1 Introduction

The rapid outbreak of Internet of Things (IoT) is one of the astounding technologies that has made a high impact in the modern life and livelihood of people. IoT was invented by Kevin Ashton from Massachusetts Institute of Technology (1998) [20]. It is not a standalone technology, rather, it is a mixture of many other technologies, platforms, cyber-physical systems and so on and so forth. More specifically, it is an extended network of physical objects or “things” combined with different components such as sensors, actuators, micro-controllers, many cyberunits, internet and other connectivity enablers so that “things” can transmit data among each other from anywhere and everywhere in the form of image, audio, video, signal, text etc.

IoT comes with broader challenges of synchronization among different platforms that are limited by their own constraints in terms of framework, connectivity, power consumption, bandwidth, communication range and compatibility. However, once developed, it can perform the herculean tasks of surveillance, healthcare monitoring, industry automation, agricultural automation, environment monitoring, etc., with minimum human intervention. The number of connected “things” are increasing expeditiously day by day and is expected to reach 29 billion by the end of 2020 [46].

Industry 4.0, also known as the fourth revolution of industry is also empowered by IoT applications [16]. It has made way for systematic deployment of advanced Information and Communication Technologies (ICT), Future oriented Techniques (FoT) and Intelligent Information Processing (IIP) for continuous monitoring and enhancement of various automatic processes. One of the major challenges in context of Industry 4.0 is providing security to the underlying independent applications. Industry 4.0 has wide range of contributions in industrial wireless sensor networks, smart healthcare, diary industries, agricultural industries, automobile industries, defense research etc. [14, 15].

In recent times, with the advent of multimedia technologies, where images are playing important role in conveying large number of information very easily at a time, it is important to preserve the privacy of these data. Needless to say, these multimedia data are often sent through insecure public platform by camera sensors. It gives rise to the potential risk of the vulnerable data sent by these sensors [42].

In cloud enabled IoT infrastructure, at the perception layer or at the physical layer, tiny sensory devices gathers data in different forms and transfer them to the cloud storage via the Internet. These information is further processed at network layer and are used for analysis at application layer [45, 67]. However, interconnection of many cyber-physical units or “things” gives rise to various threats and attacks [19, 28]. The vulnerabilities of such interconnections where sensitive data exchanges happen at a rapid rate [71], get exposed to the adversaries. Apart from that, the sensors have their own constraints in terms of less memory size, low computing capability, short battery life, bandwidth, etc. [69]. As a consequence, conventional and widely used symmetric key block ciphers such as Advanced Encryption Standard (AES), Data Encryption Standard (DES) [51] or public key ciphers such as Rivest-Shamir-Adleman (RSA) [50], Diffie-Hellman [9] cryptosystems cannot be implemented because of their complex structures and heavy resource consumption. Hence, developing lightweight algorithms for providing security to these applications is of utmost importance.

An attacker can manipulate sensitive image data during its transmission from perception layer to the network layer, where these data are processed intermediately before sending them to cloud servers [32]. As mentioned earlier, the widely used ciphers such as AES, DES, RSA, Diffie-Hellman etc., can be implemented at the network layer and cloud empowered application layer. On the other hand, since perception layer consists of resource constrained sensory devices, there are not much available lightweight cipher for image encryption. Image encryption often requires chaotic map, DNA computing, quantum computing etc., for producing high degree of randomness in the cipher images at the cost of memory, computing power, battery life, etc [12, 25, 70].

There are image encryption techniques that use chaotic maps along with one-time keys [33, 34], chaotic maps along with DNA rules [35] or chaotic maps along with neural network [64] for efficiently generating cipher image from a given plain image. The cipher images contain good cryptanalysis attack resistance properties and they are robust against certain noise levels. All of these cipher images show good NPCR and UACI values when differential analysis is performed on them. But, majority of the techniques are resource consuming in nature. Consequently, although those techniques can be implemented for conventional applications that color image encryption, but these cannot be applied in IoT applications where recourse constraints exist in the sensory devices.

In this work, an image encryption scheme called IEVCA has been developed and implemented in IoT applications that use camera sensors for surveillance purpose. The proposed cipher makes use of 2-D Von-Neumann Cellular Automata (2VCA) with five neighbors [8]. The 2VCA cells can store one bit value at a time. All the five neighbors of a cell can store one bit at a time. These neighbors together participate in changing the bit value from ‘1’ to ‘0’ or vice-versa at next time stamp [6]. When it is applied to an image, it shows complex and random arrangements of the image pixels. Moreover, it can exhibit the globally complex nature by using only at most five bits at a time. This characteristic of 2VCA makes it suitable for utilizing in developing lightweight image cipher for IoT applications. 2VCA cells can generate highly chaotic sequence that can be used in image encryption or pseudo random number generation [30]. Since, CA are highly convenient to be applied in hardware and consists of simple operations locally, the proposed scheme is lightweight and it can be easily implemented in sensor devices at physical level or perception layer.

1.1 Contribution

We have performed many standard analyses and randomness tests to check the performance of the proposed scheme against other state-of-the-art image ciphers. The comparison results have confirmed its capability to generate high degree of randomness in cipher image. Further, it is also proved that the proposed scheme can prevent many cryptanalysis attacks like brute-force attacks, known plaintext, chosen plaintext, known ciphertext and chosen ciphertext attacks. It makes IEVCA capable of being deployed for securing device to network communication. In short, the major contributions of this work are:

  • IEVCA is a symmetric key block encryption technique that uses 2VCA rule vectors for encryption of color images captured by the camera sensors at the physical/perception layer. The encryption happens at the physical layer and decryption at the network layer. The encryption is done through efficient selection of rule vectors and iteration number.

  • It is totally a lossless encryption scheme that uses pixel substitution of color images to achieve high amount of confusion and diffusion property. IEVCA has undergone majority of the analysis that are conventionally applied for any image cipher. The analyses include key space analysis, correlation coefficient, histogram, key sensitivity, differential analysis, image quality analysis etc., that show that the generated cipher image has low correlation, it achieves high amount of confusion and diffusion, the technique is highly key sensitive, as is expected from any conventional image cipher. In addition to these, IEVCA has undergone the NIST and DIEHARD randomness tests. The results are compared to other similar types of existing works. The comparison shows that IEVCA achieved expected level of p-values ensuring the presence of high randomness in cipher images as compared to the existing techniques.

  • IEVCA is implemented using Raspberry Pi 3 and camera sensors. The execution time of the proposed scheme is also compared with state-of-the-art ciphers. The comparison result justifies that the performance of our scheme is better than in terms of execution time without compromising with the other essential security criteria. It makes IEVCA suitable for implementation in real time sensitive IoT applications.

1.2 Paper organization

The subsequent sections of this paper is organized as follows. Section 2 presents state-of-the-art of various image encryption techniques using 2VCA. Section 3 presents a brief description of the essential concepts required for understanding of the current work. Section 4 presents the proposed model and algorithms of this work. Section 5 presents the results of the proposed scheme. Section 6 presents various security and performance analyses of our scheme and the comparison with other existing works. Finally, Section 7 concludes the work by suggesting some future research directions.

2 Related works

The study of Cellular Automata started long ago by John Von-Neumann et al., who popularized it as an abstract model for studying self reproduction [56] along with his mathematician friend Stanislaw M. Ulam [4]. Since then, many researchers continuously put efforts to simulate complex behavior of biological systems through CA.

Later, 2-D CA characterization, reversibility and VLSI architecture for CA Machines (CAM) were proposed by [6, 26]. Dihidar et al. [10] proposed some exceptional rules of 2-D CA with matrix algebra. Afterwards, study of 2-D CA was extended to find issues in drawing state transitions, finding decidable properties, linear rules, analysis of 2-D CA rules in ternary fields [52] and many mathematical theorems and corollaries were derived. All of these works have ensured the capability of 2-D CA in generating complex patterns through simple local transition rules.

In [2], an image encryption scheme with authentication capability has been proposed by applying three different techniques – chaotic map, permutation-diffusion architecture and memory CA. Produced cipher images contain both confusion and diffusion properties. Additionally, their scheme can detect any tampering during transmission. In [61], the authors proposed an image cipher with intertwining chaotic map for achieving confusion and periodic-boundary reversible CA for achieving diffusion property. The authors have considered only highest 4 bits of the image pixels for diffusion as they contain maximum amount of information. The runtime and operational complexities of these methods are comprehensibly resource consuming. Hence, they cannot be implemented in sensory devices.

Chen et al. [7] proposed a 2-D CA architecture for VLSI implementation in hardware. The proposed cipher was constructed using re-configurable Von-Neumann 2-D CA. In these works, security analysis using different standard metrics, randomness tests in generated cipher images were not performed. In [48], authors have proposed 1-D CA based encryption methods both for images and ECG hash codes. In spite of having large key space that helps preventing naive brute-force attacks, their performances against different types of statistical analyses are not good, making them not suitable for implementation in sensitive IoT devices.

Application of 2-D CA for text compression was proposed by Khan et al. [27]. They designed an abstract algebraic model through matrices for periodic-boundary 2-D CA. Further, a VLSI architecture for text compression was also proposed by the authors. An architecture of lightweight image cipher was proposed by Torres et al. [54]. This architecture was useful for implementing image encryption method in mobile devices with resource limitations. The proposed encryption method is a stream cipher based image cipher implemented using field programmable gate array (FPGA) devices.

Some novel image encryption techniques using DNA sequence, hybrid hyper chaotic systems, chaotic skew tent map and genetic operations are proposed in [1, 18, 39, 43, 60, 65]. Each technique have utilized CA for incorporation of permutation and diffusion. Their schemes are robust and capable of generating high quality cipher image when ample amount of computing resources are available. In [23], an image cipher is proposed using elementary CA rules. Different statistical tests and standard analyses proved their technique a good choice for image encryption.

In [44], the authors have presented a lightweight cipher that can be used for image encryption in resource constrained environment. It has significantly less execution time and can mitigate majority of security attacks such as known plaintext, chosen plaintext attacks. This scheme can be deployed with very low memory and with combination of static and dynamic keys.

In [29], a lightweight selective encryption scheme is proposed to encrypt the edge maps of medical images. This scheme uses chaotic map to generate a big key space. A one-time pad is also proposed for enciphering the detected image blocks. This scheme is lightweight and can prevent many security attacks, making it a good candidate to be implemented in IoT applications.

In [24], an unification technique is proposed for image compression and encryption in a single module. The unification is done through hyper-chaotic sequences and sparse representation of frames of any input image. This technique is able to provide a higher compression ratio (CR) compared to the state-of-the-art techniques. It also increases security level by using key-sequence in various steps of encryption. The output after unification is stronger than simple encryption techniques that use chaotic systems.

In [63], a visually secure encryption technique is proposed. This technique uses parallel compressive sensing (PCS) counter mode and embedding technique. In this technique, Logistic-Tent system is used to construct the measurement metrics. 3-D Cat maps are used to jumble the the order of embedded information. The scheme has achieved superior imperceptibility.

In [38] an image encryption scheme has been proposed using reversible CA. The scheme is a parallel block encryption scheme generating highly random cipher images. In [13] an image encryption scheme using a 2-D Tinkerball chaotic map, DNA sequences and CA has been proposed. Their proposed scheme is a gray image encryption scheme. In [68], a gray image encryption technique using quantum CA has been proposed. The invertible quantum CA operations enabled the scheme to achieve runtime complexity of θ(n) which is better than other schemes using quantum CA. The security analyses of all the schemes are good enough to be implemented in high-end computers, but not in resource limited sensory devices.

In [57] a fast image encryption algorithm based on parallel computing has been proposed. Here, cycle shift and permutation methods are combined to get good permutation results. Diffusion method is implemented using parallel computing and it shows good performance in terms of time and space complexities. Recently some image encryption algorithms have been proposed [58, 59] that use matrix semi-tensor product with a compound secret key. This key is produced by a Boolean network. Here, chaotic system has been used to generate random key streams. The produced cipher images exhibit good security characteristics when compared to other existing image encryption techniques.

In the state-of-the-art of image encryption, it can be found that there exist many techniques that are capable of generating high degree of randomness in the cipher images and show good resilience against standard cryptanalysis attacks. However, the implementation strategies of these techniques consist of chaotic sequences, DNA computing, quantum CA, parallel computing, etc. each of which has enough resource consumption. Consequently, they are not suitable for the resource constrained devices used in perception layer of typical IoT applications such as healthcare, defense, surveillance and so forth. To overcome such limitations, in this paper, a lightweight image cipher, named as IEVCA has been proposed using 2-D VCA in Section 4. The proposed cipher is capable of resisting most of the standard cryptanalysis attacks and shows ample amount of randomness in cipher images. It can also be implemented in real time sensory devices in critical and sensitive IoT applications.

3 Preliminaries of 2-D cellular automata

CA are mathematical model through which behavior of a complex system can be explained through simple components acting together under a transformation rule. CA can be of many dimensions such as 1-D CA, 2-D CA, etc. Detailed description of 1D CA can be found in [40] and the references therein. In this work, 2-D Von-Neumann CA has been considered.

A 2VCA can have periodic-boundary or null-boundary considerations [26]. In periodic-boundary, the extreme boundary cells are considered as adjacent to each other while finding neighbor. On the contrary, in null-boundary CA, the extreme cells are considered to be connected to logic “zero”. Figure 1 shows the neighborhood considerations of a 2-D VCA.

Fig. 1
figure 1

Von Neumann neighborhood

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The periodic-boundary and null-boundary conventions of Von-Neumann CA are shown in Fig. 2a and 2b respectively. The red colored cell (i,j) is the cell under consideration in Fig. 1 and Fig. 2. The positions of the neighbors are in North, South, East, West, and in the diagonal positions as shown in the figure. Each cell can have states or state-values as either ‘0’ or ‘1’. The state of a cell at position (i,j) at time t, can be changed depending on the states of its neighbors at time (t + 1) [55]. In this work, both periodic-boundary and null-boundary conventions of 2-D VCA are considered.

Fig. 2
figure 2

Different types of Von Neumann CA and their representations

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Figure 3 shows the block diagrammatic representation of 2-D periodic boundary Von Neumann CA, where the cells can be implemented through a D flip-flop and each input panel has 9 different lines connected through a XOR combination logic. The same for periodic boundary VCA can be designed if the horizontal and vertical boundary cells are connected to each other.

Fig. 3
figure 3

Hardware implementation of 2-D Von Neumann CA with periodic boundary

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3.1 Mathematical model

2-D CA are an arrangement of m × n cells in matrix form, where state of each cell can be either ‘0’ or ‘1’. A configuration means allocation of states to each and every cells of a 2-D CA. Each of such configurations can determine a next configuration through a local CA transformation rule. In other words, the state of a cell at time (t + 1) depends only on the state of the cell and its neighbors (in any convention) at time t. Now, the state of (i,j)th cell at time (t + 1) can be defined through (1). Table 1 lists all the abbreviations and notations used in the paper to describe the mathematical model.

$$ {\mathit{s_{i,j}^{t+1}} = \mathit{w_{1} \times s_{i,j}^{t} + w_{2} \times s^{t}_{i,j+1} + w_{4} \times s^{t}_{i+1,j}+ w_{8} \times s^{t}_{i,j-1}+ w_{16} \times s^{t}_{i-1,j}}} $$
(1)

where, wi ∈ {0,1}. It further means that, for two-state 2-D CA, any value other than ‘0’ or ‘1’ will not be considered. The arithmetic summation of the cell values denoted in Table 2 denote the rule number over the field \(\mathbb {Z}^{2}\).

Table 1 List of Abbreviation and Notations
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Table 2 2-D Cellular Automta Rule Convention
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There are 5 fundamental rules: 1, 2, 4, 8 and 16. The position of the cells are illustrated in Table 2. As mentioned in the table, rule 1 signifies that the central cell has dependency on itself for next state transition. If the central cell depends on left cell for next state transition, it becomes rule 8. Similarly other rules can be constructed.

Now, in case of 2-D Von Neumann CA, highest possible rule number is 31, following the convention depicted in Table 2. The other rule numbers can be realized by taking arithmetic summation of the other rule numbers. For example, 2-D CA rule 23N (1 + 2 + 4 + 16) signifies that the central cell changes its state depending on the states of its neighbors situated at the positions (i,j − 1),(i − 1,j),(i,j + 1) as shown in Fig. 2b under null-boundary consideration. Whereas, rule 23P will do so under periodic-boundary consideration.

The behavior of such types of CA can be analyzed using mathematical model using matrices. Suppose, St is the matrix with initial configuration with a particular rule. The next state configuration can be obtained by suitable XOR operations of its respective neighbors under a specific rule. The global transitions can be expressed through the matrices M1 and M2 as given below:

$$ M_{1} =\left( \begin{array}{lll} 0 & 1 & 0\\ 0 & 0 & 1\\ 0 & 0 & 0 \end{array}\right)\qquad \qquad \qquad M_{2} = \left( \begin{array}{lll} 0 & 0 & 0\\ 1 & 0 & 0\\ 0 & 1 & 0 \end{array}\right) $$

The next states of the Primary Rules〈1, 2, 4, 8, 16〉 can be computed as follows[27]:

$$ Rule~1: [S_{t+1}] = [S_t]; ~~~Rule~2: [S_{t+1}] = [S_t][M_2];~~~Rule~4: [S_{t+1}] = [M_1][S_t]; $$
$$ Rule~8: [S_{t+1}] = [S_t][M_1]; ~~Rule~16: [S_{t+1}] = [M_2][S_t]; $$

Here, St+ 1 denotes the state of the CA at time stamp t + 1. Detailed proof of the matrix representations of each primary rules over \(\mathbb {Z}^{2}\) and \(\mathbb {Z}^{3}\) can be found in [26].

For example, let us take [St] = \(\left (\begin {array}{lll} 1 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 &1 \end {array}\right )\). Now, [St+ 1] can be computed using rule 23N as shown in (2). On the other hand using rule 23P, [St+ 1] is computed as shown in Equation

$$ [S_{t}] = \left( \begin{array}{lll} 1 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 &1 \end{array}\right)\quad\overset{23N}{\rightarrow}\quad \left( \begin{array}{lll} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 1 & 1 & 1 \end{array}\right) = [S_{t+1}] $$
(2)
$$ [S_{t}] = \left( \begin{array}{lll} 1 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 &1 \end{array}\right)\quad\overset{23P}{\rightarrow}\quad \left( \begin{array}{lll} 1 & 1 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right) = [S_{t+1}] $$
(3)

Here, we have applied same rule 23N or 23P to all cells of [St] to obtain [St+ 1]. Hence, these are examples of uniform 2-D VCA. If different rules were applied in different cells, it would become hybrid 2-D VCA and in that case, the rules would be termed as 2-D CA rule vector, altogether.

4 IEVCA - the proposed technique

In a three layer IoT deployment scenario as depicted in Fig. 4, sensitive images are captured by camera sensors at the lowest layer, called physical layer or perception layer [32]. The captured images are then transmitted to the upper layer, called network layer through wi-fi or other public communication channels.

Fig. 4
figure 4

Three layer IoT architecture

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The network layer consists of gateway devices, router etc., with comparatively higher computing capabilities and storage than sensory devices deployed at perception layer. The nodes deployed in the network layer are also known as fog nodes that restricts huge network traffic towards application layer and thus increases the quality of service (QoS). In the application layer, there are high-end computers and servers for cloud storage. The users interact with the IoT applications through this layer and can obtain required data or analytical results available.

In this Section, at first we have generated the rule vectors and they are validated mathematically through state transition matrices in Section 4.1. After validation of the rule vectors, they are used in the IEVCA. Section 4.2 explains the detailed algorithm of rule generation by using both periodic and null boundary conditions. Section 4.3 and 4.4 describe encryption and decryption algorithm respectively in details.

4.1 2-D CA rule generation

The rule generation has been done by Algorithm 1. The detailed methods and technical specifications are explained in Section 4.2. Here, the illustrations regarding detailed operation of GCA is shown.

Any rule can be constructed through the primary rules, as mentioned earlier. For example, rule number 11P, 24P, 25P and 30P are constructed using the primary rules as shown in (4), (5), (6) and (7), respectively. Similarly, the other rules can be generated with periodic boundary or null boundary considerations.

$$ \begin{array}{ll} Rule~11P &= Rule~1P + Rule~2P + Rule~8P \\ \therefore ~~[S_{t+1}] &= [S_{t}] + [S_{t}][M_{2}] + [S_{t}][M_{1}] \end{array} $$
(4)
$$ \begin{array}{ll} Rule~24P &= Rule~8P + Rule~16P \\ \therefore ~~[S_{t+1}] &= [S_{t}][M_{1}] + [M_{2}][S_{t}] \end{array} $$
(5)
$$ \begin{array}{ll} Rule~25P &= Rule~1P + Rule~8P + Rule~16P \\ \therefore ~~[S_{t+1}] &= [S_{t}] + [S_{t}][M_{1}] + [M_{2}][S_{t}] \end{array} $$
(6)
$$ \begin{array}{ll} {Rule~30P} &{= Rule~2P + Rule~4P + Rule~8P + Rule~16P} \\ \therefore {~~[S_{t+1}]} &{= [S_{t}][M_{2}] + [M_{1}][S_{t}] + [S_{t}][M_{1}] + [M_{2}][S_{t}]} \end{array} $$
(7)

A CA is uniform CA if all the cells transit under same rule; otherwise it is called hybrid CA. A CA is termed as group CA (GCA), if after certain transitions, say k the initial configuration is obtained back. In this case, k is the order of the group. Each CA has a characteristic matrix [40] through which it can be verified whether a CA is GCA. In case of GCA, (8) is satisfied.

$$ [T]_{i \times j}^{k} = I_{i \times j} $$
(8)

A collection of different rules to form a GCA is called a GCA rule vector. For example, the rule vector given below is a 2-D GCA rule vector under null-boundary condition:

$$ Rule~Vector = \left( \begin{array}{lll} 7N & 25N & 22N\\ 26N & 3N & 26N\\ 15N & 15N & 26N \end{array}\right) $$
$$ \begin{array}{@{}rcl@{}} \left( \begin{array}{lll} \mathbf{1} & \mathbf{0} & \mathbf{1}\\ \mathbf{0} & \mathbf{1} & \mathbf{1}\\ \mathbf{1} & \mathbf{1} & \mathbf{0} \end{array}\right) \rightarrow \left( \begin{array}{lll} 1 & 1 & 1\\ 0 & 0 & 0\\ 0 & 0 & 0 \end{array}\right) \rightarrow \left( \begin{array}{lll} 0 & 0 & 0\\ 1 & 0 & 1\\ 0 & 0 & 0 \end{array}\right) \rightarrow \left( \begin{array}{lll} 1 & 0 & 1\\ 0 & 1 & 0\\ 0 & 0 & 1 \end{array}\right)\\ \rightarrow \left( \begin{array}{lll} 1 & 1 & 0\\ 0 & 1 & 0\\ 0 & 1 & 0 \end{array}\right)\rightarrow \left( \begin{array}{lll} 0 & 0 & 0\\ 0 & 1 & 1\\ 1 & 1 & 1 \end{array}\right)\rightarrow \left( \begin{array}{lll} 0 & 0 & 1\\ 1 & 0 & 1\\ 0 & 1 & 0 \end{array}\right)\rightarrow \left( \begin{array}{lll} \mathbf{1} & \mathbf{0} & \mathbf{1}\\ \mathbf{0} & \mathbf{1} & \mathbf{1}\\ \mathbf{1} & \mathbf{1} & \mathbf{0} \end{array}\right) \end{array} $$
(9)

The transition matrices for an initial configuration under above RuleV ector are shown in (9). Here, the initial configuration has been re-generated after 6 rounds. So, it can be noted that for k = 6, \([T]^{6}_{3 \times 3} = I_{3 \times 3}\).

Based on the dependency of central cell on the number of neighbors, the CA rules can be classified into many classes. The rule vectors used in this work are combination of rules that belong to different classes. This is done to ensure high degree of confusion and diffusion property in the cipher images.

In this work, we have generated Von Neumann, GCA rule vectors under both null-boundary and periodic-boundary conditions. Some of the null-boundary GCA rule vectors with value of k = 6 are given below:

$$ \begin{array}{@{}rcl@{}} CARV1=\left( \begin{array}{lll} 31N & 11N & 22N\\ 26N & 3N & 26N\\ 15N & 15N & 26N \end{array}\right) \quad CARV2=\left( \begin{array}{lll} 15N & 9N & 5N\\ 26N & 2N & 26N\\ 15N & 15N & 26N \end{array}\right)\\\\ CARV3=\left( \begin{array}{lll} 31N & 15N & 21N\\ 26N & 2N & 26N\\ 15N & 15N & 26N \end{array}\right)\quad CARV4 = \left( \begin{array}{lll} 7N & 25N & 22N\\ 26N & 3N & 26N\\ 15N & 15N & 26N \end{array}\right) \end{array} $$

Some of the periodic-boundary rule vectors with value of k = 6 used in this work are given below:

$$ \begin{array}{@{}rcl@{}} CARV1=\left( \begin{array}{lll} 4P & 5P & 10P\\ 11P & 9P & 26P\\ 9P & 29P & 24P \end{array}\right) \quad CARV2=\left( \begin{array}{lll} 6P & 14P & 7P\\ 11P & 9P & 26P\\ 9P & 29P & 24P \end{array}\right)\\\\ CARV3=\left( \begin{array}{lll} 10P & 5P & 6P\\ 11P & 9P & 26P\\ 9P & 29P & 24P \end{array}\right)\quad CARV4=\left( \begin{array}{lll} 23P & 30P & 12P\\ 11P & 9P & 26P\\ 9P & 29P & 24P \end{array}\right) \end{array} $$

4.2 2-D VCA rule generation algorithm

There are many algorithms for providing high degree of security at the network layer and cloud layer, but communication from perception layer to network layer is the area of concern due to resource constraints and power limitations of the sensory devices. The traditional ciphers cannot be implemented at this layer.

Hence, the data sent from this layer are vulnerable to any adversary. To cope up with this, in this work a security model is proposed where the raw images sensed at physical layer are encrypted before sending them to the network layer, where they are decrypted. The block diagram of encryption and decryption processes are shown in Figs. 5 and 6, respectively.

Fig. 5
figure 5

Encryption process

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Fig. 6
figure 6

Decryption process

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The proposed algorithm is a symmetric key encryption technique, that performs encryption through pixel substitution by applying 2-D CA rule vectors having GCA property. Firstly, R, G and B channels are extracted from an input color image and are converted into binary matrices. Then, the rule scheduler randomly selects any three random CA rule vectors (CARVs), K1,K2 and K3 from 2D CARVList, where rule vectors are previously stored.

Then, these three channels are encrypted with K1,K2 and K3 randomly. The number of rounds to run for encryption is also selected at random by the encryption module. Finally, the encrypted matrices for R, G and B channels are combined to generate the cipher image for the input color image.

Subsequently, the cipher image is sent to the network layer where 2D CARVList and secret key, K are already stored. Here, it can be noted that the secret key used for encryption is K = 〈 K1, K2, K3, ritr 〉. We assume that this K can be shared between the physical layer and the network layer through some key management authority. Since, this issue falls beyond the scope of this work, we have made this assumption.

figure a

Algorithm 4.2 is used to find 2-D CARVList based on periodic-boundary or null-boundary VCA. The all of 511 CA rules can be filled either by considering periodic-boundary or null-boundary exclusively at a time, without mixing both. Algorithm 4.2 considers all possible CA rules (for a 3 × 3 matrix, all possible rules are (511)9= 281 with repetitions) and produces a list containing valid GCA rule vectors along with the number of rounds, called iteration, the rule takes to cycle back to the original initial data. The validation of 2-D CA rules are shown in Section 4.1 with proper example. Step 14 of Algorithm 4.2 calls Algorithm 4.2 or 4.2 for selecting CARV considering null boundary or periodic boundary conditions respectively. These algorithms are considered on at a time. They should be mixed; otherwise CARV cannot be generated.

Algorithm 4.2 takes a rule vector 〈 r1, r2, … r9 〉 at random using “SelectRandom” method and verifies it for all data combinations possible for a 3 × 3 matrix to guarantee data independence, i.e., the initial data can be any random bits. The algorithm will consider any random 3 × 3 matrix and apply the randomly selected rule. Data independence signifies that the selected 2-D CARV will show GCA property for any 3 × 3 data. Step 9 iteratively selects a data value which is converted into 9 bits and then stored in a 3 × 3 matrix form, say Dt, where t is the time-stamp value. Step 9 iteratively selects a data value which is converted into 9 bits and then it is stored in a 3 × 3 matrix form, say Dt where t is the time-stamp value.

figure b
figure c

Step 13 of Algorithm 1 applies the selected periodic-boundary or null-boundary rule vector on this matrix by calling Algorithm 2 or Algorithm 3 respectively, that finds the neighbors to compute the next states of the matrix at time-stamp t + 1. Algorithm 2 takes an input matrix, Data of size m × n and produces a matrix, Data_applied of the same size, i.e., m × n by applying the selected periodic boundary cellular automata rule vector. Algorithm 3 does the same but it considers null boundary conditions while generating Data_applied.

As mentioned earlier, for a 2-D VCA, there are 9 possible neighbors. For implementation purpose, a neighbor is identified from the bit string, if the respective bit is ‘1’ in the binary representation of the selected rule. Algorithm 2 and 3 initialize the neighbors as shown in Fig. 2a and b respectively. Upon finding the neighbors, “fetchData” method finds the corresponding state values (either ‘0’ or ‘1’), on which EXOR operation is performed to compute the next state. This process is repeated for each cell of 3 × 3 matrix and then matrix Dt+ 1 is obtained. Dt+ 1 contains next state value after application of CARV. Finally, Dt+ 1 is compared to D0 and if Dt+ 1 = D0, the rule vector is tested for another 3 × 3 matrix having other set of data. This process guarantees data independence for the CARV. If the CARV under consideration is tested for all possible values and for each case Dt+ 1 = D0, the CARV is added to CARVList.

On the other hand, if Dt+ 1 ≠ D0, step 13 continues until a match is found or the maximum number of iteration is reached. At last, if no match is found even after reaching maximum value of iteration, the randomly selected periodic-boundary or null-boundary CARV at step 5 of Algorithm 1 is discarded and a new CARV is selected. The CARV is added to the CARVList only if Dt+ 1 = D0 for all data values and for same iteration. Once the 2D CARVList is generated, it is stored in the ROM of sensor devices and shared with the network layer devices.

This rule generation process is executed only once before the encryption/ decryption processes commence. It can be noted that the periodic-boundary or null-boundary rules are considered separately at a time, i.e., the periodic-boundary and null-boundary 2-D CARVs are generated separately by running Algorithm 2 or Algorithm 3 respectively with Algorithm 1.

4.3 Image encryption algorithm

Algorithm 4 is used to encrypt an input color image I of size m × n using three 2D CA rule vectors (CARVs) generated by Algorithm 1 and ritr selected by rule scheduler. Algorithm 4 generates the encrypted image, Ienc and the secret key, K to be used for decryption at receiver end. The decryption process is carried out through Algorithm 6. First, red, green and blue channels are extracted from I. Then each channel is transformed into binary format by converting each pixel value into 8 bits.

The binary form of each Channel is stored in matrix “BinImage” of dimension p × q, where p = m and q = 8 × n. Then, “BinImage” is passed to “FindBlock” method that returns an integer, NBlocks containing 3 × 3 blocks of “BinImage”.Apparently, the value of NBlocks is \(\left \lceil \frac {p}{3}\right \rceil \) × \(\left \lceil \frac {q}{3}\right \rceil \). These blocks will be actually substituted using CARVs 〈 r1, r2, … r9 〉 to incorporate high level of confusion and diffusion property.

u blocks are combined together for encryption in step 5 of Algorithm 4. It increases the length of CARVs to 9 × u, increasing the key space to 232×u. Rule Scheduler selects a random CARV from CARVList at step 6. Step 7 chooses randomly the number of rounds, ritr for which selected Ki should be applied. In each round, for each block, Algorithm 5 is called. It takes “BinImage”, u and the CARV to be used for encryption. It returns the next state values which are stored in the respective positions of “BinImage”. After the completion of step 16, we get encrypted “BinImage”. Upto this step, every operation is executed for each Channel, i.e., red, green and blue of I.

figure d
figure e

Then, for each Channel, the decimal values are obtained using “getDecImage” procedure and these are stored into the matrix, EncryptedPixel. One more shuffling is done at Step 20, to obtain encrypted cipher image, Ienc. Finally, K is generated by combining values of Ki of red, green and blue channels along with ritr. Algorithm 5 is called each time when a block needs to be encrypted. It gets the required input from Step 11 of Algorithm 4. Finally, it enciphers the image block and then Algorithm 4 generates the cipher image after final round of shuffling, as mentioned in Step 20.

figure f

4.4 Decryption algorithm

In network layer, the decryption process is done through Algorithm 6. Since this is a symmetric key algorithm, the secret key K is used for dercryption of Ienc. The decryption process follows similar steps as that of encryption. At first, the pixels of Ienc are unshuffled and red, green and blue channels are extracted from the encrypted color image, Ienc. The unshuffling is done by following the reverse of Step 20 of Algorithm 4. The respective channels are converted into BinImage. The secret key, K is obtained from perception layer. The receiver applies the same CARVs for (iteration − ritr) times. Furthermore, in Step 12 of Algorithm 6, the EncryptBlock function is called to get decrypted blocks of cipher image. Subsequently, the decrypted red, green and blue channels are merged to get back the original color image. Thus, plain image is obtained at the network layer by the shared secret key, K.

5 Experimental results

To strengthen the claim of proposed IEVCA , we evaluated the performance of it using real simulation platform. Several analyses like correlation coefficient, histogram analysis, entropy, cipher image quality analysis, differential analysis, key space analysis, sensitivity analysis, etc. are performed for IEVCA as they are important evaluation parameters for any image encryption scheme. Since it is a lightweight encryption scheme, to assess the real time energy consumption and execution time, we have used Raspberry Pi 3, model B with Python language for implementing the algorithms. The Raspberry Pi 3 had WiFi and Bluetooth Low Energy (BLE) capabilities to increase the functionality and to power more powerful devices over the USB ports.

The detailed specifications of Raspberry Pi 3 are Quad Core 1.2GHz ARMv8 64bit CPU, 1GB RAM, WiFi and Bluetooth Low Energy (BLE) on board, 40-pin Extended GPIO, 4× USB 2 ports, 4 Pole stereo output and composite video port, Full size HDMI, CSI camera port for connecting a Raspberry Pi camera, DSI display port for connecting touchscreen display, Micro SD port for loading operating system and storing data. The part of connections with system and Raspberry Pi setup is shown in Fig. 7. The NIST and DIEHARD randomness tests and other performance comparisons, once the cipher image is generated, were carried out in a system with Intel (R) Core (TM) i5-8265U 1.60 GHz and 1.80 GHz CPU, 8 GB RAM, WINDOWS 10 Pro operating system.

Fig. 7
figure 7

Experimental setup for testing of proposed scheme

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Rule generation is carried out on the same machine, but having two NVIDIA GeForce GT 920M Graphics Processing Units (GPU). Operating system used is Ubuntu version 18.04.3. To speedup the process we have used Compute Unified Device Architecture (CUDA) compilation tools, release 9.1, V9.1.85. A total of 227 threads are spanned to find GCA rules and each thread is responsible for verifying 254 rules when considering Von-Neumann neighbors.

The plain color images used in this work are Baboon, Lena and Peppers as they contain essential features to be used for image processing experiments [41]. Figure 8 shows the plain, encrypted and decrypted images used in this work. Here, Periodic VCA and Null VCA represent the encryption method by using periodic-boundary VCA and null-boundary VCA, respectively. Cipher_PB and Cipher_NB denotes the cipher images obtained by Periodic VCA and Null VCA respectively, whereas, Dec_PB and Dec_NB represent the decrypted images through periodic VCA and Null VCA respectively. From Fig. 8, it can be observed that cipher images do not disclose any information regarding the plain images as per expectation.

Fig. 8
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Plain, encrypted and decrypted Images using periodic-boundary and null-boundary VCA

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6 Security analysis

Here, a detailed discussion about the robustness of the work based on various metrics is presented. This analysis confirms the effectiveness in preventing security attacks. IEVCA has been compared with state-of-the-art techniques to establish it as a better one. All these analysis confirms the feasibility of real-time implementation of the scheme in a constrained environment.

6.1 Analysis of key space

Key space represents the possible number of keys used for encryption algorithm. A higher key space makes the algorithm secure against brute force attacks making the key finding calculations computationally infeasible within a given interval of time. In this work, 3×3 2-D CA with Von-Neumann neighborhood is considered where there are 9 neighbors of the central cell under consideration, including itself.

Each cell can be filled with the values ‘0’ or ‘1’. Hence, there are a total of 281 of encryption keys for hybrid rule vectors that are used in this work. Now, suppose encryption is performed by considering P random blocks altogether, where P is a non zero integer. So, the total key-space becomes 281×P, which is large enough to resist brute-force attacks with modern digital computers.

6.2 Resilience against cryptanalysis attacks

The proposed IEVCA is a symmetric key cipher that encrypts P number of blocks at a time, as mentioned in Section 4. While developing the proposed scheme, Kerckhoff’s principle [47, 62] has been obeyed. According to Kerckhoff’s principle, the encryption and decryption algorithms are known to public; only the encryption key is secret. In proposed scheme, every algorithm except the key is public. Below, we analyze the security of our proposed scheme against four classical attacks [62], provided the attacker knows the design and working principle of IEVCA.

  1. 1.

    Ciphertext only attack: In this kind of attack, the adversary has only a set of ciphertexts.

  2. 2.

    Known plaintext attack: Here, the adversary has a set of plaintexts and their corresponding ciphertexts.

  3. 3.

    Chosen plaintext attack: Here, we assume that the adversary has obtained ciphertexts for arbitrary plaintexts.

  4. 4.

    Chosen ciphertext attack: Here, the attacker has obtained the decrypted plaintexts of some chosen ciphertexts.

It can be easily understood from the description of the above mentioned classical attacks that the chosen plaintext attack is the most powerful attack among all. Hence, if a cryptosystem is resistant to this attack, it can prevent the other three types of attacks.

IEVCA is developed by using 2VCA that changes its configuration depending on 5 different neighbors dynamically. The rule vectors used exhibit GCA property. Now, in this scheme, three crucial components are chosen randomly - (1) the rule vectors K1,K2 and K3 from 2D CARVList (2) the particular Ki to be applied to each channel (R, G and B) and (3) the number of rounds, ritr for which encryption method needs to be run. Consequently, the plain image to cipherimage mapping would be one-to-many, i.e., two same plain images can generate completely different cipher images depending on components of K. Even if same rule vectors of K is considered, then also the cipher images will be different based on ritr. This has enabled IEVCA to achieve high degree of confusion and diffusion properties. Subsequently, it prevents the adversary from obtaining any meaningful information even if the adversary has the accessed the ciphertexts for some arbitrary plaintexts. Thus, IEVCA resists chosen plaintext, the most powerful cryptanalysis attack and hence it can resist the other three classical attacks.

6.3 Key sensitivity analysis

This analysis shows the sensitivity of the proposed scheme to the key used in the experiment. It indicates that a tiny alteration in private key can make the recovered image fully non-intelligible [61].

In other word, the modified key will generate a completely different cipher image. Figure 9 shows the decrypted image after a tiny alteration in the secret key.

Fig. 9
figure 9

Decryption of images with a small change in key

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It can be observed that the scheme is highly sensitive to the secret key. IEVCA has been compared with the scheme proposed by Babaei et al. [1] and the result is shown in Table 3. It can be seen that the performance of the proposed scheme is better.

Table 3 Key sensitivity test of proposed scheme (%)
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6.4 Information entropy analysis

Information entropy, α is one crucial metric for measuring the randomness in encrypted image. It can be calculated by (10) [66].

$$ \alpha = \sum\limits_{x=0}^{ij}S(T_{x})\log_{2} \frac{1}{S(T_{x})} $$
(10)

Here, histogram count is denoted by S(Tx). Total number of rows and columns of encrypted image are denoted by i and j respectively.

Table 4 provides the information entropy values of our scheme for red, green and blue channels of plain, encrypted and decrypted images. We have compared these values with the works of Babaei et al. [1], Jin et al. [23], Mondal et al. [39] and Fu et al. [18].

Table 4 Entropy analysis of proposed scheme
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Table 5 shows the comparison data. It can be easily noticed from the table that IEVCA outperforms majority of the existing schemes and most of the attacks are infeasible in our case, as the entropy value is close to ideal values [22, 72].

Table 5 Comparison of information entropy values of the proposed scheme with existing techniques
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6.5 Analysis of cipher image qality

Quality of cipher image generated after encryption is tested using two widely used metrics called, Mean Sqaured Error (MSE) and Peak Signal to Noise Ratio (PSNR). MSE and PSNR values have been computed using Equation (11) and (12) respectively.

$$ MSE = \frac{{\sum}_{X,Y}[K_{p}(x,y)-K_{c}(x,y)]^{2}}{X\times Y} $$
(11)
$$ PSNR = 10~log_{10}\left( \frac{P^{2}}{MSE}\right) $$
(12)

Here, Kp and Kc denote original and encrypted images respectively. X, Y signify dimensions of the image in row and column. P is the value of maximum supported pixel of image matrix [41].

High value of MSE denotes that plain image is not understandable from cipher image. Similarly, PSNR value around 30 denotes presence of high degree of randomness in cipher image. A comparison has been performed with the encryption schemes of Jin et al. [23], Fu et al. [18], Tong et al. [53] and Mondal et al. [39]. The comparison result is listed in Table 6.

Table 6 Comparison of image quality through MSE and PSNR between plain and cipher images
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The values of MSE and PSNR between different plain images and decrypted images are provided in Table 7. This result is same for both periodic-boundary and null-boundary conditions. The ‘0’ value of MSE and ∞ value of PSNR confirms that proposed IEVCA is a lossless image encryption technique.

Table 7 MSE and PSNR between plain and decrypted images
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6.6 Correlation coefficient analysis

Correlation coefficient is another statistical parameter of measuring the similarity of two images. It can be represented as β, to find out the relationship of two pixels of an image. a high value of β signifies the images are almost same, whereas, a very low value signifies that the images are completely different. The correlation coefficient β is computed through (13) [41].

$$ \beta =\frac{{\sum}_{i}{\sum}_{j}(P_{ij}-\bar{P})(Q_{ij}-\bar{Q})}{\sqrt{({\sum}_{i}{\sum}_{j}(P_{ij}-\bar{P})^{2})({\sum}_{i}{\sum}_{j}(Q_{ij}-\bar{Q})^{2})}} $$
(13)

Here, \(\bar {P}\) and \(\bar {Q}\) denote the mean pixel value. Pij represents the value at ith row and jth column.

Table 8 shows the values of correlation coefficient of plain image and cipher image and it also shows the comparison with the works done by Niyat et al. [43] and Babei et al. [1]. It can be observed that IEVCA has achieved better values of β.

Table 8 Comparison of correlation coefficient values of cipher images in horizontal, vertical and diagonal spectrum
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Additionally, we have provided the plot of correlation coefficient values by taking 4000 pixel-value pairs at a time of plain image and cipher image. Figure 10 shows the correlation coefficient plots in horizontal, vertical and diagonal directions for the images of Baboon and Lena. The different plots of correlation coefficients of Peppers image are shown in Fig. 11.

Fig. 10
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Correlation coefficient of plain and encrypted baboon and lena images

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Fig. 11
figure 11

Correlation coefficient of plain and encrypted pepper images

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Here, Enc_Baboon_Periodic and Enc_Baboon_Null represent the encrypted images by periodic-boundary and null-boundary VCA, respectively. Similarly, the nomenclatures are used for other images.

It can be noted from Fig. 10 and Fig. 11 that the encrypted images have uniformly distributed pixel values, making them non-understandable for any attacker and it rightly justifies the efficacy of the proposed scheme.

6.7 Analysis of histogram

Histogram is a decisive feature of any digital color image as far as its encryption is concerned. It is the plot of tonal distribution of a color image.

It also represents graphically the distribution of number of pixel-values for each tone-value. The uniform and flat histogram indicates the presence of high degree of randomness in the pixel-values of cipher image. Table 9 shows the histogram of plain and encrypted cipher images of Baboon, Lena and Peppers respectively. Here, Enc_Baboon_Periodic and Enc_Baboon_Null signify the encrypted image using periodic-boundary VCA and null-boundary VCA, respectively. Similarly, the other images are denoted. The uniform and flat histogram of encrypted images represent the capability of generating random cipher image by IEVCA.

Table 9 Histograms of different channels of plain and cipher images using periodic and null-boundary VCA
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6.8 Robustness test against different levels of noise

The proposed scheme is tested with different noise level to check its robustness. At first “Salt and Pepper” noise is added to the plain images at different percentage, then these images are encrypted and sent to the receiver end.

After decryption, the original images are recovered at the network layer. Figure 12 and 13 show the plain images, encrypted images and recovered images using periodic-boundary VCA and null-boundary VCA, respectively when 1% noise level is considered. Subsequently, Fig. 14 and Fig. 15 show the respective images when 10% noise level is considered. The figures clearly show that the plain images can be easily recognized by observing the recovered images.

Fig. 12
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Robustness test with 1% noise level for periodic-boundary VCA

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Fig. 13
figure 13

Robustness test with 1% noise level for null-boundary VCA

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Fig. 14
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Robustness test with 10% noise level for periodic-boundary VCA

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Fig. 15
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Robustness test with 10% noise level for null-boundary VCA

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6.9 Differential analysis

An ideal characteristic of the encrypted image is its sensitivity to tiny changes in the plain image. An adversary tries to observe the change in cipher image when a tiny change occurs in the plain image. Then she tries to establish a relationship between plain image and the secret key. In fact, this process is called differential analysis where an adversary tries to find out the key. Number of Pixels Change Rate (NPCR) and Unified Average Changing Intensity (UACI) are two key criteria for testing the effect of a minor change in input image pixel on the cipher image. Higher values signifies the better efficiency of a image cipher [1]. NPCR and UACI values can be computed using (15) and (16) [39].

$$ D(x,y)= \begin{cases} 0 & \text{ if } D_{1}(x,y)=D_{2}(x,y) \\ 1& \text{ if } D_{1}(x,y) \neq D_{2}(x,y) \end{cases} $$
(14)
$$ NPCR,~ N(D_{1},D_{2}) = \sum \frac{D(x,y)}{M\times N} \times 100 <percent> $$
(15)
$$ UACI,~ U(D_{1},D_{2}) = \sum\limits_{x,y}\frac{\left | D_{1}(x,y) - D_{2}(x,y) \right |}{P\times M\times N}\times100<percent> $$
(16)

Here, D1 and D2 are the encrypted images before and after one pixel change in plain image. D1(x, y) and D2(x, y) are positional pixel values of D1 and D2 respectively and are computed by (14). Here, M and N denotes dimension of the image and P is the highest value of a pixel in cipher image matrix.

The proposed scheme is compared with other existing schemes of Jin et al. [23], Fu et al. [18], Tong et al. [53], Nayak et al. [41] and Dong et al. [11]. The detailed result is listed in Table 10. It can be observed from the table that the values obtained are over and above the acceptable values [21] and outperforms majority of the existing schemes. Hence, the proposed scheme is capable to resist the differential cryptanalysis attacks.

Table 10 Comparison of NPCR and UACI values with existing schemes
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6.10 DIEHARD tests

The proposed scheme has undergone the statistical DIEHARDFootnote 1 randomness tests, introduced by G. Marsaglia (1995). The acceptable range of p-values is [0,1). The results are shown in Table 11. It can be seen that the p-values of our scheme is under the acceptable range, that denotes the cipher image is highly random.

Table 11 DIEHARD test result
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6.11 NIST randomness tests

The randomness of the bit sequence generated in the cipher image is one of the key criteria to assess security of any image encryption scheme. There are many methods of testing randomness, but no algorithm has passed all of them. The most widely used set of randomness tests is SP800-22 published by the National Institute of Standards and Technology (NIST)Footnote 2.

The statistical test suit (STS) consists of 15 different tests aiming to find non-randomness in a sequence. The tests are - I) Approximate Entropy, II)Block Frequency (m = 20000), III) Cumulative Sums (Forward), IV) Frequency, V) Linear Complexity (m = 500), VI) Longest Runs of 1s, VII) Maurer’s Universal, VIII) Non-overlapping Templates, IX) Overlapping Templates, X) Random Excursions (x=-1), XI) Random Excursions Variant (x=-1), XII) Rank, XIII) Runs (Forward), XIV) Serial (m = 16, delsi2m ) and XV)Spectral DFT. NIST has provided two parameters of interpretation of the result: (1) proportion and (2) p-value. More details about these parameters can be found at [48]. In Table 12, the serial numbers of these tests are mentioned. The significance level, α is 0.01 for p-values obtained at each test. It means that if the p-value ≥ α, the sequence is random, otherwise it is non-random.

Table 12 NIST test result
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In our experiment, the value of m = 100 and hence acceptable proportion range is [0.96015, 1.01985] [48]. The proposed scheme is compared with [48] in terms of obtained values of proportions and p-values. The results are listed in Table 12. Here, proportion and result are represented by Pr. and Re. It can be observed that the proportion value is under the acceptable range and the p-value is also > 0.001 that signify presence of high degree of randomness in cipher image.

6.12 Comparison of runtime and energy consumption

In this section, a detailed comparison has been performed in terms of runtime and energy consumption for the proposed scheme. Here, symmetric block ciphers such as AES, DES, 3DES are considered along with lightweight stream cipher, Chacha for comparison purpose.

6.12.1 Runtime comparison

IEVCA has been compared with AES, DES, 3-DES which are symmetric key block ciphers [17] and one lightweight stream cipher, called Chacha, from Sala20 family [3]. The result is shown in Fig. 16. Because of their complex fiestel structures, AES, DES and 3DES have higher runtime. Though Chacha is a lightweight stream cipher, but still it has higher runtime than IEVCA.

Fig. 16
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Runtime comparison

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It can be observed from Fig. 16 that proposed scheme has the least runtime under similar implementation platform, making it suitable for implementation in realtime IoT applications. The the previous subsections, the proposed scheme has been compared with the existing schemes in terms of MSE, PNSR values for assessing the quality of encrypted image. It has been compared with respect to UACI and NPCR for evaluating its performance against differential attack. The entropy values, correlation coefficient comparisons confirms the security and resistance against cryptanalysis attacks like known plaintext, chosen plaintext, known ciphertext and chosen ciphertext. Hence, the proposed scheme manifests high randomness and resilience against cryptanalysis attacks and also achieves lesser runtime than other ciphers.

6.12.2 Energy consumption

The proposed method has been experimented using Raspberry Pi 3 model B, that has recommended power supply unit (PSU) current capacity of 2.5A. The typical bare board active current consumption was 400mAFootnote 3. The supply voltage was provided to the board through microUSB power connector. The energy consumption was computed through the method described by [49]. According to their method, the energy consumed can be calculated by taking product of input supply voltage, power drawn by hardware and the average execution time of the algorithm. The supply voltage is 5V and it is constant for all the algorithms under consideration. We have compared the power consumption of IEVCA with the aforementioned algorithms. The result is shown in Fig. 17. It can be observed from Fig. 17 that as the size of the input increases, the energy consumption also increases. Among the aforementioned algorithms, our proposed scheme, IEVCA consumes the least amount of energy. It justifies one of the most important characteristics of lightweight algorithm.

Fig. 17
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Comparison of Energy Consumption

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7 Conclusion and future works

Proposed work presents an image encryption technique called, IEVCA using 2-D Von-Neumann Cellular Automata. The lightweight feature of IEVCA makes its runtime faster as compared to its existing counterparts. Hence, it is more appropriate for the IoT applications developed for sensitive fields like defense, healthcare, etc., which require encryption in the perception layer. The IoT sensory devices could able to run the encryption routine with very less resource consumption. Many security and performance analyses are performed on IEVCA which confirm its robustness and resistance against various security attacks. Additionally, NIST and DIEHARD statistical test suites are used to check the randomness of the cipher image generated and we found that the cipher image passed all the tests.

In future, an efficient version of IEVCA may be planned with the use of cache efficient algorithms. The locality of reference feature of cache will be utilized for faster fetching of the rule vectors, as a result less resources of the IoT devices will be used. Further, IEVCA can be used along with trust management [37] and key management [31] to deploy secure applications. IEMCA will be complete when the secret key sharing between sender and receiver will be taken care of and will be optimized according to the requirements of the IoT deployment. The proposed scheme can be used to secure ambient agents [5, 36], as they also require similar type of security requirements.