ASB-CS: Adaptive sparse basis compressive sensing model and its application to medical image encryption

Recent advances in intelligent wearable devices have brought tremendous chances for the development of healthcare monitoring system. However, the data collected by various sensors in it are user-privacy-related information. Once the individuals’ privacy is subjected to attacks, it can potentially cause serious hazards. For this reason, a feasible solution built upon the compression-encryption architecture is proposed. In this scheme, we design an Adaptive Sparse Basis Compressive Sensing (ASB-CS) model by leveraging Singular Value Decomposition (SVD) manipulation, while performing a rigorous proof of its effectiveness. Additionally, incorporating the Parametric Deformed Exponential Rectified Linear Unit (PDE-ReLU) memristor, a new fractional-order Hopfield neural network model is introduced as a pseudo-random number generator for the proposed cryptosystem, which has demonstrated superior properties in many aspects, such as hyperchaotic dynamics and multistability. To be specific, a plain medical image is subjected to the ASB-CS model and bidirectional diffusion manipulation under the guidance of the key-controlled cipher flows to yield the corresponding cipher image without visual semantic features. Ultimately, the simulation results and analysis demonstrate that the proposed scheme is capable of withstanding multiple security attacks and possesses balanced performance in terms of compressibility and robustness

Novel compressive sensing image encryption using the dynamics of an adjustable gradient Hopfield neural network

In this contribution, the nonlinear dynamics of a non-autonomous model of two neurons based on the Hopfield neural network is considered. Using activation gradients as bifurcation control parameters, the properties of the model include dissipation with the existence of attractors and equilibrium points with their stability. Using traditional nonlinear analysis tools such as bifurcation diagrams, the graph of the maximum Lyapunov exponent, phase portraits, two-parameter diagrams, and attraction basins, the complex behaviour of the two-dimensional Hopfield neural network has been investigated and several windows of multistability involving the coexistence of up to four coexisting attractors have been found. Besides, the results of our numerical simulation of the multistability have been further supported using some Pspice simulation. The effect of the fractional-order derivative is also explored, and it is found that the route toward chaos is completely different when the order q of the HNN is varied between $$0<q<1$$. Finally, a compressive sensing approach is used to compress and encrypt color images based on the sequences of the above-mentioned system. The plain color image is decomposed into Red, Green, and Blue components. The Discrete Wavelet Transform (DWT) is applied to each component to obtain the corresponding sparse components. Confusion keys are obtained from the proposed chaotic system to scramble each sparse component. The measurement matrices obtained from the chaotic sequence are used to compress the confused sparse matrices corresponding to the Red, Green, and Blue components. Each component is quantified and a diffusion step is then applied to improve the randomness and, consequently, the information entropy. Experimental analysis of the proposed method yields a running time (t) of 6.85 ms, a maximum entropy value of 7.9996 for global and 7.9153 for local, an encryption throughput (ET) value of 114.80, and a number of cycles (NC) of 20.90. Analysis of these metrics indicates that the proposed scheme is competitive with some recent literature

Block Cipher Nonlinear Confusion Components Based on New 5-D Hyperchaotic System

The security strengths of block ciphers greatly rely on the confusion components which have the tendency to transform the data nonlinearly into the perplexed form. This paper proposes to put forward a novel scheme of generating cryptographically strong nonlinear confusion components of block ciphers, usually termed as substitution-boxes (S-boxes). The anticipated S-box design scheme is based on a novel five-dimensional (5-D) chaotic system analyzed in this paper. The proposed 5-D dynamical system consists of hyperchaotic phenomenon, KY dimension, conservativity, unstable equilibrium point, and complex phase attractors which are suited for cryptographic applications. The S-box based on hyperchaotic system is made to evolve in order to generate an optimized S-box for high nonlinearity score to make it robust against many linear attacks. The performance analysis of proposed S-box demonstrates that it has bijectivity, high nonlinearity; satisfied strict avalanche criterion and bits independent criterion; low differential and linear probabilities. Moreover, performance appraisal of proposed S-box justifies its better strength and features over many recently investigated S-boxes

Control of multistability with selection of chaotic attractor: application to image encryption

Dynamic systems exhibiting chaos with periodic windows and multistability are not recommended for cryptography due to the lack of security in these regimes. In this work, we use a linear augmentation control scheme to control a periodic attractor in the windows of multistability to a final chaotic attractor which survives to the variation of initial seed useful for image encryption. The empirical Chua’s system with piecewise linear nonlinearity is used as a sample dynamical system but the idea can be applied using any other dynamical system. First, this system is analyzed to reveal multistability dynamics. Second, the technique of linear augmentation combined with the nonlinear system invariant sets like equilibrium points is used to choose a desired survive attractor among the coexisting ones. It is found that annihilation of multistability in the Chua’s system when varying the coupling strength is obtained through several crises among which interior crisis and border collision. Finally, a survived chaotic attractor is jointly used with SHA-512 for image encryption algorithm using a simple diffusion-confusion structure. Security analysis shows that the encryption process based on control theory can resist various forms of attack

A Novel Compound-Coupled Hyperchaotic Map for Image Encryption

Considering a nonlinear dynamic oscillator, a high Lyapunov exponent indicates a high degree of randomness useful in many applications, including cryptography. Most existing oscillators yield very low Lyapunov exponents. The proposed work presents a general strategy to derive an n-D hyperchaotic map with a high Lyapunov exponent. A 2D case study was analyzed using some well-known nonlinear dynamic metrics including phase portraits, bifurcation diagrams, finite time Lyapunov exponents, and dimension. These metrics indicated that the state of the novel map was more scattered in the phase plane than in the case of some traditional maps. Consequently, the novel map could produce output sequences with a high degree of randomness. Another important observation was that the first and second Lyapunov exponents of the proposed 2D map were both positive for the whole parameter space. Consequently, the attractors of the map could be classified as hyperchaotic attractors. Finally, these hyperchaotic sequences were exploited for image encryption/decryption. Various validation metrics were exploited to illustrate the security of the presented methodology against cryptanalysts. Comparative analysis indicated the superiority of the proposed encryption/decryption protocol over some recent state-of-the-art methods

A New 4D Hyperchaotic System with Dynamics Analysis, Synchronization, and Application to Image Encryption

In this paper, a new 4D hyperchaotic nonlinear dynamical system with two positive Lyapunov exponents is presented. Exhaustive dynamic analyses of the novel hyperchaotic model using several dynamical studies are described. The dynamics of the system considered are first investigated analytically and numerically to explore phenomena and the selection of hyperchaotic behavior utilized for designing image cryptosystem. Since the proposed hyperchaotic model has rich dynamics, it displays hidden attractors. It emerges from this dynamic the existence of a single unstable equilibrium point giving rise to self-excited attractors, hysteresis phenomenon, and hyperchaotic behavior strongly recommended for securing information by its character. Furthermore, the feasibility and synchronization of the proposed system are also presented by developing, respectively, Raspberry surveys and an adaptive synchronization approach of two identical hyperchaotic systems. By employing the hyperchaotic behavior of the 4D map, an image encryption scheme is proposed as well. It is one round of a pixel-based permutation and a bit-wise diffusion phase. The secret key of the 4D map is derived from the SHA-256 value of the input image. It acts as the signature of the input image. Hence, the secret key exhibits high sensitivity to single-bit alteration in the image, which makes the cryptosystem robust against chosen/known-plaintext attacks. Performance analyses prove that the proposed cryptosystem provides the best in terms of the performance/complexity trade-off, as compared to some recently published algorithms