This thesis presents a novel work on hardware realization of symmetric image encryption utilizing chaos based continuous systems as pseudo random number generators. Digital implementation of chaotic systems results in serious degradations in the dynamics of the system. Such defects are illuminated through a new technique of generalized post proceeding with very low hardware cost. The thesis further discusses two encryption algorithms designed and implemented as a block cipher and a stream cipher. The security of both systems is thoroughly analyzed and the performance is compared with other reported systems showing a superior results. Both systems are realized on Xilinx Vetrix-4 FPGA with a hardware and throughput performance surpassing known encryption systems.

Yes / Fractional-order chaotic systems have more complex dynamics than integer-order chaotic systems. Thus, investigating fractional chaotic systems for the creation of image cryptosystems has been popular recently. In this article, a fractional-order memristor has been developed, tested, numerically analyzed, electronically realized, and digitally implemented. Consequently, a novel simple three-dimensional (3D) fractional-order memristive chaotic system with a single unstable equilibrium point is proposed based on this memristor. This fractional-order memristor is connected in parallel with a parallel capacitor and inductor for constructing the novel fractional-order memristive chaotic system. The system’s nonlinear dynamic characteristics have been studied both analytically and numerically. To demonstrate the chaos behavior in this new system, various methods such as equilibrium points, phase portraits of chaotic attractor, bifurcation diagrams, and Lyapunov exponent are investigated. Furthermore, the proposed fractional-order memristive chaotic system was implemented using a microcontroller (Arduino Due) to demonstrate its digital applicability in real-world applications. Then, in the application field of these systems, based on the chaotic behavior of the memristive model, an encryption approach is applied for grayscale original image encryption. To increase the encryption algorithm pirate anti-attack robustness, every pixel value is included in the secret key. The state variable’s initial conditions, the parameters, and the fractional-order derivative values of the memristive chaotic system are used for contracting the keyspace of that applied cryptosystem. In order to prove the security strength of the employed encryption approach, the cryptanalysis metric tests are shown in detail through histogram analysis, keyspace analysis, key sensitivity, correlation coefficients, entropy analysis, time efficiency analysis, and comparisons with the same fieldwork. Finally, images with different sizes have been encrypted and decrypted, in order to verify the capability of the employed encryption approach for encrypting different sizes of images. The common cryptanalysis metrics values are obtained as keyspace = 2648, NPCR = 0.99866, UACI = 0.49963, H(s) = 7.9993, and time efficiency = 0.3 s. The obtained numerical simulation results and the security metrics investigations demonstrate the accuracy, high-level security, and time efficiency of the used cryptosystem which exhibits high robustness against different types of pirate attacks.

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In this work we study two aspects of image security: improper usage and illegal access of images. In the first part we present our results on steganalysis – protection against improper usage of images. In the second part we present our results on image encryption – protection against illegal access of images. Steganography is the collective name for methodologies that allow the creation of invisible –hence secret– channels for information transfer. Steganalysis, the counter to steganography, is a collection of approaches that attempt to detect and quantify the presence of hidden messages in cover media. First we present our studies on stego-images using features developed for data stream classification towards making some qualitative assessments about the effect of steganography on the lower order bit planes(LSB) of images. These features are effective in classifying different data streams. Using these features, we study the randomness properties of image and stego-image LSB streams and observe that data stream analysis techniques are inadequate for steganalysis purposes. This provides motivation to arrive at steganalytic techniques that go beyond the LSB properties. We then present our steganalytic approach which takes into account such properties. In one such approach, we perform steganalysis from the point of view of quantifying the effect of perturbations caused by mild image processing operations–zoom-in/out, rotation, distortions–on stego-images. We show that this approach works both in detecting and estimating the presence of stego-contents for a particularly difficult steganographic technique known as LSB matching steganography. Next, we present our results on our image encryption techniques. Encryption approaches which are used in the context of text data are usually unsuited for the purposes of encrypting images(and multimedia objects) in general. The reasons are: unlike text, the volume to be encrypted could be huge for images and leads to increased computational requirements; encryption used for text renders images incompressible thereby resulting in poor use of bandwidth. These issues are overcome by designing image encryption approaches that obfuscate the image by intelligently re-ordering the pixels or encrypt only parts of a given image in attempts to render them imperceptible. The obfuscated image or the partially encrypted image is still amenable to compression. Efficient image encryption schemes ensure that the obfuscation is not compromised by the inherent correlations present in the image. Also they ensure that the unencrypted portions of the image do not provide information about the encrypted parts. In this work we present two approaches for efficient image encryption. First, we utilize the correlation preserving properties of the Hilbert space-filling-curves to reorder images in such a way that the image is obfuscated perceptually. This process does not compromise on the compressibility of the output image. We show experimentally that our approach leads to both perceptual security and perceptual encryption. We then show that the space-filling curve based approach also leads to more efficient partial encryption of images wherein only the salient parts of the image are encrypted thereby reducing the encryption load. In our second approach, we show that Singular Value Decomposition(SVD) of images is useful from the point of image encryption by way of mismatching the unitary matrices resulting from the decomposition of images. It is seen that the images that result due to the mismatching operations are perceptually secure.

In this study, a new method is proposed to protect JPEG still images through encryption by employing integer-to-integer transforms and frequency domain scrambling in DCT channels. Different from existing methods in the literature, the encrypted image can be further compressed, i.e. transcoded, after the encryption. The method provides selective encryption/security level with the adjustment of its parameters. The encryption method is tested with various images and compared with the methods in the literature in terms of scrambling performance, bandwidth expansion, key size and security. Furthermore this method is applied to the H.263 video sequences for the encryption of I-frames.

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La sécurité est un problème important dans la transmission et le stockage de l'image, tandis que le cryptage est un moyen d'assurer la sécurité qui est requise dans de nombreuses applications (télévision par câble, la communication d'images militaires, systèmes d'imagerie confidentielle, etc.). Toutefois, à l'instar du message texte, les données images présentent des caractéristiques spéciales telles que la haute capacité, la redondance et la haute corrélation entre les pixels, et nécessite souvent une transmission et des traitements temps réel pour certaines applications. Construire un système rapide et efficace de cryptographie d'images suscite un intérêt considérable. C'est dans ce contexte qu’ont été menés ces travaux thèse qui portent sur l’élaboration d’un corrélateur optique en termes de cryptage/décryptage des données pour son implémentation dans un montage optique innovant. L’objectif de ces travaux est de réaliser un système optique de chiffrement sur la base d'exploitation de transformation optique et de générateurs chaotiques. L'idée originale des travaux consiste à exploiter la non-linéarité des systèmes chaotiques comme clés de chiffrement pour les systèmes optiques de chiffrement d'images multispectrales. Dans ces travaux de thèse, nous avons proposés et évalués plusieurs chiffrements d'images à base d’un système hyperchaotique et de transformées optiques (gyrator, Fourier, Baker , Arnold et Gerchberg- Saxton) à partir d’un processus de cryptage reposant sur une décomposition composants RVB et un encodage dans un flux dimensionnel d’images couleurs. L'originalité des solutions de chiffrement adoptée reposent sur l'exploitation de signaux réellement aléatoires à travers la mise en œuvre de générateurs hyperchaotiques pour la génération de données aléatoires sous forme images comme base de matrices de clés de chiffrement. En effet, ces générateurs présentent des propriétés et des caractéristiques fondamentales en termes de cryptage car il présente une non-linéarité, une imprédictibilité et une extrême sensibilité aux conditions initiales les rendant très intéressantes pour le développement de clés de chiffrement par flot. L’algorithme mis en œuvre permet d'extraire en temps réel les caractéristiques de texture dans les différentes bandes spectrales d'images en vue d’évaluer et de détecter les teneurs potentielles en information et dont les transmissions doivent être sécurisée via une transmission optique / Optical information security is one of the most important research directions in information science and technology, especially in the field of copyright protection, confidential information transmission/storage and military remote sensing. Since double random phase encoding technology (DRPE) was proposed, optical image encryption technology has become the main topic of optical information security and it has been developed and studied deeply. Optical encryption techniques offer the possibility of high-speed parallel processing of two dimension image data and hiding information in many different dimensions. In this context, much significant research and investigation on optical image encryption have been presented based on DRPE or further optical operation, such as digital holography, Fresnel transform, gyrator transform. Simultaneously, the encrypted image has been extended from single gray image to double image, color image and multi-image. However, the hyperspectral image, as a significant element in military and commercial remote sensing, has not been deeply researched in optical encryption area until now. This work extends the optical encryption technology from color image to hyperspectral image. For better comprehension of hyperspectral image encryption, this work begins with the introduction and analysis of the characteristics of hyperspectral cube. Subsequently, several kinds of encryption schemes for color image, including symmetric and asymmetric cryptosystem, are presented individually. Furthermore, the optical encryption algorithms for hyperspectral cube are designed for securing both the spatial and spectral information simultaneously. Some numerical simulations are given to validate the performance of the proposed encryption schemes. The corresponding attack experiment results demonstrate the capability and robustness of the approaches designed in this work. The research in this dissertation provides reference for the further practicality of hyperspectral image encryption

Based on the generating matrix to the Tribonacci sequence, the Tribonacci cat map is a discrete chaotic dynamical system, similar to Arnold's discrete cat map, but on three dimensional space. In this thesis, this new mapping is introduced and the properties of its matrix are presented. The main results of the investigation prove how the size of the domain of the map affects its period and explore the orbit lengths of non-trivial points. Different upper bounds to the map are studied and proved, and a conjecture based on numerical calculations is proposed. The Tribonacci cat map is used for applications such as 3D image encryption and colour encryption. In the latter case, the results provided by the mapping are compared to those from a generalised form of the map.

This thesis presents a computationally efficient cryptosystem based on chaotic continuous-interval cellular automata (CCA). This cryptosystem increases data protection as demonstrated by its flexibility to encrypt/decrypt information from distinct sources (e.g., text, sound, and images). This cryptosystem has the following enhancements over the previous chaos-based cryptosystems: (i) a mathematical model based on a new chaotic CCA strange attractor, (ii) integration of modules containing dynamical systems to generate complex sequences, (iii) generation of an unlimited number of keys due to the features of chaotic phenomena obtained through CCA, which is an improvement over previous symmetric cryptosystems, and (iv) a high-quality concealment of the cryptosystem strange attractor. Instead of using differential equations, a process of mixing chaotic sequences obtained from CCA is also introduced. As compared to other recent approaches, this mixing process provides a basis to achieve higher security by using a higher degree of complexity for the encryption/decryption processes. This cryptosystem is tested through the following three methods: (i) a stationarity test based on the invariance of the first ten statistical moments, (ii) a polyscale test based on the variance fractal dimension trajectory (VFDT) and the spectral fractal dimension (SFD), and (iii) a surrogate data test. This cryptosystem secures data from distinct sources, while leaving no patterns in the ciphertexts. This cryptosystem is robust in terms of resisting attacks that: (i) identify a chaotic system in the time domain, (ii) reconstruct the chaotic attractor by monitoring the system state variables, (iii) search the system synchronization parameters, (iv) statistical cryptanalysis, and (v) polyscale cryptanalysis.