陈聪 英文翻译文献初稿.docx

陈聪 英文翻译文献初稿.docx

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陈聪英文翻译文献初稿

对一类超混沌图像加密算法的密码分析与改进

摘要

ThisLetterproposestwodifferentattacksonarecentlyproposedimagebasedonhyper-chaos.Thecryptosystemunderstudyproceedfirstbyshufflingtheimagerowsandcolumnstodisturbthehighcorrelationamongpixelsbyiteratingthelogisticmap.Second,akeystreamisgeneratedtomixitwiththepixelsoftheshuffledimageusinghyper-chaos.Thesetwoprocessesintheencryptionstagepresentweakness,andachosenplaintextattackandachosenciphertextattackcanbedonetorecovertheciphered-imagewithoutanyknowledgeofthekeyvalue.Itjustdemandsthreecouplesofplaintext/ciphertexttobreaktotallythecryptosystem.

关键字：

Cryptanalysis，Chaoticencryption，Keystream，Hyper-chaos，Shuffle

1介绍

Someresearchershavepointedoutthatthereexiststightrelationshipbetweenchaosandcryptography[1–7].Manyfundamentalcharacteristicsofchaos,suchastheergodicity,mixingandexactnesspropertyandthesensitivitytoinitialconditions,canbeconnectedwiththe“confusion”and“diffusion”propertyincryptography.Soitisanaturalideatousechaostoenrichthedesignofnewciphers.Asaconsequence,therehavebeenproposedmanychaoticciphersinaveryhugevarietyofdesign.Weareinterestedonthosededicatedtotheimageencryption.Imageencryptionissomehowdifferentfromtextencryptionduetosomeinherentfeaturesofimage,suchasbulkdatacapacityandhighcorrelationamongpixels.Sofar,manychaos-basedimagecryptosystemshavebeenproposed[8–18].Althoughanumberofthemhavebeencryptanalyzed,manyothershavenotbeeneffectivelyattackedliketheonein[8].InthisLetter,weproposetobreaktheimageencryptionalgorithmproposedbyT.GaoandZ.Chenin[8].First,thispapergivesadetailedintroductionofthecryptosystem,asabasisofthewholeLetter.Theimageencryptionschemeunderstudyconsistsoftwoparts:

Theimageencryptionbasedontotalshufflingmatrix,andthemixingoperationoftheshuffledimagewithakeystreamgeneratedfromahyper-chaoticsystem.First,animageofsizeN×Misconsidered,everypixelofthisplainimageisnotedPi,j,withi=0,...,M−1andj=0,...,N−1.ByusingthelogisticmapgivenbyEq.

（1）departingfromaninitialconditionx0:

Aftersomeiterationsn,anewx0isderivedfromthefinaliterationxnandanumberhiiscalculated:

TheiterationofthelogisticmapwillcontinueuntilgettingMdifferentdatabetween0andM−1notedhi,i=0,...,M−1.ThenrearrangetherowsoftheplainimagePaccordingto{hi,i=0,...,M−1}.hiwillbetheithrowintheshuffledrowsimagenotedPh.Then,thisprocessisrepeatedtoshufflethecolumnpositionofeveryrowinPhtoobtainatotallyshuffledimageinrowsandcolumnsPhl.Theequationusedtocalculatethepositionoftheshuffledcolumnofeveryrowis:

foreverycolumni=1,...,Mandrowj=1,...,N.

Second,anhyper-chaoticsystemgivenby（4）isused:

Theencryptionschemeisbasedonthecombinationofstatevariablesoftheabovehyper-chaoticsystemaccordingtothesesteps:

（1）First,thesystemon（4）isiteratedforN0times.

（2）Fourvariablesaregeneratedfromthehyper-chaoticsystemandthentransformedtointegersapplyingthefollowing:

（3）Generate.x1usingthefollowing:

Accordingtothevalueof.x1,threevariables（B1,B2,B3）fromthefourvariables（x1,x2,x3,x4）generatedfrom（5）arechosentoperformencryptionoperationusinganassociationtable（formoredetailstoperformthisstep,thereaderisadvisedtoseeTable2inRef.[8]）.Andthen,threepixelsfromtheplainshuffledimagePhlaremixedwiththekeystreamBk,k=1,...,3,likethefollowing:

PiandCi,i=1,2,...,N×M,representthepixeloftheplainshuffledimagePhlandthecipheredimageC,respectively.

（4）Continueoniteratingthehyper-chaoticsystem,andgotostep

（2）untilthewholeimageistotallyciphered.

Thedecryptionalgorithmissimilartotheencryptionalgorithm.hatis,fortheencryptedimage,firstly,decrypttheimageusinghyper-chaoticsystemwiththesameparametersandinitialvaluesasthatusedinencryption,andthenanti-shuffletheresultingimage,wewillgettheoriginalimage.Asclaimedin[8],theinitial

valuesofLogisticmapandhyper-chaoticsystemareusedassecretkeys.Formoredetails,thereaderisreferredto[8].

2.Classicaltypesofattacks

Whencryptanalyzingacryptosystem,thegeneralassumptionmadeisthatthecryptanalystknowsexactlythedesignandworkingofthecryptosystemunderstudy,i.e.,heknowseverythingaboutthecryptosystemexceptthesecretkey.Thisisanevidentrequirementintoday’ssecurecommunicationsnetworks,usuallyreferredtoasKerchoff’sprinciple[19].Therearefourclassicaltypesofattacksanditispossibletodifferentiatebetweendifferentlevelsoftheseattacksbasedonthelevelofknowledgeoftheattackertothecryptosystemandifornothehastheencryption/decryptionmachineryorknowledgeofsomecoupleofplaintext/ciphertext.So,weenumeratethemorderedfromthehardesttypesofattacktotheeasiest:

（1）Ciphertextonly:

theopponentpossessesjustastringofciphertext.

（2）Knownplaintext:

theopponentpossessesastringofplaintext,M,andthecorrespondingciphertext,D.

（3）Chosenplaintext:

theopponenthasobtainedtemporaryaccesstotheencryptionmachinery.Hencehecanchooseaplaintextstring,M,andconstructthecorrespondingciphertextstring,D.

（4）Chosenciphertext:

theopponenthasobtainedtemporaryaccesstothedecryptionmachinery.Hencehecanchooseaciphertextstring,D,andconstructthecorrespondingplaintextstring,M.

Ineachofthesefourattacks,theobjectiveistodeterminethekeythatwasused.Itsufficesthatoneoftheattacksissuccessful

toconsideranalgorithminsecure.

3.Weaknessofthecryptosystembasedonthehyper-chaoticmap

Thecipherunderstudybehavesasastreamcipher[19].Theoperationofthealgorithmasastreamciphercanbeexplainedasfollows.AssumethatKisthekey,givenbynitialconditionsofthehyper-chaoticsystemandthatPcomposedbyPiistheplaintext.AkeystreamB=B1B2...isgeneratedusingEqs.（4）and（6）.This

keystreamisusedtoencrypttheplaintextaccordingtotherule:

DecryptingtheciphertextstringCcanbeaccomplishedbycomputingthekeystreamBgiventheknowledgeofthekeyKandundoingtheoperationseBi.

Themostseriousproblemofthiscryptosystemistomakethegenerationofthekeystreamthesameforeveryplaintext/ciphertext.Next,itisshownhowtorecoverthekeystreamusingchosenciphertextandchosenplaintextattacks.WenotethatknowingthekeystreamBgeneratedbyacertainkeyKisentirelyequivalenttoknowingthekey[20].Moreover,theshufflingprocess（1stprocessoftheencryptionprocedure）oftheplainimageisweakandcanbeguessedwithachosenplaintextandchosenciphertextattacks

3.1.ChosenplaintextattackCPA

AssumethatwehaveaciphertextC=C1C2...（thecipheredimagewrittenasaectoroflengthN×M）,todecryptwithoutknowingthekeyK.Weassumethatwehaveobtainedtemporaryaccesstotheencryptionmachinery.WedescribethestepsleadingtorecovertheplainimagePfromthecipheredimageC:

（1）WerequesttheciphertextoftheplaintextM=m1m2...=00000...:

aplaintextofthesamesizeoftheciphertextCconstructedbythepixelsofvaluesmi=0foreveryi=1,2,...,N×M.WeobtaintheciphertextD=d1d2....ThekeystreamB=B1B2...canbegeneratedfromDby:

foreveryi=1,2,...,N×M.

TherecoveredshuffledimagePhl=Phl1Phl2...canbeobtainedusing

thecalculatedkeystreamBandtheciphertextC:

foreveryi=1,2,...,N×M.

（2）WerequestnowtheciphertextofanimageM×NnotedJwhosealltherowsofitsfirstcolumniscomposedbythevaluepixel1,alltherowsofthesecondcolumniscomposedby2,andsoon,untilthelastcolumnNwhoseallitsrowsiscomposedwiththevalueN:

Toshowanexample,wewillconsiderthatM=N=4,so

ThecorrespondingcipheredimageisnotedJc=Jc1Jc2....WiththecalculatedkeystreamBinstep

（1）,wegeneratetheshuffledimageJhl=J1J2...ofJbyapplyingthefollowing:

Withthegivenexample,wefindthat

Fig.1.Chosenplaintextattack

So,fora4×4matrix,forthefirstrow,thecolumnswereorderedintheformof{li,1,i=1,...,N}=1,2,3,4.Forthesecondrow,thecolumnswereorderedintheformof{li,2,i=1,...,N}=1,4,3,2.Forthethirdrow,thecolumnswereorderedintheformof{li,3,i=1,...,N}=2,1,3,4.Andforthelastrow,thecolumnswereorderedintheformof{li,4,i=1,...,N}=4,2,3,1.Wewillusetheseli,jtogeneratetheimagePhbyrearrangingthecolumnsofeveryrowintheshuffledimagePhlwhichwasrecoveredfromthecipheredimageinstep

（1）.Thiscanbegeneralizedforanymatrixwithrowslessorequalthan256.

（3）WerequestnowtheciphertextofanimageM×NnotedIwhoseallthecolumnsofitsfirstrowiscomposedbythevaluepixel1,allthecolumnsofthesecondrowiscomposedby2,andsoon,untilthelastrowMwhoseallitscolumnsiscomposed

withthevalueM:

Toshowanexample,wewillconsiderthatM=N=4,so

ThecorrespondingcipheredimageisnotedIc=Ic1Ic2....WiththecalculatedkeystreamBinstep

（1）,wegeneratetheshuffledimageIhl=I1I2...ofIbyapplyingthefollowing:

Withthegivenexample,wefindthat

OnecanverifyeasilythatIh=Ihlbecausethecolumnsvaluesarethesameforeveryrow.So,foramatrixcomposedby4rows,therowswereorderedinthef