Abstract

During the past decades, chaos-based permutation-diffusion type image cipher has been widely investigated to meet the increasing demand for real-time secure image transmission over public networks. However, the existing researches almost exclusively focus on the improvements of the permutation and diffusion methods independently, without consideration of cooperation between the two processes. In this paper, an improved permutation-diffusion type image cipher with a chaotic orbit perturbing mechanism is proposed. In the permutation stage, pixels in the plain image are shuffled with a pixel-swapping mechanism, and the pseudorandom locations are generated by chaotic logistic map iteration. Furthermore, a plain pixel related chaotic orbit perturbing mechanism is introduced. As a result, a tiny change in plain image will be spread out during the confusion process, and hence an effective diffusion effect is introduced. By using a reverse direction diffusion method, the introduced diffusion effect will be further diffused to the whole cipher image within one overall encryption round. Simulation results and extensive cryptanalysis justify that the proposed scheme has a satisfactory security with a low computational complexity, which renders it a good candidate for real-time secure image storage and distribution applications.

© 2013 Optical Society of America

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2012

C. X. Zhu, “A novel image encryption scheme based on improved hyper chaotic sequences,” Opt. Commun.285(1), 29–37 (2012).
[CrossRef]

W. Zhang, K. W. Wong, H. Yu, and Z. L. Zhu, “An image encryption scheme using lightweight bit-level confusion and cascade cross circular diffusion,” Opt. Commun.285(9), 2343–2354 (2012).
[CrossRef]

X. J. Tong, “The novel bilateral - diffusion image encryption algorithm with dynamical compound chaos,” J. Syst. Software85(4), 850–858 (2012).
[CrossRef]

C. Fu, J. J. Chen, H. Zou, W. H. Meng, Y. F. Zhan, and Y. W. Yu, “A chaos-based digital image encryption scheme with an improved diffusion strategy,” Opt. Express20(3), 2363–2378 (2012).
[CrossRef] [PubMed]

2011

C. Fu, B. B. Lin, Y. S. Miao, X. Liu, and J. J. Chen, “A novel chaos-based bit-level permutation scheme for digital image encryption,” Opt. Commun.284(23), 5415–5423 (2011).
[CrossRef]

Z. L. Zhu, W. Zhang, K. W. Wong, and H. Yu, “A chaos-based symmetric image encryption scheme using a bit-level permutation,” Inf. Sci.181(6), 1171–1186 (2011).
[CrossRef]

2009

Y. Wang, K. W. Wong, X. F. Liao, T. Xiang, and G. R. Chen, “A chaos-based image encryption algorithm with variable control parameters,” Chaos Solitons Fractals41(4), 1773–1783 (2009).
[CrossRef]

K. W. Wong, B. S. H. Kwok, and C. H. Yuen, “An efficient diffusion approach for chaos-based image encryption,” Chaos Solitons Fractals41(5), 2652–2663 (2009).
[CrossRef]

Y. Wang, K. W. Wong, X. F. Liao, T. Xiang, and G. R. Chen, “A chaos-based image encryption algorithm with variable control parameters,” Chaos Solitons Fractals41(4), 1773–1783 (2009).
[CrossRef]

S. T. Liu and F. Y. Sun, “Spatial chaos-based image encryption design,” Sci. China, Ser. G52(2), 177–183 (2009).
[CrossRef]

C. K. Huang and H. H. Nien, “Multi chaotic systems based pixel shuffle for image encryption,” Opt. Commun.282(11), 2123–2127 (2009).
[CrossRef]

S. Mazloom and A. M. Eftekhari-Moghadam, “Color image encryption based on Coupled Nonlinear Chaotic Map,” Chaos Solitons Fractals42(3), 1745–1754 (2009).
[CrossRef]

R. Rhouma, S. Meherzi, and S. Belghith, “OCML-based colour image encryption,” Chaos Solitons Fractals40(1), 309–318 (2009).
[CrossRef]

2008

F. Y. Sun, S. T. Liu, Z. Q. Li, and Z. W. Lu, “A novel image encryption scheme based on spatial chaos map,” Chaos Solitons Fractals38(3), 631–640 (2008).
[CrossRef]

T. G. Gao and Z. Q. Chen, “A new image encryption algorithm based on hyper-chaos,” Phys. Lett. A372(4), 394–400 (2008).
[CrossRef]

S. Behnia, A. Akhshani, H. Mahmodi, and A. Akhavan, “A novel algorithm for image encryption based on mixture of chaotic maps,” Chaos Solitons Fractals35(2), 408–419 (2008).
[CrossRef]

A. N. Pisarchik and M. Zanin, “Image encryption with chaotically coupled chaotic maps,” Physica D237(20), 2638–2648 (2008).
[CrossRef]

K. W. Wong, B. S. H. Kwok, and W. S. Law, “A fast image encryption scheme based on chaotic standard map,” Phys. Lett. A372(15), 2645–2652 (2008).
[CrossRef]

2007

T. Xiang, K. W. Wong, and X. F. Liao, “Selective image encryption using a spatiotemporal chaotic system,” Chaos17(2), 023115 (2007).
[CrossRef] [PubMed]

F. Y. Sun, S. T. Liu, and Z. W. Lu, “Image encryption using high-dimension chaotic system,” Chin. Phys.16(12), 3616–3623 (2007).
[CrossRef]

Y. Wang, X. F. Liao, T. Xiang, K.-W. Wong, and D. Yang, “Cryptanalysis and improvement on a block cryptosystem based on iteration a chaotic map,” Phys. Lett. A363(4), 277–281 (2007).
[CrossRef]

J. Wei, X. F. Liao, K. W. Wong, and T. Zhou, “Cryptanalysis of a cryptosystem using multiple one-dimensional chaotic maps,” Commun. Nonlinear Sci. Numer. Simul.12(5), 814–822 (2007).
[CrossRef]

2006

G. Alvarez and S. Li, “Some basic cryptographic requirements for chaos-based cryptosystems,” Int. J. Bifurcat. Chaos16(8), 2129–2151 (2006).
[CrossRef]

2005

S. G. Lian, J. S. Sun, and Z. Q. Wang, “A block cipher based on a suitable use of chaotic standard map,” Chaos Solitons Fractals26(1), 117–129 (2005).
[CrossRef]

2004

Y. B. Mao, G. R. Chen, and S. G. Lian, “A novel fast image encryption scheme based on 3D chaotic baker maps,” Int. J. Bifurcat. Chaos14(10), 3613–3624 (2004).
[CrossRef]

G. R. Chen, Y. B. Mao, and C. K. Chui, “A symmetric image encryption scheme based on 3D chaotic cat maps,” Chaos Solitons Fractals21(3), 749–761 (2004).
[CrossRef]

1998

J. Fridrich, “Symmetric ciphers based on two-dimensional chaotic maps,” Int. J. Bifurcat. Chaos8(6), 1259–1284 (1998).
[CrossRef]

1949

C. E. Shannon, “Communication theory of secrecy systems,” Bell Syst. Tech. J.28(4), 656–715 (1949).
[CrossRef]

Akhavan, A.

S. Behnia, A. Akhshani, H. Mahmodi, and A. Akhavan, “A novel algorithm for image encryption based on mixture of chaotic maps,” Chaos Solitons Fractals35(2), 408–419 (2008).
[CrossRef]

Akhshani, A.

S. Behnia, A. Akhshani, H. Mahmodi, and A. Akhavan, “A novel algorithm for image encryption based on mixture of chaotic maps,” Chaos Solitons Fractals35(2), 408–419 (2008).
[CrossRef]

Alvarez, G.

G. Alvarez and S. Li, “Some basic cryptographic requirements for chaos-based cryptosystems,” Int. J. Bifurcat. Chaos16(8), 2129–2151 (2006).
[CrossRef]

Behnia, S.

S. Behnia, A. Akhshani, H. Mahmodi, and A. Akhavan, “A novel algorithm for image encryption based on mixture of chaotic maps,” Chaos Solitons Fractals35(2), 408–419 (2008).
[CrossRef]

Belghith, S.

R. Rhouma, S. Meherzi, and S. Belghith, “OCML-based colour image encryption,” Chaos Solitons Fractals40(1), 309–318 (2009).
[CrossRef]

Chen, G. R.

Y. Wang, K. W. Wong, X. F. Liao, T. Xiang, and G. R. Chen, “A chaos-based image encryption algorithm with variable control parameters,” Chaos Solitons Fractals41(4), 1773–1783 (2009).
[CrossRef]

Y. Wang, K. W. Wong, X. F. Liao, T. Xiang, and G. R. Chen, “A chaos-based image encryption algorithm with variable control parameters,” Chaos Solitons Fractals41(4), 1773–1783 (2009).
[CrossRef]

G. R. Chen, Y. B. Mao, and C. K. Chui, “A symmetric image encryption scheme based on 3D chaotic cat maps,” Chaos Solitons Fractals21(3), 749–761 (2004).
[CrossRef]

Y. B. Mao, G. R. Chen, and S. G. Lian, “A novel fast image encryption scheme based on 3D chaotic baker maps,” Int. J. Bifurcat. Chaos14(10), 3613–3624 (2004).
[CrossRef]

Chen, J. J.

C. Fu, J. J. Chen, H. Zou, W. H. Meng, Y. F. Zhan, and Y. W. Yu, “A chaos-based digital image encryption scheme with an improved diffusion strategy,” Opt. Express20(3), 2363–2378 (2012).
[CrossRef] [PubMed]

C. Fu, B. B. Lin, Y. S. Miao, X. Liu, and J. J. Chen, “A novel chaos-based bit-level permutation scheme for digital image encryption,” Opt. Commun.284(23), 5415–5423 (2011).
[CrossRef]

Chen, Z. Q.

T. G. Gao and Z. Q. Chen, “A new image encryption algorithm based on hyper-chaos,” Phys. Lett. A372(4), 394–400 (2008).
[CrossRef]

Chui, C. K.

G. R. Chen, Y. B. Mao, and C. K. Chui, “A symmetric image encryption scheme based on 3D chaotic cat maps,” Chaos Solitons Fractals21(3), 749–761 (2004).
[CrossRef]

Eftekhari-Moghadam, A. M.

S. Mazloom and A. M. Eftekhari-Moghadam, “Color image encryption based on Coupled Nonlinear Chaotic Map,” Chaos Solitons Fractals42(3), 1745–1754 (2009).
[CrossRef]

Fridrich, J.

J. Fridrich, “Symmetric ciphers based on two-dimensional chaotic maps,” Int. J. Bifurcat. Chaos8(6), 1259–1284 (1998).
[CrossRef]

Fu, C.

C. Fu, J. J. Chen, H. Zou, W. H. Meng, Y. F. Zhan, and Y. W. Yu, “A chaos-based digital image encryption scheme with an improved diffusion strategy,” Opt. Express20(3), 2363–2378 (2012).
[CrossRef] [PubMed]

C. Fu, B. B. Lin, Y. S. Miao, X. Liu, and J. J. Chen, “A novel chaos-based bit-level permutation scheme for digital image encryption,” Opt. Commun.284(23), 5415–5423 (2011).
[CrossRef]

Gao, T. G.

T. G. Gao and Z. Q. Chen, “A new image encryption algorithm based on hyper-chaos,” Phys. Lett. A372(4), 394–400 (2008).
[CrossRef]

Huang, C. K.

C. K. Huang and H. H. Nien, “Multi chaotic systems based pixel shuffle for image encryption,” Opt. Commun.282(11), 2123–2127 (2009).
[CrossRef]

Kwok, B. S. H.

K. W. Wong, B. S. H. Kwok, and C. H. Yuen, “An efficient diffusion approach for chaos-based image encryption,” Chaos Solitons Fractals41(5), 2652–2663 (2009).
[CrossRef]

K. W. Wong, B. S. H. Kwok, and W. S. Law, “A fast image encryption scheme based on chaotic standard map,” Phys. Lett. A372(15), 2645–2652 (2008).
[CrossRef]

Law, W. S.

K. W. Wong, B. S. H. Kwok, and W. S. Law, “A fast image encryption scheme based on chaotic standard map,” Phys. Lett. A372(15), 2645–2652 (2008).
[CrossRef]

Li, S.

G. Alvarez and S. Li, “Some basic cryptographic requirements for chaos-based cryptosystems,” Int. J. Bifurcat. Chaos16(8), 2129–2151 (2006).
[CrossRef]

Li, Z. Q.

F. Y. Sun, S. T. Liu, Z. Q. Li, and Z. W. Lu, “A novel image encryption scheme based on spatial chaos map,” Chaos Solitons Fractals38(3), 631–640 (2008).
[CrossRef]

Lian, S. G.

S. G. Lian, J. S. Sun, and Z. Q. Wang, “A block cipher based on a suitable use of chaotic standard map,” Chaos Solitons Fractals26(1), 117–129 (2005).
[CrossRef]

Y. B. Mao, G. R. Chen, and S. G. Lian, “A novel fast image encryption scheme based on 3D chaotic baker maps,” Int. J. Bifurcat. Chaos14(10), 3613–3624 (2004).
[CrossRef]

Liao, X. F.

Y. Wang, K. W. Wong, X. F. Liao, T. Xiang, and G. R. Chen, “A chaos-based image encryption algorithm with variable control parameters,” Chaos Solitons Fractals41(4), 1773–1783 (2009).
[CrossRef]

Y. Wang, K. W. Wong, X. F. Liao, T. Xiang, and G. R. Chen, “A chaos-based image encryption algorithm with variable control parameters,” Chaos Solitons Fractals41(4), 1773–1783 (2009).
[CrossRef]

Y. Wang, X. F. Liao, T. Xiang, K.-W. Wong, and D. Yang, “Cryptanalysis and improvement on a block cryptosystem based on iteration a chaotic map,” Phys. Lett. A363(4), 277–281 (2007).
[CrossRef]

T. Xiang, K. W. Wong, and X. F. Liao, “Selective image encryption using a spatiotemporal chaotic system,” Chaos17(2), 023115 (2007).
[CrossRef] [PubMed]

J. Wei, X. F. Liao, K. W. Wong, and T. Zhou, “Cryptanalysis of a cryptosystem using multiple one-dimensional chaotic maps,” Commun. Nonlinear Sci. Numer. Simul.12(5), 814–822 (2007).
[CrossRef]

Lin, B. B.

C. Fu, B. B. Lin, Y. S. Miao, X. Liu, and J. J. Chen, “A novel chaos-based bit-level permutation scheme for digital image encryption,” Opt. Commun.284(23), 5415–5423 (2011).
[CrossRef]

Liu, S. T.

S. T. Liu and F. Y. Sun, “Spatial chaos-based image encryption design,” Sci. China, Ser. G52(2), 177–183 (2009).
[CrossRef]

F. Y. Sun, S. T. Liu, Z. Q. Li, and Z. W. Lu, “A novel image encryption scheme based on spatial chaos map,” Chaos Solitons Fractals38(3), 631–640 (2008).
[CrossRef]

F. Y. Sun, S. T. Liu, and Z. W. Lu, “Image encryption using high-dimension chaotic system,” Chin. Phys.16(12), 3616–3623 (2007).
[CrossRef]

Liu, X.

C. Fu, B. B. Lin, Y. S. Miao, X. Liu, and J. J. Chen, “A novel chaos-based bit-level permutation scheme for digital image encryption,” Opt. Commun.284(23), 5415–5423 (2011).
[CrossRef]

Lu, Z. W.

F. Y. Sun, S. T. Liu, Z. Q. Li, and Z. W. Lu, “A novel image encryption scheme based on spatial chaos map,” Chaos Solitons Fractals38(3), 631–640 (2008).
[CrossRef]

F. Y. Sun, S. T. Liu, and Z. W. Lu, “Image encryption using high-dimension chaotic system,” Chin. Phys.16(12), 3616–3623 (2007).
[CrossRef]

Mahmodi, H.

S. Behnia, A. Akhshani, H. Mahmodi, and A. Akhavan, “A novel algorithm for image encryption based on mixture of chaotic maps,” Chaos Solitons Fractals35(2), 408–419 (2008).
[CrossRef]

Mao, Y. B.

G. R. Chen, Y. B. Mao, and C. K. Chui, “A symmetric image encryption scheme based on 3D chaotic cat maps,” Chaos Solitons Fractals21(3), 749–761 (2004).
[CrossRef]

Y. B. Mao, G. R. Chen, and S. G. Lian, “A novel fast image encryption scheme based on 3D chaotic baker maps,” Int. J. Bifurcat. Chaos14(10), 3613–3624 (2004).
[CrossRef]

Mazloom, S.

S. Mazloom and A. M. Eftekhari-Moghadam, “Color image encryption based on Coupled Nonlinear Chaotic Map,” Chaos Solitons Fractals42(3), 1745–1754 (2009).
[CrossRef]

Meherzi, S.

R. Rhouma, S. Meherzi, and S. Belghith, “OCML-based colour image encryption,” Chaos Solitons Fractals40(1), 309–318 (2009).
[CrossRef]

Meng, W. H.

Miao, Y. S.

C. Fu, B. B. Lin, Y. S. Miao, X. Liu, and J. J. Chen, “A novel chaos-based bit-level permutation scheme for digital image encryption,” Opt. Commun.284(23), 5415–5423 (2011).
[CrossRef]

Nien, H. H.

C. K. Huang and H. H. Nien, “Multi chaotic systems based pixel shuffle for image encryption,” Opt. Commun.282(11), 2123–2127 (2009).
[CrossRef]

Pisarchik, A. N.

A. N. Pisarchik and M. Zanin, “Image encryption with chaotically coupled chaotic maps,” Physica D237(20), 2638–2648 (2008).
[CrossRef]

Rhouma, R.

R. Rhouma, S. Meherzi, and S. Belghith, “OCML-based colour image encryption,” Chaos Solitons Fractals40(1), 309–318 (2009).
[CrossRef]

Shannon, C. E.

C. E. Shannon, “Communication theory of secrecy systems,” Bell Syst. Tech. J.28(4), 656–715 (1949).
[CrossRef]

Sun, F. Y.

S. T. Liu and F. Y. Sun, “Spatial chaos-based image encryption design,” Sci. China, Ser. G52(2), 177–183 (2009).
[CrossRef]

F. Y. Sun, S. T. Liu, Z. Q. Li, and Z. W. Lu, “A novel image encryption scheme based on spatial chaos map,” Chaos Solitons Fractals38(3), 631–640 (2008).
[CrossRef]

F. Y. Sun, S. T. Liu, and Z. W. Lu, “Image encryption using high-dimension chaotic system,” Chin. Phys.16(12), 3616–3623 (2007).
[CrossRef]

Sun, J. S.

S. G. Lian, J. S. Sun, and Z. Q. Wang, “A block cipher based on a suitable use of chaotic standard map,” Chaos Solitons Fractals26(1), 117–129 (2005).
[CrossRef]

Tong, X. J.

X. J. Tong, “The novel bilateral - diffusion image encryption algorithm with dynamical compound chaos,” J. Syst. Software85(4), 850–858 (2012).
[CrossRef]

Wang, Y.

Y. Wang, K. W. Wong, X. F. Liao, T. Xiang, and G. R. Chen, “A chaos-based image encryption algorithm with variable control parameters,” Chaos Solitons Fractals41(4), 1773–1783 (2009).
[CrossRef]

Y. Wang, K. W. Wong, X. F. Liao, T. Xiang, and G. R. Chen, “A chaos-based image encryption algorithm with variable control parameters,” Chaos Solitons Fractals41(4), 1773–1783 (2009).
[CrossRef]

Y. Wang, X. F. Liao, T. Xiang, K.-W. Wong, and D. Yang, “Cryptanalysis and improvement on a block cryptosystem based on iteration a chaotic map,” Phys. Lett. A363(4), 277–281 (2007).
[CrossRef]

Wang, Z. Q.

S. G. Lian, J. S. Sun, and Z. Q. Wang, “A block cipher based on a suitable use of chaotic standard map,” Chaos Solitons Fractals26(1), 117–129 (2005).
[CrossRef]

Wei, J.

J. Wei, X. F. Liao, K. W. Wong, and T. Zhou, “Cryptanalysis of a cryptosystem using multiple one-dimensional chaotic maps,” Commun. Nonlinear Sci. Numer. Simul.12(5), 814–822 (2007).
[CrossRef]

Wong, K. W.

W. Zhang, K. W. Wong, H. Yu, and Z. L. Zhu, “An image encryption scheme using lightweight bit-level confusion and cascade cross circular diffusion,” Opt. Commun.285(9), 2343–2354 (2012).
[CrossRef]

Z. L. Zhu, W. Zhang, K. W. Wong, and H. Yu, “A chaos-based symmetric image encryption scheme using a bit-level permutation,” Inf. Sci.181(6), 1171–1186 (2011).
[CrossRef]

Y. Wang, K. W. Wong, X. F. Liao, T. Xiang, and G. R. Chen, “A chaos-based image encryption algorithm with variable control parameters,” Chaos Solitons Fractals41(4), 1773–1783 (2009).
[CrossRef]

K. W. Wong, B. S. H. Kwok, and C. H. Yuen, “An efficient diffusion approach for chaos-based image encryption,” Chaos Solitons Fractals41(5), 2652–2663 (2009).
[CrossRef]

Y. Wang, K. W. Wong, X. F. Liao, T. Xiang, and G. R. Chen, “A chaos-based image encryption algorithm with variable control parameters,” Chaos Solitons Fractals41(4), 1773–1783 (2009).
[CrossRef]

K. W. Wong, B. S. H. Kwok, and W. S. Law, “A fast image encryption scheme based on chaotic standard map,” Phys. Lett. A372(15), 2645–2652 (2008).
[CrossRef]

J. Wei, X. F. Liao, K. W. Wong, and T. Zhou, “Cryptanalysis of a cryptosystem using multiple one-dimensional chaotic maps,” Commun. Nonlinear Sci. Numer. Simul.12(5), 814–822 (2007).
[CrossRef]

T. Xiang, K. W. Wong, and X. F. Liao, “Selective image encryption using a spatiotemporal chaotic system,” Chaos17(2), 023115 (2007).
[CrossRef] [PubMed]

Wong, K.-W.

Y. Wang, X. F. Liao, T. Xiang, K.-W. Wong, and D. Yang, “Cryptanalysis and improvement on a block cryptosystem based on iteration a chaotic map,” Phys. Lett. A363(4), 277–281 (2007).
[CrossRef]

Xiang, T.

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