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Most algorithms of image scrambling transformation based on Logistic map are currently dedicated to permutation rules and methods without considering design philosophy. In this paper, we propose a new image bit permutation algorithm based on the Logistic map. This algorithm with firmly mathematic theory is designed by following the scientific course from theory to practice. According to the characteristics of chaotic sensitivity to initial condition and large key space, starting from Logistic map, the transformation which can generate uniformly distributed random variable in the interval based on Logistic at =4 is developed. Utilizing this generated uniform random variable, random permutation algorithm based on interchange position is obtained. For measuring permutation strength of the proposed random permutation algorithm, the corresponding permutation strength testing algorithm is designed. Based on this permutation algorithm, the image bit permutation algorithm is described. When used to image and compared with Baker Ye and Yoon algorithm, the proposed image bit permutation method exhibits large key space, extreme sensitivity to initial condition, effective capability for dissipating high correlation among pixels and increasing information about entropy value. Results show that this proposed scrambling scheme with firmly theoretical foundation can enhance image security significantly.
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Keywords:
- image permutation /
- chaos sequence /
- random permutation /
- bit permutation
[1] Claude E S 1949 Bell Sys. Tech. Journal 28 656
[2] Shi Z, Lee R 2000 12th IEEE International Conference on Application-Specific Systems, Architectures, and Processors (ASAP 2000) Boston MA USA, IEEE Computer Society, July 10-12 2000 p138
[3] Lee R, Shi Z, Yang X 2001 IEEE Micro. 21 56
[4] Socek D, Li S, Magliveras S S 2005 International Conference on Security and Privacy for Emerging Areas in Communications Networks Athens Greece, IEEE Computer Society, September 5-9 2005 p208
[5] Ye G D 2010 Patt. Recogn. Lett. 31 347
[6] Yoon J W, Kim H 2010 Commun. Nonlinear Sci. Numer. Simulat. 15 3998
[7] Lasota A, Mackey M C 1997 Chaos, Fractals and noise-Stochastic Aspects of Dynamics (2nd Ed)(New York:Springer-Verlag)p230
[8] Shahram E B, Mohammad E 2009 Math. Prob. Engin. 2009 1
[9] Liu X D, Zhang J X 2008 International Journal of Computer Science and Network Security 8 64
[10] Lorenz E 1963 J. Atmospheric Sciences 20 130
[11] Li T Y, Yorke J A 1975 Amer. Math. 82 481
[12] Edward O 1993 Chaos in dynamical systems (2nd Ed.) (Cambridge: Cambridge University Press) p34
[13] Sheng L Y, Cao L L, Sun K H, Wen J 2005 Acta Phys. Sin. 54 4031 (in Chinese) [盛利元、曹莉凌、孙克辉、闻 姜 2005 物理学报 54 4031]
[14] Wang L, Wang F P, Wang Z J 2006 Acta Phys. Sin. 55 3964 (in Chinese) [王 蕾、汪芙平、王赞基 2006 物理学报 55 3964]
[15] Sheng L Y, Xiao Y Y, Sheng Z 2008 Acta Phys. Sin. 57 4007 (in Chinese) [盛利元、肖燕予、盛 喆 2008 物理学报 57 4007]
[16] Fridrich J 1998 Int. J. Bifurcation and Chaos 8 1259
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[1] Claude E S 1949 Bell Sys. Tech. Journal 28 656
[2] Shi Z, Lee R 2000 12th IEEE International Conference on Application-Specific Systems, Architectures, and Processors (ASAP 2000) Boston MA USA, IEEE Computer Society, July 10-12 2000 p138
[3] Lee R, Shi Z, Yang X 2001 IEEE Micro. 21 56
[4] Socek D, Li S, Magliveras S S 2005 International Conference on Security and Privacy for Emerging Areas in Communications Networks Athens Greece, IEEE Computer Society, September 5-9 2005 p208
[5] Ye G D 2010 Patt. Recogn. Lett. 31 347
[6] Yoon J W, Kim H 2010 Commun. Nonlinear Sci. Numer. Simulat. 15 3998
[7] Lasota A, Mackey M C 1997 Chaos, Fractals and noise-Stochastic Aspects of Dynamics (2nd Ed)(New York:Springer-Verlag)p230
[8] Shahram E B, Mohammad E 2009 Math. Prob. Engin. 2009 1
[9] Liu X D, Zhang J X 2008 International Journal of Computer Science and Network Security 8 64
[10] Lorenz E 1963 J. Atmospheric Sciences 20 130
[11] Li T Y, Yorke J A 1975 Amer. Math. 82 481
[12] Edward O 1993 Chaos in dynamical systems (2nd Ed.) (Cambridge: Cambridge University Press) p34
[13] Sheng L Y, Cao L L, Sun K H, Wen J 2005 Acta Phys. Sin. 54 4031 (in Chinese) [盛利元、曹莉凌、孙克辉、闻 姜 2005 物理学报 54 4031]
[14] Wang L, Wang F P, Wang Z J 2006 Acta Phys. Sin. 55 3964 (in Chinese) [王 蕾、汪芙平、王赞基 2006 物理学报 55 3964]
[15] Sheng L Y, Xiao Y Y, Sheng Z 2008 Acta Phys. Sin. 57 4007 (in Chinese) [盛利元、肖燕予、盛 喆 2008 物理学报 57 4007]
[16] Fridrich J 1998 Int. J. Bifurcation and Chaos 8 1259
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