A novel image encryption scheme using both pixel level and bit level permutation with chaotic map

doi:10.1016/j.asoc.2020.106162

Applied Soft Computing

Volume 90, May 2020, 106162

https://doi.org/10.1016/j.asoc.2020.106162 Get rights and content

Highlights

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The key stream generated by the proposed method is large enough to resist various attacks.
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The NPCR , UACI and Entropy values are nearly 99.6094% , 33.4635% and 8 respectively.
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Double scrambling not only permutes pixel positions but also changes the pixel values.

Abstract

In cryptography, chaotic cryptosystem is one of the methods to carry out encryption and decryption of images. This paper introduces a new symmetric key encryption technique based on chaotic map, scan method and cyclic shift operation. The confusion and diffusion techniques are implemented using Hilbert curve and Henon map. To ensure image scrambling, both pixel level and bit level permutations are performed. A novel method is adopted for bit level permutation using cyclic shift operation. The key streams for cyclic shift and diffusion operations are generated from the Henon map. Final encrypted image is generated from the double scrambled image. The performance of the proposed method has been analyzed using various analyses like statistical analysis, entropy analysis, differential attack analysis, key sensitivity analysis and known plain text attack analysis. Experimental results show that the proposed image encryption technique resists various attacks and ensures high security. It also provides better performance when compared with several traditional and state-of-the-art image encryption methods.

Introduction

It is necessary to protect multimedia information transmitted through the communication network from illegal access. In cryptography, data protection is ensured using confusion and diffusion techniques proposed by Claude Shannon [1]. Image encryption is one of the methods in cryptography which ensures image security. Most of the image crypto systems are based on confusion and diffusion techniques.

While developing a cryptosystem for image encryption, we must consider certain features of images like larger size, higher redundancy, and strong adjacent pixel correlation. Because of these reasons, traditional symmetric and asymmetric algorithms are not suitable for image encryption. In 1963, Edward Lorenz [2] introduced the concept of Chaos theory. Chaos-based systems are suitable for image encryption, due to their properties such as sensitivity to initial conditions, unpredictability and ergodicity [3], [4].

Recently, chaotic cryptosystem has become a widely acceptable research area for image encryption. The existing image encryption techniques are classified in to three categories: pixel position permutation, pixel value transformation and combined approach. Pixel position permutation method is simple and it scrambles the original pixels according to some predefined scheme. These schemes usually have low data security. Pixel value transformation scheme [5], [6] changes the image pixel values. The hardware cost and complexity of operations are reduced with this type of transformation. In [5], a cyclic bit shift called Bit Recirculation Image Encryption (BRIE) is used as an encryption technique. Since this method uses permutation operations alone, it is vulnerable to known and chosen plaintext attacks [7]. The scheme proposed in [5] is crypt analyzed in [8]. In [6] the cipher is generated by the permutation process using cyclic shift operation on bit level and is crypt-analyzed in [9]. The combined scheme has high data security. Our proposed encryption algorithm is a combination of pixel position permutation and pixel value transformation techniques.

Many research studies have implemented DNA encoding for image encryption due to their properties such as low power consumptions, high density and parallelism. In the past several years a number of research papers [10], [11], [12], [13], [14], [15], [16] have combined DNA encoding with chaotic maps to improve the image security. In [10] hyper chaotic Lorenz system is adopted for key stream generation where as in [11] coupled map lattice is used.

The premium properties of chaos ensure high security in image encryption. The chaotic crypto systems may use one, two or multi dimensional chaotic maps. One dimensional chaotic map is applied in [17], [18], [19], [20], [21], [22], [23], [24], [25], [26] to ensure security through confusion and diffusion. One dimensional (1-D) chaotic methods may be attacked easily [27], [28] as they suffer from lack of efficiency, insufficient security and reduced key size. The chaotic sequence of 1-D chaotic maps is simple and the initial values of the maps may be easily predictable [29], [30], [31] using certain methods [32], [33]. Higher dimensional chaotic map is adopted in [34], [35] for performing encryption. The higher dimensional systems have higher implementation cost and complex performance analysis. To overcome the above mentioned drawbacks, the proposed method introduces a 2-D chaotic map.

In some other image encryption schemes [36], [37], [38], [39] SCAN patterns are used for pixel scrambling process. In paper [39], image scrambling is performed using Hilbert curve that ensures only pixel level permutation. The encryption scheme using simple scrambling method is prone to brute-force attack. Our proposed image scrambling technique introduces double scrambling process to ensure both pixel level and bit level permutation. Also in [39], the random key stream is generated from randomized bit pattern method. In contrast to that our scheme employs chaotic Henon map to generate pseudorandom numbers for confusion and diffusion process. Chaotic Henon map generate excellent random sequence because of its uniform invariant distribution and good ergodicity. Chaos based systems have been applied for several image processing functions because of their better security and effectiveness.

Motivated from the above discussions, this paper proposes a new image encryption technique using 2-D chaotic Henon map, Hilbert curve and cyclic shift operation. The proposed image scrambling technique introduces double scrambling process to ensure both pixel level and bit level permutation. At first, pixel level permutation can be performed using Hilbert curve. Then for bit level permutation the concept of cyclic shift is employed. A novel approach is introduced to perform cyclic shift operation in such a manner that it will transform image pixel values. The cyclic shift can resist some common cryptographic attacks and hence increase the image encryption security. Image scrambling will ensure confusion phase of the system. Henon map is utilized for cyclic shift operation and diffusion phase. Experimental results and security analysis show the feasibility and resistance against various attacks of the proposed method.

The main contributions of this paper are summarized as:

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Efficient confusion technique: Double scrambling technique introduced here using SCAN method and cyclic shift operation benefits better permutation results than single phase scrambling. Double scrambling not only changes the pixel positions but also alters the value of each pixel.
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Efficient diffusion technique: To generate the current pixel the proposed method uses the previous pixel value, one element from the key stream and a secret value. This will ensure that the cipher image is extremely sensitive to the changes in plain image. That is one bit change in the plain image will reflect in multiple pixels of cipher image with higher probability.
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The proposed method can achieve good confusion and diffusion properties since the principle of confusion and diffusion are fulfilled.
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Novel method for key stream generation: A methodology for generating two key streams is implemented. These key streams are used in confusion and diffusion process.
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The proposed encryption technique can efficiently resist some common security attacks such as statistical attack, entropy attack, differential attack and chosen plaintext attack. Thus it ensures high security and outperforms other state-of-the-art methods.
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Simplicity of the concept, practical significance, robustness, trouble free implementation and fast encryption speed are some salient features of the proposed methodology.

The rest of the paper is organized as follows: Section 2 briefly introduces the SCAN method and Hilbert curve. Section 3 describes Henon map. Section 4 presents the proposed image encryption method. Section 5 presents the analysis of various security aspects and simulation outcomes. Finally, the conclusions are drawn in Section 6.

Section snippets

SCAN method

The SCAN is a two-dimensional spatial accessing methodology to generate distinct number of scanning paths. It specifies the order to access each and every elements of the array exactly once. Some commonly used scan patterns [38] in different encryption techniques are shown in Fig. 1.

Henon map

Henon map is a discrete-time dynamical system with chaotic behavior. It is a two-dimensional dynamic system proposed by [40] and is defined by Eq. (1). $\begin{matrix} x_{n + 1} = 1 - α x_{n}^{2} + y_{n} \\ y_{n + 1} = β y_{n} \end{matrix}$ Where $α$ and $β$ are the parameters of the Henon map and when $α = 1.4$ and $β = 0.3$ , the map becomes chaotic in nature. Each point ( $x_{n}$ , $y_{n}$ ) is mapped to a new point ( $x_{n + 1}$ , $y_{n + 1}$ ) through Henon map. Fig. 3 shows an example of Henon map obtained from the initial conditions ( $x_{0}$ , $y_{0}$ ) as (0.0000013778, 0.0061).

The proposed cryptosystem

The architecture of the proposed cryptosystem is shown in Fig. 4. It consists of three phases viz. pixel permutation phase, diffusion phase and key stream generation phase. Pixel permutation phase is implemented through double scrambling process to ensure confusion. The first round scrambling is performed in pixel level using Hilbert curve and second round scrambling in bit level using cyclic shift operation. A novel method is implemented for key stream generation. The key stream $K 1$ is used in

Experimental results and security analysis

For conducting experiments eight different test images (Lena, Baboon, Pepper, fruits, Jet plane, Camera man, Boat and Barbara) with size 256 × 256 are taken. The initial values and parameters ( $x_{0}$ , $y_{0}$ , $μ$ , $ρ$ ) $=$ (7.396016084688671e−06, 0.003380886664354, 5.28825609906277e $+$ 14, 6.59901762952245e $+$ 14) are obtained from Eqs. (2), (3), (4), (5). Several simulations effects and security analysis are discussed in the following sections.

Conclusions

In this paper, we have proposed a symmetric cryptographic system to encrypt grayscale images using the concepts of Hilbert curve, bit level cyclic shift and the Henon map. A novel approach is implemented for key stream generation. Image pixel scrambling is performed in both pixel level and bit level to ensure double scrambling. This is achieved with the help of Hilbert curve and cyclic shift operation. The nearby pixel correlation values are decreased by the method of double scrambling. For

Future enhancement

In future we want to develop a chaotic cryptosystem for color images with better performance and security aspects.

CRediT authorship contribution statement

Shahna K.U.: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Data curation, Writing - original draft, Writing - review & editing, Visualization. Anuj Mohamed: Supervision, Writing - review & editing, Validation.

Declaration of Competing Interest

No author associated with this paper has disclosed any potential or pertinent conflicts which may be perceived to have impending conflict with this work. For full disclosure statements refer to https://doi.org/10.1016/j.asoc.2020.106162.

Acknowledgment

The authors acknowledge the support extended by DST-PURSE (Phase-II), Government of India .

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View full text

A novel image encryption scheme using both pixel level and bit level permutation with chaotic map

Highlights

Abstract

Introduction

Section snippets

SCAN method

Henon map

The proposed cryptosystem

Experimental results and security analysis

Conclusions

Future enhancement

CRediT authorship contribution statement

Declaration of Competing Interest

Acknowledgment

Phys. Lett. A

Signal Process., Image Commun.

Signal Process.

Opt. Lasers Eng.

Opt. Lasers Eng.

Signal Process.

Appl. Soft Comput.

Opt. Commun.

Signal Process.

Opt. Laser Technol.

Inform. Sci.

Phys. Lett. A

Inform. Sci.

Opt. Commun.

Pattern Recognit.

Pattern Recognit.

Communication theory of secrecy systems

Bell Labs Tech. J.

The essence of chaos

Pure Appl. Geophys.

Chaos and cryptography: Block encryption ciphers based on chaotic maps

IEEE Trans. Circuits Syst. I

A new image encryption algorithm and its VLSI architecture