2015毕业设计（翻译原文）基于混沌小波的图像加密算法研究

ANewHyper-chaoticAlgorithmforImageEncryptionYongliangXiaoP1,2P,LiminXiaP1,*PP1PSchoolofInformationScienceandEngineering,CentralSouthUniversity,Changsha410083,China;P2PDepartmentofInformationManagement,HunanCollegeofFinanceandEconomics,Changsha410205,China;P*PCorrespondingauthor:AbstractThispaperpresentsanewimageencryptionalgorithm,whichusesanimagesorttransformationtoshufflethepositionsofimagepixels,andthenthestatesofhyper-chaosareusedtochangethegreyvaluesoftheshuffledimageaccordingtothechangeddistancesofeachpixelduringtheprocessofshuffled.Theexperimentalresultsdemonstratethatthesuggestedencryptionalgorithmofimagehastheadvantagesoflargekeyspaceandhighsecurity,andmoreover,thedistributionofgreyvaluesoftheencryptionmagehasarandom-likebehavior.Comparedwithsomeencryptionalgorithms,theencryptionalgorithmismoresecure.Keyword:Hyper-chaotic,imageencryption,keyspace,sort,shuffling1.IntroductionWiththerapidgrowthofcomputernetworktechnology,itissoeasytoobtaindigitalimagesthroughnetworkandfurtheruse,process,reproduceanddistributethem.Protectionofdigitalimagesagainstillegalcopyinganddistributionhasbecomeextremelyimportant.Generally,therearetwomajorapproachesthatareusedtoprotectdigitalimages.Oneisinformationhidingwhichincludeswatermarking,anonymityandcoverchannelH1,2H.TheotherisencryptionthatincludesconventionalencryptionandotherssuchaschaoticencryptionH3,4H.AfterMatthewsproposedthechaoticencryptionalgorithmin1989H5H,therearemanyimageencryptiontechnologybasedonchaoticsystemsH6-9H,whichhavemanyimportantproperties,suchasthesensitivedependenceoninitialconditionsandsystemparameters,pseudorandomproperty,non-periodicityandtopologicaltransitivity.Theencryptiontechnologyconsistsoftwoindependentprocesses:shuffledandencryptionH4,10,11H.Intheseschemes,peopleoftenuseachaoticmaptogenerateachaoticsequence,andthenquantifythissequencetogettheshuffleaddresses.Theshuffledaddressesarentachaoticsequence,sowehavetoiteratethemapmanytimestogettheonlyaddress.Meantime,theprocessedofshuffledandencryptionisindependent.Duringtheprocessofencryptingimage,wedontutilizeanyresultofshuffled.Sowecangetthecorrecthistogramwiththecorrectchaoskeysofencryption,whichiseasytoattackbystatisticalanalysisH10H.Toovercomethesedrawbacks,anewhyper-chaoticalgorithmissuggested.Theencryptionproposedconsistsoftwoprocesses.Firstly,weuseanimagesorttransformationtoshufflethepositionsofimagepixels.Thenthestatesofhyper-chaosareusedtochangethegreyvaluesoftheshuffled-imageaccordingtothechangeddistancesofeverypixelduringtheprocessofshuffling.Therestofthispaperisorganizedasfollows.InSection2,weproposeanewchaoticshufflealgorithmandimageencryptionalgorithmthroughcombinationofstatesofchaoticsystems.Section3describestheresultsofencryptionalgorithmbasedonthehyper-chaoticsystem.InSection4,securityofthehyper-chaoticencryptionalgorithmisdiscussed.Itisprovedthatthenewalgorithmhastheadvantagesofhigh-levelsecurity,largekeyspace.Finally,Section5concludesthepaper.2.Theproposedencryptionalgorithm2.1.ImageshufflealgorithmImagedatahavestrongcorrelationsamongadjacentpixels,inordertodisturbthehighcorrelationamongpixels,one-dimensionalchaoticsystemwiththeThe9thInternationalConferenceforYoungComputerScientists978-0-7695-3398-8/08$25.002008IEEEDOI10.1109/ICYCS.2008.4112814advantagesofhigh-levelefficiencyandsimplicityHT12TH,suchasLogisticmap,hasbeenwidelyusednow.Buttheirweakness,suchassmallkeyspaceandweaksecurity,isalsodisturbingHT13TH.Sothispaperweuseanewnonlinearchaoticalgorithm(NCA),theNCAisdefinedas44(1)(1)()(1)1xtgtgxxnnng69g69g68g69g68g16g16g32g16g152g152g16g152g152g16g152g144(1(1)()(1)tgxxnng69g69g69g68g16g16g16g152g152g16(1)where(0,1)xng143,(0,1.4g68g143,(5,43g69g143,or(0,1)xng143,(1.4,1.5g68g143,(9,38g69g143,or(0,1)xng143,(1.5,1.57g68g143,(3,15g69g143.ThismapcanapplymorelargekeyspacethanLogisticmap.Formoreinformationaboutthesystem,pleaseseerelativereferenceHT14TH.Withoutlossofgenerality,weassumethatthedimensionoftheplainimageNMg117,thegreymatrixofpixelsis(,)Pij,0,1,1iMg32g16g33;0,1,1jNg32g16g33.Theprocedureofgenerationforshufflingmapisdescribedasfollows:Step1.Fromlefttorightandtoptobottom,wetransformtwo-dimensionalimagePtoone-dimensionalsequence1()Pi,1,2,g32g117g33iNM.Step2.Startingfromcertaininitialcondition0xandparameterg68,g69.AfteriteratedKtimes,wecontinuetoiteratetheaboveNCANMg117timestoobtainchaoticsequenceg94g9612NMXx,xxg117g32g33,thenorderXascending,wegetanewsequenceg94g9612NMYy,yyg117g32g33.Step3.AccordingtotheaddressmapofYtoX,wetransform1()Pi,1,2,g32g117g33iNMto2()Pi,1,2,g32g117g33iNMandrecordthemovabledistancesg94g9612NMDd,ddg117g32g33,wedefinethemovabledistanceequalingtothecoordinatedifferencebetween1Pand2Pforthesamepixel.Step4.Transform2Ptoshuffledimage0PbasedontheinverseprocessesofStep1.2.2.ChuaschaoticsystemIntheproposedencryptionscheme,anewhyper-chaoticsystemgeneratedfromChuaschaoticsystemisusedinkeyscheming,whichismodeledbyHT15TH1211213354324544545665()()()g88g90g88g90g32g152g16g16g173g176g32g16g14g14g152g16g176g176g32g16g152g176g174g32g152g16g16g176g176g32g16g14g176g32g16g152g176g175g5g5g5g5g5g5xxxfxxxxxmxxxxxxxfxxxxxxx(2)()()(11)/2fxbxabxxg32g14g16g152g16g16g14.Whereg88,g90,a,b,mareparameters,when10.0g88g32,14.87g90g32,1.27ag32g16,0.68bg32g16,0.02mg32,thehyper-chaoshastwopositiveLyapunovexponents10.431g79g32and20.412g79g32,sothepredictiontimeofahyper-chaoticsystemislongerthanthatofachaoticsystemHT16TH,asaresult,itissaferthanchaosinsecurityalgorithm.Thehyper-attractorsareshowninHTFig1TH.Formoredetailedanalysisofthecomplexdynamicsofthesystem,pleaseseerelativereferenceHT15TH.-4-3-2-101234-6-4-20246x3x1-4-3-2-101234-0.8-0.6-0.4-0.20.00.8x5x4(a)(b)Fig1.Hyper-chaosattractors:(a)xB1B-xB3Bplaneand(b)xB4B-xB5Bplane.2.3.EncryptionalgorithmdesignAfterwegettheshuffledimage0PbasedontotalshufflingmapusingNCA,theabovehyper-chaosisusedtoencrypttheshuffledimage0P.Theencryptionschemeisbasedonthestatevariablesoftheabovehyper-chaoticsystem,whichisgiveninHTTable1TH.Table1.Differentstateofhyper-chaosdxdx0xB1B3xB4B1xB2B4xB5B2xB3B5xB6BThen,theencryptionprocessisgivenasfollows:Step1.Iteratethehyper-chaoticsystemfor0KtimesbyRungeKuttaalgorithmtoavoidtheharmfuleffectoftransientprocedure.2815Step2.Thehyper-chaoticsystemisiterated,andasaresult,sixdecimalfractions1x,2x,3x,4x,5x,6xwillbegenerated.Thesedecimalvaluesarepreprocessedfirstlyasfollows14mod()()10,256)g32g16g117xAbsxFloorxiii1,2,3,4,5,6g32i(3)where()Absxreturnstheabsolutevalueofx.()Floorxreturnsthevalueofxtothenearestintegerslessthanorequaltox,mod(,)xyreturnstheremainderafterdivision.Step3.Generatedbyusingthefollowingformula:dmod(D,6)g32.Asd0,5g143,sofromTable1,wecanselectthecorrespondingstatethatareusedtoperformencryptionoperationifdequalstotheserialnumberofsequenceofthegroup.Forexample,ifd1g32,then2xisusedtodoencryption.TheencryptionoperationistodoXORbetween2xandthispixel.Step4.RepeatingStep2andStep3,eachpixelofimageP0isencryptedbyorderfromlefttorightandtoptobottom.3.ExperimentalanalysisExperimentalanalysisoftheproposedimageencryptionalgorithminthispaperhasbeendone.Theplainimagewiththesize256256g117isshowninHTFig2(aTH)andthehistogramoftheplainimageisshowninHTFig2(bTH).ImagewegetthroughchangeofimagetotalshufflingmapisshowninHTFig2(cTH)andthecorrespondinghistograminshowninHTFig2(dTH).TheencryptionimageisshowninHTFig2(eTH)andthehistogramisshowninHTFig2(fTH).Fromthefigure,wecanseethatthehistogramofthecipheredimageisfairlyuniformandissignificantlydifferentfromthatoftheoriginalimage.(a)(b)(c)(d)(e)(f)Fig2.Experimentalresult:(a)originalimage;(b)histogramof(a);(c)imageencryptedbytotalshufflingmapbasedonNCA;(d)histogramof(c);(e)cipheredimageand(f)histogramof(e).4.SecurityanalysisSecurityisamajorissueofacryptosystem.Agoodcryptosystemshouldbesensitivetothesecretkeys,andhavelargekeyspacetoresistallkindsofknownattacks.Somesecurityanalysishasbeenperformedontheproposedimageencryptionscheme.4.1.KeyspaceanalysisKeyspacesizeisthetotalnumberofdifferentkeysthatcanbeusedinthecryptosystem.Cryptosystemiscompletelysensitivetoallsecretkeys.Iftheprecisionis10P-14P,thekeyspacesizeforinitialconditionsandisoverthan10P98P.Moreover,theinitialiterationnumberK,Nandstructureparametersg68,g69alsobeusedasthesecretkeys.TheskyspaceislargethanthespaceofRef.HT4,9,11,17TH.Apparently,thekeyspaceislargeenoughtoresistallkindsofbrute-forceattacks.4.2.KeysensitivitytestSeveralkeysensitivitytestsareperformed.HTFig3(a)-(d)THillustratethesensitivityofourschemetothesecretkey0x,1x,2x,3x,4x,5x,6x,g68,g69,Kand0K.HTFig3(a)THistheencryptionimagewiththesameparametersasthatusedinencryptionalgorithms,thatisxB0B=0.3,xB1B=-0.56,xB2B=0.1,xB3B=0.1,xB4B=0.56,xB5B=-0.1,xB6B=-0.1,0.02g68g32,5g69g32,2000Kg32and05000Kg32.HTFig3(b)THisthedecryptedimagewithalltheparameterstobesameasthatusedinencryptionalgorithmexceptxB0B=0.30000000000001.HTFig3(d)THisthedecrypted2816imagewithadifferentinitialiterationtimes05001Kg32.HTFig3(c)THand(e)arecorrespondinghistogramsofthedecryptedimage,respectively.Wecanseethatthehistogramofthecipheredimageisfairlyuniformandissignificantlydifferentfromthatoftheoriginalimage,andthehyper-chaosencryptionalgorithmissensitivetothekey,asmallchangeofthekeywillgenerateacompletelydifferentdecryptionresultandcannotgetthecorrectplainimage.Moreover,withoutthekeysofhyper-chaoticsystemandNCA,wecantobtainthecorrectencryptionimageandhistogram.ButinotherschemesHT8,11TH,wecangetthecorrecthistogramwiththecorrecthyper-chaoskeys,whichiseasytoattackbystatisticalanalysisHT10TH.Soitcanbeconcludedthattheencryptionalgorithmismoresecure.(a)(b)(c)(d)(e)Fig3.Experimentalresult:(a)decryptedimagewithcorrectparameters;(b)decryptedimagewithdifferentinitialvalue;(c)histogramofimage(b);(d)decryptedimagewithdifferentiterationvalueand(e)histogramofimage(d).4.3.AnalysisofcorrelationoftwoadjacentpixelsStatisticalanalysishasbeenperformedontheproposedimageencryptionalgorithm.Thisisshownbyatestofthecorrelationbetweentwoadjacentpixelsinplainimageandcipheredimage.Werandomlyselect5000pairsoftwo-adjacentpixels(invertical,horizontal,anddiagonaldirection)fromplainimagesandcipheredimages,andcalculatethecorrelationcoefficientsHT18,19TH,respectivelybyusingthefollowingtwoformulas(seeHTTable2THandHTFig4(a)THandHT(b)TH):(a)(b)Fig4.Correlationoftwohorizontallyadjacentpixelsintheoriginalimageandinthecipheredimage:(a)correlationanalysisofplainimageand(b)correlationanalysisofcipheredimage.cov(,)()()xyrxyDxDyg32(4)Where1()1NExxiNig32g166g32,12()()1NDxxExiNig32g16g166g32,1cov(,)()()1NxyxExyEyiiNig32g16g16g166g32,xandyaregreyvaluesoftwoadjacentpixelsintheimage.HTFig4THshowsthecorrelationdistributionoftwoadjacentpixelsintheoriginalimageandthatinthecipheredimage.Thecorrelationcoefficientsare0.9317and0.0102,respectively.OthertestresultsareshowninHTTable2TH.Table2.CorrelationcoefficientoftwoadjacentpixelsintwoimagesModelOriginalCipheredimageHorizontal0.93170.0102Vertical0.95320.0070Diagonal0.90420.01685.ConclusionsInthispaper,anewschemeforimageencryptionbasedonhyper-chaoshasbeenpresented.Weuseanewsorttransformationtoshufflethepixelpositionoftheplainimageandthenthestatesofhyper-chaosareusedtochangethegreyvaluesoftheshuffled-imageaccordingtothechangeddistancesofeverypixelduringtheprocessingofshuffle.Somesecurityanalysissuchaskeyspaceanalysis,keysensitivityanalysis,correlationanalysisoftwoadjacentpixelsisgiventoshowthattheproposedcryptosystemhasa2817highsecuritylevel.Moreover,withoutthekeysofhyper-chaoticsystemandNCA,wecantobtainthecorrectdecryptedimageandhistogram.Butinotherschemes,wecangetthecorrecthistogramwiththecorrecthyper-chaoskeys,whichiseasytoattackbystatisticalanalysis.Soitcanbeconcludedthattheencryptionalgorithmismoresecure,whichmayhassomepotentialapplicationslikeinternetimageencryptionandsecuretransmissionofconfidentialinformationintheInternet.AcknowledgementsTheauthorswouldliketothankthereviewersfortheirconstructivesuggestions.ThisworkwassupportedbytheKeyProgramofNationalNaturalScienceFoundationofChinaunderGrantNO.79816101andHunanNaturalScienceFoundationunderGrantNO.05JJ30121.References1X.J.Qi,J.Qi,Arobustcontent-baseddigitalimagewatermarkingscheme,SignalProcessing,Volume87,Issue6,June2007,pp.1264-1280.2S.S.Maniccam,N.Bourbakis,Losslesscompressionandinformationhidinginimages,PatternRecognition,Volume37,Issue3,March2004,pp.475-486.3X.J.Tong,M.G.Cui,Imageencryptionwithcompoundchaoticsequenceciphershiftingdynamically,ImageandVisionComputing,Volume26,Issue6,June2008,pp.843-850.4Z.H.Guan,F.J.Huang,andW.J.Guan,Chaos-basedimageencryptionalgorithm,PhysicsLettersA,Volume346,Issues1-3,October2005,pp.153-157.5R.A.J.Matthews,Onethederivationofachaoticencryptionalgorithm,Cryptologia,Volume1,Issues8,1989,pp.29-42.6F.Y.Sun,S.T.Liu,Z.Q.Li,etal,Anovelimageencryptionschemebasedonspatialchaosmap,Chaos,Solitons&Fractals,Volume38,Issue3,November2008,pp.631-640.7S.Behnia,A.Akhshani,S.Ahadpour,etal,A.AkhavanAfastchaoticencryptionschemebasedonpiecewisenonlinearchaoticmaps,PhysicsLettersA,Volume366,Issues4-5,July2007,pp.391-396.8T.G.Gao,Z.Q.Chen,Imageencryptionbasedonanewtotalshufflingalgorithm,Chaos,Solitons&Fractals,Volume38,Issue1,October2008,pp.213-220.9L.H.Zhang,X.F.Liao,andX.B.Wang,Animageencryptionapproachbasedonchaoticmaps,Chaos,Solitons&Fractals,Volume24,Issue3,