图像加密英文翻译 译文Word文档格式.docx

图像加密英文翻译 译文Word文档格式.docx

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学生姓名：

覃洁文

学号：

1000710222

指导教师单位：

姓名：

王东

职称：

副教授

2014年6月7日

Parallelimageencryptionalgorithmbasedondiscretizedchaoticmap

Abstract

Recently,avarietyofchaos-basedalgorithmswereproposedforimageencryption.Nevertheless,noneofthemworksefficientlyinparallelcomputingenvironment.Inthispaper,weproposeaframeworkforparallelimageencryption.Basedonthisframework,anewalgorithmisdesignedusingthediscretizedKolmogorovflowmap.Itfulfillsalltherequirementsforaparallelimageencryptionalgorithm.Moreover,itissecureandfast.Thesepropertiesmakeitagoodchoiceforimageencryptiononparallelcomputingplatforms.

1.Introduction

Inrecentyears,thereisarapidgrowthinthetransmissionofdigitalimagesthroughcomputernetworksespeciallytheInternet.Inmostcases,thetransmissionchannelsarenotsecureenoughtopreventillegalaccessbymaliciouslisteners.Thereforethesecurityandprivacyofdigitalimageshavebecomeamajorconcern.Manyimageencryptionmethodshavebeenproposed,ofwhichthechaos-basedapproachisapromisingdirection[1–9].

Ingeneral,chaoticsystemspossessseveralpropertieswhichmakethemessentialcomponentsinconstructingcryptosystems:

（1）Randomness:

chaoticsystemsgeneratelong-period,random-likechaoticsequenceinadeterministicway.

（2）Sensitivity:

atinydifferenceoftheinitialvalueorsystemparametersleadstoavastchangeofthechaoticsequences.

（3）Simplicity:

simpleequationscangeneratecomplexchaoticsequences.

（4）Ergodicity:

achaoticstatevariablegoesthroughallstatesinitsphasespace,andusuallythosestatesaredistributeduniformly.

Inadditiontotheaboveproperties,sometwo-dimensional（2D）chaoticmapsareinherentexcellentalternativesforpermutationofimagepixels.PichlerandScharingerproposedawaytopermutetheimageusingKolmogorovflowmapbeforeadiffusionoperation[1,2].Later,Fridrichextendedthismethodtoamoregeneralizedway[3].Chenetal.proposedanimageencryptionschemebasedon3Dcatmaps[4].Lianetal.proposedanotheralgorithmbasedonstandardmap[5].Actually,thosealgorithmsworkunderthesameframework:

allthepixelsarefirstpermutedwithadiscretizedchaoticmapbeforetheyareencryptedonebyoneunderthecipherblockchain（CBC）modewherethecipherofthecurrentpixelisinfluencedbythecipherofpreviouspixels.Theaboveprocessesrepeatforseveralroundsandfinallythecipher-imageisobtained.

Thisframeworkisveryeffectiveinachievingdiffusionthroughoutthewholeimage.However,itisnotsuitableforrunninginaparallelcomputingenvironment.Thisisbecausetheprocessingofthecurrentpixelcannotstartuntilthepreviousonehasbeenencrypted.Thecomputationisstillinasequentialmodeevenifthereismorethanoneprocessingelement（PE）.ThislimitationrestrictsitsapplicationplatformsincemanydevicesbasedonFPGA/CPLDordigitalcircuitscansupportparallelprocessing.Withtheparallelcomputingtechnique,thespeedofencryptionisgreatlyaccelerated.

Anothershortcomingofchaos-basedimageencryptionschemesistherelativelyslowcomputingspeed.Theprimaryreasonisthatchaos-basedciphersusuallyneedalargeamountofrealnumbermultiplicationanddivisionoperations,whichcostvastofcomputation.Thecomputationalefficiencywillbeincreasesubstantiallyiftheencryptionalgorithmscanbeexecutedonaparallelprocessingplatform.

Inthispaper,weproposeaframeworkforparallelimageencryption.Undersuchframework,wedesignasecureandfastalgorithmthatfulfillsalltherequirementsforparallelimageencryption.Therestofthepaperisarrangedasfollows.Section2introducestheparalleloperatingmodeanditsrequirements.Section3presentsthedefinitionsandpropertiesoffourtransformationswhichformtheencryption/decryptionalgorithm.InSection4,theprocessesofencryption,decryptionandkeyschedulingwillbedescribedindetail.ExperimentalresultsandtheoreticalanalysesareprovidedinSections5and6,respectively.Finally,weconcludethispaperwithasummary.

2.Parallelmode

2.1Parallelmodeanditsrequirements

Inparallelcomputingmode,eachPEisresponsibleforasubsetoftheimagedataandpossessesitsownmemory.Duringtheencryption,theremaybesomecommunicationbetweenPEs（seeFig.1）.

Toallowparallelimageencryption,theconventionalCBC-likemodemustbeeliminated.However,thiswillcauseanewproblem,i.e.howtofulfillthediffusionrequirementwithoutsuchmode.Besides,therearisesomeadditionalrequirementsforparallelimageencryption:

1.ComputationloadbalanceThetotaltimeofaparallelimageencryptionschemeisdeterminedbytheslowestPE,sinceotherPEshavetowaituntilsuchPEfinishesitswork.ThereforeagoodparallelcomputationmodecanbalancethetaskdistributedtoeachPE.

2.CommunicationloadbalanceThereusuallyexistslotsofcommunicationbetweenPEs.Forthesamereasonasofcomputationload,thecommunicationloadshouldbecarefullybalanced.

3.CriticalareamanagementWhencomputinginaparallelmode,manyPEsmayreadorwritethesameareaofmemory（i.e.criticalarea）simultaneously,whichoftencausesunexpectedexecutionoftheprogram.Itisthusnecessarytousesomeparalleltechniquestomanagethecriticalarea.

2.2Aparallelimageencryptionframework

Tofulfilltheaboverequirements,weproposeaparallelimageencryptionframework,whichisafour-stepprocess:

Step1:

Thewholeimageisdividedintoanumberofblocks.Step2:

EachPEisresponsibleforacertainnumberofblocks.Thepixelsinsideablockareencryptedadequatelywitheffectiveconfusionanddiffusionoperations.Step3:

Cipher-dataareexchangedviacommunicationbetweenPEstoenlargethediffusionfromablocktoabroaderscope.Step4:

Gotostep2untilthecipherimagereachestherequiredlevelofsecurity.

Instep2,diffusionisachieved,butonlywithinthesmallscopeofoneblock.Withtheaidofstep3,however,suchdiffusioneffectisbroadened.Notethatfromthecryptographicpointofview,dataexchangeinstep3isessentiallyapermutation.Afterseveraliterationsofsteps2and3,thediffusioneffectisspreadtothewholeimage.Thismeansthatatinychangeinoneplain-imagepixelwillspreadtoasubstantialamountofpixelsinthecipher-image.Tomaketheframeworksufficientlysecure,tworequirementsmustbefulfilled:

1.Theencryptionalgorithminstep2shouldbesufficientlysecurewiththecharacteristicofconfusionanddiffusionaswellassensitivitytobothplaintextandkey.

2.Thepermutationinstep3mustspreadthelocalchangetothewholeimageinafewroundsofoperations.

ThefirstrequirementcanbefulfilledbyacombinationofdifferentcryptographicelementssuchasS-box,Feistel-structure,matrixmultiplicationsandchaosmap,etc.,orwecanjustuseaconventionalcryptographicstandardsuchasAESorIDEA.Thesecondone,however,isanewtopicresultedfromthisframework.Furthermore,suchpermutationshouldhelptoachievethethreeadditionalgoalspresentedinSection2.1.Hence,thepermutationoperationisoneofthefocusesofthispaperandshouldbecarefullystudied.

Underthisparallelimageencryptionframework,weproposeanewalgorithmwhichisbasedonfourbasictransformations.Therefore,wewillfirstintroducethosetransformationsbeforedescribingouralgorithm.

3.Transformations

3.1A-transformation

InA-transformation,‘A’standsforaddition.Itcanbeformallydefinedasfollow:

a+b=c,wherea,b,cϵG,G=GF（28）,andtheadditionisdefinedasthebitwiseXORoperation.ThetransformationAhasthreefundamentalproperties:

（2.1）a+a=0

（2.2）a+b=b+a

（2）（2.3）（a+b）+c=a+（b+c）

3.2M-transformation

InM-transformation,‘M’standsformixingofdata.First,weintroducethesumtransformation:

sum：

m×

n→G

thensum（I）isdefinedas:

sum

（1）=a（ij）

NowwegivethedefinitionofM-transformationasfollows:

M：

n→m×

n

LetM（I）=CI=a（ij）C=（c（ij）（3）c（ij）=a（ij）+sum（I）

ItiseasytoprovethefollowingpropertiesoftheM-transformation:

（5.1）M（M（I））=I（5）（4）

（5.2）M（I+J）=M（I）+M（J）

（5.3）M（kj）=kM（I），wherekI=1，k∈N

ItshouldbenotedthatalltheadditionoperationsfromaretheA-transformationindeed.

3.3S-transformation

InS-transformation,‘S’standsforS-boxsubstitution.TherearelotsofwaystoconstructanS-box,amongwhichthechaoticapproachisagoodcandidate.Forexample,TangetalpresentedamethodtodesignS-boxbasedondiscretizedlogisticmapandBakermap[10].Followingthiswork,Chenetal.proposedanothermethodtoobtainanS-box,whichleadstoabetterperformance[11].Theprocessisdescribedasfollows:

Step1:

SelectaninitialvaluefortheChebyshevmap.TheniteratethemaptogeneratetheinitialS-boxtable.

Step2:

Pileupthe2Dtabletoa3Done.

Step3:

Usethediscretized3DBakermaptoshufflethetableformanytimes.Finally,transformthe3Dtablebackto2DtoobtainthedesiredS-box.ExperimentalresultsshowthattheresultantS-boxisidealforcryptographicapplications.Theapproachisalsocalled‘dynamic’asdifferentS-boxesareobtainedwhentheinitialvalueofChebyshevmapischanged.However,forthesakeofsimplicityandperformance,weuseafixedS-box,i.e.theexamplegivenin[11]（seeTable1）.

3.4K-transformation

InK-transformation,‘K’standsforKolmogorovflow,whichisoftencalledgeneralizedBakermap[3].TheapplicationofKolmogorovflowforimageencryptionwasfirstproposedbyPichlerandScharinger[1,2].ThediscreteversionofK-flowisgivenby:

whered=（n1,