Efficient neural chaotic generator for image encryption
Introduction
Drastic growth in multimedia communication resulted to numerous security issues in the data transmission over the Internet. To meet this challenge, a variety of encryption schemes have been proposed [1], [2], [3], [4], [5], [6]. Among them, chaos-based algorithms emerged to be promising. They have shown some exceptionally good properties regarding complexity, speed, computing power and computational overhead, especially in domain of image encryption. Due to some intrinsic features of images, such as bulk data capacity and high correlation among pixels, traditional encryption algorithms such as DES, AES and RSA are not suitable for practical image encryption. The main obstacle in designing image encryption algorithms is that it is rather difficult to swiftly shuffle and diffuse data by traditional means of cryptology: traditional cryptographic algorithms shuffle and diffuse data by rounds of encryption, while chaotic maps spread the initial region over the entire phase space via iterations.
Chaos has been widely studied in secure communications [7], [8], [9], [10], and the idea of using digital chaotic systems to construct cryptosystems has been extensively studied since 1989 [11], and attracts more and more attention in the last years [12], [13]. In order to use chaotic systems in image encryption, chaotic sequences must seem absolutely random (practically very close to random) and have some properties such as: balance on {0, 1}, long cycleʼs length, high linear complexity, δ-like auto-correlation, cross-correlation near to zero, and fully distributed phase space. Existing digital chaotic generators satisfy some of these properties, but most of them suffer from short cycleʼs length due to the dynamical degradation caused by -dimensional finite space [14], [15]. Usually some perturbation techniques are used to avoid such degradation [16], [17], [18], [19]. Good dynamical and randomness properties allow chaotic generators to have a resistance against analysis and correlation attacks. However, enhancing dynamical properties do not prevent brute-force attack if the generator has few parameters.
In this paper, we firstly propose a new perturbation technique based on neural network: a neural network is trained to learn a certain chaotic function, then the neural network is called every a certain period to take the place of the chaotic generator during the generation of the chaotic sequence. As chaotic generators are very sensitive to any small variation in the current iteration, the error between the neural network response and the exact response of the chaotic generator leads to a deviation from the chaotic orbit, and thus acting as a good source of perturbation that enlarges the cycle length of the chaotic sequence. Moreover, the neural network parameters (network structure, activation functions, weights and biases) enlarge key space, and thus result in a robust chaotic generator in term of security. Our techniques can be implemented in any chaotic generator. Second, we propose a neural chaotic generator based on the neural perturbation technique. Third, we propose a new image encryption algorithm based on three-dimensional (3D) chaotic map. The new algorithm, first shuffles the positions of pixels (pixels permutation) in order to fast de-correlate relations among them. Then, to confuse the relationship between cipher image and plain image, a diffusion process among pixels is performed (permutation at bits level).
Many perturbation techniques are proposed [16], [17], [18], [19], most of them based on maximal length LFSR. These perturbation techniques allow to elongate the cycle length and to obtain better dynamical properties of the chaotic sequences [17], [18]. But it has been found many guess and correlation attacks on LFSR [19], [20], [21], [22], [23]. Moreover, they do not solve an important problem of chaotic generators that is fewness of parameters.
Our work follows the spirit of [24] where they model the dynamics of Chuaʼs circuit using artificial neural network aiming to enlarge the key space. They show that the neural network can deliver a similar response as the numerical solution of Chuaʼs circuit with a small error. Note that modeling a certain chaotic generator by a neural network does not solve the dynamical degradation. However, to the best of our knowledge, no body use neural network as a source of perturbation in order to avoid the dynamical degradation caused by the digital chaotic systems. We take the advantage of neural network error to use it as a source of perturbation in order to solve the dynamical degradation problem, at the same time enlarging the key space of the chaotic generator.
In Section 2, we present some known chaotic generators. In Section 3, we present the general implementation of neural network in any chaotic generator. Then in Section 4, a new chaotic generator is proposed. In Section 5, some experimental results and comparisons are made to illustrate the efficiency of the proposed neural chaotic generator. Finally before concluding, we propose a new image encryption method in Section 6.
Section snippets
Presentation of known chaotic generators
In this section, we present some of the well-known chaotic generators.
Artificial neural network: a brief overview
An artificial Neural Network (ANN) [25] is a highly parallel distributed network of connected processing units called neurons. It is motivated by the human brain which is a highly complex, nonlinear and parallel computer. The network has a series of external inputs and outputs which take or supply information to the surrounding environment. Weights and biases of the network are used to store knowledge acquired from the environment. Learning is achieved by adjusting these parameters in
Proposed neural chaotic generator
In this section, we propose a new chaotic generator using a nonlinear digital IIR filter similar to the one used in Frey map [7]. However, we use PWCLM as a nonlinear function instead of left circulate function to remove any correlation between successive iterations. To improve the dynamical properties and elongate the orbit of the final chaotic sequence, we apply our neural network perturbation technique. The neural chaotic generator is presented in Fig. 9. It takes as an input two parameters k
Experimental results
In order to evaluate and quantify the cryptographic properties of the proposed generator, we make some experiments and comparisons between our generator, Frey map and Frey map perturbed by LFSR. The results concerning Frey map perturbed by LFSR are taken from [18]. The precision used is and the period adopted for perturbation is for both NN and LFSR techniques.
New image encryption technique based on neural chaotic generator
We propose a novel image encryption method based on chaotic sequence. It consists of two operations, first operation is permutation at the pixel level, and second operation is masking followed by permutation at bit level. In our context, denotes the pixel in the ith row and jth column of the plain image ( resolution). , and represent the red, green and blue components of the pixel respectively, each recorded by 8 bits.
Conclusion
In a cryptosystem, the use of a good chaotic generator with desirable dynamical and statistical properties is very important. In this paper, we present a general implementation of neural network in any chaotic generator to increase the cycleʼs length and enlarge the key space to overcome the weakness of the chaotic generators concerning the digital degradation parameter fewness. Then, we propose a new chaotic generator based on neural network. A comparative study using standard criteria (system
Ali Kassem received the engineering diploma in Telecommunication and Computer from the Lebanese University, Beirut, Lebanon in 2011. In 2012, he received the master degree in Security, Cryptology and Coding of Information from Joseph Fourier University, Grenoble, France. He started his PhD in security analysis of cryptographic protocols, in October 2012, at VERIMAG laboratory, employed by the University of Grenoble. His research interests include formal verification, run time verification,
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2018, Digital Signal Processing: A Review JournalCitation Excerpt :For protection, encryption and information hiding are the two basic approaches. Image encryption converts the image information into invisible cipher text [1–7], so that the illegal identity can not obtain the message without the correct key. But the drawback is that the encrypted file is a meaningless representation and easily causes the attention of attackers during the transmission.
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2017, OptikCitation Excerpt :Finally, the last section summarizes the results of the previous sections and concludes the paper. Kassem et al. proposed an image encryption method based on neural chaotic generator [16]. In this algorithm two operations (first operation is permutation at the pixel level, and second operation is masking followed by permutation at bit level) are used for encryption of the color-image P of size 3 × M × N. So, Pr(i,j), Pg(i,j), and Pb(i,j) denote the gray scale in the ith row and jth column of the red, green and blue components of the pixel P(i,j), respectively.
Ali Kassem received the engineering diploma in Telecommunication and Computer from the Lebanese University, Beirut, Lebanon in 2011. In 2012, he received the master degree in Security, Cryptology and Coding of Information from Joseph Fourier University, Grenoble, France. He started his PhD in security analysis of cryptographic protocols, in October 2012, at VERIMAG laboratory, employed by the University of Grenoble. His research interests include formal verification, run time verification, security of ad-hoc network routing protocols, image security, and trusted platform modules.
Hussein Al Haj Hassan is currently a PhD candidate at Network, Security and Multimedia department at Telecom Bretagne, Rennes, France. He earned his diploma in Telecommunication and Computer Engineering and his master in Networks of Telecommunication from the Lebanese University, Beirut, Lebanon. In his PhD, he works on mobile networks powered by renewable energy. His fields of interest are in wireless networks, energy efficiency, artificial intelligence and security.
Youssef Harkouss received the PhD degree in telecommunications from the University of Limoges, France, in 1998. From 1999 to 2000, he was research engineer at the CNRS, France. He joined the Department of Telecommunications of the Lebanese University, Faculty of Engineering, Branch III, as professor in 2001. His research interests include neural networks, fuzzy logic, fuzzy neural network modeling and optimization for microwave devices and circuits, CAD of passive devices, equalization, intelligent systems, and information security.
Rima Assaf received the PhD degree in telecommunications from the University of Nantes, France, in 2009. She joined the Lebanese University, Faculty of Engineering, Branch III, in 2010 as an associate professor of telecommunications. Her research interests include neural networks, equalization, intelligent systems, and information security.