23-2 Industrial Communication Systems
by.chaos.synchronization..But.before.1990,.chaos.synchronization.was.very.dicult.and.nearly.impos-
sible.
.e.ground-breaking.scheme,.called.Pecara.and.Carroll.scheme.[PC90],.rstly.oered.a.method.
to.control.and.realize.chaos.synchronization..From.then.on,.chaos.synchronization.and.its.application.
to.secure.communication.have.seen.a.urry.of.research.activities.for.decades.
e
.main.advantage.of.a.chaotic.secure.communication.system.over.conventional.cryptosystems.is.
that.chaotic.secure.communication.schemas.can.oen.be.realized.using.very.simple.circuits.on.a.part.
of.a.chip.[GHGS00].and.they.can.be.used.in.applications.that.do.not.require.a.high.level.of.information.
security.such.as.remote.keyless.entry.system,.video.phone,.and.wireless.telephone.[GHGS00]..In.this.
chapter,.some.typical.control.methods.for.chaos.synchronization.will.be.presented.rst,.and.then.how.
they.are.applied.to.secure.communication.will.be.illustrated.
23.2 Chaos Synchronization
A.number.of.methods.have.been.proposed.for.the.synchronization.of.chaotic.systems,.including.the.
linear.and.nonlinear.feedback.control,.fuzzy.control,.adaptive.control,.sliding.mode.control,.and.impulsive.
control..In.this.section,.some.typical.synchronization.control.methods.are.introduced.with.the.Chua’s.
circuit.as.an.illustrated.example.
23.2.1 Feedback Control for Chaos Synchronization via Partial States
One.of.the.important.aspects.to.evaluate.the.eectiveness.of.the.secure.communication.schema.is.the.
transmission.eciency,.i.e.,.the.ratio.of.the.data.information.to.the.entire.transferred.information..In.
order.to.achieve.chaos.synchronization,.it.is.unavoidable.to.occupy.the.communication.channel.by.syn-
chronization
.control.information.of.the.driving.system.that.needs.to.be.transmitted.to.the.receiver..In.
the.full-order.synchronization.control.schema.in.which.synchronization.is.achieved.by.controlling.all.
the.system.states,.information.on.all.the.states.of.the.driving.system.should.be.sent.to.the.receiver,.which.
leads.to.a.poor.transmission.eciency..In.addition,.the.full-order.synchronization.control.schema.is.not.
feasible.for.the.case.when.some.of.the.system.states.are.not.available.or.controllable..In.order.to.over-
come
.the.problem.for.such.a.case.and.to.improve.the.transmission.eciency,.one.may.wish.to.transmit.
Original
Original signal
Encrypter
Chaotic
system
Decrypter
~
p(t)
~
k(t)
Synchronization
drive impulses
Synchronization
drive impulses
Digital signal
Channel
Intruder
Cryptographic
scheme e()
p(t)
v
R
(t)
v
R
(t)
k(t)
Chaotic
system
Magnifying-
glass
Composition
Decomposition
Magnifying-
glass
Cryptographic
scheme d()
Digital signal
Compressed and D/A A/D and decompressed
FIGURE 23.1 System. block. diagram. of. the. chaotic. cryptosystem.. (Reprinted. from. Li,. Z.G.. et. al.,. IEEE
Trans.Commun.,
.51(8),.1306,.2003..Copyright.@.2003.by.e.Institute.of.Electrical.and.Electronics.Engineers..
With..permission.)
© 2011 by Taylor and Francis Group, LLC