A DWT Based Steganography Approachhome.iitk.ac.in/~kanirudh/Reports/ee604.pdf · 1. Spatial Methods: the processing is applied on the image pixel values directly. This easy and computationally

ADWTBasedSteganographyApproach

EE604TermPaper

Instructor:Prof.SumanaGupta

GroupNo.1

GroupMembers

AnirudhKumarAgrawal,11907098

PratikLikhar,11531

RadhikaRavi,11553

Introduction

ImageSteganographyreferstohidingofdatainsideanimageinwhichthechangesshouldbeimperceptibletohumaneye.Acommonuseofsteganographyisinwatermarkingwhichisusedtopreventillegaldistributionofcontentbyhidingasignatureintheimageofthecopyright.Watermarkingtechniquesgenerallyhavefollowingfeatures:

1. Imperceptibility:Humaneyecannotdistinguishbetweenthewatermarkedandoriginalimage2. Security:Thewatermarkedimagecannotbecopied,deletedormodifiedbyananimusobserver3. Robustness:Thewatermarkstillcanbeextractedoutwithincertainacceptablequalityeventheimage

hasenduredsomesignalprocessingornoisesbeforeextraction4. Statistically Undetectable : It is extremely hard or impossible to detect watermark using statistical

methods5. BlindDetection:Theextractinghavenotaccesstotheoriginalimage

Themethodscanbebrokendownintotwomainbroadcategories:

1. Spatial Methods: the processing is applied on the image pixel values directly. This easy andcomputationallyfast,butisaffectedbysignalprocessingandnoises

2. FrequencyDomainMethods:thefirststepistotransformtheimagedataintofrequencydomain coefficients by some mathematicaltools (e.g. FFT, DCT, or DWT). Then, accordingto thedifferentdatacharacteristicsgeneratedbythesetransforms,embedthewatermarkintothecoefficientsin frequencydomain. After the watermarked coefficientsare transformed back to spatial domain,theentireembeddingprocedure is completed.Theadvantageof this typeofwatermarking isthehighability to face some signal processingor noises. However,methods of this type are computationallycomplexandhenceslower.

Algorithm

ThefrequencydomaintransformusedhereistheHaar-DWTwhichisappliedasfollowing

Step 1: At first, scan the pixels from left toright in horizontal direction. Then, perform the addition andsubtractionoperationsonneighboringpixels.Storethesumonthe leftandthedifferenceontheright.Thepixelsumsrepresentthe lowfrequencypart (denotedassymbolL)whilethepixeldifferencesrepresentthehighfrequencypartoftheoriginalimage(denotedassymbolH).Step2:Secondly,scanthepixelsfromtoptobottominverticaldirection.Performadditionandsubtractionoperationsonneighboringpixelsandthenstorethesumonthetopandthedifferenceonthebottom as illustrated in Figure 3. Repeat this operation until all thecolumns are processed. Finally wewillobtain4sub-bandsdenotedasLL,HL,LH,andHHrespectively.Therearemultiplemodesbasedontherelationbetweenimagesizesandthetexttobeembedded1.FixModeThereisafixembeddingcapacityrequirementn=MxNx(2/4)x4bits,followingstepsareusedtoachievethesameEmbeddingProcedureStep1:ApplyDiscreteWaveletTransform(DWT)onthegrayscale imageandobtainthefoursub-bands(LL,HL,LH,andHH)Step2:Combineeverytwobitstoformadecimalvaluerangingfrom0to3.EverytwodecimalvaluepairissubtractedtoformasequenceofvaluesStep3:TheembeddingprocessfollowstherasterscanordertheabsolutedifferencesvaluesInthiscase,weembed the absolutedifference values at two rightmost LSBs in LH andHL (LH sub-band first, thenHL sub-band)andthestatusvaluesatthoseinHHandfurthermore(thethirdone,andthefourthoneifneeded)LSBsinLHandHLsub-bands.BasedonFigure1,thecodingontherightTable isdesignedtorecordthepossiblesubtraction pairs. The codes underlined are embedded in the third or fourth LSBs in LH andHL sub-bandswhile the others are embedded in HH (and the first LSB for LH and the second for HL if needed). TheembeddingpositionsinHHarejustthosecorrespondingpositionsinLHandHL

Figure1Step4:AfterembeddingallthemessagebitsweobtainmodifiedDWTcoefficients,weperformIDWTonthestegoimageduetoLSBsubstitutionsomepixelsarenotintegersandwillresultinthefloatingpointvalues,akeymatrixwasusedtostorethe4possiblenon-integerssituations(0.0,0.25,0.50,0.75).Step5:TheroundedversionisthefinalimageFandthekeymatrixisstoredintheexample,the”Description”taginTIFFformatandthe“Comment”taginJPGformatExtractionProcedureStep1:ExtractthekeyMatrixfromthefiletagandtransformalltheelementsofKinto0.0,0.25,-0.5,-0.25toK’Step2:ObtainH’matrixbyperformingDWTtransformonE=F+K’Step3:Extracttheabsolutevalues(0,1,2and3)fromthe2rightmostLSBsinHHsub-band.Accordingtothevalueextracted,LSBsofcorrespondingpositionsinLHandHLareusedtodeterminethesubtractionpair.Baseon themapping rules defined in Figure 1, we can reconstruct 2 values (former and latter) of the decimalsequence.Cuethesedecimalvaluesincorrectorderandthenexpandthemtoabinarybitstream.2.VaryingMode

Invaryingmodenumberofembeddedbitsbelongstospecificrange

EmbeddingProcedure

Step1:ApplyDWTonthegrayscaleimageandobtainthefoursub-bandsLL,HL,LHandHH

Step2:Combineeverytwobitstoformadecimalvaluerangingfrom0to3.Everytwodecimalvaluepairissubtracted to forma sequenceof values. Thereareonly4possible absolute values (0, 1, 2, and3) for theelements in this differential sequence. Record these absolute values in HH by substituting the 2 LSBs ofcoefficientsinHHHwith00,01,10,and11respectively.However,sameabsolutevaluemightbeconsequenceofdifferentsubtractionpairs.Hence,weneedmorebitstodistinguishthesubtractionstatus.InFigure1,therightTablecodingisdesignedtorecordthepossiblesubtractionpairs.ThecodesunderlinedareembeddedinLH and the others are embedded in HL. Embedding positions in HLH and HHL are just the correspondingpositionsinHH.

Step3:TheremainingbitsofSareembeddedatthoseunusedLSBsinLHandthenHLbitbybit.Forexample,ifthevalueembeddedinHHis1,wecannotembedanymoremessagebitatthecorrespondingpositionofLHbut1morebitatthecorrespondingpositioninLH.

Step4:Afterembeddingallmessagebits,weobtaintheslightlymodifiedcoefficientsmatrixH'.ByperformingtheinverseDWT(IDWT)onH',thestego-imageEisobtained.Nowweemploya“Keymatrix”-Ktorecordthe4possiblenon-integersituations(0.0,0.25,0.5and0.75).TheroundedpixelvaluesofEareusedtoshowthestego-image. In order to perfectly reconstruct the secret message bits, K is necessary in the extractingprocedure

Step5:TheroundedversionofE,denotedasF,isthenstoredinaspecificimagefileformatwhileKisfilledintheunusedtags(forexample,the”Description”taginTIFFformatorthe“Comment”taginJPGformat.

ExtractionProcedure

Step1:ExtractthekeyMatrixfromthefiletagandtransformalltheelementsofKinto0.0,0.25,-0.5,-0.25toK’

Step2:ObtainH’matrixbyperformingDWTtransformonE

Step3:Extracttheabsolutevalues(0,1,2and3)fromthe2rightmostLSBsinH'HHsub-band.Accordingtothevalueextracted,LSBsofcorrespondingpositionsinH'LHandH'HLareusedtodeterminethesubtractionpair.Basedonthemappingrulesdefined inTable1,wecanreconstruct2values (formerand latter)of thedecimalsequence.Cuethesedecimalvaluesincorrectorderandthenexpandthemtoabinarybitstream.

Step4:ByextractingsomemoresecondLSBsinH'LHandH'HLaccordingtotheruleillustratedinFigure14,weobtain the remainingportionofS.Cascade itwith thesequenceobtained in step3, thewholemessagebitstreamSiscompletelyextracted.

Results

FixedMode

Followingpicturesareobtainedwhenrunningthealgorithmforfixedmode

ThefollowingtableshowsthePSNRobtainedfordifferentimages

Images PSNR(dB)Lena 40.4420

Peppers 40.8364Barbara 40.4688Mandril 40.5798Boat 40.5428

VaryingMode

Followingpicturesareobtainedwhenrunningthealgorithmforvaryingmode

LENA

CASE1:n≤(3/4)MxN CASE2:(3/4)MxN≤n≤MxN CASE3:MxN≤n≤(9/8)MxN

MANDRIL

ThefollowingtableshowsthePSNRobtainedfordifferentimages

Images PSNR(dB) Case-1 Case-2 Case-3

Lena 49.2008 46.2553 44.2926Peppers 49.2477 46.1719 44.3210Mandril 49.0497 46.2782 44.4409Barbara 49.0302 46.1832 44.3737

LivingRoom 49.0077 46.2201 44.4061

Tothechecktherobustnessofthealgorithmwithfixedmodecaseunderexternalattacks,wetriedthefollowingcases

1. Noise

Noisecanbeaddedtotheimagewhiletransmission,weusedAdditiveGaussianNoiseforsimulatingthefactorbasedonwhichfollowingresultswereobtained

Image ErrorLena 60.56%Mandril 60.55%Barbara 60.58%

Table1:ErrorwithGaussianNoise(sigma=2)

Image ErrorLena 69.55%Mandril 69.54%Barbara 69.54%

Table2:ErrorwithGaussianNoise(sigma=5)

Thuswecanseethattheproceduredoesnotfarewellunderadditionofnoise

2. RotationTheimagemightberotatedbysomeangletheta,forsimplicityweassumethattheimagewhenreceivedwasrotatedbyanangleof90degrees.Thus,afterrotatingtheimageby-90degreesweruntheextractionalgorithmonceagain,theresultsarerecordedintable3.

Image ErrorLena 0.29%Mandril 0.29%Barbara 0.29%

Table3:Errorwithrotationofimageby90degrees

Image ErrorLena 73.78%Mandril 73.56%Barbara 73.45%

Table4:Errorwithrotationangleoftheimage63degrees

Aboveresultsleadustobelieveiftheangleofrotationisanintegermultipleof90degreeswecanextractthemessagereasonably,butinothercaseswefailtodoso.

Discussion

Haar Transform was chosen because of the computational simplicity and the fact that we can accuratelyreproducethemessageusingthekeymatrixwhichwouldhavebeendifficultusingothertransform.Alsonotethat the LH represents horizontal edges, HL represents vertical edges and HH sub-band represents thediagonal edges. Hence the good performance of the algorithm can be attributed to the fact that is onlychangesthevaluesoftheedges.

In terms of the capacity of the givenmethod for an image of size 256 x 256we are able to embedded amessageofsize256*256*(2/4)*4=131072bitsusing256*256*(2/4)+256*256*(2/4)*4=163840bits in the image, while the total no. of bits in the original image is 256*256*8 = 524288. The spacerequirementoftheprocessisnearly=0.3125.

Anoteonthesecurityissue,anobservercannotsuccessfullydecryptthemessagewithoutknowingthe‘KeyMatrix’andevenifthepersonknowthekeymatrixhealsoneedstoknowthemappingruleswhichdifferfromcasetocase.Hencemakingthemethodsecure.

Conclusion

Theproposedsteganographytechniquewasimplementedanditscorrectnesswasverified.Furthertestsonthestabilityofthealgorithmunderexternalattacksgivetheconclusionthatthealgorithm