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Chaotic Generator in Digital Secure Communicatio
n
張 書 銘交通大學應用數學系
smchang@math.nctu.edu.tw2008 年 12 月 20 日
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Chaos Secure Communication Chaotic Generator Conclusions
Outline
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Chaos
Chaos is “ mess, disorder, uncontrollable ! ?
Smoke of Cigarette Mike in coffee
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Lorenz strange attractor
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Three planar charged particles
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Three planar charged particles
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Three planar charged particles
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Henon map
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Discrete predator-prey map
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Logistic map
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Secure Communication
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Digital secure communication
Transmitter Receiver
SourceDigital Data
Chaotic Encryption
Unit
AcquireDigital DataCiphertext
Plaintext
Encryption Decryption
ChaoticDecryption
Unit
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Applications - 1
CommunicationCommunication InformationInformation
EntertainmentEntertainmentTransactionTransaction
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Applications - 2
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Chaotic Generator
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Logistic map
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Modified Logistic map
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Properties of MLM
• Chaotic map
• No windows
• Uniform distribution
• Equivalent
• Pseudorandom
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MLM: chaotic map
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MLM: no windows
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MLM: no windows
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MLM: uniform distributionr = 5.9
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MLM: uniform distributionr = 10.8
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MLM: equivalent
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MLM: equivalent
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MLM: pseudorandom
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MLM: pseudorandom
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Conclusions
•Propose Modified Logistic Map (MLM)•Show that MLM is a chaotic map (Devaney's definition)•No windows•Uniform distribution, equivalent•Pseudorandom
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Thank you for your attention!
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Random vs. Chaos
,...,...,, 10 nxxx
,...,...,, 10 nyyy
Identity ： 1. Continuous Spectrum
2. Correlation Function ：
1nnknk xxC
Random numbers:
Chaotic signals:
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Random vs. Chaos
Observable:
Temporal Average for (1):
Perturbation:
Temporal Average for (2):
rnn Ryfy )(1)1(
:A ractorstrangeatt ,attractor dA dim
r
yyz
rnn
n
)()1( ...
N
iNi az
N 1
1
,)ˆ(ˆ 1 nnn yfy )2( noisen :
N
iNi az
N 1
ˆˆ1
11ˆ difaa nn
3. Stability ：
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Random vs. Chaos
Distinction：
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Further
•Based on MLMs, we establish Modified Logistic Hyper-Chaotic System (MLHCS)•Apply MLHCS to develop a symmetric cryptography algorithm•Asymptotic Synchronization of Modified Logistic Hyper-Chaotic System (ASMLHCS)
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Digital secure communication
Transmitter Receiver
SourceDigital Data
MLHCS Encryption
Unit
AcquireDigital DataCiphertext
Plaintext
Encryption Decryption
ASMLHCSDecryption
Unit
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S. M. Chang, M. C. Li and W. W. Lin, Asymptotic synchronization of modified logistic hyper-chaotic systems and its applications. Nonlinear Analysis: Real World Applications, Vol. 10, Issue 2 (2009), pp. 869–880.
S. M. Chang, T. C. Lin and W. W. Lin, Chaotic and Quasiperiodic Motions of Three Planar Charged Particles. Int. J. Bifurcation Chaos, Vol. 11, No. 7 (2001), pp. 1937–1951.
S. L. Chen, S. M. Chang, T. T. Hwang and W. W. Lin, Digital secure-communication using robust hyper-chaotic systems. Int. J. Bifurcation Chaos, Vol. 18, No. 11 (2008), pp. 1–14.
References
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