A novel algorithm for image encryption based on mixture of chaotic maps. (English) Zbl 1134.94356

Summary: Chaos-based encryption appeared recently in the early 1990s as an original application of nonlinear dynamics in the chaotic regime. In this paper, an implementation of digital image encryption scheme based on the mixture of chaotic systems is reported. The chaotic cryptography technique used in this paper is a symmetric key cryptography. In this algorithm, a typical coupled map was mixed with a one-dimensional chaotic map and used for high degree security image encryption while its speed is acceptable. The proposed algorithm is described in detail, along with its security analysis and implementation. The experimental results based on mixture of chaotic maps approves the effectiveness of the proposed method and the implementation of the algorithm. This mixture application of chaotic maps shows advantages of large key space and high-level security. The ciphertext generated by this method is the same size as the plaintext and is suitable for practical use in the secure transmission of confidential information over the Internet.


94A60 Cryptography
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37N99 Applications of dynamical systems
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
Full Text: DOI


[1] Hao, B., Starting with parabolas: an introduction to chaotic dynamics (1993), Shanghai Scientific and Technological Education Publishing House: Shanghai Scientific and Technological Education Publishing House Shanghai China
[2] Brown, R.; Chua, L. O., Clarifying chaos: examples and counterexamples, Int J Bifurcat Chaos, 6, 2, 219-242 (1996) · Zbl 0874.58038
[3] Fridrich, J., Symmetric ciphirs based on two-dimensional chaotic maps, Int J Bifurcat Chaos, 8, 6, 1259-1284 (1998) · Zbl 0935.94019
[4] Pecora, L. M.; Carroll, T. L., Synchronization in chaotic systems, Phys Rev Lett, 64, 821-824 (1990) · Zbl 0938.37019
[5] Feki, M., An adaptive chaos synchronization scheme applied to secure communication, Chaos, Solitons & Fractals, 18, 141-148 (2003) · Zbl 1048.93508
[6] Parlitz, U.; Chua, L. O.; Kocarev, L.; Halle, K. S.; Shang, A., Transmission of digital signals by chaotic synchronization, Int J Bifurcat Chaos, 2, 973-977 (1992) · Zbl 0870.94011
[7] Morgul, O.; Feki, M., A chaotic masking scheme by using synchronized chaotic systems, Phys Lett A, 251, 169-176 (1999)
[8] Cuomo, K. M.; Openheim, A. V., Circuit implementation of synchronized chaos with applications to communications, Phys Rev Lett, 71, 65-68 (1993)
[9] Chen, J. Y.; Wong, K. W.; Cheng, L. M.; Shuai, J. W., A secure communication scheme based on the phase synchronization of chaotic systems, Chaos, 13, 508-514 (2003)
[10] Xiao, D.; Liao, X.; Wong, K., An efficient entire chaos-based scheme for deniable authentication, Chaos, Solitons & Fractals, 23, 1327-1331 (2005) · Zbl 1070.94023
[11] Tang, G.; Liao, X.; Chen, Y., A novel method for designing S-boxes based on chaotic maps, Chaos, Solitons & Fractals, 23, 413-419 (2005) · Zbl 1068.94017
[12] Xiang, T.; Liao, X.; Tang, G.; Chen, Y.; Wong, K. W., A novel block cryptosystem based on iterating a chaotic map, Phys Lett A, 349, 109-115 (2006) · Zbl 1195.81041
[13] Lü, H.; Wang, S.; Li, X.; Tang, G.; Kuang, J.; Ye, W., A new spatiotemporally chaotic cryptosystem and its security and performance analyses, Chaos, 14, 617-629 (2004) · Zbl 1080.94011
[14] Huang, F.; Guan, Z. H., Cryptosystem using chaotic keys, Chaos, Solitons & Fractals, 23, 851-855 (2005) · Zbl 1068.94013
[15] Lee, P. H.; Pei, S. C.; Chen, Y. Y., Generating chaotic stream ciphers using chaotic systems, Chin J Phys, 41, 559-581 (2003)
[16] Baptista, M. S., Cryptography with chaos, Phys Lett A, 240, 50-54 (1998) · Zbl 0936.94013
[17] Chen, G.; Mao, Y.; Chui, C., A symmetric image encryption scheme based on 3d chaotic cat maps, Chaos, Solitons & Fractals, 21, 749-761 (2004) · Zbl 1049.94009
[18] Kocarev, L., Chaos-based cryptography: a brief overview, IEEE Circ Syst, 1, 6-21 (2001)
[19] Parker, A. T.; Short, K. M., Reconstructing the keystream from a chaotic encryption scheme, IEEE Trans Circuits Syst I, 48, 5, 104-112 (2001) · Zbl 1001.94030
[20] Zhou, Ch. S.; Lai, C. H., Extracting messages masked by chaotic signals of time-delay systems, Phys Rev E, 60, 320-323 (1999)
[21] Dachselt, F.; Schwarz, W., Chaos and cryptography, IEEE Trans Circuits Syst, 48, 12, 1498-1509 (2001) · Zbl 0999.94030
[22] Jafarizadeh, M. A.; Behnia, S.; Khorram, S.; Nagshara, H., Hierarchy of chaotic maps with an invariant measure, J Stat Phys, 104, 516, 1013-1028 (2001) · Zbl 1143.82308
[23] Jafarizadeh, M. A.; Behnia, S., Hierarchy of chaotic maps with an invariant and their coupling, Physica D, 159, 1-21 (2001) · Zbl 0986.37026
[24] Li, Wentian, Phenomenology of non-local cellular automata, J Stat Phys, 68, 829 (1992) · Zbl 0900.68317
[25] Cosenza, M. G.; Parravano, A., Dynamics of coupling functions in globally coupled maps: Size, periodicity, and stability of clusters, Phys Rev E, 64, 036224 (2001)
[26] dos Santosa, A. M.; Vianaa, R. L.; Lopesa, S. R.; Pintob, S. E. de S.; Batista, A. M., Chaos synchronization in a lattice of piecewise linear maps with regular and random couplings, Physica A (2005)
[27] Monteb, S.; Dovidioc, F.; Chate, H.; Mosekildea, E., Effects of microscopic disorder on the collective dynamics of globally coupled maps, Physica D, 205, 25-40 (2005)
[28] Coca, D.; Billings, S. A., Analysis and reconstruction of stochastic coupled map lattice models, Phys Lett A, 315, 61-75 (2003) · Zbl 1028.60035
[29] Devancy, R. L., An introduction to chaotic dynamical systems (1982), Addison Wesley
[30] Keller, G., Equilibrium states in a ergodic theory (1998), Cambridge University Press, p. 23-30
[31] Shannon, C. E., A mathematical theory of communication, Bell Syst Tech J, 27, 3, 379-423 (1948), 623-56 · Zbl 1154.94303
[32] Shannon, C. E., Communication theory of secrecy systems, Bell Syst Tech J, 28, 656-715 (1949) · Zbl 1200.94005
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