2015毕业设计（翻译原文）基于混沌小波的图像加密算法研究1

AHYPERCHAOSBASEDIMAGEENCRYPTIONALGORITHMCHENZAIPING,LIHAIFEN,DONGENZENG,DUYANGTIANJINKEYLABORATORYFORCONTROLTHEORYIMAGEENCRYPTIONSECURITYANALYSISKEYSPACEIINTRODUCTIONWITHTHEDEVELOPMENTOFNETWORKTECHNOLOGYANDMULTIMEDIATECHNOLOGY,ECOMMERCE,ELECTRONICADVERTISING,VIDEOANDOTHERTYPESOFNETWORKSERVICESANDMODEOFOPERATIONFORTHEBUSINESSEARNEDPROFITSATTHESAMETIMEHOWEVER,THEINTERNETMULTIMEDIAINFORMATIONTOBRINGCONVENIENCETOPEOPLEBUTALSOEXPOSEDMOREANDMORESERIOUSSECURITYPROBLEMSFOREXAMPLEMULTIMEDIAWORKSOFCOPYRIGHTINFRINGEMENT,ILLEGALCOPIESOFSOFTWARETOSOLVETHISPROBLEM,MANYENCRYPTIONALGORITHMSHAVEBEENPROPOSED18AMONGTHEM,CHAOSBASEDALGORITHMSHASSUGGESTEDANEWANDEFFICIENTWAYTODEALWITHTHEINTRACTABLEPROBLEMOFFASTANDHIGHLYSECUREIMAGEENCRYPTION,ANDITHASBEENPROVEDTHATINMANYASPECTSAGOODENCRYPTIONSHOULDINCLUDETHEFOLLOWINGASPECTSFIRSTLY,THEKEYMUSTHAVESENSITIVITYTOTHECIPHERKEYSSECOND,THEKEYSPACESHOULDBELARGEENOUGHTOMAKEBRUTEFORCEATTACKSINFEASIBLE9HYPERCHAOSHASMORETHANONEPOSITIVELYAPUNOVEXPONENT,ANDTHEREAREMORECOMPLEXDYNAMICALCHARACTERISTICSTHANCHAOS,THEREFORETHESTUDYOFHYPERCHAOSBASEDENCRYPTIONALGORITHMSMAYBEMOREVALUABLETHEENCRYPTIONALGORITHMSECURECOMMUNICATIONSCHEMESBASEDONHYPERCHAOTICSYSTEMSWASPROPOSED10,BUTNOWTHEREISALITTLESTUDYINTHEHYPERCHAOSENCRYPTIONALGORITHMINTHISPAPER,ANEWENCRYPTIONALGORITHMISPROPOSEDTHISENCRYPTIONALGORITHMOFIMAGEHASTHEADVANTAGESOFLARGEKEYSPACEANDHIGHSECURITYIITHEPROPOSEDENCRYPTIONALGORITHMAAHYPERCHAOTICCHENSSYSTEMINTHEPROPOSEDENCRYPTIONSCHEME,ANEWHYPERCHAOTICSYSTEMGENERATEDFROMCHENSCHAOTICSYSTEMISUSEDINKEYSCHEMING,WHICHISMODELEDBY11UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020RWYZWBZXYZCWXZDXYWXYAX1WHEREX,Y,ZANDWARESTATEVARIABLES,A,B,C,DANDRAREPARAMETERS,WHENA35,B3,C12,D7AND0085R0789,THESYSTEMISHYPERCHAOTICTHEHYPERCHAOSATTRACTORSARESHOWNINFIG1201510505101520252520151050510152025201510505101520250510152025303540FIGURE1CHENSHYPERCHAOTICATTRACTORAXYPLANE,BXZPLANEWHENA35,B3,C12,D7ANDR06ASTHEHYPERCHAOSHASTWOPOSITIVELYAPUNOVEXPONENTS,SOTHEPREDICTIONTIMEOFAHYPERCHAOTICSYSTEMISSHORTERTHANTHATOFACHAOTICSYSTEM,ASARESULT,ITISSAFERTHANCHAOSINSECURITYALGORITHMBIMAGEENCRYPTIONBASEDONSHUFFLINGMATRIXIMAGEVALUEHASSTRONGCORRELATIONSAMONGADJACENTPIXELSINORDERTODISTURBTHEHIGHCORRELATIONAMONGPIXELS,ANIMAGESHUFFLINGMATRIXISUSEDTOSHUFFLETHEPOSITIONOFTHEPLAINIMAGEWEASSUMETHATTHEDIMENSIONOFTHEPLAINIMAGEISNM,THEPOSITIONMATRIXOFPIXELIS,IPJI,MJMI2,1,2,1,WHERE,IPJISTANDSFORTHEGREYVALUEOFTHEIMAGETHEPROCEDUREOFSHUFFLINGIMAGEISDESCRIBEDASFOLLOWSSTEP1FORHYPERCHAOTICSYSTEM,GIVENINITIALVALUE,IWIZIYIX,AFTERDOINGSOMEITERATIONSFOREACHITERATION,WECANGETFOURVALUES,IWIZIYIXWHEREMI2,1REPRESENTSTHEITHITERATIONOFTHEHYPERCHAOTICSYSTEMTHENLET1,0,2,1,10MOD14MIXMIMIXIXUNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF02021,0,2,1,10MOD14MIYMIMIYIY3UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF0201,0,2,1,10MOD14MIZMIMIZIZUNIF020UNIF020UNIF020UNIF02042010SECONDINTERNATIONALCONFERENCEONINTELLIGENTHUMANMACHINESYSTEMSANDCYBERNETICS9780769541518/1026002010IEEEDOI101109/IHMSC20101472021881,0,2,1,10MOD14MIWMIMIWIWUNIF020UNIF020UNIF0205STEP2GENERATEMBYUSINGTHEFOLLOWINGFORMULAUNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF0206,MODIXMUNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF0206AS5,0M,SOFROMTABLE1,WECANSELECTTHECORRESPONDINGGROUPTHATAREUSEDTOPERFORMSHUFFLINGMATRIXIFMEQUALSTOTHESERIALNUMBEROFSEQUENCEOFTHEGROUPFOREXAMPLE,IF2M,THENCHOOSEIXANDIWSTEP3WHENWEGETIXANDIW,THESEDATACANBEREORDEREDINTHEFORMOFIX,WHEREJXIX,MJ2,1,IFJI,THENREARRANGETHEROWOFMATRIXPI,JACCORDINGTOIX,THATIS,MOVETHE1XTOTHEFIRSTROW,2XTOTHESECONDROW,THUSANEWIMAGEPOSITIONMATRIXXJIP,ISGENERATEDBASEDONROWTRANSFORMATIONSTEP4FOREVERYROWOFTHENEWMATRIXXJIP,WEWILLSHUFFLETHECOLUMNPOSITIONOFTHEIMAGEFORIW,THESEDATACANBEREORDEREDINTHEFORMOFIW,WHEREJWIW,IFJI,THENREARRANGETHEDATAOFEVERYCOLUMNFORTHEFIRSTROWOFMATRIXXJIP,ACCORDINGTOIW,MOVETHE1WTOTHEFIRSTCOLUMN,2WTOTHESECONDCOLUMN,THUSANEWCOLUMNTRANSFORMATIONOFTHEFIRSTROWOFMATRIXWXJIP,ISGENERATEDSTEP5FORTHENEWWXJIP,GOTOEQ5,STEP4TODOCOLUMNTRANSFORMATIONFORTHESECONDROW,TILLTHELASTROWTRANSFORMATIONISFINISHED,THUSANEWIMAGETOTALSHUFFLINGMATRIXWXJIP,ISPRESENTEDTABLEIDIFFERENTCOMBINATIONOFSTATESSERIALNUMBERCOMBINATIONOFSTATES0,IYIX1,IZIX2,IWIX3,IZIY4,IWIY5,IWIZCENCRYPTIONALGORITHMDESIGNFORTHEHYPERCHAOTICCHENSSYSTEMAFTERWEGETTHESHUFFLINGMATRIXWXJIP,THEHYPERCHAOSISUSEDTOENCRYPTTHESHUFFLEIMAGETHEENCRYPTIONSCHEMEISBASEDONTHECOMBINATIONOFSTATEVARIABLESOFTHEABOVEHYPERCHAOTICSYSTEMONEOFTHEFOURVARIABLESARECOMBINEDDIFFERENTLY,WHICHMAYPRODUCEFOURDIFFERENTCOMBINATIONS,WHICHISGIVENINTABLE2STEP1THESYSTEMON1ISITERATEDFOR0NTIMESSTEP2THEHYPERCHAOTICSYSTEMISITERATED,ASARESULT,FOURFRACTIONWILLBEGENERATEDTHESEDECIMALVALUESAREPREPROCESSEDFIRSTLYASFOLLOWS256,10MODX14IXABSFLOORIXABSIUNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF0207256,10MODY14IYABSFLOORIYABSIUNIF020UNIF020UNIF020UNIF020UNIF020UNIF0208256,10MODZ14IZABSFLOORIZABSI9UNIF020UNIF020UNIF020UNIF020UNIF020256,10MODW14IWABSFLOORIWABSIUNIF020UNIF02010WHEREMI2,1REPRESENTSTHEITERATIONOFTHEHYPERCHAOTICSYSTEMWHEREXABSRETURNSTHEABSOLUTEVALUEOFXXFLOORRETURNSTHEVALUEOFXTOTHENEARESTINTEGERSLESSTHANOREQUALTOX,MODYXRETURNSTHEREMAINDERAFTERDIVISIONSTEP3GENERATEIXUSINGTHEFOLLOWINGFORMULAMODXI,4IXUNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF02011SO3,0IXFROMTABLE2,WHEREIXREPRESENTSTHEITHITERATIONOFTHEHYPERCHAOTICSYSTEMWECANSELECTTHECORRESPONDINGGROUPTHATISUSEDTOPERFORMENCRYPTIONOPERATIONIFIXEQUALSTOTHESERIALNUMBEROFSEQUENCEOFTHEGROUPFOREXAMPLE,IF1IX,THENIYISUSEDTODOENCRYPTIONACCORDINGTOTHEFOLLOWINGFORMULAUNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020IYIPIWUNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF02012THEPROCESSDOESNOTENDUNTILTHESET2,1NMPPPPISALLENCRYPTEDTHENTHEENCRYPTEDPIXELSET2,1NMWWWWISWRITTENTOTHECIPHERIMAGETHEDECRYPTIONALGORITHMISSIMILARTOTHEENCRYPTIONALGORITHMITISFORTHEENCRYPTEDIMAGE,FIRSTLY,DECRYPTTHEIMAGEUSINGHYPERCHAOTICSYSTEMWITHTHESAMEPARAMETERSANDINITIALVALUESASTHATUSEDINENCRYPTION,WEWILLGETTHEORIGINALIMAGETHESEIMAGESWILLBESHOWINTHEFIG2TABLEIIDIFFERENTCOMBINATIONOFSTATESOFHYPERCHAOSSERIALNUMBERCOMBINATIONOFSTATES0IX1IY2IZ3IW0501001502002500100200300400500600700800AB2031890501001502002500100200300400500600CD0501001502002500100200300400500600700800EF0501001502002500100200300400500600GHFIGURE2IMAGEENCRYPTIONANDDECRYPTIONEXPERIMENTALRESULTAORIGINALIMAGE,BORIGINALIMAGEHISTOGRAM,CCIPHEREDIMAGE,DCIPHEREDIMAGEHISTOGRAM,EDECRYPTEDIMAGE,FDECRYPTEDIMAGEHISTOGRAM,GDECRYPTEDIMAGEWITHDIFFERENTINITIALVALUE,HERRORDECRYPTEDIMAGEHISTOGRAMIIISECURITYANALYSISSECURITYISAMAJORISSUEOFACRYPTOSYSTEMAGOODENCRYPTIONALGORITHMSHOULDBESENSITIVETOTHESECRETKEYS,ANDHAVELARGEKEYSPACETORESISTALLKINDSOFKNOWNATTACKSSOMESECURITYANALYSISHASBEENPERFORMEDONTHEPROPOSEDIMAGEENCRYPTIONSCHEMEAKEYSPACEANALYSISINTHEALGORITHM,THEINITIALVALUESOFHYPERCHAOTICSYSTEMAREUSEDASSECRETKEYS,IFTHEPRECISIONIS1014,THEKEYSPACESIZEIS1070MOREOVER,THEINITIALITERATIONNUMBERN0,THEKEYHAVELARGEENOUGHASTHESECRETKEYSTHISISENOUGHTORESISTALLKINDSOFBRUTEFORCEATTACKSBKEYSENSITIVITYTESTSEVERALKEYSENSITIVITYTESTSAREPERFORMEDFIG3ILLUSTRATETHESENSITIVITYOFOURSCHEMETOTHESECRETKEYNWZYX,X102,Y101,Z113,W111ANDN300FIG3AISTHEDECRYPTEDIMAGEWITHALLTHEPARAMETERSTOBESAMEASTHATUSEDINENCRYPTIONALGORITHMEXCEPTW110000001FIG3BISTHEDECRYPTEDIMAGEWITHADIFFERENTINITIALITERATIONTIMESN301SOITCANBECONCLUDEDTHATHYPERCHAOSENCRYPTIONALGORITHMISSENSITIVETOTHEKEY,ASMALLCHANGEOFTHEKEYWILLGENERATEACOMPLETELYTHESEIMAGESWERESHOWNINFIGURE3ABFIGURE3IMAGEENCRYPTIONANDDECRYPTIONEXPERIMENTALRESULTADECRYPTEDIMAGEWITHDIFFERENTINITIALVALUE,BDECRYPTEDIMAGEWITHDIFFERENTINITIALVALUECSTATISTICALANALYSIS1HISTOGRAMTHEFIGUREISTHEORIGINALIMAGEANDTHEENCRYPTEDIMAGEHISTOGRAM,FROMFIG2WECANSEETHEENCRYPTEDIMAGEHASUNIFORMHISTOGRAM,WHICHMEANSTHATITISAGOODENCRYPTIONALGORITHM2RELATIVITYANALYSISTOTESTTHECORRECTIONBETWEENTWOADJACENTPIXELSINPLAINIMAGEANDCIPHEREDIMAGE,THEFOLLOWINGPROCEDUREWASCARRIEDOUTFIRST,RANDOMLYSELECT512PAIRSOFTWOADJACENTPIXELSFROMANIMAGETHEN,CALCULATETHECORRELATIONCOEFFICIENTOFEACHPAIRBYUSINGTHEFOLLOWINGFORMULAS12,COVYEYXEXEYXUNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF02013UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020,COVYDXDYXRXYUNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF02014UNIF020UNIF020UNIF020UNIF020UNIF020NIIXNXE11UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF02015NIIXEXNXD121UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF020UNIF02016UNIF0201,COV1YEYXEXNYXINII17WHEREXANDYAREGREYVALUESOFTWOADJACENTPIXELSINTHEIMAGETHESEIMAGESWERESHOWNINFIGURE420419040608010012014016018020022020406080100120140160180200220THERELATIVITYRELATIONOFORIGINALIMAGEPIXELGRAYVALUELOCATIONX,YPIXELGRAYVALUELOCATIONX,Y1050100150200250300050100150200250300THERELATIVITYRELATIONOFCIPHEREDIMAGEPIXELGRAYVALUELOCATIONX,YPIXELGRAYVALUELOCATIONX,Y1ABFIGURE4SHOWTHERELATIVITYRELATIONOFORIGINALANDTHEENCRYPTEDIMAGEARELATIVITYRELATIONOFORIGINALIMAGE,BRELATIVITYRELATIONOFENCRYPTEDIMAGEACCORDINGTOTHEABOVEIMAGESHOWSTHECORRELATIONDISTRIBUTIONOFTWOVERTICALDIRECTIONADJACENTPIXELSINTHEORIGINALIMAGEANDTHATINTHECIPHEREDIMAGETHECORRELATIONCOEFFICIENTSARE09650AND00579TABLEIIICORRELATIONCOEFFICIENTSOFTWOADJACENTPIXELSINTWOIMAGESDIRECTIONPLAINIMAGECIPHEREDIMAGEHORIZONTAL0965000579VERTICAL0945600256DIAGONAL0923700014FROMTABLE3,WEFINDTHATALLTHERELATIVITYCOEFFICIENTSOFENCRYPTEDELEMENTSAREREDUCEDGREATLYTHEENCRYPTIONALGORITHMCANDESTRUCTRELATIVITYEFFECTIVELYDANTICUTTINGTESTINTHEPROCESSOFTRANSMISSION,IMAGEMAYBEDAMAGED,THUSCAUSINGLOSSOFIMAGEINFORMATIONINTHISPAPER,THEENCRYPTIONALGORITHMISINANENCRYPTEDUNDERTHECONDITIONSOFLACKOFINFORMATIONCANSTILLBERECOVEREDMAJORINFORMATIONASSHOWNINFIG5AANDFIG5B,ALTHOUGHENCRYPTEDIMAGESHAVEBEENCUTINSOMEDEGREE,THEDECRYPTEDIMAGEHASMINORNOISE,BUTITDOESNTINFLUENCETHEOVERALLIMAGEITPROVESTHATTHISMETHODCANINACERTAINEXTENTBERESTOREDBYMALICIOUSDAMAGEABFIGURE5IMAGEBEINGCUTANDDECRYPTEDIMAGEACUTINTOPLEFT,BDECRYPTEDTHROUGHTHEABOVEEXPERIMENTSWECANSEE,THISALGORITHMCANRESISTAGAINSTNOISEATTACK,CUTTINGATTACK,ANDHASASTRONGROBUSTNESSIVCONCLUSIONSINTHISPAPER,ANEWIMAGEENCRYPTIONALGORITHMBASEDONHYPERCHAOSISPROPOSED,ITUSESANIMAGESHUFFLINGMATRIXTOSHUFFLETHEPIXELPOSITIONSOFTHEPLAINIMAGEANDTHENTHESTATESCOMBINATIONOFHYPERCHAOSISUSEDTOCHANGETHEGREYVALUESOFTHESHUFFLEDIMAGESOMESECURITYANALYSISSUCHASKEYSPACEANALYSIS,KEYSENSITIVITYANALYSIS,CORRELATIONANALYSISOFTWOADJACENTPIXELSISGIVENTOSHOWTHATTHEPROPOSEDCRYPTOSYSTEMHASAHIGHSECURITYLEVELACKNOWLEDGMENTTHEAUTHORSACKNOWLEDGEWITHTHANKSTHEFINANCIALSUPPORTBYTIANJINDEVELOPMENTFOUNDATIONOFSCIENCEANDTECHNOLOGYKEYPROJECTGRANT10ZCKFGX03000,TIANJINSCIENCEANDTECHNOLOGYFOUNDATIONPROJECTGRANT09ZXCXGX19300,CHINANATIONALINNOVATIONFUNDFORTECHNOLOGYBAS