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

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.

Abstract: In 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.

...read more

##### Citations

108 citations

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....

[...]

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....

[...]

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

[...]

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

[...]

...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....

[...]

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....

[...]

...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....

[...]

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)....

[...]

##### References

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....

[...]

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....

[...]

594 citations

554 citations