(Luận án) Research and development of digital watermarking methods for authentication and copyright protection

MINISTRYOFEDUCATIONANDTRAINING MINISTRYOF NATIONALDEFENCE ACADEMYOFMILITARYSCIENCEANDTECHNOLOGY Cao Thi Luyen RESEARCH AND DEVELOPMENT OF DIGITALWATERMARKING METHODS FORAUTHENTICATIONANDCOPYRIGHTPROTECT ION Major: Mathematical Foundation for informationCode:9460110 SUMMARYOFMATHEMATICALDOCTORALDISSERTATION HANOI-2018 Theworkwascompletedat: AcademyofMilitaryScienceandTechnology ScienceConsultantCadres: Assoc.Prof.Dr.PhamVan At Dr NguyenDucThao Reviewer1: Assoc.Prof.Dr.Ngo QuocTao VietnamAcademyofScienceandTechnology Reviewer2: Assoc.Prof.Dr.NguyenLinhGiang HanoiUniversityofScienceandTechnology Reviewer3:Dr TaMinhThanh MilitaryTechnicalAcademy Thed i s s e r t a t i o n w i l l b e d e f e n d e d i n f r o n t o f D o c t o r E x a m i n i n g Committee held atAcademyofMilitaryScienceandTechnologyat…,… … … …, 2018 Forfurtherdetails: - Libraryof AcademyofMilitaryScienceandTechnology - VietnamNationalLibrary INTRODUCTION Necessities Nowadays,thestorageandtransmissionofdataismadepopularthroughthe Internet environment The problem of digital product infringementcauses a lot of negative impacts to economy, politics, society etc On theotherhand,thedigitalproductistransformedbeforereachingtherecipient,if the received data has been transformed previously, then which area ischanged.Thatistheproblem ofdigitaldataauthentication.Findingeffectivemethodstosolvetheproblemsofcopyr ightprotectionandcontentauthenticationbecomesanurgentneedandreceivesmuchatte ntionsfromboth academia and society Watermarking is one of the most effectiveremediestodealwiththeseproblems Currentwatermarkingstudiesaimtosuccessfullydevelopawatermarkingsyste mthatbestsatisfiesthebasicrequirementsofawatermarkingsystemsuchaswaterma rkingimagequality,computationalcomplexity,safety.Theresultsofpublickeywaterm arkingarestilllimited This thesis focuses on watermarking and proposes robust and fragilewatermarkingschemesusingpublickeysinordertoenhancethesecurityandimp rovetheaccuracyofimagevalidationaswellasenhancerobustnessof the watermarking scheme besidesenhancingthewatermarkingimagequality Researchobjectivesandscope  Researchobjectives: - Watermarkingmethods,datahidingtechniques - Matrixdecompositions - Publickeymodels  ResearchScope:Digitalwatermarkingscheme ResearchObjectives • Proposepublickey robustwatermarkingmethodsthatareresistant tointentionalattacksonthedigitalimage • Proposepublicfragilewatermarkingmethodsthatcandetectanysmallchangesi nthedigitalimage • Developanumberofsharedlibrarymodulesthatembedandextract watermarkusingtheproposedmethods Researchmethodology • Surveya n d t h o r o u g h l y s t u d y t h e e x i s t i n g m e t h o d s o f d a t a h i d i n g , watermarking,inordertofindoutaspecificresearchdirection • Usemat hem atical me t hods toa nal yse andevaluatet he effectiveness, robustness,confidentiality,fragilityandlatencyofwatermarkingmethods Exploit the limitations of several widely used watermarkingschemesandproposenewwaystoimprovethem • Designdatasetsandexperimentalmannerstocomparedifferentwatermark ingmethods Researchcontents • Makingresearch,analysis,evaluationofalgorithms,algorithms,systemsofw atermarkinganddatahidingonexistingdigitalimage,especiallytheSVDdom ain,reversibleand publickeywatermarking • ProposingsomepublickeyrobustwatermarkingmethodsbasedonSVDtransfor mations • StudyingwatermarkingschemesforJPEGimages,makeevaluationandenhancement stodevelopahigh-embeddingfracturepublickeywatermarkingscheme • Research and proposing a fragile, public-key, reversible watermarkingapproachbasedonthedifferenceextensioncandetectanysmall change • Developing a number of library modules using proposed algorithms tosolvecopyrightprotectionandimagevalidationproblems Scientificandpracticalvalueoftheresearch The study of public key watermarking methods has implications on bothscientificand practicalaspects:  On the scientific aspect: The watermarking methods now commonlyshare a secret key in both the embedded process and the watermarkingtest This method has the disadvantage of being vulnerable to exposureduring the exchange between the submerger and the user,t h e r e f o r e , the safety is not high In the public key watermarking method, we usetwokeys:thesecretkeytoembedandthepublickeytotestwatermarking Thus,Noneedtoexchangekeyswillhelpthewatermarkingsystemmoresec ure.Thewatermarkingm e t h o d proposedbytheresearcherwillbebothe asytouseandsafe.Inaddition,theproposedwatermarkingschemewillhavegoo dwatermarking quality as well as reduced computational complexitycompared tothecurrentmethod  On the practical aspect: Based on current technology research, NCSwillproposesomenewpublickeywatermarkingmethods.Thesemeth ods will be expressed on a mathematical basis and implementedby library mudules, software that performs embedded functions andseparatesthewatermarkingsignonthedigitalimagedata.Thesemodule sandsoftwarecanbeappliedtoanyinformationservice provider to protect the integrity of information, restrict distortion, orotherwise misuse them in a public exchange environment as well ascontributetothe preventionof fake photos Structureofthethesis Thethesisconsistsofthreechapters,includingintroduction,conclusion,listsof w or ks a nd a p pe n di c e s Thepr oduct of thethe sisis07scientificarticleswhichhavebeen publishedintheseminarsandmagazines in as well as internationally, of which 01 have SCOPUSindex CHAPTER1:OVERVIEWOFDIGITALWATERMARKING 1.1 Conceptsofwatermarkinganddatahiding Data hiding [36] is a technique for embedding information A intoenvironmentB.AandBcanbetext,image,audio,orvideofiles.Informationembedde dAmaycontainconfidentialmessagesthatneedtobeexchangedorinformationaboutco pyright,multimediaproducts Digitalwatermarkingisthetechniqueofembeddinginformation(watermark)in toanobject(adatahidingenvironment)beforeitisdistributedover thenetworktoprotect themessage objects Messageobjectscanalsobedigitalphotos,textfiles,soundfiles, Watermarkcanthen be restored as evidence to prove legal rights as well as to test digitalproductswhichareinintegrityor notorthereisunauthorizedaccessbeforereachingtheuser 1.2 Importantcharacteristicsofthewatermarkingscheme Accordingto[36],thewatermarkingsystemshouldmeetthefollowingbasicrequire ments: - Robustness: Watermark must be robust that means, it can be detectedaftercommonsignalprocessingoperations.Therobustnessrequire mentoften is used for selective authentication systems such as semifragilewatermarkings y s t e m s [ ] , [ ] , [ ] , [ ] , [ ] , [73]orrobust watermarking[3],[6],[62],[72],[83] - Sensitivity: The authentication system should be able to detect anymodifications to the contents or to detect any operation on the imageeven if it is small For sensitive watermarking systems [4], [5], [19],[34], [45], the watermark will be lost after any signal processingapplication - Capacity:Thewatermarksareusuallysmallinsize,butthewatermarkingsc hememustbeabletodiptheidentifiedwatermark.Themoredataareembedde d,thebetterwatermarkingschemeis - Localization: The watermarking system should be able to identify thelocationoftheimagethathaschanged - Abilitytorestore:Thewatermarkingsystemmustbeabletopartiallyorcomp letelyrestoretheimagethathasbeentamperedwith - Security:Thewatermarkingsystemmusthavetheabilitytoprotecttheauthenti cdataagainstanyattemptedtampering - Complexity:Thewatermarkingsystemshouldusetimetoimplementalgorit hmsbutnottoocomplicatedandslow Depending on the type of watermarking system, which feature areconcerned For example, for robust watermarking, the robustness of theschemeisimportantbutsensitivityisignored,whileforfragilewatermarkingsch emes,itsensitivityisimportantandtherobustnessisnotconsideredinthistypeofwatermarkin g 1.3 Principlesofdevelopingwatermarkingscheme A watermarking scheme consists of two processes [36]: watermarkembedding process and watermark sign test During the embedding ofwatermark,theownerembedsthewatermarkWintotheoriginalimage𝐹toreceiveawa termarkedimage𝐹’.Forextrasecurity,itispossibletouseK1key The exchange of watermarked images𝐹’on the Internet can betransformed into an image𝐹* The procedure to verify the copyright orverify the integrity of the image𝐹*may need to restore the watermark orrestoretheoriginalimage.TestingmayalsorequiretheuseofK2key.Ifthetesting image𝐹*is restored to its original image𝐹, it is called reversiblewatermarking.IftheK1keyusedintheembeddingprocessisasecretkey,theK2ke yforcheckingthewatermarkingsignisapublickeywatermarking, if isK1the same asK2, it is called a symmetric keywatermarkingmodel.Adetailedwatermarkingclassificationismentionedbelow 1.4 ApplycationofWatermarking 1.5 Overviewofnationalandinternationalresearchondigitalwaterma rking Inthecountry,thereareanumberofarticlesanddoctoralthesesondatahiding and watermarkingbut mostly robust watermarking, watermarkingschemesusingsecretkeys In the world, every year, there is the annualInternationalWorkshoponDigitalForensicsandWatermarking(IWDW),which arepublishedbySpringerPublishingHousingonLectureNotesinComputerSciences For simplicity, the thesis investigates watermarkingschemesinthecurrentresearchdirections 1.5.1 Datahidingandwatermarkingonthespatialdomain This group of methods, presented on binary images, is completelyapplicabletograyandcolorimagesbyseparatinglowbitstoformbinarymatri ces Its advantage is low computational speed and fragile, which isoftenappliedtotheproblemofdatahidingordataintegrity 1.4.1.1 Datahiding,watermarkingbasedontheparity In 1998, M.Wu and J.Lee proposed a simple data hiding schemeforparitybasedbinary(WLalgorithm)andwascitedbymanyworks[54].In2000,Y.Chengetal.[80]expanded the WL algorithm to embed amaximum of r bits per element block𝑚 × 𝑛 that only changes elements(𝑟=⌊𝑙𝑜𝑔2(𝑚× 𝑛+ 1)⌋) 1.4.1.2 DatahidingandwatermarkingbasedonLSBtechnique This technique is based on the observation that if only low bit ischanged, change of image can not be detected visually This techniqueinsertsconfidentialinformationintothelowbitof8bitpixels.Thetypicalscheme using this technique F5 was proposed by Andress Westfeld in1999,JstegproposedbybyJ.Fridrichetal.[37]proposedin2003,andetc.Theadvantageof thismethodishighcapacity(3-bitsembeddedperoneimage colour) Its biggest limitation is that it is easy to detect imagescontainingstatisticalinformationbecausetheimagecontainsahistogramchanges, aswellasthismethodisnotrobustpriortogeometrictransformation.Dataembedding andwatermarkingschemesbasedonlowbit inserting or parity are fragile so this technique is often used in fragilewatermarkingschemes 1.5.2 Datahidingandwatermarkingonthefrequencydomain Formorerobustwatermarkingscheme,DCT,DWT,DFT,SVD,QR areusedinth erobustwatermarkingscheme 1.5.3 Fragilewatermarking Fragilewatermarking[4],[5],[34],[36], [45]isatypeofwatermarkingthatthewatermarkiseasilydistortediftheimageisattack edevenbysmallchanges Based on that variation of the watermark to conclude that theimagehasbeenaccessedillegally,aswellastheintegrityoftheimage.Ifthe image is altered, determine which area of the image is changed Thisusuallyusesimagingtechniquesembeddedinspatialdomainandisappliedtotheinte grityproblemoftheimage 1.5.4 Robustwatermarking Contrarytothefragilewatermarking,therobustwatermarkingistheonethat requires a watermark to survive persistence against conventionalattacksto e l i m i n a t e w a t e r m a r k i n g (JPEG c om pr e s s i o n, n oi s e , f i l t e r i n g, rotation, ,orinthecaseofremovingthewatermark,theimageaftertheattackisnolonger valid.Robustwatermarkingtypes[3],[6],[63],[73], [83] commonly embed watermark on the frequency domain Frequencydomains are usually performed through transformations such as DCT(DiscreteCosineTransform)[4],[33], [56],SVD(singularvaluedecomposition)[8],[40],[54],[58],[54],[60], [73],DWT(discretewavelettransform), [6], QR (quick responsion) [31] or a combination of saidtransformations [9], [15] , [23], [31], [54], [72] to create new schemes.Next,SVDisnotonlybeusedinlinearalgebra,butalsoinmanydifferentapplicatio ns,suchasinimageprocessing,ispresentasbelow The main benefits of SVD in image processing are that it provides amethod to decompose a large matrix to smaller and more manageablematricesandthesingularvalues(SVs)ofananalyzedmatriceshaveagood stability.Thus,whenamanipulationisappliedtoanimage,itsSVsdonotsignificantlychanged Concretely,anm×nimageblock(canbeconsideredasamatrix)isdecomposedintothre ematricesU,DandV[28,pp448]: 𝐴= 𝑈 ×𝐷×𝑉 𝑇= 𝑈 1𝐷(1,1)𝑉𝑇+ 𝑈 2𝐷(2,2)𝑉𝑇+ ⋯+𝑈 𝑠𝐷(𝑠,𝑠)𝑉𝑇, 𝑠 wheres = min(m,n),𝑈 ∈ 𝑅 ,𝑉 ∈ 𝑅 are normalized orthogonalmatrices and𝐷 ∈ 𝑅 𝑚×𝑛is a diagonal matrix The main diagonal ofDconsistsofthesingularvaluesofA,whereD(1,1)≥D(2,2)≥ ≥D(s,s)≥0(sisc alledtherankofthematrixD) 1.5.5 Publickeywatermarking Most of the schemes presented are secret key watermarking schemes[47], [52],[58],[62],[65],[83].Theseschemessharethesamesecretkeyfor both the embedded process and the watermarking test(Key K2= K inFigure1.2Figure1.5).Therefore,thereshouldbeakeyexchangebetweenthe embedder and the watermark tester Maintaining confidentiality ofinformationaboutthekeyisnotdifficult.However,thislimitationwillbesolvedusingap ublickeywatermarkingmodel.Forthepublickeywatermarking[33],[59],[78],[79],[81],twokeyswill be used, K secretkeyusedinthedipstickdipprocess,arestillintestingofthewatermarking,usethepubl ickeyK2 For robust watermarking scheme, public keys have spread spectrumdirections, using pseudorandom numbers; For the sensitive public keywatermarking,theschemeproposedbyKimin2004willbeapplied 1.5.6 Reversiblewatermarking All most above watermarking schemes are irreversible Reversiblewatermarkingisatypeofwatermarkingwhich,besidesrestoringawater marking,a l s o a l l o w s t h e or i g i na l i m a g e t o b e r e s t o r e d R e c e n t l y , 𝑚×𝑚 𝑛×𝑛 reversiblewatermarkinghasbeenstudiedextensivelyforitsapplicabilityinpractice,partic ularly inhealth,military,security andeducation.Thereversible watermarking methods follow the principle that the inversetransformexists.Somereversiblewatermarkingmethodsare:usingcompre ssionfeatures[11],[17],[67],histogramshifting[30],[68],[85] differenceexpansion[5],[22],[39],[42],[47],[51],[78],predictions[24], [25]orcombinationsofthosemethods[10],[20] 1.5.7 Zerowatermarking Traditionalwatermarkingimplementsimportantinformationintotheimage to protecttheimageorvalidatetheintegrityoftheimage.Thisaffects the image quality Often one must accept a slight reduction inrobustness,orpayapriceforsensitivityinordertoobtaintheappropriatewatermarking image quality The zero watermarkingwill solve the problemthankstothewatermarkingbut notembeddinganyinformationintheimage Therefore, how to secure the copyright of the owner as well asverify that the image has been accessed illegally The feature of a zerowatermarkingistofindtherobustnessoftheimage,whichcanbestoredorcombine dwithconfidentialinformationtomakewatermarkingevidenceaspartofacopyrightv erificationoridentificationprocessfortheintegrityoftheimage.Thedisadvantageofthisty peofwatermarkingistherobustnessof the scheme, which depends on the feature extraction methods SomeselectiveextractionmethodsaresuchasDCT,SVD,QR,DWTorcombinations ofthesetransformations[6],[67],[68],[82],[83] 1.6 Parametersforevaluation PSNR:Hệsốnàyđểđánhgiáchấtlượngảnhthủyvânđượctínhtheocơngthức: 𝑃𝑆𝑁𝑅=20𝑙𝑜𝑔 10(𝑀𝐴K) √𝑀𝑆 𝐸 (1.1) TrongđóMAXlàgiátrịcựcđạicủađiểmảnhvàMSEđượcxácđịnhtheocơngthức: 𝑀𝑆𝐸= 𝑚×𝑛 ∑𝑚∑ 𝑛(𝐼(i,j)−𝐼′(i,j))2 i=1j=1 ERR:làtỷ lệsaikhácgiữathủyvântríchđượcW*sovớithủy vâgốcW đượctínhtheocơngthức: (1.2) 𝐸𝑅𝑅= ∑𝑡 |i− * | 𝑡 i=1 i (1.3)Lư (1.3)LLERRcàngnh3)LLLLcơngthức:đócàngbcàngnh3 1.7 Conclusionofthechapter1 This chapter explores the background knowledge of watermarking:the concept of watermarking, the concealment of information; importantpropertiesofwatermarkingscheme;applicationofwatermarking;research directions; principles of watermarkingplanning; Survey thesituation of research at home and abroad Current watermarkingstudiesaim tosuccessfully developawatermarking system thatb e s t s a t i s f i e s thebasicrequirementsofthewatermarkingsystem,suchas watermarkingimagequality,highembeddingcapability,lowcomputational complexity, high safety mentioned in Section 1.2 Thethesisfocusesoninvestigatingcurrentwatermarkingschemestoimprove, develop public key watermarking schemes, and new reversiblewatremarkingschemewithgoodimperceptibility,lowcalculationcomp lexity as well as enhance embedding capacity of scheme This is atwo-way researchthatiscurrent,scientificandhighly applicableinpractice.Thenextsectionofthisthesiswillresearchtherobustwaterma rkingbasedontheSVDtransformationinChapter2,thereversiblewatermarkingbas edondifferenceexpansionofthepixelvectorseriesandthepublickey fragile watermarkinginthechapter CHAPTER ROBUST WATERMAKRING BASED ON SVDDEVELOPMENT Robustwatermarkingisaneffectivesolutionforcopyrightprotection.Thewatermar kembeddingprocessandlicensingofrobustwatermarkingschemesareoftenperforme dontransformeddomainsbytransformations.Thethesisselects theSingularValueDecomposition(SVD)forthefollowing reasons: SVD is a flexible transformation that can partition amatrixofsquareorrectangularmatriceswhileDCTandDWTonlyallowtodividetheim ageintosquarematrices;SVDisenergy-centric,therefore,theycanbeusedforavarietyofpurposes: information encapsulation,image compression, feature extraction, watermarking, etc This chapterdiscusses SVD; Application of SVD in robust features extraction and itsapplicationinwatermarking;Improveextractionmethodtogetmorerobustwatermarkin g scheme; The robust public key watermarking proposal hasgoodimagequalityandlowcomputationalcomplexity 𝑥′=𝑙′𝜃 i +Changing𝑈ii(1,1),𝑈 i ′ ′ )𝑥 𝑈 i(1,1 (2,1)to𝑈 𝑈 i(2,1)𝑥 (2,1): ′ ′ i(1,1)and𝑈 𝑈 (1,1)= 𝘍,𝑈 (2,1)= 𝘍i i i i Step4:Figuringou 𝑥i i 𝑥i 𝐼′= 𝐷 ( 1,1)×𝑈 ′(1)×𝑉 ′𝑇(1)+𝐼− 𝐷 ( 1,1)×𝑈 ( 1)×𝑉 𝑇(1)(Eq.1) i i i i i i i i Ata r e s u l t , Ii ′canb e c o m p u t e d w i t h o u t usingconventionalSVD analysis TheExtractingProcedure: The watermarked image𝐼′may be attacked by different * operations.Therefore,thereceiverobtainedanattackedimage𝐼 ,whichisnotquitethe same as𝐼′ The extracted watermarkW*(from𝐼*) can be compared to theoriginalwatermarkWinordertoevaluatetherobustnessofthewatermarkingscheme Firstly, the attacked image𝐼*is partitioned into noni * overlapped𝐼 blockswiththesizeofm×n.Watermarkbitsareextractedfromembedde dblocks(selectedblockswithhighcomplexity)infollowingsteps: Step1:Computethematrices: 𝐴*=𝐼 *×𝐼*𝑇∈𝑅 𝑚×𝑚 i i i 𝐵*=𝐼 *𝑇×𝐼*∈𝑅 𝑛×𝑛 i i 𝑚 *i * 𝑛 Theeigenvectors𝑈i(1)∈𝑅,𝑉i( ) ∈𝑅, c o r r e s p o n d i n g t o t h e largeste v aa lt ur ei cs oe sf t𝐴h e*and n o𝐵n -*were n e g a it gi ve ne m i determined[56] Step2:𝑤 *bitisextractedfrom𝑃 *and𝑄*: i i i *i * If𝑘i= 0then𝑥i=* 𝑈 i( 2* , ) +𝑈i( 1*, ) * If𝑘 i= then𝑥 = 𝑉 (2,2)+𝑉 (1,1) Calculatew*i𝑥: 𝑙*=⌊i +* 𝜃 ⁄2 ⌋ i 𝜃 𝑤*=𝑙*𝑚𝑜𝑑2 i i i i i Step3: Wec o m p a r e t h e o b t a i n e d w a t e r m a r k W *= (𝑤*,𝑤*,…,𝑤*)witht h e originalwatermarkW = (𝑤1,𝑤2, … , 𝑤𝑡)by using theerrorrate(ERR)betweenW*andW ThevalueofERRcanbecomputedas: 𝐸𝑅𝑅= ∑𝑡i=1 𝑤iX𝑂𝑅 𝑤i * 𝑡 𝑡 If the value of ERR is smaller than a predefined threshold τ then weconclude that the watermarkWwas embedded in𝐼*and𝐼*belongs to theownersof𝐼′ Thea u t h o r o f [ ] p r o v e d t h a t t h e a n a l y s i s o f S V D f o r a m a t rix 𝐴∈𝑅 𝑚×𝑛canbesolvedbycomputingalleigenvaluesandeigenvectorsofthe matrix with size of(m+n)×(m+n).This problem is much more complexthan finding only the largest eigenvalues and eigenvectors Thus, thecomputational complexity of the proposedscheme is lower than that ofotherSVDbasedschemes ThethesisalsoproposesSVD1andSVD2schemes.ComparedwiththeSVD3schem e,SVD1differsinthatithasanembeddedalgorithmsimilarto the ChungSVD scheme, but only embedded in blocks of high blockcompexity.TheSVD2schemeisembeddedinChungSVD'stechnique,butthe embedding elements areU (1,1)andU(2,1)instead ofU (2,1)andU(3,1) The proposed scheme adds a key to enhance the integrity of thewatermarkingschemeandusesthebestvaluemethodinsteadoftheSVDexpansiontored ucecomputationalcomplexity 2.3 Therobust featuresextracting SVDisnotonlyusedinembeddedschemes,butisalsousedinimagecompression algorithmsordataextraction.Thissectionintroducestheselective extraction methods using the SVD analysis associated with theDWTtransformationofYaxunZhouetal[82]andtheschemeofT.Ye[67]incorpora tingSVDdevelopmentwithDCTtransformation.Thetestshowsthatthecharacteristic sselectedbyalgorithms[67], [82]areconsistentwithsomeimagetransformationattacks.Inordertobemorerobust[67] ,[82],thethesisaddstheT-bufferintotheextractedformula,sothatiftheimageis attacked, it still accurately extracts the characteristics of the image.Subsequently,theproposedselectiveextractionmethodwillbeusedintherobustp ublickeywatermarkingschemeextendingthesensitivepublickeywatermarkingmodel[8 0],[81] Theselectionoffeaturesin[67], [82]isbasedonthedirectcomparativerelationshipof𝐷2i−1(1,1)> 𝐷2i(1,1)or𝐷𝐶2i−1(1,1)> 𝐷𝐶2i(1,1).Iftheimage is attacked, then the comparative relationship will not be satisfied,resultingintheselectionofthecharacteristicsofthewatermarkingimageafter the deviationfromthecharacteristicsoftheoriginalimage.Thesolution proposed by the thesis is to create a T-buffer to increase therobustness of the image extraction method Furthermore, the selection ofYaxunZhouetal'saliasesandtheproposedalgorithmisbasedonlyonthemaximumval ue𝐷i(1,1)oft h e characteristic matrix,t h e r e f o r e , i t is possibletousethesolution oftheproblemtofindthe greatestindividualvalueandthevectorEquivalentofthenonnegativematrixtolookdirectly 𝐷i(1,1)(Section 2.2) instead of SVD development to reduce computationalcomplexity.Thedetailsoftheproposedalgorithmareasfollows: Step1:DividinganoriginalimageIintonon-overlappedm×nblocks𝐼i,i=1 𝑘 Step2:Applyingthementionedalgorithm(inSection2.2)toeachblock𝐼i inordertocompute𝐷i(1,1) Step3:Determiningrobustfeaturesofthecoverimagebytheformulasasbelow: If|𝐷2i−1(1,1)−𝐷2i(1,1)|>𝑇 t h e n B(i)=1elseB(i)=0,wherei= ⌊𝑘⌋ Experimentalresultsshowthattheproposedalgorithmismorerobust thansomeotherrelatedschemes[67],[82] Thethesisusestheproposedextracting algorithmtodeveloparobustpublickeywatermarkingscheme 2.4 TheproposedpublickeywatermarkingschemebasedonSVD Toimprovetheusabilityofwatermarkinginpractice,variouswatermarkingsche mesborrowedsomeideasfrompublickeycryptography[31], [32].Inthissection,weutilizetheproposedalgorithmandpublickeyinordertodesignar obustpublickeywatermarkingscheme 2.4.1 Theembeddingwatermarkalgorithm The input of the algorithm is an original imageI This private keybelongstothelegalownerofI.Theoutputisthewatermarkedimage𝐼′ Theembeddingprocessisperformedasbelow: Step1:Dividingtheoriginalimage𝐼intotwoseparatedpart𝐼1and𝐼2 Step2:CreatingthewatermarkWbyusingtheproposedalgorithm(Section2.3)to extract robust features (denoted byW) from𝐼2 Assuming that, thelengthofWisk(bits) Step3:EmbeddingthewatermarkWintothepart𝐼1followingtheproposedalgorithminSect ′ ion2.2.Consequently,weget𝐼 Step4:Combining𝐼′and𝐼 𝐼′ 2toreceivethewatermarkedimage 2.4.2 Theextractinganddetectingalgorithms The input of thealgorithm is an attacked image𝐼*and a pre-definedthreshold𝑟 (𝑟[0,1])).Theoutputisthe conclusionthattheimageI*legallybelongstotheownersof𝐼 ′ Thep r o c e s s o f d e t e r m i n i n g t h e c o p y r i g h t o f 𝐼 *i s c o n d u c t e d i n t h e followi ngsteps: Step1:Dividingtheattackedimage𝐼 *i n t o twoseparatedpart𝐼 *a n d 𝐼 * followsthesamewayinStep1oftheembeddingwatermarkingprocess * * Step2:R t r a c t i en cg o v e r i n g 𝐵 f r o m 𝐼 b y a p p l y i n g t h e p r o p o s e d e x 1 procedure(inSection2.2) Step3:Extractingthefeaturesof𝐼*byemployingtheextractingalgorithm(presentedinSec 𝐵 tion2.3)toobtain* Step4:InspiredbytheformulatocalculateERR(Eq.2,Section2.2),wewillverifyth ecopyrightofattackedimagesbythefollowingsub-steps: * - Computing𝐶= 𝑆𝑈𝑀(𝐵 X𝑂𝑅 𝐵 *)/𝑘 -If𝐶