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.
Keywords: 4f system; Fresnel domain; Hopfield neural network; double random phase encoding; optical image encryption; single neuronal dynamic system; wavelet packet transform.