Plaintext Related Optical Image Hybrid Encryption Based on Fractional Fourier Transform and Generalized Chaos of Multiple Controlling Parameters

Combining optical image encryption with digital image encryption, we propose a composed optical image hybrid encryption scheme in this paper. The scheme consists of two main parts. In the first part, the original image is encrypted in 4f optical system in the pattern of double random phase encoding. In the second stage, the result of optical encryption is divided into the real part image and the imaginary one. Then, pixels diffusion and confusion are successively carried out on the two images in parallel. Fractional Fourier transform and a generalized chaos, as well as nonlinear transform of matrices are composited to brace the core computation of the algorithm. Plaintext related cipher technology is fully applied to cryptosystem. Moreover, other tools including cumulative sum and modular operation, random matrices, dot operation of matrices, sequence rearrangement, etc., are employed to support the algorithm. Cipher statistical analysis according to SP800 R1a shows that the cryptosystem is secure. Encryption simulations and performance analysis show that the algorithm performs well in effectiveness, feasibility, safety and robustness. The innovation of this work includes two aspects: firstly, the high-dimensional chaotic digital image encryption method is integrated into 4f optical image encryption system, and a new idea of optical image encryption is proposed; Secondly, a separate encryption paradigm of real and imaginary images in frequency domain is proposed, which greatly improves the security of image encryption and transmission. Other contributions of this paper consist in: a novel chaos with multiple free parameters is introduced to sustain the cryptosystem; the algorithm has a super large scale key space to ensure the security of the algorithm. Compared with other known schemes, the proposed algorithm shows relatively overall advantages. So, it is a nice candidate for image protection.