Image encryption algorithm based on Tent-Dynamics coupled map lattices and diffusion of Household

doi:10.1016/j.chaos.2020.110309

Chaos, Solitons & Fractals

Volume 141, December 2020, 110309

https://doi.org/10.1016/j.chaos.2020.110309 Get rights and content

Highlights

•
A new spatiotemporal chaotic system is proposed: Tent-Dynamics Coupled Map Lattices chaotic system.
•
Experimental tests prove that the performance of the Tent-Dynamics Coupled Map Lattices model is better than the traditional coupled mapping lattice model.
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Applying the Household method to the diffusion process of image matrix.
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The security analysis experiment proves that the image encryption algorithm based on Tent-Dynamics Coupled Map Lattices and diffusion of Household has good performance.

Abstract

This paper presents an image encryption algorithm based on Tent-Dynamics Coupled Map Lattices (TDCML) system and diffusion of Household. All aspects of the TDCML spatiotemporal chaotic system proposed in this paper meet the cryptographic characteristics and are suitable for studying image encryption. The specific image encryption algorithm first generates chaotic sequences according to the TDCML system. The image scrambling uses a cyclic shift algorithm, and the movement of each row and column is determined by the chaotic sequence. Then the image diffusion is improved according to the Household orthogonal decomposition method. Think of each column of the image matrix as a row vector, and then operate according to part of the formulas in the Household transformation to obtain a new row vector. Finally, perform the bitwise XOR operation with the specified chaotic sequence to obtain the final encrypted image. Theoretical analysis and experimental results have proved the security of this encryption algorithm.

Introduction

With the rapid development of digital image processing technology, people pay more and more attention to improve the security of information. Image encryption is an important means to ensure information security. Therefore, more and more scholars are keen to study image encryption algorithms. Chaotic systems have many features suitable for cryptography, including pseudo-randomness, initial value sensitivity, parameter sensitivity, ergodicity, and unpredictability. Therefore, in recent years, the use of chaotic systems to study encryption algorithms [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23] has become one of the hot spots in the field of computer science and cryptography. Among many chaotic systems, spatiotemporal chaotic systems [24] have better performance than low-dimensional chaotic systems, such as a larger parameter space, better randomness, more diverse chaotic sequences, and a wider range of initial condition.

After studying and analyzing many image encryption algorithms based on coupled-map lattice space-time chaotic systems [25], [26], [27], [28], it is found that these models have some defects. First of all, the coupled mapping lattice models commonly used for encryption are all statically coupled. This coupling method has an obvious disadvantage, which is that the chaos of the different lattices in the system varies greatly, and some lattices can exhibit strong chaotic characteristics. And the chaotic characteristics of some lattices are not obvious or even lose chaotic characteristics, which will cause that in the process of using it for encryption, we can not determine whether all the lattices are in the best state of chaos, so there is no guarantee of encryption Image security.

Aiming at the shortcomings of these algorithms, an image encryption algorithm based on Tent-Dynamics Coupled Map Lattices (TDCML) chaotic system and Household diffusion is proposed. First, the TDCML chaotic system is proposed. Next, perform scrambling operations on the ordinary image, calculate the number of left shifts of a row and the number of shifts of a column according to certain rules according to the chaotic sequence generated by the chaotic system, and then perform cyclic shift transformation on the corresponding rows and columns. Then, each column of the image matrix is regarded as a row vector, and then a diffusion operation is performed on it. Specifically, it calculates a new row vector according to part of the formula in Household method, and then performs bit-wise XOR calculation with the specified chaotic sequence. Finally, combining all the row vectors into a new matrix is the final encrypted image. The key space and sensitivity analysis, histogram analysis, correlation analysis, information entropy, NPCR, UACI and other experiments prove that the algorithm has superior security performance.

The rest of the article is organized as follows. Section 2 introduces the performance of TDCML spatiotemporal chaotic system and the process of Household decomposition method. Section 3 introduces the steps of image encryption and decryption algorithms. Part 4 shows the simulation results of encryption algorithms and various security performance analysis. The fifth part is about the security analysis of color images. Finally, the full text is summarized in Section 6.

Section snippets

The TDCML system

The traditional coupled mapping lattice model (CML) proposed by Kaneko [25] is shown in Eq. (1): $x_{n + 1} (i) = (1 - e) f (x_{n} (i)) + (e / 2) (f (x_{n} (i - 1)) + f (x_{n + 1} (i + 1)))$ wheree (0 ≤ e ≤ 1) is the coupling coefficient, n( $n = 1, 2, 3, \dots$ ) is the time series, i(1 ≤ i ≤ L) is the space grid points, $i - 1$ and $i + 1$ is the two grid points adjacent to i. $f (x) = μ x (1 - x)$ is a Logistic model proposed by May [29]. The boundary conditions is taken as when $i = L$ , let $i + 1 = 1$ , when $i = 1$ , let $i - 1 = L$ . This is done to ensure that the grid points and

Generation of chaotic system parameters and initial values

In this algorithm, the hash value of the original image is obtained by using the SHA-256 hash algorithm, and the resulting hash value is a 256-bit binary number. In this way, even if there is only one pixel difference between the two images, their hash values will be completely different, which means that the algorithm proposed in this paper is very sensitive to the original image. Convert the resulting 256-bit hash value to a decimal number for every eight-bit value, and you can obtain the

Performance analysis

This section shows the simulation experiment results of the algorithm and the performance analysis of the algorithm. A good encryption algorithm can resist various attacks, so as to ensure the security of the image during transmission. Common attacks include statistical attacks, selective attacks, and differential attacks. This section uses key space analysis, sensitivity analysis, statistical feature analysis, correlation analysis, NPCR and UACI, information entropy, cropping attack, noise

Color image simulation

Color images are different from gray images. Each pixel of a color image usually consists of three components: R, G, and B. To encrypt the color image, it is necessary to encrypt the three components R, G and B separately, and then combine the encrypted images of the three components to obtain the final encrypted image. This paper takes the ``Lena'' color image of size 512 × 512 as an example. The keys used in this experiment are as follows: $μ = 3.999$ , $μ_{1} = 1.23456789$ , $e = 0.222$ , $x_{1} = 0.123456789$ , $x_{2} =$

Conclusions

Tent-Dynamics Coupled Map Lattices (TDCML) is proposed. The Kolmogorov–Sinai entropy, bifurcation graph and mutual information analysis prove that the spatiotemporal chaotic system has good chaotic performance. An image encryption algorithm based on TDCML chaotic system and Household diffusion is proposed. Through the key space and sensitivity analysis, histogram analysis, correlation analysis, information entropy, NPCR, UACI, PSNR, robustness analysis and χ² test of the experimental results,

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This research is supported by the National Natural Science Foundation of China (No: 61672124), the Password Theory Project of the 13th Five-Year Plan National Cryptography Development Fund (No: MMJJ20170203), Liaoning Province Science and Technology Innovation Leading Talents Program Project (No: XLYC1802013), Key R&D Projects of Liaoning Province (No: 2019020105-JH2/103), Jinan City ‘20 universities’ Funding Projects Introducing Innovation Team Program (No: 2019GXRC031).

References (33)

XY Wang et al.
Image encryption algorithm for synchronously updating Boolean networks based on matrix semi-tensor product theory
Inf Sci
(2020)
TG Gao et al.
Image encryption based on a new total shuffling algorithm
Chaos Solitons Fractals
(2008)
XY Wang et al.
Fast image encryption algorithm based on parallel computing system
Inf Sci
(2019)
Y Wang et al.
A new chaos-based fast image encryption algorithm
Appl Soft Comput
(2011)
XY Wang et al.
Image encryption algorithm based on the matrix semi-tensor product with a compound secret key produced by a Boolean network
Inf Sci
(2020)
SM Ismail et al.
Generalized double-humped logistic map-based medical image encryption
J Adv Res
(2018)
Y Wang et al.
A new chaos-based fast image encryption algorithm
Appl Soft Comput
(2011)
S Tedmori et al.
Image cryptographic algorithm based on the Haar wavelet transform
Inf Sci
(2014)
YQ Zhang et al.
A new image encryption algorithm based on non-adjacent coupled map lattices
Appl Soft Comput
(2015)
YQ Zhang et al.
Spatiotemporal chaos in mixed linear-nonlinear coupled logistic map lattice
Physica A
(2014)

YQ Zhang et al.

A symmetric image encryption algorithm based on mixed linear-nonlinear coupled map lattice

Inf Sci

(2014)

F Khellat et al.

Li-Yorke chaos and synchronous chaos in a globally nonlocal coupled map lattice

Chaos Solitons Fractals

(2011)

YH Chen et al.

Optimal windows of rewiring period in randomly coupled chaotic maps

Phys Lett A

(2010)

YQ Zhang et al.

Spatiotemporal chaos of fractional order logistic equation in nonlinear coupled lattices

Commun Nonlinear Sci Numer Simul

(2017)

ST Liu et al.

Nonlinear feedback-controlled generalized synchronization of spatial chaos

Chaos Solitons Fractals

(2004)

K. Kaneko

Pattern dynamics in spatiotemporal chaos: pattern selection, diffusion of defect and pattern competition intermettency

Physica D

(1989)

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ReviewImage encryption algorithm based on Tent-Dynamics coupled map lattices and diffusion of Household

Highlights

Abstract

Introduction

Section snippets

The TDCML system

Generation of chaotic system parameters and initial values

Performance analysis

Color image simulation

Conclusions

Declaration of Competing Interest

Acknowledgements

Inf Sci

Chaos Solitons Fractals

Inf Sci

Appl Soft Comput

Inf Sci

J Adv Res

Appl Soft Comput

Inf Sci

Appl Soft Comput

Physica A

Inf Sci

Chaos Solitons Fractals

Phys Lett A

Commun Nonlinear Sci Numer Simul

Chaos Solitons Fractals

Physica D

Review
Image encryption algorithm based on Tent-Dynamics coupled map lattices and diffusion of Household