zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
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.

37D45Strange attractors, chaotic dynamics
37N99Applications of dynamical systems
94A08Image processing (compression, reconstruction, etc.)
Full Text: DOI
[1] Chang, H. K. C.; Liu, J. L.: A linear quadtree compression scheme for image encryption. Signal process image commun. 10, No. 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) · Zbl 0908.93005
[4] Chen, G.; Ueta, T.: Yet another chaotic attractor. Int. J. Bifurcat. chaos 9, No. 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, No. 8, 2439-2451 (2000)
[6] Bourbakis, N.; Alexopoulos, C.: Picture data encryption using SCAN patterns. Pattern recognit. 25, No. 6, 567-581 (1992)
[7] Fridrich, J.: Symmetric ciphers based on two-dimensional chaotic maps. Int. J. Bifurcat. chaos 8, No. 6, 1259-1284 (1998) · Zbl 0935.94019
[8] Kocarev, L.: Chaos-based cryptography: a brief overview. IEEE circ. Syst. mag. 1, No. 3, 6-21 (2001)
[9] Kocarev, L.; Jakimovski, G.: Chaos and cryptography: from chaotic maps to encryption algorithms. IEEE trans. Circ. syst.----I 48, No. 2, 163-169 (2001) · Zbl 0998.94016
[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, No. 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, No. 2, 318-325 (1998)
[18] Schneier, B.: Applied cryptography: protocols, algorithms, and source code in C. (1995) · Zbl 0789.94001
[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, No. 8, 1917-1931 (2000)
[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