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 secure communication scheme using projective chaos synchronization. (English) Zbl 1060.93530
Summary: Most secure communication schemes using chaotic dynamics are based on identical synchronization. In this paper, we show the possibility of secure communication using projective synchronization (PS). The unpredictability of the scaling factor in projective synchronization can additionally enhance the security of communication. It is also showed that the scaling factor can be employed to improve the robustness against noise contamination. The feasibility of the communication scheme in high-dimensional chaotic systems, such as the hyperchaotic Rössler system, is demonstrated. Numerical results show the success in transmitting a sound signal through chaotic systems.

93C10Nonlinear control systems
37D45Strange attractors, chaotic dynamics
Full Text: DOI
[1] Pecora, L. M.; Carroll, T. L.: Synchronization in chaotic systems. Phys. rev. Lett. 64, 821-824 (1990) · Zbl 0938.37019
[2] Kocarev, L.; Halle, K. S.; Eckert, K.; Chua, L. O.; Parlitz, U.: Experimental demonstration of secure communications via chaotic synchronization. Int. J. Bifurcat. chaos 2, 709-713 (1992) · Zbl 0875.94134
[3] Parlitz, U.; Chua, L.; Kocarev, L. J.; Halle, K. S.; Shang, A.: Transmission of digital signals by chaotic synchronization. Int. J. Bifurcat. chaos 2, 973-977 (1992) · Zbl 0870.94011
[4] Cuomo, K. M.; Oppenheim, A. V.: Circuit implementation of synchronized chaos with applications to communications. Phys. rev. Lett. 71, 65-68 (1993)
[5] Lu, J.; Wu, X. Q.; Lu, J. H.: Synchronization of a unified chaotic system and the application in secure communication. Phys. lett. A 305, 365-370 (2002) · Zbl 1005.37012
[6] Cuomo, K. M.; Oppenheim, A. V.; Strogatz, S. H.: Robustness and signal recovery in a synchronized chaotic system. Int. J. Bifurcat. chaos 3, 1629 (1993) · Zbl 0884.94008
[7] Feki, M.; Robert, B.; Gelle, G.; Colas, M.: Secure digital communication using discrete-time chaos synchronization. Chaos, solitons & fractals 18, 881-890 (2003) · Zbl 1069.94016
[8] Kocarev, L.; Parlitz, U.: General approach for chaotic synchronization with applications to communication. Phys. rev. Lett. 74, 5028-5031 (1995)
[9] Parlitz, U.; Kocarev, L.; Stojanovski, T.; Preckel, H.: Encoding messages using chaotic synchronization. Phys. rev. E 53, 4351-4361 (1996)
[10] Yang, T.; Chua, L. O.: Channel-independent chaotic secure communication. Int. J. Bifurcat. chaos 6, 2653-2660 (1996) · Zbl 1298.94112
[11] Xiao, J. H.; Hu, G.; Qu, Z. L.: Synchronization of spatiotemporal chaos and its application to multichannel pread-spectrum communication. Phys. rev. Lett. 77, 4162-4165 (1996)
[12] Boccaletti, S.; Farini, A.; Arecchi, F. T.: Adaptive synchronization of chaos for secure communication. Phys. rev. E 55, 4979-4981 (1997)
[13] Carroll, T. L.; Pecora, L. M.: Synchronizing hyperchaotic volume-preserving maps and circuits. IEEE trans. Circuits systems I----fundament. Theory appl. 45, 656-659 (1998)
[14] Minai, A. A.; Anand, T.: Synchronization of chaotic maps through a noisy coupling channel with application to digital communication. Phys. rev. E 59, 312-320 (1999)
[15] Sundar, S.; Minai, A. A.: Synchronization of randomly multiplexed chaotic systems with application to communication. Phys. rev. Lett. 85, 5456-5459 (2000)
[16] Garcia-Ojalvo, J.; Roy, R.: Spatiotemporal communication with synchronized optical chaos. Phys. rev. Lett. 86, 5204-5207 (2001)
[17] Short, K. M.: Steps toward unmasking secure communications. Int. J. Bifurcat. chaos 4, 959-977 (1994) · Zbl 0875.94002
[18] Perez, G.; Cerdeira, H. A.: Extracting messages masked by chaos. Phys. rev. Lett. 74, 1970-1973 (1995)
[19] Short, K. M.: Unmasking a modulated chaotic communications scheme. Int. J. Bifurcat. chaos 6, 367-375 (1996) · Zbl 0870.94004
[20] Mainieri, R.; Rehacek, J.: Projective synchronization in three-dimensional chaotic systems. Phys. rev. Lett. 82, 3042-3045 (1999)
[21] Li, Z. G.; Xu, D. L.: Stability criterion for projective synchronization in three-dimensional chaotic systems. Phys. lett. A 282, 175-179 (2001) · Zbl 0983.37036
[22] Xu, D. L.: Control of projective synchronization in chaotic systems. Phys. rev. E 63, 027201 (2001)
[23] Xu, D. L.; Li, Z. G.; Bishop, S. R.: Manipulating the scaling factor of projective synchronization in three-dimensional chaotic systems. Chaos 11, 439-442 (2001) · Zbl 0996.37075
[24] Xu, D. L.; Li, Z. G.: Controlled projective synchronization in nonpartially-linear chaotic systems. Int. J. Bifurcat. chaos 12, 1395-1402 (2002)
[25] Xu, D. L.; Ong, W. L.; Li, Z. G.: Criteria for the occurrence of projective synchronization in chaotic systems of arbitrary dimension. Phys. lett. A 305, 167-172 (2002) · Zbl 1001.37026
[26] Kocarev, L.; Parlitz, U.; Stojanovski, T.: An application of synchronized chaotic dynamic arrays. Phys. lett. A 217, 280-284 (1996) · Zbl 1298.94105
[27] Carroll, T. L.; Heagy, J. F.; Pecora, L. M.: Transforming signals with chaotic synchronization. Phys. rev. E 54, 4676-4680 (1996)
[28] Lorenz, E. N.: Deterministic non-periodic flow. J. atmos. Sci. 20, 130-141 (1963)
[29] Rössler, O. E.: An equation for hyperchaos. Phys. lett. A 71, 155-167 (1976)