Book ChapterDOI

# A novel image encryption framework based on markov map and singular value decomposition

22 Jun 2011-pp 286-296

TL;DR: A novel yet simple encryption technique is proposed based on toral automorphism, Markov map and singular value decomposition (SVD) and a reliable decryption scheme is proposed to construct original image from encrypted image.

AbstractIn this paper, a novel yet simple encryption technique is proposed based on toral automorphism, Markov map and singular value decomposition (SVD). The core idea of the proposed scheme is to scramble the pixel positions by the means of toral automorphism and then encrypting the scrambled image using Markov map and SVD. The combination of Markov map and SVD changed the pixels values significantly in order to confuse the relationship among the pixels. Finally, a reliable decryption scheme is proposed to construct original image from encrypted image. Experimental results demonstrate the efficiency and robustness of the proposed scheme.

##### Citations
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Journal ArticleDOI
TL;DR: A novel encryption scheme is proposed for securing multiple images during communication and transmission over insecure channel by discretizing continuous fractional wavelet transform and chaotic maps.
Abstract: The fractional wavelet transform is a useful mathematical transformation that generalizes the most prominent tool in signal and image processing namely wavelet transform by rotation of signals in the time-frequency plane. The definition of discrete fractional wavelet transform is not reported yet in the literature. Therefore, a definition of the discrete fractional wavelet transform is consolidated by discretizing continuous fractional wavelet transform in the proposed work. Possible applications of the transform are in transient signal processing, image analysis, image transmission, biometrics, image compression etc. In this paper, image transmission is chosen as the primary application and hence a novel encryption scheme is proposed for securing multiple images during communication and transmission over insecure channel. The proposed multiple image encryption scheme is consolidated by fractional wavelet transform and chaotic maps. First, all the images are encrypted followed by their sharing. The sharing process is done considering numerical techniques by making the sharing process a system of linear equations. Experimental results and security analysis demonstrate the efficiency and robustness of the proposed primary application.

108 citations

Journal ArticleDOI
TL;DR: Experimental results prove the first ETC approach for processing ECG data using the singular value decomposition technique to be an effective technique for assuring data security as well as compression performance forECG data.
Abstract: Electrocardiogram (ECG) monitoring systems are widely used in healthcare. ECG data must be compressed for transmission and storage. Furthermore, there is a need to be able to directly process biomedical signals in encrypted domains to ensure the protection of patients’ privacy. Existing encryption-then-compression (ETC) approaches for multimedia using the state-of-the-art encryption techniques inevitably sacrifice the compression efficiency or signal quality. This paper presents the first ETC approach for processing ECG data. The proposed approach not only can protect data privacy but also provide the same quality of the reconstructed signals without sacrificing the compression efficiency relative to unencrypted compressions. Specifically, the singular value decomposition technique is used to compress the data such that the proposed system can provide quality-control compressed data, even though the data has been encrypted. Experimental results prove the proposed system to be an effective technique for assuring data security as well as compression performance for ECG data.

39 citations

### Cites methods from "A novel image encryption framework ..."

• ...In [30], the SVD is exploited to produce an orthogonal key matrix which is used to encrypt images....

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Proceedings ArticleDOI
, Li Li2, Qiong Li2
01 May 2012
TL;DR: Simulation results justify the feasibility of the proposed scheme in image encryption purpose and show the ability to enforce security in chaotic systems and singular value decomposition.
Abstract: This paper presents an efficient image encryption scheme based on chaotic systems and singular value decomposition. In this scheme, the image pixel's positions are scrambled using chaotic systems with variable control parameters. To further enforce the security, the pixel gray values are modified using a combination between singular value decomposition (SVD) and chaotic polynomial map. Simulation results justify the feasibility of the proposed scheme in image encryption purpose.

10 citations

### Cites methods from "A novel image encryption framework ..."

• ...Scrambling is done by various methods based on toral automorphism ([3]), two or high-dimentional chaotic system with fixed control parameters [4] etc....

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• ..., and the diffusion is done through the diffusion cipher like chaos based methods ([2-5]), DNA based methods ([6]), and other assorted methods [7, ....

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• ...[3] Considered items Bhantnagar et al....

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• ...3 Resistance to differential attack To test the influence of a one-pixel change in cipher image, two common measures [1-5] are used, i....

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Proceedings ArticleDOI
01 Nov 2014
TL;DR: Experimental results shows that the proposed algorithm is lossless in nature, robust against statistical attacks and has high key sensitivity, and low PSNR values indicate thatThe proposed algorithm provides a high level of perceptual security for the biometric data.
Abstract: In the recent past we have been facing security challenges towards the transmission of biometric data over unsecured data channels. A lot of techniques have been developed and implemented for the secure transmission of the data. Taking the security concept in mind we introduce an efficient method based on chaotic theory for secured data transmission. The core idea of the proposed method is to shuffle the adjacent pixel correlation using the combination of Arnold Cat Map, Holmes Map and Singular Value Decomposition (SVD). The pixel values are scrambled using the Arnold Cat Map and further Holmes Map and SVD are used to alter the pixel values to complicate the relationship. Finally, decryption method is proposed to reconstruct the original data from encrypted data. Performance of proposed algorithm has been experimentally analyzed using statistical attack analysis, key sensitivity analysis and Peak Signal to Noise Ratio (PSNR). Experimental results shows that the proposed algorithm is lossless in nature, robust against statistical attacks and has high key sensitivity. Further low PSNR values indicate that the proposed algorithm provides a high level of perceptual security for the biometric data.

9 citations

### Cites background from "A novel image encryption framework ..."

• ...Although lot of research has been done in field of chaotic theory [6, 7] but still there is need for more robustness and perceptual security to make encryption schemes more efficient and secured....

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• ...Experimental results of the proposed algorithm indicates significant reduction of the correlation coefficient among adjacent pixels and significantly low PSNR values[6] makes it difficult to retrieve the original image from its encrypted one without the knowledge of correct decryption key....

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Proceedings ArticleDOI
01 Mar 2018
TL;DR: A novel image encryption technique is proposed based on reference sets with some prime numbers and polar decomposition using a recursive random number generation process, and a reliable decryption process has been presented to reconstruct the original image.
Abstract: In this paper, a novel image encryption technique is proposed based on reference sets with some prime numbers and polar decomposition. In this technique, a primary secret key and reference sets are used in the generation of feature vector using a recursive random number generation (RRNG) process. This feature vector is then used for encryption process. Finally, a reliable decryption process has been presented to reconstruct the original image. The Simulated results demonstrate the efficiency and robustness of the proposed technique.

7 citations

### Cites background from "A novel image encryption framework ..."

• ...In [7], the authors have proposed an encryption framework based on singular value decomposition (SVD)....

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##### References
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Journal ArticleDOI
Zhou Wang
TL;DR: Although the new index is mathematically defined and no human visual system model is explicitly employed, experiments on various image distortion types indicate that it performs significantly better than the widely used distortion metric mean squared error.
Abstract: We propose a new universal objective image quality index, which is easy to calculate and applicable to various image processing applications. Instead of using traditional error summation methods, the proposed index is designed by modeling any image distortion as a combination of three factors: loss of correlation, luminance distortion, and contrast distortion. Although the new index is mathematically defined and no human visual system model is explicitly employed, our experiments on various image distortion types indicate that it performs significantly better than the widely used distortion metric mean squared error. Demonstrative images and an efficient MATLAB implementation of the algorithm are available online at http://anchovy.ece.utexas.edu//spl sim/zwang/research/quality_index/demo.html.

4,687 citations

### "A novel image encryption framework ..." refers methods in this paper

• ...Peak signal to noise ration (PSNR), spectral distortion (SD), normalized singular value similarity (NSvS) [17] and Universal Image Quality Index (UIQ) [ 18 ] are used as the objective metrics to evaluate proposed technique....

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Journal ArticleDOI
TL;DR: The decomposition of A is called the singular value decomposition (SVD) and the diagonal elements of ∑ are the non-negative square roots of the eigenvalues of A T A; they are called singular values.
Abstract: Let A be a real m×n matrix with m≧n. It is well known (cf. [4]) that $$A = U\sum {V^T}$$ (1) where $${U^T}U = {V^T}V = V{V^T} = {I_n}{\text{ and }}\sum {\text{ = diag(}}{\sigma _{\text{1}}}{\text{,}} \ldots {\text{,}}{\sigma _n}{\text{)}}{\text{.}}$$ The matrix U consists of n orthonormalized eigenvectors associated with the n largest eigenvalues of AA T , and the matrix V consists of the orthonormalized eigenvectors of A T A. The diagonal elements of ∑ are the non-negative square roots of the eigenvalues of A T A; they are called singular values. We shall assume that $${\sigma _1} \geqq {\sigma _2} \geqq \cdots \geqq {\sigma _n} \geqq 0.$$ Thus if rank(A)=r, σ r+1 = σ r+2=⋯=σ n = 0. The decomposition (1) is called the singular value decomposition (SVD).

2,812 citations

### "A novel image encryption framework ..." refers background in this paper

• ...In linear algebra, the singular value decomposition(SVD) [ 14 ] is an important factorization of a rectangular real or complex matrix with many applications in signal/image processing and statistics....

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BookDOI
01 Jan 1989

2,183 citations

Journal ArticleDOI
TL;DR: In this Letter, a new image encryption scheme is presented, in which shuffling the positions and changing the grey values of image pixels are combined to confuse the relationship between the cipher-image and the plain-image.
Abstract: In this Letter, a new image encryption scheme is presented, in which shuffling the positions and changing the grey values of image pixels are combined to confuse the relationship between the cipher-image and the plain-image. Firstly, the Arnold cat map is used to shuffle the positions of the image pixels in the spatial-domain. Then the discrete output signal of the Chen's chaotic system is preprocessed to be suitable for the grayscale image encryption, and the shuffled image is encrypted by the preprocessed signal pixel by pixel. The experimental results demonstrate that the key space is large enough to resist the brute-force attack and the distribution of grey values of the encrypted image has a random-like behavior.

594 citations

Journal ArticleDOI
TL;DR: The experimental results demonstrate that the suggested encryption algorithm of image has the advantages of large key space and high security, and moreover, the distribution of grey values of the encrypted y image has a random-like behavior.
Abstract: This Letter presents a new image encryption scheme, which employs an image total shuffling matrix to shuffle the positions of image pixels and then uses a hyper-chaotic system to confuse the relationship between the plain-image and the cipher-image. The experimental results demonstrate that the suggested encryption algorithm of image has the advantages of large key space and high security, and moreover, the distribution of grey values of the encrypted y image has a random-like behavior.

554 citations