英文翻譯文獻(xiàn)初稿

1、Anewchaos-basedfastimageencryptionalgorithmABSTRACTInrecentyears,variousimageencryptionalgorithmsbasedonthepermutation-diffusionarchitecturehavebeenproposedwhere,however,permutationanddiffusionareconsideredastwoseparatestages,bothrequiringimage-scanningtoobtainpixelvalues.Ifthesetwostagesarecombined

2、,theduplicatedscanningeffortcanbereducedandtheencryptioncanbeaccelerated.Inthispaper,afastimageencryptionalgorithmwithcombinedpermutationanddiffusionisproposed.First,theimageispartitionedintoblocksofpixels.Then,spatiotemporalchaosisemployedtoshuffletheblocksand,atthesametime,tochangethepixelvalues.M

3、eanwhile,anefficientmethodforgeneratingpseudorandomnumbersfromspatiotemporalchaosissuggested,whichfurtherincreasestheencryptionspeed.Theoreticalanalysesandcomputersimulationsbothconfirmthatthenewalgorithmhashighsecurityandisveryfastforpracticalimageencryption.KeywordsSpatiotemporalchaos;Imageencrypt

4、ion;Cryptography;Informationsecurity1.IntroductionWiththerapidgrowthofimagetransmissionthroughcomputernetworksespeciallytheInternet,thesecurityofdigitalimageshasbecomeamajorconcern.Imageencryption,inparticular,isurgentlyneededbutitisachallengingtaskitisquitedifferentfromtextencryptionduetosomeintrin

5、sicpropertiesofimagessuchasbulkydatacapacityandhighredundancy,whicharegenerallydifficulttohandlebyusingtraditionaltechniques.Nevertheless,manynewimageencryptionschemeshavebeensuggestedinrecentyears,amongwhichthechaos-basedapproachappearstobeapromisingdirection1-10.Ageneralpermutation-diffusionarchit

6、ectureforchaos-basedimageencryptionwasemployedinRefs.1,11-15asillustratedinFig.1.Inthepermutationstage,theimagepixelsarerelocatedbuttheirvaluesremainunchanged.Inthediffusionstage,thepixelvaluesaremodifiedsothatatinychangeinone-pixelspreadsouttoasmanypixelsaspossible.Permutationanddiffusionaretwosepa

7、rateanditerativestages,andtheybothrequirescanningtheimageinordertoobtainthepixelvalues.Thus,intheencryptionprocess,eachroundofthepermutation-diffusionoperationrequiresatleasttwicescanningthesameimage.Thiseffortisactuallyduplicatedbutmaybeavoidedifthepermutationanddiffusionoperationscanbecombined,i.e

8、.,viachangingthevaluesofthepixelswhilerelocatingthem,asillustratedinFig.2.Asaresult,theimageonlyneedstobescannedoncesothattheencryptionspeedandefficiencyissignificantlyimproved.Ontheotherhand,spatiotemporalchaoshasattractedmoreandmoreinterestsamongresearchersinthefieldsofmathematics,physicsandengine

9、ering.Comparedwithsimplechaoticmaps,thiskindofspatiotemporalchaospossessestwoadditionalmeritsforcryptographicpurposes.First,observethatduetothefinitecomputingprecision,orbitsoftemporaldiscretechaoticsystemswilleventuallybecomeperiodic.However,theperiodofspatiotemporalchaosisfoundmuchlongerthanthatof

10、temporalchaoticmaps16sothattheperiodicityproblemispracticallyavoided17.Second,aspatiotemporalchaoticsystemishigh-dimensional,havinganumberofpositiveLyapunovexponentsthatguaranteethecomplexdynamicalbehaviororhighrandomness.Itisthereforemoredifficulttopredictthetimeseriesgeneratedbythiskindofchaoticsy

11、stems.Inthispaper,animageencryptionalgorithmwiththearchitectureofcombiningpermutationanddiffusionisproposed.Theplain-imageisfirstpartitionedintoblocksof8x8pixels.Aspatiotemporalchaoticsystemisthenemployedtogeneratethepseudorandomsequenceusedfordiffusingandshufflingtheblocks.Theobjectivesofthisnewdes

12、igninclude:(i)toefficientlyextractgoodpseudorandomsequencesfromaspatiotemporalchaoticsystemand(ii)tosimultaneouslyperformpermutationanddiffusionoperationsforfastencryption.Therestofthispaperisorganizedasfollows:Section2focusesontheefficientgenerationofpseudorandomsequencesfromspatiotemporalchaos.InS

13、ection3,theproposedalgorithmisdescribedindetail.Section4presentssimulationresultsandperformanceanalyses.InSection5,conclusionsaredrawn.RroundsFig.1.Imagecryptosystembasedonthepermutationanddiffusionoperations.Fig.2.Imagecryptosystemcombiningthepermutation-diffusionarchitecture.2.Pseudorandomsequence

14、sgeneratedfromRroundsFig.1.Imagecryptosystembasedonthepermutationanddiffusionoperations.Fig.2.Imagecryptosystemcombiningthepermutation-diffusionarchitecture.2.PseudorandomsequencesgeneratedfromspatiotemporalchaosApproachtoobtainingpseudorandomnumbersAgeneralnearest-neighboringspatiotemporalchaossyst

15、em,alsocallednearest-neighboringcoupled-maplattices（NCML）18,canbedescribedby5l=G（Ai,Aj.A3,Aq）：$12=F012mlmm14,Ais）；S13=C（W內(nèi)14,內(nèi)15,內(nèi)12）；xn+1=(1-)f(xn(i)+f(xn(i+1)wheren=1,2,.,isthetimeindex;i=1,2,.,N,isthelatticestateindex;fisachaoticmap,and(0,1)isacouplingconstant.Theperiodicboundaryconditionxn(N+i)=

16、xn(i)isimposedintothissystem.Moreover,thetentmapischosenasthelocalchaoticmap,givenbywhereb(0,1)isaconstant.Here,Nischosenas8,whiletheparametersareselectedas=0.05andb=0.4999inordertohavegoodchaoticproperties19,20.Thetraditionalapproachtoextractingpseudorandomnumbersfromtheoutputofachaoticsysteminvolv

17、esiteratingthechaoticmapandthenextractingavaluefromitscurrentstatevariable.ThesetwooperationsareperformedrepeatedlyuntilTable1Timerequiredforl0.000.000runsofvariousbasicoperationsperformedonPCIandPCI.OperatorsTimerequired(ms)PCIraAnd(a)1512Complement1512ExclusiveOR()1612InclusiveDRCv)1612Modulus(mod

18、)1612Addiricn(+)1816Multiplication(x)6347ConvertingfloatiTig-pcinttointeger210160sufficientpseudorandomnumbersareobtained.FortheNCML,thelocalchaoticmapofeachlatticeisfirstiterated.Then,thenewstatevaluesarecalculatedaccordingtothecouplingrelationshipbetweenthelattices.Obviously,iteratingtheNCMLrequir

19、esmuchmorecomputationaleffortthaniteratingasimplechaoticmap.TheefficiencywillbeverylowifonlyonevalueisextractedfromtheNCMLateachtime.Therefore,toimprovetheefficiency,morenumbersshouldbeextractedineachiteration.Thestatevalueofachaoticmapisafloating-pointnumber,butapseudorandomnumberintheformofaninteg

20、erisusuallyrequired.Thismeansthattheconversionfromfloating-pointstointegerscannotbeavoidedinpracticalapplications.However,itisfoundfromcomputersimulationsthatsuchaconversionistimeconsuming.Tojustifythis,variousbasicoperationsarerepeatedfor10,000,000timesontwopersonalcomputerswithdifferentconfigurati

21、ons,whereoneisnamedasPC1witha1.3GHzPentiumprocessorand256MRAMwhiletheotheriscalledPC2witha2.67GHzPentiumDprocessorand1GRAM.ThetimingdatalistedinTable1indicatethatmultiplicationandconversionfromfloatingpointstointegersshouldbeavoidedinordertohavehighefficiencyofgeneratingpseudorandomnumbers.Basedonth

22、eaboveanalysis,thefollowingstepsforgenerating64pseudorandomnumbersfromthelatticevaluesaresuggested.Step1.IteratetheNCMLonceandextract16bits(9thto24thbitsafterthedecimalpoint)fromeachlatticevalue.Thus,atotalof128bitsareobtained.Dividethesebitsinto16bytesanddenotethemasA0,A1,.,A15.Step2.Generate16numb

23、ers,S0,S1,.,S15fromA0,A1,.,A15accordingtothefollowingformula:5?=,A3.八口,A);S3=j.出口,占，內(nèi)工)：514=HfAl4,Ais,Al2,Al3)；515=/c15,A12,A13*A14)wherefunctionsF,G,H,IaredefinedasTOC o 1-5 h zF(a,瓦公d)=(a八5)ac)+d1mod256(4)C(g,b,c,d)=小。ac)vba(-,c,d)=&(av+d)inod256(7)Step3.ChangethevaluesofA0,A1,.,A15asA口一內(nèi)1,&f&,Ai4

24、fAi幺A5f片燈(S)If64pseudorandomnumbershavealreadybeengenerated,gotoStep4;otherwise,gotoStep2togeneratethenext16pseudorandomnumbers.Step4.Substitutethe64numbersaccordingtotheS-boxofAES21,whichareexpressedinhexadecimalforminFig.3.Step5.Generatethe64outputnumbersaccordingto&=115be為+1)mod64)-f5b(j-f2)mod64

25、3Sb(i+3mod64)mod256(9)KIVaujftcr!./AppMSoftfCNJtpd啰J(2C514-522FQ12345678g&bcdfc637e7?Thf26b5fcS3001672bEa37ks76iC32cJ7d5947fOadd4a2af9cal12cC2上7fd93363fE7cc34A3e5fl71da3L15304c723c3ie姚05Sa07IS80b2sh27h27=A09332claIB五日5aa0523bd6b329e32553dl00cd20fcbl5b6acbbe4a4c53g工dOsfSLAfh434d330545f91027f50_3c9EaS

26、S51占3406f929d38f5bebSda21LOff13d51A$edOc11ec5f574417c4a77s3d645d1973960814de222a90EB48abB14de5電gdbaeO323AOa490624Ecc2d3ac整9195el78bcS376dfidd54eA06c564sa657aas0B7951二b4Ct銘dd74Li5bd心8aFig.3.車-bOx：生ubstitUtionvaii倒fOrbyte及y二(inhe0decimaIfo)rmat).e9S1169Be54如13a7占3ee552Bdwherei=0,8c.,al63;RiiOdsthbfei,

27、th金642E8outputnumb41)era99nd52d)DfistbO34hesubsthbLtutiC(7,(i+d)mod8),wherei=0,1,2,3,exchangethelatticevaluesx(i)andx(i+d)mod8).RepeattheoperationsfromStep(i)toStep(iv)untilallblocksareencrypted.Exchangethe(7,7)pixelinthekLthblockandthe(0,s)pixelinthefirstblock,wheres=LSB3(kL).Step5.RepeatStep4for(R

28、-1)roundsaccordingtothesecurityrequirement,whereRisthetotalnumberofencryptionrounds.Thecipher-imageisobtainedbyrelocatingthepixelsintheblocksbacktotheimage.Themoreroundsareprocessed,thehighersecuritytheencryptionwillhave,butattheexpenseofcomputationaleffortandtimedelay.Anillustrationofthewholeencryp

29、tionprocessisgiveninFig.5.DecryptionalgorithmThedecryptionprocedureissimilartothatoftheencryptionprocessexceptthatsomestepsareinareversedorder.Step1andStep2arethesameasthoseoftheencryptionalgorithm.Step3.Partitiontheimageintoblocksof8x8pixelsinareversedorderofStep5inencryption.Step4.Removetheeffecto

30、fcombinedpermutationanddiffusionontheblocks.Exchangethe(0,s)pixelinthefirstblockwiththe(7,7)pixelintheLthkblock.IteratetheNCMLonce,togenerate64pseudorandomnumbers(i,j),wherei=0,1,.,7,andj=0,1,.,7.CX-IJ)|H出eW,O)0(0,0).IH(CX-IJ)|H出eW,O)0(0,0).IH(0,7)0(0.7)Fig.4.Flowchartofchangingpixelvaluesinablock.i

31、ii)CalculateknewaccordingtoEq.(15).IfitisequaltokLortheknewthblockhasalreadybeenprocessed,setknew=(knew+1)modnumuntilaneligibleoneisfound.Movetheknewthblocktopositionk.RecoverthepixelvaluesintherelocatedblockaccordingtoPfc(rj)=0(寸)cycRCt(jJ)SB3(Q(r-L(r-1脂4(G*(51Cjtti-1J+GjmodG(wherecycR(x,y)performs

32、they-bitright-cyclic-shiftoperationonthebinarysequencex;otherparametersarethesameasthoseusedinEq.(14).ExchangethelatticevaluesintheNCMLinthesamewayastheencryption.RepeattheoperationsfromStep(ii)toStep(v)untilallblocksaredecrypted.Step4.RepeatStep3for(R-1)rounds.Step5.Putthepixelsintheblocksbacktothe

33、imageinreverseorderofStep2inencryption.AnillustrationofthedecryptionprocessisgiveninFig.6.Fig.5.AnillustrationofthedecryptionprocessisgiveninFig.6.Fig.5.EncryptionprocessFig.6.Decryptionprocess.PerformanceanalysisKeyspaceanalysisAgoodimageencryptionalgorithmshouldbesensitivetothecipherkey.Thekeyspac

34、eshouldalsobesufficientlylargetomakebrute-forceattackinfeasible.Intheproposedalgorithm,a128-bitkeyisused,whichsatisfiesthegeneralrequirementofresistingbrute-forceattack.Atypicalkeysensitivitytesthasbeenperformedinthefollowingsteps:a512x512imageisencryptedbyusingthetestkey1256789125.Thekeyischangedsl

35、ightlytobe1256789126andusedtoencryptthesameimage.Thetwocipher-imagesarecomparedpixel-by-pixel.Here,thenumberofencryptionroundsisselectedasR=2.Thereisa99.622%differencebetweenthetwocipher-images.Ifaslightlymodifiedkeyisusedtodecryptthecipher-image,thedecryptionfailscompletely.Thetestresultsareshownin

36、Fig.7.DifferentialattackInordertoresistdifferentialattack,aminoralterationintheplain-imageshouldcauseasubstantialchangeinthecipher-image.Totesttheinfluenceofaone-pixelchangeonthecipher-image,twocommonquantitativemeasuresareused:numberofpixelschangerate(NPCR)andunifiedaveragechangingintensity(UACI).T

37、heyaredefinedasfollows1:E；Atj)NPCR=x100%(18)WXHU7=winSM1口吃S9)whereC1andC2arethetwocipher-imageswhosecorrespondingplain-imageshaveonlyone-pixeldifference,thegrey-scalevaluesofthepixelsatposition(i,j)ofC1andC2aredenotedasC1(i,j)andC2(i,j),respectively;WandHarewidthandheightofthecipher-image,respective

38、ly;D(i,j)isdeterminedbyC1(i,j)andC2(i,j),namely,ifC1(i,j)=C2(i,j),D(i,j)=1;otherwise,D(i,j)=0.Aplain-imageisfirstencrypted.Then,apixelinthatimageisrandomlyselectedandtoggled.Themodifiedimageisencryptedagainbyusingthesamekeysoastogenerateanewcipher-image.Finally,theNPCRandUACIvaluesarecalculated.This

39、kindoftestisperformed100timeswithdifferentimagesandnumbersofencryptionroundsR.Theresultingmaximum,minimum,andaverageNPCRandUACIvaluesarelistedinTable3.Ascanbeseenfromthesimulationresults,theproposedcryptosystemonlyneedsaminimumoftworoundstoachieveahighperformancesuchasNPCR0.995andUACI0.333.Therefore

40、,theproposedalgorithmcanresistthedifferentialattackifR2.StatisticalanalysisItiswellknownthatpassingthestatisticalanalysisonciphertextisofcrucialimportanceforacryptosystem.Indeed,anidealciphershouldberobustagainstanystatisticalattack.Inordertoprovetheecurityoftheproposedimageencryptionscheme,thefollo

41、wingstatisticaltestsareperformed.Histogram:Encryptthetestimage,Pepper,fortworounds,andthenplotthehistogramsoftheplain-imageandcipher-imageasshowninFigs.8(a)and(c),respectively.Thelatterfigureshowsthatthehistogramofthecipher-imageisnearlyflat,implyingagoodstatisticalproperty.Correlationofadjacentpixe

42、ls:Totestthecorrelationbetweentwoadjacentpixels,thefollowingproceduresarecarriedout.First,randomlyselect10,000pairsoftwohorizontallyadjacentpixelsfromanimageandthencalculatethecorrelationcoefficientrxyofeachpairusingthefollowingequations:(20)(21)CQvfx,y)=E(x-E(x)(y-E(y)J(20)(21)cov(x,y)wherexandyare

43、grey-levelvaluesofthetwoadjacentpixelsintheimage,E(x)=(1/N)口nxi,andD(x)=(1/N)n(xi-E(x)2.Then,thesameoperationsareperformedalongtheverticalandthediagonaldirections,respectively.Table4liststhecorrelationcoefficientsoftheimagePepperanditscipher-image,whiletheircorrelationdistributionsareshowninFig.9.Th

44、ecorrelationcoefficientsofthecipher-imagesareverysmall,implyingthatnodetectablecorrelationsexistbetweentheoriginalimageanditscorrespondingcipher-image.Therefore,theproposedalgorithmpossesseshighsecurityagainststatisticalattacks.Fig.7.Keyse-imageusingkeyFig.7.Keyse-imageusingkey789012346”,(d)differen

45、ceimagebetweenthetwocipher-images,and(e)decryptedimageusingaslightlymodifiedkey.InformationentropyanalysisItiswellknownthattheentropyH(m)ofamessagesourcemcanbemeasuredbyWhereMisthetotalnumberofsymbolsmiem;p(mi)representstheprobabilityofoccurrenceofsymbolmiandlogdenotesthebase2logarithmsothattheentro

46、pyisexpressedinbits.Forarandomsourceemitting256symbols,itsentropyisH(m)=8bits.Forthecipher-imagesofLenaandPepper,thecorrespondingentropiesare7.9994and7.9992,respectively.Thismeansthatthecipher-imagesareclosetoarandomsourceandtheproposedalgorithmissecureagainsttheentropyattack.Resistancetoknown-plain

47、textandchosen-plaintextattacksIntheproposedalgorithm,thelatticevaluesoftheNCMLareexchangedaccordingtotheciphervaluesaftereachblockisencrypted.ThismeansthatthestatevalueofNCMLisrelatedtoTheniximum,Thiimur11M冊/eNKRu:llUCT間巳sctjfanirodnd?.MF=?P=3Mu閡電閏艇噂璃Mu閶Min則強(qiáng)他：Ainlareg1.1439L63?95553391605蛆庇4的5鴕叫艱0J

48、321127213575丑3而114J433313R43BBjwcti.的的5151.171明5而如虎4第576改i31,7430J911556?引.淑31404B47O315513334431442Bc-itKif.虬萩1.15S433M9L63499531瞿577356CE改i32,7460J8514陰罰前133344B4J5315563溺31452Lena.的1.1514426；明肥99&5J5蛔1940典班冉耶Ptppe:32,8520J9214加335543335434姐33561333993145B6.館1.171441129LE20明5用強(qiáng)即9ft07的5%3S61CFig.8.

49、(a)Plain-image,Pepper,(b)histogramoftheplain-image,(c)cipher-image,and(d)histogramofthecipher-image.初9海51.16344朋后還更5將為剛招時犯538窺theplain-image.SinCetheparameters=Ofdiffu后iOnand-permutation,i.e.；3(i,j)andknew.whichcanbeconsideredasthekeystream,arerelatedtothestatevaluesofNCML,differentimageswillhavenon

50、-identica伊(i,j)-Ondkne：.TheattaCkercannotdecryptparticularcipher-imagebyusingtheparameters(i,j)andknewobtainedfromotherimages.Therefore,theproposedalgorithmcanwellresisttheknown-andchosen-plaintextattacks(asdescribedin2325).SpeedanalysisWhenthesecurityrequirementisfulfilled,therunningspeedbecomesani

51、mportantfactorforpracticalapplications.Intheproposedalgorithm,thepermutationanddiffusionprocessesarecombined,soonlyoneimage-scanningstepisrequiredineachencryptionround.Thisleadstoaspeedadvantagewhencomparedwithalgorithmsrequiringatleasttwoimage-scanningstepsofseparatedpermutationanddiffusionoperatio

52、ns.Meanwhile,intheprocessofgeneratingpseudorandomnumbers,someintegeroperatorssuchasXOR,modulus,etc.areemployedtoreducethenumberoftime-consumingoperationssuchasmultiplicationandconversionfromfloating-pointstointegers.Thisalsoimprovestherunningspeedeffectively.InRef.10,animageencryptionalgorithmbasedo

53、nspatialchaosisproposed,whichneedstworoundstoencrypttheimage.Thealgorithmextractsthepseudorandomnumbersdirectlyfromtheeachiterationofthespatialchaosandmaskstheimagedatafromthefirstonetothelastone,thenfromthelastonetothefirstone.Sincethealgorithmextractsthepseudorandomnumberdirectlyfromthestatvalueof

54、thechaoticmap,moretimeconsumingoperationsareprocessed.Therefore,comparedwiththisalgorithm,ouralgorithmhasfasterrunningspeed.TheNPCRandUACImeasurementsreportedinRefs.1,10are50.23%,0.40%and25.23%,0.3192%,respectively.Theycanhardlysatisfyanyhighperformancerequirement.Onthecontrary,itwasshowninSection4.

55、2thattheproposedalgorithmneedsonlytwoencryptionrounds(i.e.,R=2)toachieveasatisfactoryperformance,withNPCR0.995andUACI0.333foratinychangeatanypositionoftheplain-image.Tomakeacomparisonwithotheralgorithms,theroundnumberofimage-scanning,permutationanddiffusionroundsrequiredtoachievethisperformanceareli

56、stedinTable5.Theresultsshowthattheroundnumberofimage-scanning,permutationanddiffusionrequiredbythenewschemeisfewerthanthatbyothercomparablealgorithms.Thus,theproposedalgorithmindeedleadstoafasterencryptionspeed.FurtherdiscussionAlthoughphysicalchaoticsystemsrunoverrealnumberfieldwithinfinitewordleng

57、th,manyresearchesshowthatdigitalrealizationsusingfloating-pointarithmeticarecloseapproximationsofthecontinuous-valuechaoticmodelandyieldverygoodresultsifthefractionpartissufficientlylong.Inouralgorithm,theNCMLisiteratedwithdoubleprecisionfloating-pointarithmetic.BecauseIEEE754floating-pointstandardi

58、savailableinvirtuallyalmostallcomputersproducedsince198026,theencryptionanddecryptioncanbeprocessedcorrectlyifIEEE754floating-pointstandardisimplementedincomputers,inspiteofdifferentoperatingsystems,programminglanguagesandwordlengths.However,wecannotrecovertheplain-imagefromtheencryptedimageiftheIEE

59、E754floating-pointstandardisnotimplemented.Table4CamelstioncoefficLentsoftwcadjiacentpixesinttieplain-andtheciptier-images.Plain-iiTTiag&Cipher-imageFarijonta0.986433.0707Vertical.98航39.2165Diaoml0.977623.14S8G同裁-L+K)E口130-CQ口口3AaJIH-UM-dixefgrayvslueonlocalhn伏肘piifflljwvalueontooaliDn弋出同裁-L+K)E口130

60、-CQ口口3AaJIH-UM-dixefgrayvslueonlocalhn伏肘piifflljwvalueontooaliDn弋出wrtitm:胃危如e串ceiltwpxPE號時而打己翼cotreltizn肝圖itcaadjxeErmpi詞方如cint空。(Jj的D1二dteI己(ameFd向第ial咕口:mefsFzrzbfrmagB辱口re而1口訃口版飽13da:etW3pii.fkgcbirFig.9.CorrelationsoftwoadjacentDixe才朝1溶盛onlotion(x.yiplain-image,(b)horizontaldirectionco-lc0口一匚o口口