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**A symmetric image encryption scheme based on 3D chaotic cat maps.**
*(English)*
Zbl 1049.94009

Summary: Encryption of images is different from that of texts due to some intrinsic features of images such as bulk data capacity and high redundancy, which are generally difficult to handle by traditional methods. Due to the exceptionally desirable properties of mixing and sensitivity to initial conditions and parameters of chaotic maps, chaos-based encryption has suggested a new and efficient way to deal with the intractable problem of fast and highly secure image encryption. The two-dimensional chaotic cat map is generalized to 3D for designing a real-time secure symmetric encryption scheme. This new scheme employs the 3D cat map to shuffle the positions (and, if desired, grey values as well) of image pixels and uses another chaotic map to confuse the relationship between the cipher-image and the plain-image, thereby significantly increasing the resistance to statistical and differential attacks. Thorough experimental tests are carried out with detailed analysis, demonstrating the high security and fast encryption speed of the new scheme.

### MSC:

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 |

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\textit{G. Chen} et al., Chaos Solitons Fractals 21, No. 3, 749--761 (2004; Zbl 1049.94009)

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### References:

[1] | Chang, H.K.C.; Liu, J.L., A linear quadtree compression scheme for image encryption, Signal process image commun., 10, 4, 279-290, (1997) |

[2] | Chang, C.C.; Hwang, M.S.; Chen, T.S., A new encryption algorithm for image cryptosystems, J. syst. software, 58, 83-91, (2001) |

[3] | Chen, G.; Dong, X., From chaos to order: methodologies, perspectives and applications, (1998), World Scientific Singapore |

[4] | Chen, G.; Ueta, T., Yet another chaotic attractor, Int. J. bifurcat. chaos, 9, 7, 1465-1466, (1999) · Zbl 0962.37013 |

[5] | Cheng, H.; Li, X.B., Partial encryption of compressed images and videos, IEEE trans. signal process., 48, 8, 2439-2451, (2000) |

[6] | Bourbakis, N.; Alexopoulos, C., Picture data encryption using SCAN patterns, Pattern recognit., 25, 6, 567-581, (1992) |

[7] | Fridrich, J., Symmetric ciphers based on two-dimensional chaotic maps, Int. J. bifurcat. chaos, 8, 6, 1259-1284, (1998) · Zbl 0935.94019 |

[8] | Kocarev, L., Chaos-based cryptography: a brief overview, IEEE circ. syst. mag., 1, 3, 6-21, (2001) |

[9] | Kocarev, L.; Jakimovski, G., Chaos and cryptography: from chaotic maps to encryption algorithms, IEEE trans. circ. syst.–I, 48, 2, 163-169, (2001) |

[10] | Li SJ, Zheng X. Cryptanalysis of a chaotic image encryption method. In: IEEE Int Symposium Circuits and Systems, Scottsdale, AZ, USA, 2002 |

[11] | Li SJ, Zheng X, Mou X, Cai Y. Chaotic encryption scheme for real-time digital video. In: Proc SPIE on Electronic Imaging, San Jose, CA, USA, vol. 4666, 2002 |

[12] | Mao YB, Chen G. Chaos-based image encryption. Handbook of Computational Geometry for Pattern Recognition, Computer Vision, Neurocomputing and Robotics. New York: Springer-Verlag; in press, 2004 |

[13] | Mao YB, Chen G, Lian SG. A novel fast image encryption scheme based on the 3D chaotic baker map, Int J Bifurcat Chaos, accepted, 2003 |

[14] | http://mathworld.woffram.com/ArnoldsCatMap.html |

[15] | Matthews, R., On the derivation of a “chaotic” encryption algorithm, Cryptologia, 8, 1, 29-41, (1989) |

[16] | Peterson G. Arnold’s cat map, 1997. Available from: http://online.redwoods.cc.ca.us /instruct/ darnold/ maw/catmap.htm |

[17] | Scharinger, J., Fast encryption of image data using chaotic Kolmogorov flows, J. electron. imaging, 7, 2, 318-325, (1998) |

[18] | Schneier, B., Applied cryptography: protocols, algorithms, and source code in C, (1995), Wiley New York |

[19] | Shannon, C.E., Communication theory of secrecy system, Bell syst. tech. J., 28, 656-715, (1949) · Zbl 1200.94005 |

[20] | Uehara T, Safavi-Naini R, Ogunbona P. Securing wavelet compression with random permutations. In: IEEE Pacific Rim Conference on Multimedia, 2000. p. 332-5 |

[21] | Ueta, T.; Chen, G., Bifurcation analysis of chens equation, Int. J. bifurcat. chaos, 10, 8, 1917-1931, (2000) · Zbl 1090.37531 |

[22] | Yen JC, Guo JI. A new chaotic key-based design for image encryption and decryption. In: Proc IEEE Int Conference Circuits and Systems, vol. 4, 2000. p. 49-52 |

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