A novel fast image encryption scheme based on 3D chaotic Baker maps. (English) Zbl 1064.94509

Summary: Symmetric block encryption schemes, designed on invertible two-dimensional chaotic maps on a torus or a square, prove feasible and secure for real-time image encryption according to the commonly used criteria given in the literature. In this paper, a typical map of this kind, namely, the Baker map, is further extended to be three-dimensional and then used to speed up image encryption while retaining its high degree of security. The proposed algorithm is described in detail, along with its security analysis and implementation. Experimental results show that this three-dimensional Baker map is 2–3 times faster than the two-dimensional one, showing its great potential in real-time image encryption applications.


94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37N99 Applications of dynamical systems
81Q50 Quantum chaos
68P25 Data encryption (aspects in computer science)
68U10 Computing methodologies for image processing
Full Text: DOI


[1] Chen G R, Mao Y. Chaos-based Image Encryption. Handbook of Computational Geometry for Pattern Recognition. Berlin: Springer-Verlag, 2005. 231-265
[2] Mao Y B, Chen G, Lian S G. A novel fast image encryption scheme based on the 3D chaotic baker map. Int J Bifurcat Chaos, 2004, 14: 3613-3624 · Zbl 1064.94509
[3] Zhang Y W, Wang Y M, Shen X B. Chaos-based image encryption algorithm using alternate structure. Sci China Ser F-Inf Sci, 2007, 50: 334-341 · Zbl 1142.94001
[4] Li H D, Feng D G. Composite nonlinare discrete chaotic dynamical systems and keyed hash functions. Chin J Comput, 2003, 26: 460-464
[5] Tao X, Liao X F, Tang G P. A novel block cryptosystem based on iterating a chaotic map. Phys Lett A, 2006, 34: 109-115 · Zbl 1195.81041
[6] Zhang W T, Qing S H, Wu W L. Security evaluation for a class of block ciphers based on chaotic maps (in Chinese). J Softw, 2003, 14: 512-517
[7] Li P, Li Z, Wolf G A, et al. Analysis of a multiple-output, pseudo-random bit generator based on a spatiotemporal chaotic system. Int J Bifurcat Chaos, 2006, 16: 2949-2963
[8] Huang F J. Information security research based on discrete chaotic theory (in Chinese). Dissertation for the Doctoral Degree. Wuhan: Huazhong Science and Technology University, 2005. 1-10
[9] Li S J, Zheng X. On the security of an image encryption method. Proc 2002 Int Conf Image Process, 2002, (2): 925-928
[10] Chuang T J, Lin J C. A new multi-resolution approach to still image encryption. Patt Recognit, 1999, 9: 431-436
[11] Chen G R, Mao Y B, Charles K C. A symmetric image encryption scheme based on 3D chaotic cat maps. Chaos Solit Fractal, 2004, 21: 749-761 · Zbl 1049.94009
[12] Xiang T, Liao X F, Tang G P, et al. A novel block cryptosystem based on iterating a chaotic map. Phys Lett A, 2006, 349: 109-115 · Zbl 1195.81041
[13] Lian S G, Mao Y B, Wang Z Q. 3D extension of Baker map and its application to multimedia information encryption (in Chinese). Control Decision, 2004, 19: 714-717 · Zbl 1097.94021
[14] Li S J. Chaos-based Image and Video Encryption. Chapter 4. Multimedia Encryption Handbook. Furht B, Kirovski D, eds., New York: CRC Press, 2005. 133-168
[15] Zhao G, Fang J Q, Yan H, et al. Design of changeable P-box and two modules structure block cryptosystem based on chaos. In: Proceedings of APWCCS, 2007. 174-183
[16] Lu K, Sun J H, Ouyang R B, et al. Chaotic Dynamics (in Chinese). Shanghai: Shanghai Translation Press, 1990. 17-51
[17] Tong X J, Cui M. Image encryption with compound chaotic sequence cipher shifting dynamically. Image Vision Comput, 2008, 26: 843-850
[18] Hao B L. Staring from Parabola-Chaotic Dynamics Introduction (in Chinese). Shanghai: Shanghai Education Press, 1993. 122-123
[19] Hone B, Tang Q Y, Yang F S, et al. ApEn and cross-ApEn: property, fast algorithm and preliminary application to the study of EEG and cognition (in Chinese). Signal Process, 1999, 15: 100-108
[20] Zhou H, Ling X T. Realizing finite precision chaotic systems via perturbation of \(m\) sequences (in Chinese). Acta Electron Sin, 1997, 25: 95-97
[21] Rukhin A,
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.