AFusionofMaximumLikelihood andStructuralSteganalysis AndrewKer - - PowerPoint PPT Presentation

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a fusion of maximum likelihood and structural steganalysis
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AFusionofMaximumLikelihood andStructuralSteganalysis AndrewKer

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AFusionofMaximumLikelihood andStructuralSteganalysis

AndrewKer

  • InformationHidingWorkshop,StMalo

12June2007

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AFusionofMaximumLikelihood andStructuralSteganalysis

Outline

  • Maximumlikelihood&structuralsteganalysis
  • Newstructuralanalysis% likelihoodfunction
  • Maximization
  • Experimentalresults
  • Conclusions&furtherwork
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SteganalysisofLSBReplacement

Replacementoflow*orderbitsisparticularlyinsecuresteganographybecause

  • fcombinatorialstructure.

MaximumLikelihoodSteganalysis !"#"$ % &'$ ( )'&

  • Foundedonsoundstatisticalprinciples,
  • Requiresknowledge/estimationofcoversourcePMF/transitionmatrix/etc,
  • Inaccurateestimatorinpractice.

Dabeeretal,*+++, -,2004. Hoganetal.-*+"*.,+*,2005. Draperetal.*/0&,2005. Sullivanetal.*+++, *,2006.

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SteganalysisofLSBReplacement

Replacementoflow*orderbitsisparticularlyinsecuresteganographybecause

  • fcombinatorialstructure.

StructuralSteganalysis !""$ % 1$ ( 2'

  • Dubiousstatisticalrigour,
  • Requireslessknowledgeaboutcovers,
  • Highlysensitiveinpractice.

Dumitrescuetal,*+++, -,2003. Luetal.*/0&,2004. Ker,*/0&,2005. Ker,*+++, *,2007.

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SLIDE 5

SteganalysisofLSBReplacement

Replacementoflow*orderbitsisparticularlyinsecuresteganographybecause

  • fcombinatorialstructure.

StructuralSteganalysis !""$ % 1$ ( 2'

  • Dubiousstatisticalrigour,
  • Requireslessknowledgeaboutcovers,
  • Highlysensitiveinpractice.

CanwemergethestatisticalrigourofMLdetection withthesensitivefeaturesfoundinstructuralsteganalysis?

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TraceSubsets

Everypair ofadjacentsamplesisclassifiedaccordingtotheirvalues: forexample, Itisalsousefultowritei.e.pairs

  • wouldbeclassified
  • wouldbeclassified
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TraceSubsets

Everypair ofadjacentsamplesisclassifiedaccordingtotheirvalues:

EmbeddingProcess

Suppposeacoverofsize. Uncorrelatedpayloadofsize embeddedbyreplacingLSBsofapseudo' random selectionofvalues,so LSBflipsareindependentwithprobability'''*

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Coverobject Stegoobject flipneither: probability LSBflipsareindependentwithprobability'''*

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Coverobject Stegoobject flipboth: probability LSBflipsareindependentwithprobability'''*

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Coverobject Stegoobject LSBflipsareindependentwithprobability'''*

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Coverobject Stegoobject

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Toestimate

  • :
  • 1. Assumecovermodel:

innaturalimages;

  • 2. Consideronlyodd;
  • 3. Assume

Coverobject Stegoobject

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NewStructuralAnalysis

  • Recallthat.Supposethepartitionisrandom.

i.e.,imaginethatacoverobjectisderivedfroma“pre*cover”,inwhich arefixed,withpairsmovingindependentlyatrandom: Thismodelisvalidatedintheliterature,exceptfor

A.Ker,2+2#3$IEEETrans.InformationForensicsand Security2(2):140*148,2007.

“Pre'cover” Coverobject

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“Pre'cover” Coverobject Stegoobject

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“Pre'cover” Coverobject Stegoobject

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“Pre'cover” Coverobject Stegoobject

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Stegoobject “Pre'cover”

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# # Vectorofprobabilities Stegoobject “Pre'cover”

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# # Vectorofprobabilities Vectorofprobabilities Vectorofprobabilities Vectorofprobabilities Vectorofprobabilities Stegoobject “Pre'cover”

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LikelihoodFunction

Giventhesizesofthetracesubsetsinthepre*cover

  • ,and,thedistributionof
  • isasumofmultinomials:

well*approximatedby Thelog*likelihoodofanobservation

  • f
  • istherefore

where isthelengthofthevector

  • .
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Σ

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MaximumLikelihood

Estimator:find (and

  • )tomaximize
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MaximumLikelihood

Estimator:find (and

  • )tomaximize

Difficulties:

  • Noanalyticalmaximum(can’tevendifferentiate!)

)

  • Dimensionality:

512dimensionalmaximizationproblem eachlikelihoodevaluationinvolvesaquadraticformoflength1020

  • Overfitting

)!-4 24 44 33

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ExperimentalResults

Experimentsconductedon3000never*compressedgrayscalebitmapimages, size0.3Mpixels. ComparedStructural/MLestimatorswithstandardstructuralestimatorsby (asestimatesfor).

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ExperimentalResults

SamplePairsAnalysis(SPA)1

  • 1S. Dumitrescu. 25.IEEETransactionsonSignal

Processing51(7):1995–2007.2003.

2P.Lu !5.6th InformationHidingWorkshop,

SpringerLNCS3200:116–127.2004

LeastSquaresSPA2 MLPairs

  • meansquareerror
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ExperimentalResults

SamplePairsAnalysis(SPA)1 LeastSquaresSPA2 MLPairs

  • meansquareerror

For1Mpixelimages,benchmarks: ‒ SPAandLeastSquaresSPA:21images/sec ‒ MLPairs:0.4images/sec

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WideningtheApplication

Otherstructuralsteganalyses,e.g.

  • ofLSBreplacementintripletsofpixels1
  • ofreplacementoftwo*leastsignificantbits2(“2LSB”)

canreceivethesametreatment. &6$

1A.Ker.!&5.7th InformationHiding

Workshop,SpringerLNCS3727:296–311.2005.

2A.Ker.+,5.IEEETrans.InformationForensicsandSecurity

2(1):46–54.2007.

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ExperimentalResults(2LSB)

WSfor2LSB1

1X.Yu.+'5.IEEEInternationalConferenceonImage

Processing,vol.2:1102–1105.2005

2A.Ker.+,5.IEEETrans.InformationForensicsandSecurity

2(1):46–54.2007.

LeastSquaresfor2LSB2 MLPairsfor2LSB

  • meansquareerror
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NewStructuralAnalysis

  • Recallthat.Supposethepartitionisrandom.

i.e.,imaginethatacoverobjectisderivedfroma“pre*cover”,inwhich arefixed,withpairsmovingindependentlyatrandom: Thismodelisvalidatedintheliterature,exceptfor “Pre'cover” Coverobject

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Conclusions

  • Itispossibletoproduceastatistically*rigorouslikelihoodanalysisofthe

structureofbitreplacement. ,

  • EstimationviatheML/structuralcombinationisusuallymoreaccuratethan

MLorstructuralsteganalysisalone…

  • Sometimesthemaximizationiscomputationallyinfeasible.

,1&7 – #8 – '8

  • Needtorefinethecovermodeltoimproveperformanceonlargepayloads.

,1&

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End