Image encryption based on higher-order singular value decomposition

Li Yong; Xun Xianchao; Wang Qingzhu

Volume 43 Issue S1

Jan. 2015

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Article Navigation > Infrared and Laser Engineering > 2014 > 43(S1): 243-247

Li Yong, Xun Xianchao, Wang Qingzhu. Image encryption based on higher-order singular value decomposition[J]. Infrared and Laser Engineering, 2014, 43(S1): 243-247.

Citation:

Li Yong, Xun Xianchao, Wang Qingzhu. Image encryption based on higher-order singular value decomposition[J]. Infrared and Laser Engineering, 2014, 43(S1): 243-247.

Image encryption based on higher-order singular value decomposition

1.
College of Information Engineering,Jilin Teathers' Institute of Engineering & Technology,Changchun 130052,China;
2.
Basic Department of Basic Flight Traiming Base,Air Force Aviation University,Changchun 130022,China;
3.
School of Information Engineering,Northeast Dianli University,Jilin 132012,China

Received Date: 2014-04-26
Rev Recd Date: 2014-04-15
Publish Date: 2015-01-25

Abstract

The existing Singular Value Decomposition (SVD) based color information encryption system provided an optical matrix composition scheme, secure ciphertexts and very sensitive keys. As the Higher-order SVD (HOSVD) is a natural multi-linear extension of the matrix SVD, an HOSVD based color image encryption algorithm was proposed. In the encryption procedure, HOSVD can generate more multiplication orders of the ciphertexts (decomposition parts) than what SVD provides. These multiplication orders can be used as effective keys to make unauthorized decryption harder. In the decryption procedure, the reconstruction accuracy of HOSVD is higher than that of SVD. These advantages enhance the accuracy, security and robustness. Numerical simulations based on a test dataset of 100 images support the viability of the proposed algorithm.
- higher-order dingular value decomposition,
- three dimensional matrix,
- gyrator transform

References

[1]
[2]	Matoba O, Nomura T, Perez C E, et al. Optical techniques for information security[J]. Proceedings of IEEE, 2009, 97(6): 1128-1148.
[3]
[4]	Liu S, Guo C L, Sheridan J T. A review of optical image encryption techniques[J]. Optics and Laser Technology, 2014, 57: 327-342.
[5]	Refregier P, Javidi B. Optical image encryption based on input plane and Fourier plane random encoding[J]. Optics Letters, 1995, 20(7): 767-769.
[6]
[7]
[8]	Javidi B, Nomura T. Securing information by use of digital holography[J]. Optics Letters, 2000, 25(1): 28-30.
[9]
[10]	Taajahuerce E, Javidi B. Encrypting three-dimensional information with digital holography[J]. Applied Optics, 2000, 39(35): 6595-6601.
[11]	Haw J W, Park C S, Ryu D H. Optical image encryption based on XOR operations[J]. Optical Engineering, 1999, 38(1): 47-54.
[12]
[13]
[14]	Chen L F, Zhao D M. Optical color image encryption by wavelength multiplexing and lensless Fresnel transform holograms[J]. Optics Express, 2006, 14(19): 8552-8560.
[15]	Unnikrishnan G, Joseph J, Singh K. Optics encryption by double-random phase encoding in the fractional Fourier domain[J]. Optics Letters, 2000, 25: 887-889.
[16]
[17]
[18]	Chen L F, Zhao D M, Ge F. Image encryption based on singular value decomposition and arnold transform in fractional domain[J]. Optics Communications, 2013, 291: 98-103.
[19]	Liu Z, Liu S. Random fractional Fourier transform[J]. Optics Letters, 2007, 32: 2088-2090.
[20]
[21]	Hennelly B M, Sheridan J T. Generalizing, optimizing, and inventing numerical algorithms for the fractional Fourier, Fresnel, and linear canonical transforms[J]. Journal of the Optical Society of America A, 2005, 22(5): 917-927.
[22]
[23]
[24]	Liu S, Sheridan J T. Optical encryption by combining image scrambling techniques in fractional fourier domains[J]. Optics Communications, 2013, 287(10): 73-80.
[25]	Tao R, Lang J, Wang Y. Optical image encryption based on the multiple parameter fractional Fourier transform[J]. Optics Letters, 2008, 33: 581-583.
[26]
[27]	Alieva T, Bastiaans J. Alternative representation of the linear canonical integral transform[J]. Optics Letters, 2005, 30(24): 3302-3304.
[28]
[29]	Rodrigo J A, Alieva T. Calvo M L. Applications of gyrator transform for image processing[J]. Optics Communications, 2007, 278(2): 279-284.
[30]
[31]	Rodrigo J A, Alieva T, Calvo M L. Experimental implementation of the gyrator transform[J]. Journal of Optical Society of America A, 2007, 24(10): 3135-3139.
[32]
[33]
[34]	Liu Z J, Chen D Z, Ma J P. Fast algorithm of discrete gyrator transform based on convolution operation[J]. Optik, 2011, 122: 864-867.
[35]	Muhammad R A. An asymmetric color image cryptosystem based on schur decomposition in gyrator transform domain[J]. Optics and Lasers in Engineering, 2014, 58: 39-47.
[36]
[37]
[38]	Muhammad R A. Color information verification system based on singular value decomposition in gyrator transform domains[J]. Optics and Lasers in Engineering, 2014, 57: 13-19.
[39]
[40]	Lieven D L. A multilinear singular value decomposition[J]. Siam Journal on Matrix Analysis and Application, 2000, 21 (4): 1253-1278.
[41]	Vannieuwenhoven N. A new truncation strategy for the higher-order singular value decomposition[J]. Siam Journal on Scientific Computing, 2012, 34(2): 1027-1052.
[42]
[43]
[44]	Rajwade A, Rangarajan A, Banerjee A. Image denosing using the higher order singular value decomposition[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2013, 35(4): 849-862.
[45]	Xiao H S, Wang Z L, Fan Z G. Optical distortion Evaluation of an aerodynamically heated window, based on the higher-order singular value decomposition with the influence of elasto-optical effect excluded[J]. Applied Optics, 2012, 51(16): 3269-3278.
[46]
[47]	Jussi S, Andreas R, Visa K. Sequential unfolding SVD for tensors with applications in array signal processing[J]. IEEE Transactions on Signal Processing, 2009, 57(12): 4719-4733.
[48]
[49]
[50]	Chen Y L, Hsu C T. Multilinear graph embedding: representation and regularization for images[J]. IEEE Transactions on Image Processing, 2014, 23(2): 741-754.
[51]	Li Q, Shi X Q, Schonfeld D. Robust HOSVD-based higher-order data indexing and retrieval[J]. IEEE Signal Processing Letters, 2013, 20(10): 984-987.
[52]
[53]	Fan D S, Meng X F, Wang Y R. Optical information encoding and image watermarking scheme based on phase-shifting interferometry and singular value decomposition[J]. Journal of Modern Optics, 2013, 60(9): 749-756.

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通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

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Image encryption based on higher-order singular value decomposition

1. College of Information Engineering,Jilin Teathers' Institute of Engineering & Technology,Changchun 130052,China;

2. Basic Department of Basic Flight Traiming Base,Air Force Aviation University,Changchun 130022,China;

3. School of Information Engineering,Northeast Dianli University,Jilin 132012,China

Received Date: 2014-04-26

Rev Recd Date: 2014-04-15

Publish Date: 2015-01-25

Key words:

higher-order dingular value decomposition /
three dimensional matrix /
gyrator transform

Abstract: The existing Singular Value Decomposition (SVD) based color information encryption system provided an optical matrix composition scheme, secure ciphertexts and very sensitive keys. As the Higher-order SVD (HOSVD) is a natural multi-linear extension of the matrix SVD, an HOSVD based color image encryption algorithm was proposed. In the encryption procedure, HOSVD can generate more multiplication orders of the ciphertexts (decomposition parts) than what SVD provides. These multiplication orders can be used as effective keys to make unauthorized decryption harder. In the decryption procedure, the reconstruction accuracy of HOSVD is higher than that of SVD. These advantages enhance the accuracy, security and robustness. Numerical simulations based on a test dataset of 100 images support the viability of the proposed algorithm.

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Reference (53)

[1]
[2]	Matoba O, Nomura T, Perez C E, et al. Optical techniques for information security[J]. Proceedings of IEEE, 2009, 97(6): 1128-1148.
[3]
[4]	Liu S, Guo C L, Sheridan J T. A review of optical image encryption techniques[J]. Optics and Laser Technology, 2014, 57: 327-342.
[5]	Refregier P, Javidi B. Optical image encryption based on input plane and Fourier plane random encoding[J]. Optics Letters, 1995, 20(7): 767-769.
[6]
[7]
[8]	Javidi B, Nomura T. Securing information by use of digital holography[J]. Optics Letters, 2000, 25(1): 28-30.
[9]
[10]	Taajahuerce E, Javidi B. Encrypting three-dimensional information with digital holography[J]. Applied Optics, 2000, 39(35): 6595-6601.
[11]	Haw J W, Park C S, Ryu D H. Optical image encryption based on XOR operations[J]. Optical Engineering, 1999, 38(1): 47-54.
[12]
[13]
[14]	Chen L F, Zhao D M. Optical color image encryption by wavelength multiplexing and lensless Fresnel transform holograms[J]. Optics Express, 2006, 14(19): 8552-8560.
[15]	Unnikrishnan G, Joseph J, Singh K. Optics encryption by double-random phase encoding in the fractional Fourier domain[J]. Optics Letters, 2000, 25: 887-889.
[16]
[17]
[18]	Chen L F, Zhao D M, Ge F. Image encryption based on singular value decomposition and arnold transform in fractional domain[J]. Optics Communications, 2013, 291: 98-103.
[19]	Liu Z, Liu S. Random fractional Fourier transform[J]. Optics Letters, 2007, 32: 2088-2090.
[20]
[21]	Hennelly B M, Sheridan J T. Generalizing, optimizing, and inventing numerical algorithms for the fractional Fourier, Fresnel, and linear canonical transforms[J]. Journal of the Optical Society of America A, 2005, 22(5): 917-927.
[22]
[23]
[24]	Liu S, Sheridan J T. Optical encryption by combining image scrambling techniques in fractional fourier domains[J]. Optics Communications, 2013, 287(10): 73-80.
[25]	Tao R, Lang J, Wang Y. Optical image encryption based on the multiple parameter fractional Fourier transform[J]. Optics Letters, 2008, 33: 581-583.
[26]
[27]	Alieva T, Bastiaans J. Alternative representation of the linear canonical integral transform[J]. Optics Letters, 2005, 30(24): 3302-3304.
[28]
[29]	Rodrigo J A, Alieva T. Calvo M L. Applications of gyrator transform for image processing[J]. Optics Communications, 2007, 278(2): 279-284.
[30]
[31]	Rodrigo J A, Alieva T, Calvo M L. Experimental implementation of the gyrator transform[J]. Journal of Optical Society of America A, 2007, 24(10): 3135-3139.
[32]
[33]
[34]	Liu Z J, Chen D Z, Ma J P. Fast algorithm of discrete gyrator transform based on convolution operation[J]. Optik, 2011, 122: 864-867.
[35]	Muhammad R A. An asymmetric color image cryptosystem based on schur decomposition in gyrator transform domain[J]. Optics and Lasers in Engineering, 2014, 58: 39-47.
[36]
[37]
[38]	Muhammad R A. Color information verification system based on singular value decomposition in gyrator transform domains[J]. Optics and Lasers in Engineering, 2014, 57: 13-19.
[39]
[40]	Lieven D L. A multilinear singular value decomposition[J]. Siam Journal on Matrix Analysis and Application, 2000, 21 (4): 1253-1278.
[41]	Vannieuwenhoven N. A new truncation strategy for the higher-order singular value decomposition[J]. Siam Journal on Scientific Computing, 2012, 34(2): 1027-1052.
[42]
[43]
[44]	Rajwade A, Rangarajan A, Banerjee A. Image denosing using the higher order singular value decomposition[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2013, 35(4): 849-862.
[45]	Xiao H S, Wang Z L, Fan Z G. Optical distortion Evaluation of an aerodynamically heated window, based on the higher-order singular value decomposition with the influence of elasto-optical effect excluded[J]. Applied Optics, 2012, 51(16): 3269-3278.
[46]
[47]	Jussi S, Andreas R, Visa K. Sequential unfolding SVD for tensors with applications in array signal processing[J]. IEEE Transactions on Signal Processing, 2009, 57(12): 4719-4733.
[48]
[49]
[50]	Chen Y L, Hsu C T. Multilinear graph embedding: representation and regularization for images[J]. IEEE Transactions on Image Processing, 2014, 23(2): 741-754.
[51]	Li Q, Shi X Q, Schonfeld D. Robust HOSVD-based higher-order data indexing and retrieval[J]. IEEE Signal Processing Letters, 2013, 20(10): 984-987.
[52]
[53]	Fan D S, Meng X F, Wang Y R. Optical information encoding and image watermarking scheme based on phase-shifting interferometry and singular value decomposition[J]. Journal of Modern Optics, 2013, 60(9): 749-756.

Image encryption based on higher-order singular value decomposition

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