1 chaotic generator in digital secure communication 張 書 銘 交通大學應用數學系...
TRANSCRIPT
2
Chaos Secure Communication Chaotic Generator Conclusions
Outline
3
Chaos
Chaos is “ mess, disorder, uncontrollable ! ?
Smoke of Cigarette Mike in coffee
4
Lorenz strange attractor
5
Three planar charged particles
6
Three planar charged particles
7
Three planar charged particles
8
Henon map
9
Discrete predator-prey map
10
Logistic map
11
Secure Communication
12
Digital secure communication
Transmitter Receiver
SourceDigital Data
Chaotic Encryption
Unit
AcquireDigital DataCiphertext
Plaintext
Encryption Decryption
ChaoticDecryption
Unit
13
Applications - 1
CommunicationCommunication InformationInformation
EntertainmentEntertainmentTransactionTransaction
14
Applications - 2
15
Chaotic Generator
16
Logistic map
17
Modified Logistic map
18
Properties of MLM
• Chaotic map
• No windows
• Uniform distribution
• Equivalent
• Pseudorandom
19
MLM: chaotic map
20
MLM: no windows
21
MLM: no windows
22
MLM: uniform distributionr = 5.9
23
MLM: uniform distributionr = 10.8
24
MLM: equivalent
25
MLM: equivalent
26
MLM: pseudorandom
27
MLM: pseudorandom
28
Conclusions
•Propose Modified Logistic Map (MLM)•Show that MLM is a chaotic map (Devaney's definition)•No windows•Uniform distribution, equivalent•Pseudorandom
29
Thank you for your attention!
30
Random vs. Chaos
,...,...,, 10 nxxx
,...,...,, 10 nyyy
Identity ： 1. Continuous Spectrum
2. Correlation Function ：
1nnknk xxC
Random numbers:
Chaotic signals:
31
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 ：
32
Random vs. Chaos
Distinction：
33
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)
34
Digital secure communication
Transmitter Receiver
SourceDigital Data
MLHCS Encryption
Unit
AcquireDigital DataCiphertext
Plaintext
Encryption Decryption
ASMLHCSDecryption
Unit
35
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