A New Family of Generalized 3D Cat Maps

Since the 1990s chaotic cat maps are widely used in data encryption, for their very complicated dynamics within a simple model and desired characteristics related to requirements of cryptography. The number of cat map parameters and the map period length after discretization are two major concerns in many applications for security reasons. In this paper, we propose a new family of 36 distinctive 3D cat maps with different spatial configurations taking existing 3D cat maps [1]-[4] as special cases. Our analysis and comparisons show that this new 3D cat maps family has more independent map parameters and much longer averaged period lengths than existing 3D cat maps. The presented cat map family can be extended to higher dimensional cases.

[1]  Zhengjun Liu,et al.  Double image encryption by using Arnold transform and discrete fractional angular transform , 2012 .

[2]  Xiao Liu,et al.  A novel chaos-based bit-level permutation scheme for digital image encryption , 2011 .

[3]  W. Tang,et al.  A fast image encryption system based on chaotic maps with finite precision representation , 2007 .

[4]  Ljupco Kocarev,et al.  Theory and practice of chaotic cryptography , 2007 .

[5]  Shiguo Lian,et al.  3D Extensions of Some 2D Chaotic Maps and Their Usage in Data Encryption , 2003, 2003 4th International Conference on Control and Automation Proceedings.

[6]  Qing-xin Zhu,et al.  A DCT Domain Color Watermarking Scheme Based on Chaos and Multilayer Arnold Transformation , 2009, 2009 International Conference on Networking and Digital Society.

[7]  Zhiliang Zhu,et al.  A Novel Image Encryption Algorithm Based on Improved 3D Chaotic Cat Map , 2008, 2008 The 9th International Conference for Young Computer Scientists.

[8]  Joseph Ford,et al.  The Arnol'd cat: failure of the correspondence principle , 1991 .

[9]  Anil Kumar,et al.  Substitution-Diffusion Based Image Cipher Using Chaotic Standard Map and 3D Cat Map , 2010, BAIP.

[10]  Nithin Nagaraj,et al.  Increasing average period lengths by switching of robust chaos maps in finite precision , 2008, 0811.1823.

[11]  Tian Gong Pan,et al.  A New Algorithm of Image Encryption Based on 3D Arnold Cat , 2011 .

[12]  Daomu Zhao,et al.  Color component 3D Arnold transform for polychromatic pattern recognition , 2011 .

[13]  Wallace Kit-Sang Tang,et al.  Formulation and analysis of high-dimensional chaotic maps , 2008, 2008 IEEE International Symposium on Circuits and Systems.

[14]  Vinod Patidar,et al.  Image encryption using chaotic logistic map , 2006, Image Vis. Comput..

[15]  C. Chui,et al.  A symmetric image encryption scheme based on 3D chaotic cat maps , 2004 .

[16]  Pan Tian-gong,et al.  A New Algorithm of Image Encryption Based on 3 D Arnold Cat , 2011 .

[17]  A. Kanso,et al.  A novel image encryption algorithm based on a 3D chaotic map , 2012 .