Optical image encryption using different twiddle factors in the butterfly algorithm of fast Fourier transform

Song, Jaehun; Lee, Yeonho

doi:10.1016/j.optcom.2020.126707

Cited by 12 publications

(3 citation statements)

References 25 publications

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“…Step 8 Do the backward functions of add and XOR under modulus operation for the vector 𝑍 and vector 𝑏 to get vector 𝑒, as follows: 𝑒(MN) = (𝑒 0 ⊕ 𝑏 (MN) + 𝑍(i)) mod 256, 𝑒( j) = (𝑒( j + 1) ⊕ 𝑏 ( j) + 𝑍( j)) mod 256, (13) where j = MN − 1, . .…”

Section: Image Encryption Processmentioning

confidence: 99%

“…Image encryption algorithms mentioned above are all in spatial domain. Furthermore, frequency domain transform based encryption schemes [13][14][15][16][17] has also been studied recently. For example, Ding et al [14] presented a multiple chaotic systems based image encryption algorithm together with discrete wavelet transform (DWT), in which the plain image is first transformed by DWT operation, and permuted by low-dimensional chaotic system, then followed by diffusion with high-dimensional chaotic system.…”

Section: Introductionmentioning

confidence: 99%

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Asymmetric image encryption algorithm based on a new three-dimensional improved logistic chaotic map

Ye¹,

Wu²,

Huang³

et al. 2023

Chinese Phys. B

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Based on some analyses of existing chaotic image encryption frameworks and a new designed 3D-ILM chaotic map, an asymmetric image encryption algorithm using public-key RSA is presented in this paper. In the first stage, a new 3D-ILM chaotic map is proposed to enhance the chaotic behavior considering analysis of time sequence, Lyapunov exponent and Shannon entropy. In the second stage, combined with the public key RSA algorithm, a new key acquisition mathematical model (MKA) is constructed to obtain the initial keys for the 3D-ILM. Consequently, the keystream can be produced depending on the plain image for a higher security. Moreover, a novel process model (NPM) for the input of the 3D-ILM is built, which is built to improve the distribution uniformity of the chaotic sequence. In the third stage, to encrypt the plain image, a pre-process by XOR operation with a random matrix is applied. Then, the pre-processed image is performed by a permutation for rows, a downward modulo function for adjacent pixels, a permutation for columns, a forward direction XOR addition-modulo diffusion, and a backward direction XOR addition-modulo diffusion to achieve the final cipher image. Moreover, experiments show that the the proposed algorithm has a better performance. Especially, the number of pixels change rate (NPCR) is near to ideal case 99.6094%, with the unified average changing intensity (UACI) near to 33.4634% and the information entropy (IE) near to 8.

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Section: Image Encryption Processmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Asymmetric image encryption algorithm based on a new three-dimensional improved logistic chaotic map

Ye¹,

Wu²,

Huang³

et al. 2023

Chinese Phys. B

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“…Lin et al [ 17 ] also proposed a new form of butterfly transform, called deformable butterflies, as a replacement for convolutional or fully connected layers in neural networks. Song et al [ 18 ] instead used the butterfly algorithm to encrypt optical images.…”

Section: Related Workmentioning

confidence: 99%

Butterfly Transforms for Efficient Representation of Spatially Variant Point Spread Functions in Bayesian Imaging

Eberle

Frank

Stadler

et al. 2023

Entropy

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Bayesian imaging algorithms are becoming increasingly important in, e.g., astronomy, medicine and biology. Given that many of these algorithms compute iterative solutions to high-dimensional inverse problems, the efficiency and accuracy of the instrument response representation are of high importance for the imaging process. For efficiency reasons, point spread functions, which make up a large fraction of the response functions of telescopes and microscopes, are usually assumed to be spatially invariant in a given field of view and can thus be represented by a convolution. For many instruments, this assumption does not hold and degrades the accuracy of the instrument representation. Here, we discuss the application of butterfly transforms, which are linear neural network structures whose sizes scale sub-quadratically with the number of data points. Butterfly transforms are efficient by design, since they are inspired by the structure of the Cooley–Tukey fast Fourier transform. In this work, we combine them in several ways into butterfly networks, compare the different architectures with respect to their performance and identify a representation that is suitable for the efficient representation of a synthetic spatially variant point spread function up to a 1% error. Furthermore, we show its application in a short synthetic example.

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A synergetic image encryption method based on discrete fractional random transform and chaotic maps

Deng

et al. 2022

Multimed Tools Appl

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Optical image encryption using different twiddle factors in the butterfly algorithm of fast Fourier transform

Cited by 12 publications

References 25 publications

Asymmetric image encryption algorithm based on a new three-dimensional improved logistic chaotic map

Asymmetric image encryption algorithm based on a new three-dimensional improved logistic chaotic map

Butterfly Transforms for Efficient Representation of Spatially Variant Point Spread Functions in Bayesian Imaging

A synergetic image encryption method based on discrete fractional random transform and chaotic maps

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