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Double-image encryption algorithm based on discrete fractional angular transform and fractional Fourier transform

Qiu Tian, Dai Wei-Hua, Chen Su-Hua, Zhou Hang, Gong Li-Hua

Optica Applicata

2022

Vol. 52, nr 4

669--684

By combining fractional Fourier transform with discrete fractional angular transform, a double-image encryption algorithm is designed. The discrete cosine transform is performed on two grayscale images to generate a spectrum image, and then the generated spectrum image is compressed into an image with Zigzag scanning. The compressed image is processed with the discrete fractional angular transform, and then fractional Fourier transform and double random phase coding are executed on the image. The DNA operation controlled by chaotic system is introduced to change the pixel values. Finally, the ciphertext image is obtained through bit-level permutation and pixel adaptive diffusion. The statistical information of the plaintext images is employed as the input of the SHA-256 to calculate the initial conditions of the chaotic map. Simulation experiments demonstrate that the double-image encryption algorithm can effectively reduce the correlation among adjacent pixels of the plaintext images.

Digital watermarking algorithm based on 4-level discrete wavelet transform and discrete fractional angular transform

Li Jing-You, Zhao Chun-Hui, Zhang Guang-Da

Optica Applicata

2021

Vol. 51, nr 4

605--619

Nowadays, there are many watermarking algorithms based on wavelet transform. The simple one is to insert directly the watermark into the wavelet transform coefficients. However, most of the existing watermarking schemes can only resist traditional signal processing attacks, such as image compression, noise and filtering. When the watermarked image is subject to geometric transformations, especially rotation attack, it is hard to detect the watermark successfully. In this paper, a digital watermarking algorithm is proposed based on 4-level discrete wavelet transform and discrete fractional angular transform. To enhance the security of the algorithm, the watermark is scrambled with the simplicity of Arnold transform and chaos-based mix optical bistability model, since the chaos is pseudorandom and sensitive to the initial values. And the watermark is embedded into the medium frequency sub-band of the 1-level wavelet decomposition according to the Harris feature point detection. Simulation results show that the proposed digital watermarking algorithm by combining 4-level discrete wavelet transform with discrete fractional angular transform could resist rotation attack and other common attacks.

Image encryption combining discrete fractional angular transform with Arnold transform in image bit planes

Zhou Z., Yu J., Liao Q., Gong L.

Optica Applicata

2018

Vol. 48, nr 2

225--236

A new image encryption algorithm by using a discrete fractional angular transform and Arnold transform in image bit planes is investigated. In the image encryption algorithm, the original image is encrypted by the Arnold transform in image bit planes firstly, and then the resulting image is encrypted by the discrete fractional angular transform further. The key of the image encryption algorithm includes the parameters of the Arnold transform and the order of the discrete fractional angular transform. It is shown that the proposed image encryption algorithm is of high security and strong enough to counteract some conventional image attack manners.

Image encryption algorithm by using the logistic map and discrete fractional angular transform

Yu J., Li Y., Xie X., Zhou N., Zhou Z.

Optica Applicata

2017

Vol. 47, nr 1

141--155

A new image encryption scheme based on logistic map and discrete fractional angular transform has been proposed. In the proposed scheme, the original image is encrypted with the random sequence generated by the logistic map, and the encrypted image is subsequently processed by the discrete fractional angular transform, which produces the ciphertext after double encryptions. The parameters of the logistic map and the order of the discrete fractional angular transform serve as the main keys of the image encryption algorithm. Simulation results show that the proposed image encryption algorithm can effectively resist the attacks of statistical analysis, and has acceptable encryption effect and security.