Application of the Chaotic Ergodicity of Standard Map in Image Encryption and Watermarking

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Ruisong Ye 1,* Huiqing Huang 2

1. Department of Mathematics, Shantou University Shantou, Guangdong, 515063, China

2. School of Mathematics, Jiaying University Meizhou, Guangdong, 514015, China

* Corresponding author.


Received: 8 Jul. 2010 / Revised: 13 Aug. 2010 / Accepted: 22 Sep. 2010 / Published: 8 Nov. 2010

Index Terms

Standard map, ergodicity, chaos, shuffling, watermarking


Thanks to the exceptionally good properties in chaotic systems, such as sensitivity to initial conditions and control parameters, pseudo-randomness and ergodicity, chaos-based image encryption algorithms have been widely studied and developed in recent years. Standard map is chaotic so that it can be employed to shuffle the positions of image pixels to get a totally visual difference from the original images. This paper proposes two novel schemes to shuffle digital images. Different from the conventional schemes based on Standard map, we disorder the pixel positions according to the orbits of the Standard map. The proposed shuffling schemes don’t need to discretize the Standard map and own more cipher leys compared with the conventional shuffling scheme based on the discretized Standard map. The shuffling schemes are applied to encrypt image and disorder the host image in watermarking scheme to enhance the robustness against attacks. Experimental results show that the proposed encryption scheme yields good secure effects. The watermarked images are robust against attacks as well.

Cite This Paper

Ruisong Ye,Huiqing Huang, "Application of the Chaotic Ergodicity of Standard Map in Image Encryption and Watermarking", IJIGSP, vol.2, no.1, pp.19-29, 2010. DOI: 10.5815/ijigsp.2010.01.03


[1]R. Matthews. “On the derivation of a chaotic encryption algorithm, Cryptrologia”, 13, 1989, pp. 29–42.

[2]M.S. Baptista. “Cryptography with chaos”, Physics Letter A, 240, 1998, pp. 50–54.

[3]J. Scharinger. “Fast encryption of image data using chaotic Kolmogorov flows”, Journal of Electronic Imaging, 7(2), 1998, pp.318–325.

[4]J. Fridrich. “Symmetric ciphers based on two-dimensional chaotic maps”, International Journal of Bifurcation and Chaos, 8(6), 1998, pp. 1259–1284.

[5]D. X. Qi, J. C. Zhou, and X. Y. Han. “A new class of scrambling transformation and its application in the image information covering”, Science in China (series E), 43, 2000, pp. 304–312.

[6]H. Cheng, X.. B. Li. “Partial encryption of compressed images and videos”, IEEE Transactions on Signal Processing, 48(8), 2000, pp. 2439–51.

[7]C. C. Chang, M. S. Hwang, and T. S. Chen. “A new encryption algorithm for image cryptosystems”, Journal of Systems and Software, 58, 2001, pp. 83–91.

[8]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, 2004, pp. 749–761.

[9]Y.B. Mao, G. Chen, S. G. Lian. “A novel fast image encryption scheme based on the 3D chaotic Baker map”, International Journal of Bifurcation and Chaos, 14(10), 2004, pp. 613-3624.

[10]Shiguo Lian, JInsheng Sun, and Zhiquan Wang. “A block cipher based on a suitable use of the chaotic standard map”, Chaos, Solitons & Fractals, 26, 2005, pp. 117–129.

[11]Ruisong Ye and Huiliang Li, “A novel digital image scrambling and watermarking scheme based on cellular automata”, Proceedings of the 2008 International Symposium on Electronic Commerce and Security, pp. 938-941

[12]I. J. Cox, J. Kilian, F. T. Leighton, and T. Shamoon, “Secure spread spectrum watermarking for multimedia”, IEEE Trans. Image Process, 6, 1997, pp. 1673–1687.

[13]J. C. Yen and J. I. Guo, “A new chaotic key-based design for image encryption and decryption”, Proceedings of IEEE International Conference Circuits and Systems, Vol. 4, 2000, pp. 49-52.

[14]Y. Wang, J. F. Doherty, and R. E. V. Dyck, “A waveletbased watermarking algorithm for ownership verification of digital images”, IEEE Trans. Image Process, 11, 2002, pp. 77–88.

[15]A. B. Watson, “DCT quantization matrices visually optimized for individual images”, Proc. SPIE 1993, pp. 202–216.

[16]A. B. Watson, G. Y. Yang, J. A. Solomon, and J. Villasenor, “Visibility of wavelet quantization noise”, IEEE Trans. Image Process, 6, 1997, pp. 1164–1175.

[17]C.-I. Podilchuk and W. Zeng, “Image-adaptive watermarking using visual models”, IEEE J. Select. Areas Commun, 16, 1998, pp. 525–539.

[18]P. H. W. Wong, O.-C. Au, and Y.-M. Yeung, “A novel blind multiple watermarking technique for images”, IEEE Trans. Circuit Syst. Video Technol, 13 (8), 2003, pp. 813–830.

[19]Ji-wu Huang, Yun Q. Shi, and Yi Shi, “Embedding image watermarks in DC components”, IEEE Trans. on Circuits and Systems for Video Technology, 10(6), 2000, pp. 974-979.

[20]Zne-Jung Lee, Shih-Wei Lin, Shun-Feng Su, and Chun-Yen Lin, “A hybrid watermarking technique applied to digital images”, Applied Soft Computing, 8, 2008, pp. 798–808.

[21]Dawei Zhao, Guanrong Chen, and Wenbo Liu, “A chaosbased robust wavelet-domain watermarking algorithm” Chaos, Solitons and Fractals, 22 , 2004, pp. 47–54.

[22]Chin-Chen Chang, Yih-Shin Hu, and Tzu-Chuen Lu, “A watermarking-based image ownership and tampering authentication scheme”, Pattern Recognition Letters, 27, 2006, pp. 439–446.

[23]Bum-Soo Kima et al. “Robust digital image watermarking method against geometrical attacks”, Real-Time Imaging, 9 , 2003, pp.139–149.

[24]Wei-Hung Lin, Yuh-Rau Wang, and Yuh-Rau Wang, “A wavelet-tree-based watermarking method using distance vector of binary cluster”, Expert Systems with Applications, 36 (6), 2009, pp. 9869-9878

[25]Ruisong Ye, “A novel digital image scrambling and watermarking scheme based on orbits of Arnold transform”, Proceedings of the 2009 Pacific-Asia Conference on Circuits, Communications and System, pp. 485-488.

[26]Liehuang Zhu, Wenzhuo Li, Lejian Liao, and Hong Li, “Novel image scrambling algorithm for digital watermarking based on chaotic sequences”, International Journal of Computer Science and Network Security, 6 (8B), 2006.

[27]C. E. Shannon, “Communication theory of secrecy system”, Bell Syst Tech J. 28, 1949, pp. 656–715.