A chaos-based digital image encryption scheme with an improved diffusion strategy |
Optics Express, Vol. 20, Issue 3, pp. 2363-2378 (2012)
http://dx.doi.org/10.1364/OE.20.002363
Acrobat PDF (2998 KB)
Abstract
Chaos-based image cipher has been widely investigated over the last decade or so to meet the increasing demand for real-time secure image transmission over public networks. In this paper, an improved diffusion strategy is proposed to promote the efficiency of the most widely investigated permutation-diffusion type image cipher. By using the novel bidirectional diffusion strategy, the spreading process is significantly accelerated and hence the same level of security can be achieved with fewer overall encryption rounds. Moreover, to further enhance the security of the cryptosystem, a plain-text related chaotic orbit turbulence mechanism is introduced in diffusion procedure by perturbing the control parameter of the employed chaotic system according to the cipher-pixel. Extensive cryptanalysis has been performed on the proposed scheme using differential analysis, key space analysis, various statistical analyses and key sensitivity analysis. Results of our analyses indicate that the new scheme has a satisfactory security level with a low computational complexity, which renders it a good candidate for real-time secure image transmission applications.
© 2012 OSA
1. Introduction
1. J. Fridrich, “Symmetric ciphers based on two-dimensional chaotic maps,” Int. J. Bifurcat. Chaos 8(6), 1259–1284 (1998). [CrossRef]
1. J. Fridrich, “Symmetric ciphers based on two-dimensional chaotic maps,” Int. J. Bifurcat. Chaos 8(6), 1259–1284 (1998). [CrossRef]
23. K. W. Wong, B. S. H. Kwok, and C. H. Yuen, “An efficient diffusion approach for chaos-based image encryption,” Chaos Solitons Fractals 41(5), 2652–2663 (2009). [CrossRef]
2. G. R. Chen, Y. B. Mao, and C. K. Chui, “A symmetric image encryption scheme based on 3D chaotic cat maps,” Chaos Solitons Fractals 21(3), 749–761 (2004). [CrossRef]
3. 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. Chaos 14(10), 3613–3624 (2004). [CrossRef]
4. F. Belkhouche, I. Gokcen, and U. Qidwai, “Chaotic gray-level image transformation,” J. Electron. Imaging 14(4), 043001 (2005). [CrossRef]
6. H. S. Kwok and W. K. S. Tang, “A fast image encryption system based on chaotic maps with finite precision representation,” Chaos Solitons Fractals 32(4), 1518–1529 (2007). [CrossRef]
7. S. Behnia, A. Akhshani, S. Ahadpour, H. Mahmodi, and A. Akhavan, “A fast chaotic encryption scheme based on piecewise nonlinear chaotic maps,” Phys. Lett. A 366(4-5), 391–396 (2007). [CrossRef]
8. S. Behnia, A. Akhshani, H. Mahmodi, and A. Akhavan, “A novel algorithm for image encryption based on mixture of chaotic maps,” Chaos Solitons Fractals 35(2), 408–419 (2008). [CrossRef]
9. T. G. Gao and Z. Q. Chen, “A new image encryption algorithm based on hyper-chaos,” Phys. Lett. A 372(4), 394–400 (2008). [CrossRef]
12. R. Rhouma, S. Meherzi, and S. Belghith, “OCML-based colour image encryption,” Chaos Solitons Fractals 40(1), 309–318 (2009). [CrossRef]
13. F. Y. Sun, S. T. Liu, Z. Q. Li, and Z. W. Lü, “A novel image encryption scheme based on spatial chaos map,” Chaos Solitons Fractals 38(3), 631–640 (2008). [CrossRef]
15. S. Mazloom and A. M. Eftekhari-Moghadam, “Color image encryption based on coupled nonlinear chaotic map,” Chaos Solitons Fractals 42(3), 1745–1754 (2009). [CrossRef]
16. 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 Fractals 41(4), 1773–1783 (2009). [CrossRef]
19. X. Ma, C. Fu, W. M. Lei, and S. Li, “A novel chaos-based image encryption scheme with an improved permutation process,” Int. J. Adv. Comput. Technol. 3(5), 223–233 (2011). [CrossRef]
20. S. G. Lian, J. S. Sun, and Z. Q. Wang, “A block cipher based on a suitable use of the chaotic standard map,” Chaos Solitons Fractals 26(1), 117–129 (2005). [CrossRef]
21. T. Xiang, K. W. Wong, and X. F. Liao, “Selective image encryption using a spatiotemporal chaotic system,” Chaos 17(2), 023115 (2007). [CrossRef] [PubMed]
22. K. W. Wong, B. S. H. Kwok, and W. S. Law, “A fast image encryption scheme based on chaotic standard map,” Phys. Lett. A 372(15), 2645–2652 (2008). [CrossRef]
23. K. W. Wong, B. S. H. Kwok, and C. H. Yuen, “An efficient diffusion approach for chaos-based image encryption,” Chaos Solitons Fractals 41(5), 2652–2663 (2009). [CrossRef]
2. Image permutation based on Chirikov standard map
3. Improved image diffusion based on Chebyshev map
- Step 1: Iterate Eq. (5) for N_{0} times to avoid the harmful effect of transitional procedure, where N_{0} is a constant.
- Step 2: The Chebyshev map is iterated continuously. Here, notice that the value of −1 is a ‘bad’ point, trapping the iterations to the fixed point 0. If this case is encountered, a tiny perturbation should apply. For each iteration, we can obtain one key stream element from the current state of the chaotic map according to
- Step 3: Calculate the cipher-pixel value according to Eq. (4). One may set initial value c(−1) as a constant.
- Step 4: Perturb the control parameter k according to the perturbing scheme illustrated by Fig. 5.
- Step 5: Return to Step 2 until a complete bidirectional diffusion process is done.
4. Security analysis
4.1 Key space analysis
4.2 Statistical analysis
4.2.1 Histogram
4.2.2 Correlation of adjacent pixels
4.2.3 Information entropy
4.2.4 Key stream statistical characteristics
27. G. Alvarez and S. Li, “Some basic cryptographic requirements for chaos-based cryptosystems,” Int. J. Bifurcat. Chaos 16(8), 2129–2151 (2006). [CrossRef]
4.3 Key sensitivity analysis
5. Efficiency analysis
6. Conclusions
Acknowledgments
References and links
1. | J. Fridrich, “Symmetric ciphers based on two-dimensional chaotic maps,” Int. J. Bifurcat. Chaos 8(6), 1259–1284 (1998). [CrossRef] |
2. | G. R. Chen, Y. B. Mao, and C. K. Chui, “A symmetric image encryption scheme based on 3D chaotic cat maps,” Chaos Solitons Fractals 21(3), 749–761 (2004). [CrossRef] |
3. | 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. Chaos 14(10), 3613–3624 (2004). [CrossRef] |
4. | F. Belkhouche, I. Gokcen, and U. Qidwai, “Chaotic gray-level image transformation,” J. Electron. Imaging 14(4), 043001 (2005). [CrossRef] |
5. | N. K. Pareek, V. Patidar, and K. K. Sud, “Image encryption using chaotic logistic map,” Image Vis. Comput. 24(9), 926–934 (2006). [CrossRef] |
6. | H. S. Kwok and W. K. S. Tang, “A fast image encryption system based on chaotic maps with finite precision representation,” Chaos Solitons Fractals 32(4), 1518–1529 (2007). [CrossRef] |
7. | S. Behnia, A. Akhshani, S. Ahadpour, H. Mahmodi, and A. Akhavan, “A fast chaotic encryption scheme based on piecewise nonlinear chaotic maps,” Phys. Lett. A 366(4-5), 391–396 (2007). [CrossRef] |
8. | S. Behnia, A. Akhshani, H. Mahmodi, and A. Akhavan, “A novel algorithm for image encryption based on mixture of chaotic maps,” Chaos Solitons Fractals 35(2), 408–419 (2008). [CrossRef] |
9. | T. G. Gao and Z. Q. Chen, “A new image encryption algorithm based on hyper-chaos,” Phys. Lett. A 372(4), 394–400 (2008). [CrossRef] |
10. | X. J. Tong and M. G. Cui, “Image encryption scheme based on 3D baker with dynamical compound chaotic sequence cipher generator,” Signal Process. 89(4), 480–491 (2009). [CrossRef] |
11. | V. Patidar, N. K. Pareek, and K. K. Sud, “A new substitution-diffusion based image cipher using chaotic standard and logistic maps,” Commun. Nonlinear Sci. Numer. Simul. 14(7), 3056–3075 (2009). [CrossRef] |
12. | R. Rhouma, S. Meherzi, and S. Belghith, “OCML-based colour image encryption,” Chaos Solitons Fractals 40(1), 309–318 (2009). [CrossRef] |
13. | F. Y. Sun, S. T. Liu, Z. Q. Li, and Z. W. Lü, “A novel image encryption scheme based on spatial chaos map,” Chaos Solitons Fractals 38(3), 631–640 (2008). [CrossRef] |
14. | C. K. Huang and H. H. Nien, “Multi chaotic systems based pixel shuffle for image encryption,” Opt. Commun. 282(11), 2123–2127 (2009). [CrossRef] |
15. | S. Mazloom and A. M. Eftekhari-Moghadam, “Color image encryption based on coupled nonlinear chaotic map,” Chaos Solitons Fractals 42(3), 1745–1754 (2009). [CrossRef] |
16. | 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 Fractals 41(4), 1773–1783 (2009). [CrossRef] |
17. | I. F. Elashry, O. S. F. Allah, A. M. Abbas, S. El-Rabaie, and F. E. A. El-Samie, “Homomorphic image encryption,” J. Electron. Imaging 18(3), 033002 (2009). [CrossRef] |
18. | S. E. Borujeni and M. Eshghi, “Chaotic image encryption design using Tompkins-Paige algorithm,” Math. Probl. Eng. 2009, 762652 (2009). |
19. | X. Ma, C. Fu, W. M. Lei, and S. Li, “A novel chaos-based image encryption scheme with an improved permutation process,” Int. J. Adv. Comput. Technol. 3(5), 223–233 (2011). [CrossRef] |
20. | S. G. Lian, J. S. Sun, and Z. Q. Wang, “A block cipher based on a suitable use of the chaotic standard map,” Chaos Solitons Fractals 26(1), 117–129 (2005). [CrossRef] |
21. | T. Xiang, K. W. Wong, and X. F. Liao, “Selective image encryption using a spatiotemporal chaotic system,” Chaos 17(2), 023115 (2007). [CrossRef] [PubMed] |
22. | K. W. Wong, B. S. H. Kwok, and W. S. Law, “A fast image encryption scheme based on chaotic standard map,” Phys. Lett. A 372(15), 2645–2652 (2008). [CrossRef] |
23. | K. W. Wong, B. S. H. Kwok, and C. H. Yuen, “An efficient diffusion approach for chaos-based image encryption,” Chaos Solitons Fractals 41(5), 2652–2663 (2009). [CrossRef] |
24. | F. Rannou, “Numerical study of discrete plane area-preserving map,” Astron. Astrophys. 31, 289–301 (1974). |
25. | A. J. Litchenberg and M. A. Lieberman, Regular and Stochastic Motion (Springer, 1983). |
26. | IEEE Computer Society, “IEEE standard for binary floating-point arithmetic,” ANSI/IEEE Std. 754–1985 (1985). |
27. | G. Alvarez and S. Li, “Some basic cryptographic requirements for chaos-based cryptosystems,” Int. J. Bifurcat. Chaos 16(8), 2129–2151 (2006). [CrossRef] |
OCIS Codes
(100.2000) Image processing : Digital image processing
(100.2960) Image processing : Image analysis
(110.1758) Imaging systems : Computational imaging
ToC Category:
Image Processing
History
Original Manuscript: September 20, 2011
Revised Manuscript: January 13, 2012
Manuscript Accepted: January 13, 2012
Published: January 19, 2012
Citation
Chong Fu, Jun-jie Chen, Hao Zou, Wei-hong Meng, Yong-feng Zhan, and Ya-wen Yu, "A chaos-based digital image encryption scheme with an improved diffusion strategy," Opt. Express 20, 2363-2378 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-3-2363
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References
- J. Fridrich, “Symmetric ciphers based on two-dimensional chaotic maps,” Int. J. Bifurcat. Chaos8(6), 1259–1284 (1998). [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]
- F. Belkhouche, I. Gokcen, and U. Qidwai, “Chaotic gray-level image transformation,” J. Electron. Imaging14(4), 043001 (2005). [CrossRef]
- N. K. Pareek, V. Patidar, and K. K. Sud, “Image encryption using chaotic logistic map,” Image Vis. Comput.24(9), 926–934 (2006). [CrossRef]
- H. S. Kwok and W. K. S. Tang, “A fast image encryption system based on chaotic maps with finite precision representation,” Chaos Solitons Fractals32(4), 1518–1529 (2007). [CrossRef]
- S. Behnia, A. Akhshani, S. Ahadpour, H. Mahmodi, and A. Akhavan, “A fast chaotic encryption scheme based on piecewise nonlinear chaotic maps,” Phys. Lett. A366(4-5), 391–396 (2007). [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]
- T. G. Gao and Z. Q. Chen, “A new image encryption algorithm based on hyper-chaos,” Phys. Lett. A372(4), 394–400 (2008). [CrossRef]
- X. J. Tong and M. G. Cui, “Image encryption scheme based on 3D baker with dynamical compound chaotic sequence cipher generator,” Signal Process.89(4), 480–491 (2009). [CrossRef]
- V. Patidar, N. K. Pareek, and K. K. Sud, “A new substitution-diffusion based image cipher using chaotic standard and logistic maps,” Commun. Nonlinear Sci. Numer. Simul.14(7), 3056–3075 (2009). [CrossRef]
- R. Rhouma, S. Meherzi, and S. Belghith, “OCML-based colour image encryption,” Chaos Solitons Fractals40(1), 309–318 (2009). [CrossRef]
- F. Y. Sun, S. T. Liu, Z. Q. Li, and Z. W. Lü, “A novel image encryption scheme based on spatial chaos map,” Chaos Solitons Fractals38(3), 631–640 (2008). [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]
- 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]
- I. F. Elashry, O. S. F. Allah, A. M. Abbas, S. El-Rabaie, and F. E. A. El-Samie, “Homomorphic image encryption,” J. Electron. Imaging18(3), 033002 (2009). [CrossRef]
- S. E. Borujeni and M. Eshghi, “Chaotic image encryption design using Tompkins-Paige algorithm,” Math. Probl. Eng.2009, 762652 (2009).
- X. Ma, C. Fu, W. M. Lei, and S. Li, “A novel chaos-based image encryption scheme with an improved permutation process,” Int. J. Adv. Comput. Technol.3(5), 223–233 (2011). [CrossRef]
- S. G. Lian, J. S. Sun, and Z. Q. Wang, “A block cipher based on a suitable use of the chaotic standard map,” Chaos Solitons Fractals26(1), 117–129 (2005). [CrossRef]
- T. Xiang, K. W. Wong, and X. F. Liao, “Selective image encryption using a spatiotemporal chaotic system,” Chaos17(2), 023115 (2007). [CrossRef] [PubMed]
- 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]
- 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]
- F. Rannou, “Numerical study of discrete plane area-preserving map,” Astron. Astrophys.31, 289–301 (1974).
- A. J. Litchenberg and M. A. Lieberman, Regular and Stochastic Motion (Springer, 1983).
- IEEE Computer Society, “IEEE standard for binary floating-point arithmetic,” ANSI/IEEE Std. 754–1985 (1985).
- G. Alvarez and S. Li, “Some basic cryptographic requirements for chaos-based cryptosystems,” Int. J. Bifurcat. Chaos16(8), 2129–2151 (2006). [CrossRef]
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