RP): Case 1: If C e P (j)== C e−1 P (j), every value of the j th column of the image matrix Ie-1 is upward, circularly shifted s4 times. Case 2: If C e P (j)== 0 and C e−1 P (j) == 1, every

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Figure 9
Permutation process based on CA == 0 and configuration vectors , R 0 P and C 0, P may selfevolve and can acquire two evolved configurations, R i P = { R 0 P , R 1 P , .. R e P … , R m P } and C i P = { C 0 P , C 1 P , .. C e P … , C n P }, where e is the e th round configuration, and m and n denote the dimensions of the big-image matrix,(I).The R P sequence is used for row permutation and the C P sequence for column permutation. Figure 9 gives an example.

Row Permutation (RP):
Case 1: If R e P (i)== R e−1 P (i), every value of the i th row of the image matrix Ie-1 is left, circularly shifted s1 times. Case 2: If R e P (i)== 0 and R e−1 P (i) == 1, every value of the i th row of the image matrix Ie-1 is left, circularly shifted s2 times. Case 3: If R e P (i)== 1 and R e−1 P (i) == 0, every value of the i th row of the image matrix Ie-1 is right, circularly shifted s3 times. s1, s2 and s3 are calculated using Equation (5): Permutation process based on CA ( j) == 1, every value of the j th column of the image matrix I e-1 is upward, circularly shifted s 5 times.

Case 3: If
{R 0 P and C 0 P } of the circular boundary ECA are obtained as presented in the key generation phase. In accordance with Rule-30, the initial configuration vectors , R 0 P and C 0, P may selfevolve and can acquire two evolved configurations, R i P = { R 0 P , R 1 P , .. R e P … , R m P } and C i P = { C 0 P , C 1 P , .. C e P … , C n P }, where e is the e th round configuration, and m and n denote the dimensions of the big-image matrix,(I).The R P sequence is used for row permutation and the C P sequence for column permutation. Figure 9 gives an example.

Row Permutation (RP):
Case 1: If R e P (i)== R e−1 P (i), every value of the i th row of the image matrix Ie-1 is left, circularly shifted s1 times. Case 2: If R e P (i)== 0 and R e−1 P (i) == 1, every value of the i th row of the image matrix Ie-1 is left, circularly shifted s2 times. Case 3: If R e P (i)== 1 and R e−1 P (i) == 0, every value of the i th row of the image matrix Ie-1 is right, circularly shifted s3 times. s1, s2 and s3 are calculated using Equation (5): Column Permutation (RP): Case 1: If C e P (j)== C e−1 P (j), every value of the j th column of the image matrix Ie-1 is upward, circularly shifted s4 times. Case 2: If C e P (j)== 0 and C e−1 P (j) == 1, every

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Figure 9
Permutation process based on CA

== 1 and
{R 0 and C 0 } of the circular boundary ECA are obtained as presented in the key generation phase.
In accordance with Rule-30, the initial configuration vectors , R 0 P and C 0, P may selfevolve and can acquire two evolved configurations, R i P = { R 0 P , R 1 P , .. R e P … , R m P } and C i P = { C 0 P , C 1 P , .. C e P … , C n P }, where e is the e th round configuration, and m and n denote the dimensions of the big-image matrix,(I).The R P sequence is used for row permutation and the C P sequence for column permutation. Figure 9 gives an example.

Row Permutation (RP):
Case 1: If R e P (i)== R e−1 P (i), every value of the i th row of the image matrix Ie-1 is left, circularly shifted s1 times. Case 2: If R e P (i)== 0 and R e−1 P (i) == 1, every value of the i th row of the image matrix Ie-1 is left, circularly shifted s2 times. Case 3: If R e P (i)== 1 and R e−1 P (i) == 0, every value of the i th row of the image matrix Ie-1 is right, circularly shifted s3 times. s1, s2 and s3 are calculated using Equation (5): Permutation process based on CA ( j) == 0, every value of the j th column of the image matrix I e-1 is downward, circularly shifted s 3 times. s 4 , s 5 and s 6 are calculated using Equation (6): Step 1: Combine all the h input images to create one large image (I).
Step 2: Create pure-image elements by segmenting the large image.
Step 3: Generate the mixed-image elements. A permutation operation is employed on the pureimage elements to create mixed-image elements. In this work, a two-stage permutation operation is performed. The first stage of the permutation operation, based on Rule-30 of the elementary cellular automata, is as follows. The permutation is performed on both rows and columns. The two different initial configuration vectors {R 0 P and C 0 P } of the circular boundary ECA are obtained as presented in the key generation phase. In accordance with Rule-30, the initial configuration vectors , R 0 P and C 0, P may selfevolve and can acquire two evolved configurations, R i P = { R 0 P , R 1 P , .. R e P … , R m P } and C i P = { C 0 P , C 1 P , .. C e P … , C n P }, where e is the e th round configuration, and m and n denote the dimensions of the big-image matrix,(I).The R P sequence is used for row permutation and the C P sequence for column permutation. Figure 9 gives an example.

Row Permutation (RP):
Case 1: If R e P (i)== R e−1 P (i), every value of the i th row of the image matrix Ie-1 is left, circularly shifted s1 times. Case 2: If R e P (i)== 0 and R e−1 P (i) == 1, every value of the i th row of the image matrix Ie-1 is left, circularly shifted s2 times. Case 3: If R e P (i)== 1 and R e−1 P (i) == 0, every th value of the j th column of the image matrix Ie-1 is upward, circularly shifted s5 times. Case 3: If C e P (j)== 1 and C e−1 P (j) == 0, every value of the j th column of the image matrix Ie-1 is downward, circularly shifted s3 times. s and s6 are calculated using � s 4 = mod(j × 250, n) s 5 = mod(j × 250, n) + 2 s 6 = mod(j × 250, n) + 2 .

Decryption Algorithm
Step 4: Transform the big image matrix into a one-dimensional vector with zigzag scanning.
Step 5: Perform the k-bit left circular shift operation on each pixel value.
Step 6: Do the bitwise exclusive-or operation. A pixel-level substitution based on the logistic map is performed in the proposed method, in which a new value is set for each pixel, as follows. The 2D logistic map (1) is iterated to obtain random sequences that are preprocessed in Equation (7) before being used. The simple exclusive-or operation is used in the pixel substitution process, as defined in Equation (8), Step 1: Combine all the h input images to create one large image (I).
Step 2: Create pure-image elements by segmenting the large image.
Step 3: Generate the mixed-image elements. A permutation operation is employed on the pureimage elements to create mixed-image elements. In this work, a two-stage permutation operation is performed. The first stage of the permutation operation, based on Rule-30 of the elementary cellular automata, is as follows. The permutation is performed on both rows and columns. The two different initial configuration vectors {R 0 P and C 0 P } of the circular boundary ECA are obtained as presented in the key generation phase. In accordance with Rule-30, the initial configuration vectors , R 0 P and C 0, P may selfevolve and can acquire two evolved configurations, R i P = { R 0 P , R 1 P , .. R e P … , R m P } and C i P = { C 0 P , C 1 P , .. C e P … , C n P }, where e is the e th round configuration, and m and n denote the dimensions of the big-image matrix,(I).The R P sequence is used for row permutation and the C P sequence for column permutation. Figure 9 gives an example.

Decryption Algorithm
Multiple-image decryption is the inverse of multiple-image encryption. The h enciphered images are combined into a big image, after which inverse pixel substitution is performed using the 2D logistic map, followed by the k-bit right circular shift operation on each pixel to restore the original pixel values. The pixel location is restored by carrying out inverse zigzag scanning and inverse pixel permutation using CA Rule-30. Finally, the big image is segmented to produce the h plain images.
Where (R, G& B) are color components.
Step 7: Segment the big image into h encrypted images.

Decryption Algorithm
Multiple-image decryption is the inverse of multiple-image encryption. The h enciphered images are combined into a big image, after which inverse pixel substitution is performed using the 2D logistic map, followed by the k-bit right circular shift operation on each pixel to restore the original pixel values. The pixel location is restored by carrying out inverse zig-

Figure 9
Permutation process based on CA

Experimental Setup
In all our experiments, we have used the MATLAB R2014a, Windows 7 software platform, the Intel Corei5-2.50GHz processor hardware platform and sixteen well-known RGB color images with pixels sized 128×128 were used. The parameters and initial seeds used for the logistic map were 1 =2.98, 2 =3.30, 1 =0.18,

Figure 10
Input images   Big image

Input Sensitivity Test
The input image sensitivity test is used to assess the effectiveness of the cipher against chosen plain-image and known plain-image attacks [14]. In these attacks, the attackers compare two encrypted images to learn the relationship patterns between plain and cipher images. Such attacks are also referred to as differential attacks. The two well-known quantitative metrics, NPCR and UACI that are utilized to calculate the sensitivity of the cipher are defined in Equations (9 & 10) [35],

Input Sensitivity Test
The input image sensitivity test is used to assess the effectiveness of the cipher against chosen plain-image and known plain-image attacks [14]. In these attacks, the attackers compare two encrypted images to learn the relationship patterns between plain and cipher images. Such attacks are also referred to as differential attacks.
The two well-known quantitative metrics, NPCR and UACI that are utilized to calculate the sensitivity of the cipher are defined in Equations (9 & 10) [35], where C 1 and C 2 are the encrypted images of the plain images,P 1 and P 2 with P 1 and P 2 differing in exactly one pixel The obtained NPCR and UACI values are displayed in Table 1.

Key Space Analysis
The security strength of a cipher chiefly relies on the this sca 2D sec our 2 622 key big

5.3
Sen goo dec out the sen is e and mad tho and key that mo rela

Input Sensitivity Test
The input image sensitivity test is used to assess the effectiveness of the cipher against chosen plain-image and known plain-image attacks [14]. In these attacks, the attackers compare two encrypted images to learn the relationship patterns between plain and cipher images. Such attacks are also referred to as differential attacks.
The two well-known quantitative metrics, NPCR and UACI that are utilized to calculate the sensitivity of the cipher are defined in Equations (9 & 10) [35], where C 1 and C 2 are the encrypted images of the plain images,P 1 and P 2 with P 1 and P 2 differing in exactly one pixel The obtained NPCR and UACI values are displayed in Table 1.

Key Space Analysis
The security strength of a cipher chiefly relies on the this sca 2D sec our 2 62 key big

5.3
Sen goo dec out the sen is and ma tho and key tha mo rel   where C 1 and C 2 are the encrypted images of the plain images, P 1 and P 2 with P 1 and P 2 differing in exactly one pixel The obtained NPCR and UACI values are displayed in Table 1.

Key Space Analysis
The security strength of a cipher chiefly relies on the keys, which demand a large key space [3]. In this system, the starting position for zigzag scanning, starting values (real numbers) for the 2D logistic map and 512bit hash constitute the secret key. Since the precision is set to 10 14 in our experiment, the key space is approximately 2 622 . Hence our proposed approach offers larger key space than schemes reported in [29,30]. A bigger space repels all key-based attacks.

Key Sensitivity Analysis
Sensitivity to keys is an excellent property of a good cipher, causing the encryption and decryption processes to produce entirely different output images when minor changes are made in the keys [33]. In our experiment, the key sensitivity is tested as follows.

Figure 13
Key sensitivity analysis the unmodified and modified keys. The results displayed in Figure 13 show that the decrypted image with the slightly modified key is absolutely unintelligible, with no relation to the original images.

Histogram Analysis
A histogram specifies the frequency occurrences of color values in an image [6]. Typically, since the histograms of plain images are different, the attacker exploits this statistical feature to compromise the cipher. To prevent such a threat, the statistical features of plain images must be destroyed by the cipher during encryption. The histograms of the 16 plain, encrypted and decrypted images are shown in Figure 14.  [6]. Typically, since istograms of plain images are different, the ker exploits this statistical feature to romise the cipher. To prevent such a threat, tatistical features of plain images must be oyed by the cipher during encryption. The grams of the 16 plain, encrypted and decrypted images are shown in Figure 14.

Correlation Analysis
Correlation analysis measures the similarity association between neighbor pixel values [16]. Given that all natural plain images have a strong correlation, it is required that the encryption method assures a weak correlation in the encrypted images. To calculate the correlation in our work, 3000 pixel pairs were selected randomly in diagonal, vertical and horizontal directions, and the correlation measured using Equation (11): The correlation test results are listed in

Correlation Analysis
Correlation analysis measures the similarity association between neighbor pixel values [16]. Given that all natural plain images have a strong correlation, it is required that the encryption method assures a weak correlation in the encrypted images. To calculate the correlation in our work, 3000 pixel pairs were selected randomly in diagonal, vertical and horizontal directions, and the correlation measured using Equation (11): The correlation test results are listed in

Correlation Analysis
Correlation analysis measures the similarity association between neighbor pixel values [16]. Given that all natural plain images have a strong correlation, it is required that the encryption method assures a weak correlation in the encrypted images. To calculate the correlation in our work, 3000 pixel pairs were selected randomly in diagonal, vertical and horizontal directions, and the correlation measured using Equation (11): The correlation test results are listed in Table 2 (where V is vertical, H is horizontal and D is

Correlation Analysis
Correlation analysis measures the similarity association between neighbor pixel values [16]. Given that all natural plain images have a strong correlation, it is required that the encryption method assures a weak correlation in the encrypted images. To calculate the correlation in our work, 3000 pixel pairs were selected randomly in diagonal, vertical and horizontal directions, and the correlation measured using Equation (11): our work, 3000 pixel pairs were selected randomly in diagonal, vertical and horizontal directions, and the correlation measured using Equation (11): The correlation test results are listed in Table 2 (where V is vertical, H is horizontal and D is (11) The correlation test results are listed in Table 2 (where V is vertical, H is horizontal and D is diagonal), and the correlation of input image1 and the corresponding encrypted image1is plotted in Figure 15. It is observed from the outcomes that the regular rel-evance between neighbor pixels is destroyed in the cipher image.
The encrypted image histograms are uniformely distributed (equal probability). Therefore, the proposed system withstands statistical attacks well.

Information Entropy (IE)
The metric, entropy, quantifies the randomness in the pixel value distribution of digital images. The standard entropy value for a true random image is 8 [3]. IE is calculated using Equation (12)

Information Entropy (IE)
The metric, entropy, quantifies the randomness in the pixel value distribution of digital images. The standard entropy value for a true random image is 8 [3]. IE is calculated using Equation (12), where p(sa) represents the emergence probability corresponding to sa. Table 3 shows the entropy test results which indicate that this method has produced random images.

PSNR
The PSN judges t Mathemat (13) [14], = wherein M The obtai Table 3. F quality o process is Table 3 Experimental results of information entropy and PSNR Information Entropy (12) where p(s a ) represents the emergence probability corresponding to s a . Table 3 shows the entropy test results which indicate that this method has produced random images.

Figure 15
Correlation coefficient of test image 8 before and after encryption diagonal), and the correlation of input image1 and the corresponding encrypted image1is plotted in Figure 15. It is observed from the outcomes that the regular relevance between neighbor pixels is destroyed in the cipher image.
The encrypted image histograms are uniformely distributed (equal probability). Therefore, the proposed system withstands statistical attacks well.

Figure 15
Correlation coefficient of test image 8 before and after encryption  Table 3 Experimental results of information entropy and PSNR Input Image Information Entropy PSNR

PSNR Analysis
The PSNR is an image quality index which judges the quality of deciphered images. Mathematically, it is calculated using Equation (13)

PSNR Analysis
The PSNR is an image quality index which judges the quality of deciphered images. Mathematically, it is calculated using Equation (13) [14], = 10 10 ( 255 ), wherein MSE represents the mean square error. The obtained PSNR test outcome is displayed in Table 3. From the results, it is concluded that the quality of images produced by the decryption process is good.

R
wherein MSE represents the mean square error. The obtained PSNR test outcome is displayed in Table 3.
From the results, it is concluded that the quality of images produced by the decryption process is good.

Time complexity analysis
The encryption time is analyzed to estimate the computation cost. To reduce the time consumption, we have used faster exclusive-or, integer addition and modulus operation in our proposed scheme. The encryption time is presented in Table 4. As can be seen in Table 4, the non-time consuming operations effectively accelerate the encryption process. The encryption speed is faster than references [13,15,39]. Therefore, this scheme can be used in real-time internet applications

NIST Statistical Test Analysis
NIST statistical test is a very important tool to assess the various aspects of randomness in a bit sequence [9]. The diversity of randomness in encrypted images was tested using NIST suite SP 800-22. This suite has 15 statistical tests. The randomness of a bit sequence is determined by p-value. The significant-level α = 0.02 is set to obtain p-value from 15 tests. Table  5 shows the statistical results of an encrypted image. The results proved that the proposed scheme has passed all the fifteen tests. Hence, the generated sequence is truly random.

Discussion
The performance test results produced by the proposed technique is analyzed and compared here with three peer image ciphers based on performance metrics like the correlation coefficient, NPCR, PSNR, UACI and information entropy. Figure 12 depicts flat cipher image histograms, which means that the pixel values appear with equal probability. The total secret key space in this technique is approximately 2 622 , which is remarkably high, and helps resist keybased attacks like brute force attacks. It is obvious from Figure 11 that the input image-based keys used in the proposed technique are so highly sensitive that even a small change in the keys produces a totally new decrypted image. From the numerical results listed in Table 2 and Figure 13, it is observed that the double permutation nature of the proposed technique excellently minimizes the correlation association among neighbor pixels, when compared to the other two techniques. The plain image sensitivity tests conducted, with the results presented in Table 1, show that the UACI and NPCR values obtained using the proposed method are optimal and counter differential attacks better than the other two methods. The PSNR image quality metric test results displayed in Table 3 show that the decrypted image quality is good, compared to that offered by the two peer schemes. The double substitution process yields the best entropy values for all the encrypted images. Overall, it is concluded that the proposed technique performs well in all tests.

Conclusion
A symmetric multiple color image encryption technique has been proposed that includes cellular automata, zigzag scanning, circular shifts, chaos and mixed-image content. This algorithm achieves twostage encryption by adopting a dual permutation and dual substitution structure. The experimental outcomes and a comparison of the findings show that the dual permutation operation significantly minimizes the correlation association between neighbor pixels. The dual substitution helps produce the true random cipher image, thereby strengthening security. The combination of cellular automata and chaos increases the key space of the system. Moreover, the input image-based key generation method offers key sensitivity much-needed strong security. Finally, it is concluded that the proposed technique can be used in several areas to secure multiple color images simultaneously.