Suggested Integral Analysis for Chaos-Based Image Cryptosystems

Murillo-Escobar, Miguel Ángel; Meranza-Castillón, Manuel Omar; López-Gutiérrez, R.M.; Cruz-Hernández, C.

doi:10.3390/e21080815

Cited by 83 publications

(38 citation statements)

References 58 publications

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“…In a similar way, the authors in [19] showed the effects of time delay on burst synchronization transitions of a neural network which was locally modeled by Hindmarsh-Rose neurons. On the one hand, the main drawback of those works was the lack of statistical tests according to the National Institute of Standard and Technology (NIST), as done in other chaotic systems given in [20][21][22], to guarantee the randomness of the chaotic sequences. On the other hand, and in addition to NIST tests, the authors in [23] recommend to improve the key space when using chaotic maps, thus enhancing the image encryption schemes.…”

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confidence: 99%

Chaotic Image Encryption Using Hopfield and Hindmarsh–Rose Neurons Implemented on FPGA

Tlelo‐Cuautle

Díaz-Muñoz

González-Zapata

et al. 2020

Sensors

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Chaotic systems implemented by artificial neural networks are good candidates for data encryption. In this manner, this paper introduces the cryptographic application of the Hopfield and the Hindmarsh-Rose neurons. The contribution is focused on finding suitable coefficient values of the neurons to generate robust random binary sequences that can be used in image encryption. This task is performed by evaluating the bifurcation diagrams from which one chooses appropriate coefficient values of the mathematical models that produce high positive Lyapunov exponent and Kaplan-Yorke dimension values, which are computed using TISEAN. The randomness of both the Hopfield and the Hindmarsh-Rose neurons is evaluated from chaotic time series data by performing National Institute of Standard and Technology (NIST) tests. The implementation of both neurons is done using field-programmable gate arrays whose architectures are used to develop an encryption system for RGB images. The success of the encryption system is confirmed by performing correlation, histogram, variance, entropy, and Number of Pixel Change Rate (NPCR) tests.In [2] J.J. Hopfield introduced the neuron model that nowadays is known as the Hopfield neural network. Ten years later, a modified model of Hopfield neural network was proposed in [3], and applied in information processing. Immediately, the Hopfield neural network was adapted to generate chaotic behavior in [4] where the authors explored bifurcation diagrams. In [5] the simplified Hopfield neuron model was designed to use a sigmoid as activation function, and three neurons were used to generate chaotic behavior. In addition, the authors performed an optimization process updating the weights of the neurons interconnections. The Hopfield neuron was combined with a chaotic map in [6] to be applied in chaotic masking. More recently, the authors in [7] proposed an image encryption algorithm using the Hopfield neural network. In the same direction, the authors in [8] detailed the behavior of Hindmarsh-Rose neuron to generate chaotic behavior. Its bifurcation diagrams were described in [9], and the results were used to select the values of the model to improve chaotic behavior. Hindmarsh-Rose neurons were synchronized in [10], optimizing the scheme of Lyapunov function with two gain coefficients. In this way, the synchronization region is estimated by evaluating the Lyapunov stability. Two Hindmarsh-Rose neurons were synchronized in [11], and the system was used to mask information in continuous time. To show that the neurons generate chaotic behavior, one must compute Lyapunov exponents, and for the Hindmarsh-Rose neuron they were evaluated by the TISEAN package in [12].The Hopfield neural network has been widely applied in chaotic systems [13][14][15]. This network consists of three neurons, and the authors in [13] proposed a simplified model by removing the synaptic weight connection of the third and second neuron in the original Hopfield network. Numerical simulations were carried out considering values from t...

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confidence: 99%

Chaotic Image Encryption Using Hopfield and Hindmarsh–Rose Neurons Implemented on FPGA

Tlelo‐Cuautle

Díaz-Muñoz

González-Zapata

et al. 2020

Sensors

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“…They measure how much the elements of a set of data vary with respect to each other around the mean. Two datasets may have the same average value (mean), but the variations can be drastically different [23].…”

Section: Histogram Statisticsmentioning

confidence: 99%

“…Quality evaluation of digital images can use the Mean Squared Error (MSE) and Peak Signal-to-Noise Ratio (PSNR) for measurement [23,24]. The MSE is a parameter to measure the difference between two images, which is described as Equation (36).…”

Section: Images Coefficientmentioning

confidence: 99%

A Novel Five-Dimensional Three-Leaf Chaotic Attractor and Its Application in Image Encryption

Wang

Song

Wang

et al. 2020

Entropy

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This paper presents a novel five-dimensional three-leaf chaotic attractor and its application in image encryption. First, a new five-dimensional three-leaf chaotic system is proposed. Some basic dynamics of the chaotic system were analyzed theoretically and numerically, such as the equilibrium point, dissipative, bifurcation diagram, plane phase diagram, and three-dimensional phase diagram. Simultaneously, an analog circuit was designed to implement the chaotic attractor. The circuit simulation experiment results were consistent with the numerical simulation experiment results. Second, a convolution kernel was used to process the five chaotic sequences, respectively, and the plaintext image matrix was divided according to the row and column proportions. Lastly, each of the divided plaintext images was scrambled with five chaotic sequences that were convolved to obtain the final encrypted image. The theoretical analysis and simulation results demonstrated that the key space of the algorithm was larger than 10150 that had strong key sensitivity. It effectively resisted the attacks of statistical analysis and gray value analysis, and had a good encryption effect on the encryption of digital images.

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“…It is possible to find at least 35 works [ 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64 , 65 , 66 , 67 , 68 , 69 , 70 , 71 , 72 , 73 , 74 , 75 , 76 , 77 , 78 , 79 , 80 , 81 , 82 , 83 , 84 , 85 , 86 , 87 , 88 , 89 , 90 , 91 ] in the Entropy journal that relate chaos theory in different areas; however, there are only five articles, from all areas, where reproducibility was mentioned [ 92 , 93 , 94 , 95 , 96 ]. From those aforementioned papers, only Funabashi [ 95 ] presented some slight relationship with the reproducibility of nonlinear dynamics fields.…”

Section: Related Workmentioning

confidence: 99%

A Note on the Reproducibility of Chaos Simulation

Nazare

Nepomuceno

Martins

et al. 2020

Entropy

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An evergreen scientific feature is the ability for scientific works to be reproduced. Since chaotic systems are so hard to understand analytically, numerical simulations assume a key role in their investigation. Such simulations have been considered as reproducible in many works. However, few studies have focused on the effects of the finite precision of computers on the simulation reproducibility of chaotic systems; moreover, code sharing and details on how to reproduce simulation results are not present in many investigations. In this work, a case study of reproducibility is presented in the simulation of a chaotic jerk circuit, using the software LTspice. We also employ the OSF platform to share the project associated with this paper. Tests performed with LTspice XVII on four different computers show the difficulties of simulation reproducibility by this software. We compare these results with experimental data using a normalised root mean square error in order to identify the computer with the highest prediction horizon. We also calculate the entropy of the signals to check differences among computer simulations and the practical experiment. The methodology developed is efficient in identifying the computer with better performance, which allows applying it to other cases in the literature. This investigation is fully described and available on the OSF platform.

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Suggested Integral Analysis for Chaos-Based Image Cryptosystems

Cited by 83 publications

References 58 publications

Chaotic Image Encryption Using Hopfield and Hindmarsh–Rose Neurons Implemented on FPGA

Chaotic Image Encryption Using Hopfield and Hindmarsh–Rose Neurons Implemented on FPGA

A Novel Five-Dimensional Three-Leaf Chaotic Attractor and Its Application in Image Encryption

A Note on the Reproducibility of Chaos Simulation

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