Table Of ContentKehuiSun
ChaoticSecureCommunication
Also of interest
CodingandCryptography
Natas˘aZ˘ivic´,2013
ISBN978-3-486-75212-0,e-ISBN978-3-486-78126-7,
Set-ISBN978-3-486-80581-9
ModernCommunicationsTechnology
Natas˘aZ˘ivic´,2016
ISBN978-3-11-041337-3,e-ISBN978-3-11-041338-0,
e-ISBN(EPUB)978-3-11-042390-7
ACourseinMathematicalCryptography
G.Baumslag,B.Fine,M.Kreuzer,G.Rosenberger
ISBN978-3-11-037276-2,e-ISBN978-3-11-037277-9,
e-ISBN(EPUB)978-3-11-038616-5
ComputationalMethodsinAppliedMathematics
CarstenCarstensen(Editor-in-Chief),4issuesperyear
ISSN1609-4840,e-ISSN1609-9389
Kehui Sun
Chaotic Secure
Communication
Principles and Technologies
Thisworkisco-publishedbyTsinghuaUniversityPressandWalterdeGruyterGmbH.
Author
Prof.KehuiSun
SchoolofPhysicsandElectronics
CentralSouthUniversity
Hunan,China
ISBN978-3-11-042688-5
e-ISBN(PDF)978-3-11-043406-4
e-ISBN(EPUB)978-3-11-043326-5
Set-ISBN978-3-11-043407-1
LibraryofCongressCataloging-in-PublicationData
ACIPcatalogrecordforthisbookhasbeenappliedforattheLibraryofCongress.
BibliographicinformationpublishedbytheDeutscheNationalbibliothek
TheDeutscheNationalbibliothekliststhispublicationintheDeutscheNationalbibliografie;detailed
bibliographicdataareavailableontheInternetathttp://dnb.dnb.de.
©2016WalterdeGruyterGmbH,Berlin/Boston
Coverimage:scanrail/iStock/thinkstock
Typesetting:IntegraSoftwareServicesPvt.Ltd.
Printingandbinding:CPIbooksGmbH,Leck
(cid:2)8Printedonacid-freepaper
PrintedinGermany
www.degruyter.com
Preface
Since meteorologist Lorenz discovered chaotic phenomenon in 1963, it has been
widelyanddeeplystudied.Chaostheoryisknownasthethirdscientifictheoretical
revolutionfollowingthetheoryofrelativityandquantumtheoryinthe20thcentury.
Especially,PecoraandCarrollreportedchaossynchronizationin1990,whicharoused
anupsurgeofstudyonchaoticsecurecommunications.Aftermorethan20yearsof
researchanddevelopment,chaoticsecurecommunicationtechnologyisbecominga
newgrowthpointinthefieldofinformationtechnology.Ononehand,theapplication
ofchaoswillcontinuetopromotepeople’sprofoundunderstandingofthenatureof
chaos.Ontheotherhand,thenewproblemsintheapplicationofchaoswillfurther
leadtothefurtherresearchofchaos.Althoughchaoticsecurecommunicationtechno-
logystillhasalongwaytogo,theapplicationofchaosinsecurecommunicationfield
showsusapromisingprospect.
Thisbookincludesninechapters.Inthefirstchapter,thehistoryofchaosresearch
isreviewed,andtheimportantcharactersandstoriesinthedevelopmentofchaosare
introduced,andtheadvancesinresearchonchaoticsynchronizationcontroltechno-
logyandchaoticsecurecommunicationmethodarereviewed.Inthesecondchapter,
themainanalysismethodsofthechaoticcharacteristicofthenonlinearsystemare
presented.Thetypicalchaoticdynamicsystemmodelsareintroducedbrieflyinthe
third chapter. In the fourth chapter, the principle and technology of the synchron-
ization control between chaotic systems are investigated. In the fifth chapter, the
technologyandschemeofsecurecommunicationbasedonchaoticsynchronization
arediscussed.Inthesixthchapter,thedataencryptiontechnologybasedonchaotic
sequences is discussed. In the seventh chapter, the audio and video real-time en-
cryptioncommunicationtechnologybasedonchaosisstudied.Intheeighthchapter,
thelatestresearchprogress,dynamiccharacteristicanalysis,andsimulationmethods
of fractional-order chaotic system are studied. In the ninth chapter, the design and
implementationtechnologyofchaoticcircuitisstudied.
Inordertofacilitatereaderstograsptheimportantknowledgepointsinthebook,
theauthorlistsafewquestionsattheendofeachchapter.Inordertofacilitatethe
searchofrelevantliteratureandtopublishtheresearchresultsontime,journalsabout
chaosresearcharelistedasAppendixAofthisbook.Inaddition,inordertofacilit-
atereaderstoquicklygraspthechaosofresearchmethods,theauthorcollectedthe
relevantanalysisprogramsasshowninAppendixB.
Basedontheresearchresultsinthefieldandalargenumberofrelatedliteratures,
thisbookiswrittenthroughrepeatedmodification.
Inthefieldofresearchofchaos,theauthorhasgottheguidanceandinspiration
of many professors including Professor Sprott J C from the University of Wisconsin
MadisonintheUnitedStates,ProfessorQiuSSfromSouthChinaUniversityofTech-
nology,ProfessorYuSMfromGuangdongUniversityofTechnology,ProfessorWang
VI Preface
GYfromHangzhouUniversityofElectronicScienceandTechnology,ProfessorZhang
TS,ProfessorShengLY,andProfessorZhuCXfromCentralSouthUniversity.Theau-
thorexpressessinceregratitudetoalltheprofessors.Inaddition,inthepreparation
ofthisbook,previousgraduatestudentsgavealotofsupport.TheyareMouJ,ZhouJ
L,TanGQ,RenJ,ShangF,WangX,BaoSQ,YangJL,ChengW,LiuX,HeSB,Wang
HH,WangY,ZuoT,AiXX,LiuWH,RuanJY,ZhangLM,XuYX,YuMY,YinYH.
Thanksfortheircontributions!
Iwouldsincerelyliketoappreciateandacknowledgethecommentsandsugges-
tionsfromthereadersforthisbook.
KehuiSun
January2015,Changsha
Contents
1 Introduction 1
1.1 Linear,Nonlinear,andChaos 1
1.2 DevelopmentofChaos 2
1.3 FamousScientistsandImportantEvents 4
1.3.1 LorenzandButterflyEffect 4
1.3.2 LiTien-YienandtheConceptofChaos 5
1.3.3 FeigenbaumandFeigenbaumConstant 6
1.3.4 LeonOngChuaandChua’sCircuit 7
1.3.5 GuanrongChenandChen’sAttractor 8
1.4 DefinitionandCharacteristicsofChaos 9
1.5 OverviewofChaosSynchronizationMethod 10
1.5.1 ChaosSynchronizationMethodsandCharacteristics 11
1.5.2 OtherSynchronizationMethodsandProblems 14
1.6 SummaryofChaosSecureCommunication 15
1.6.1 ChaoticAnalogCommunication 16
1.6.2 ChaoticDigitalCommunication 16
1.6.3 Encryption Communication based on Chaotic
Sequence 17
1.7 ChaosResearchMethodsandMainResearchContents 18
Questions 20
2 CharacteristicAnalysisMethodsforNonlinearSystem 21
2.1 PhaseDiagramAnalysisMethod 21
2.2 PowerSpectralAnalysisMethod 22
2.3 PoincaréSectionMethod 24
2.4 LyapunovCharacteristicExponentMethod 25
2.4.1 DefinitionofLyapunovCharacteristicExponent 25
2.4.2 LyapunovExponentSpectrum 27
2.4.3 PhysicalMeaningofLyapunovExponent 27
2.4.4 ConditionLyapunovExponent 29
2.5 FractalDimensionAnalysisMethod 30
2.6 0–1TestMethod 30
2.6.1 0–1TestAlgorithm 30
2.6.2 Improved0–1TestAlgorithm 32
2.6.3 Applicationof0–1TestAlgorithm 33
2.7 DividingFrequencySamplingMethod 33
2.8 Pseudo-PhaseSpaceMethod 34
2.9 ComplexityMeasureAlgorithm 35
2.9.1 SpectralEntropyComplexityAlgorithm 36
2.9.2 C ComplexityAlgorithm 38
0
Questions 40
VIII Contents
3 TypicalChaoticSystems 41
3.1 Discrete-TimeChaoticMap 41
3.1.1 LogisticMap 41
3.1.2 TentMap 44
3.1.3 HénonMap 44
3.1.4 TangentDelay-EllipseReflectingCavitySystemMap 46
3.2 Continuous-TimeChaoticSystem 47
3.2.1 DuffingOscillator 48
3.2.2 vanderPolOscillator 49
3.2.3 LorenzSystem 49
3.2.4 RösslerSystem 50
3.2.5 Chua’sCircuit 51
3.2.6 ChenSystem 55
3.2.7 LüSystem 55
3.2.8 UnifiedChaoticSystem 57
3.2.9 SimplifiedLorenzSystem 59
3.2.10 StandardforaNewChaoticSystem 62
3.3 HyperchaoticSystem 62
3.3.1 RösslerHyperchaoticSystem 62
3.3.2 ChenHyperchaoticSystem 63
3.3.3 FoldedTowelHyperchaoticMap 64
Questions 65
4 ChaoticSynchronizationPrincipleandMethod 66
4.1 DefinitionofChaosSynchronization 66
4.2 PerformanceIndexofChaoticSynchronizationSystem 67
4.3 PrincipleandPerformanceofFeedbackControlSynchronization 69
4.3.1 Multivariabledrivefeedbacksynchronizationforchaotic
system 69
4.3.2 LinearandNonlinearFeedbackSynchronizationfor
DiscreteChaoticSystem 73
4.4 ParameterAdaptiveSynchronizationBasedonPecora–Carroll
SynchronizationCriterion 84
4.4.1 PrincipleforAdaptiveSynchronization 84
4.4.2 ChooseControlLawandControlParameters 85
4.4.3 DeterminetheBoundaryandRangeoftheControl
Constant 86
4.4.4 SimulationResultsandDiscussion 87
4.5 AdaptiveSynchronizationControlBasedonLyapunovStableTheory 88
4.5.1 Adaptive Synchronization Control with Certain
Parameter 88
4.5.2 AdaptiveSynchronizationControlwithUncertain
Parameters 91
Contents IX
4.6 IntermittentFeedbackSynchronizationControl 94
4.6.1 IntermittentSynchronizationControlbetweenDifferent
Systems 94
4.6.2 Synchronization Simulation and Performance
Analysis 97
4.7 SynchronizationControlBasedonStateObserverMethod 99
4.7.1 DesignPrincipleofStateObserver 99
4.7.2 Design of State Observer for Unified Chaotic
System 101
4.7.3 SimulationandDiscussion 101
4.8 ChaosSynchronizationBasedonChaosObserver 104
4.8.1 DesignPrincipleofChaosObserver 104
4.8.2 ChaosObserveroftheUnifiedChaoticSystem 105
4.8.3 Synchronization Simulation and Performance
Analysis 106
4.9 ProjectiveSynchronization 108
4.9.1 PrincipleandSimulationofProportionalProjection
Synchronization 109
4.9.2 Principle and Simulation of Function Projective
Synchronization 113
4.9.3 PrincipleandSimulationoftheAdaptiveFunction
ProjectiveSynchronization 116
4.10 ProblemsandDevelopmentofChaosSynchronization 123
Questions 124
5 SecureCommunicationTechnology
BasedonChaosSynchronization 125
5.1 ChaoticMaskingCommunication 125
5.2 ChaosShiftKeyingCommunication 130
5.2.1 COOKCommunication 131
5.2.2 CSKCommunication 132
5.2.3 DCSKCommunication 137
5.2.4 FM-DCSKCommunication 139
5.2.5 QCSKCommunication 140
5.3 ChaosParameterModulation 145
5.4 ChaoticSpreadSpectrumCommunication 148
5.4.1 PrincipleofChaoticDS/SSCommunication 148
5.4.2 GenerationofChaoticSpreadSpectrumCode 150
5.4.3 SimulationModuleDesignofMultiuserChaoticSpread
SpectrumSystem 152
5.4.4 DesignandSimulationofMultiuserChaoticSpread
SpectrumSystemBasedonRakeReceiver 158
X Contents
5.4.5 PerformanceAnalysisofMultiuserChaoticSpread
SpectrumSystemBasedonRakeReceiver 159
Questions 163
6 DataEncryptionBasedonChaoticSequence 164
6.1 ChaosCryptography 164
6.1.1 TraditionalCryptography 164
6.1.2 RelationshipbetweenChaosCryptographyandTraditional
Cryptography 166
6.1.3 PrincipleofChaosSequenceEncryption 167
6.2 DataEncryptionAlgorithmBasedonChaoticSequence 168
6.2.1 Basic Requirements of Chaotic Encryption
Algorithm 168
6.2.2 LogisticMapandItsStatistics 170
6.2.3 ChaoticEncryptionModelandAlgorithm 170
6.2.4 ImplementofEncryptionAlgorithmBasedonChaotic
Sequence 172
6.2.5 SystemPerformanceAnalysis 175
6.3 BinaryWatermarkImageEncryptionAlgorithmBasedonChaos 176
6.3.1 ImprovementofChaoticPseudo-RandomSequence
Generator 178
6.3.2 BinaryWatermarkImageEncryptionAlgorithmBasedon
TD-ERCSMap 178
6.3.3 PerformanceAnalysisofEncryptionAlgorithm 179
6.4 ColorImageWatermarkingAlgorithmBasedonChaoticMapandWavelet
Transform 182
6.4.1 Wavelet Transformation Algorithm and Its
Application 183
6.4.2 DesignandImplementationofWatermarkEmbeddingand
ExtractionAlgorithm 186
6.4.3 SimulationandPerformanceAnalysis 190
6.5 ChaoticImageEncryptionAlgorithm 196
6.5.1 Chaos-BasedImageEncryptionTechnology 196
6.5.2 ANewChaoticImageEncryptionScheme 199
Questions 205
7 AudioandVideoChaoticEncryption
andCommunicationTechnology 206
7.1 PrincipleofReal-TimeVoiceEncryptionCommunication 206
7.1.1 Principle of Digital Encryption Communication
System 206
7.1.2 Real-Time Voice Encryption and Communication
System 208
