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