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Double-image encryption scheme based on the phase-truncated multiple-parameter Fresnel transform

Zhou Ling, Zhou Hang, Ma Yan, Zhou Nan-Run

Optica Applicata

2022

Vol. 52, nr 2

163--177

A double-image encryption algorithm is proposed with the phase-truncated multiple-parameter Fresnel transform. Firstly, the pixel positions of two plaintext images are scrambled and then the results are merged into one image with the scrambling operation. Subsequently, the resulting image is encrypted by phase truncation and phase reservation in the multiple-parameter Fresnel transform domain. The phase information is scrambled by the affine transform and then recombined with the amplitude information. The final encryption image is obtained with the pixel scrambling and diffusion methods to further enhance the security of the image encryption system, where the scrambling and diffusion operations are based on logistic map, logistic-sine system and 2D logistic-adjusted-sine map. The image encryption scheme is robust against the common attacks due to the nonlinear properties of diffusion and phase truncation. Numerical simulation results verify the performance and the security of the proposed double-image algorithm based on the phase-truncated multiple-parameter Fresnel transform.

Image encryption based on permutation polynomials over finite fields

Wu Jianhua, Liu Hai, Zhu Xishun

Optica Applicata

2020

Vol. 50, nr 3

357--376

In this paper, we propose an image encryption algorithm based on a permutation polynomial over finite fields proposed by the authors. The proposed image encryption process consists of four stages: i) a mapping from pixel gray-levels into finite field, ii) a pre-scrambling of pixels’ positions based on the parameterized permutation polynomial, iii) a symmetric matrix transform over finite fields which completes the operation of diffusion and, iv) a post-scrambling based on the permutation polynomial with different parameters. The parameters used for the polynomial parameterization and for constructing the symmetric matrix are used as cipher keys. Theoretical analysis and simulation demonstrate that the proposed image encryption scheme is feasible with a high efficiency and a strong ability of resisting various common attacks. In addition, there are not any round-off errors in computation over finite fields, thus guaranteeing a strictly lossless image encryption. Due to the intrinsic nonlinearity of permutation polynomials in finite fields, the proposed image encryption system is nonlinear and can resist known-plaintext and chosen-plaintext attacks.