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

Abstract

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 $$0<q<1$$ 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.

Novel Duffing chaotic oscillator and its application to privacy data protection

“…Since f 1 is k-sparse, the number of equations is much smaller than the number of unknowns, making equation (6) an underdetermined system without definite solutions. Therefore, the sensing matrix Θ needs to satisfy the Restricted Isometry Property (RIP) [24].…”

“…The original signal f 1 can be efficiently recovered by the reconstruction methods such as matching pursuit, orthogonal matching pursuit, and smooth l 0 norm [24].…”

Application of variable-order fractional calculus in neural networks: where do we stand?

“…Many different methods for data hiding are reported in the literature. In this issue, by means of fractional-order neural networks, some interesting approaches have been proposed [24,25]. In [18], the realization of a variable-order fractional chaotic system over a PC's sound card has been done for the first time in the literature.…”

A Novel Color Image Encryption Scheme Based on Hyperchaos and Hopfield Chaotic Neural Network

“…There are also some new directions, such as compressive sensing combined with DNA coding, compressive sensing combined with Hopfield chaotic neural networks for image encryption, quantum cryptography and DNA coding applied together in the design of encryption schemes, and memristive chaotic systems and DNA operations jointly applied in encryption [ 26 , 27 , 28 , 29 , 30 ]. These approaches can be applied to text, audio, and video encryption as well [ 31 , 32 ].…”