An Optical Image Encryption Method Using Hopfield Neural Network

Abstract

In this paper, aiming to solve the problem of vital information security as well as neural network application in optical encryption system, we propose an optical image encryption method by using the Hopfield neural network. The algorithm uses a fuzzy single neuronal dynamic system and a chaotic Hopfield neural network for chaotic sequence generation and then obtains chaotic random phase masks. Initially, the original images are decomposed into sub-signals through wavelet packet transform, and the sub-signals are divided into two layers by adaptive classification after scrambling. The double random-phase encoding in 4f system and Fresnel domain is implemented on two layers, respectively. The sub-signals are performed with different conversions according to their standard deviation to assure that the local information’s security is guaranteed. Meanwhile, the parameters such as wavelength and diffraction distance are considered as additional keys, which can enhance the overall security. Then, inverse wavelet packet transform is applied to reconstruct the image, and a second scrambling is implemented. In order to handle and manage the parameters used in the scheme, the public key cryptosystem is applied. Finally, experiments and security analysis are presented to demonstrate the feasibility and robustness of the proposed scheme.

Event-triggered controller on practically exponential input-to-state stabilization of stochastic reaction-diffusion neural networks and its application to image encryption

“…The application of chaotic systems to image encryption has become a popular research area in recent years [3][4][5][6][7]. This section will explore the implementation of chaotic SRDDHNNs through the secure transmission of cameraman image.…”

“…7 depicts the distribution correlation of adjacent pixels in three directions of plain and encrypted images. To check the correlation of two adjacent pixels in an encrypted image, apply the following mathematical Cameraman image Horizontal Vertical Diagonal Plain 0.9333 0.9569 0.9052 Encrypted (our scheme) -0.0003 -0.0001 0.0010 Encrypted [3] -0.0004 -0.0003 0.0030 Encrypted [4] -0.0031 -0.0006 0.0011 Encrypted [5] -0.0025 -0.0004 0.0035 Encrypted [6] -0.0208 -0.0011 0.0323 Encrypted [7] -0.0186 -0.0053 0.0095 Table 2 Correlation coefficients of pixels location of plain and encrypted image in three direction expressions: Thus, the results of correlation coefficients of plain and encrypted images in three direction are shown in Table 2. By virtue of Table 2 and Fig.…”

“…Neural networks (NNs) plays an significant role in many real-world applications such as image encryption [1][2][3][4][5][6][7], signal processing [8], pattern recognition [9], optimization problem [10], and secure communication [11]. Cohen-Grossberg NNs (CGNNs) was initially proposed and studied by Cohen and Grossberg in 1983 [12].…”

Random Maximum 2 Satisfiability Logic in Discrete Hopfield Neural Network Incorporating Improved Election Algorithm

“…In this context, HNN will update the neuron state until the network achieves global minimum energy to ensure the optimality of the solution for any given optimization problem. Despite having wide applicability [7][8][9][10], HNNs are prone to storage capacity issues. As proposed by various studies [11,12], the number of stored memory patterns is severely limited (about 14%) which indicates the need for optimal neuron modeling in HNNs.…”

An Algorithm Based on Hodgkin-Huxley Model and Latin Square for Image Encryption

“…Aside from traditional chaotic digital encryption methods, neuron models have also made some research results in image encryption. Xu et al [22] use Hopfield neural network applying in optical image encrypted. To generate chaotic sequences and chaotic random phase masks, the algorithm employs a Hopfield neural network.…”