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8/9/2019 Palette Stenography
http://slidepdf.com/reader/full/palette-stenography 1/15
SecureSteganographicMethodsforPaletteImages
JiriFridrich,DuRui
CenterforIntelligentSystems,Dept.ofSS&IE,SUNYBinghamton,Binghamton,NY13902-6000
{fridrich,bh09006}@binghamton.edu
Abstract. In this paper, westudynon-adaptive and adaptive steganographic
techniquesforimageswithlownumberofcolorsinpaletteimageformats.We
haveintroducedtheconceptofoptimalparityassignmentforthecolorpaletteanddesignedan efficient algorithm thatfinds theoptimal parity assignment.
Theoptimalparityisindependentoftheimagehistogramanddependsonlyon
the image palette. Thus, it can be used for increasing the security ofsteganographic techniques thatembedmessage bits into theparity of palette
colors. We have further developed two adaptive steganographic methodsdesignedtoavoidareasofuniformcolorandembedmessagebitsintotexture-
rich portionsof the carrier image. Both techniquesweretested oncomputergeneratedimageswithlargeareasofuniformcolorandwithfonts onuniform
background.Noobviousartifactswereintroducedbyeithertechnique.Thelast,
embedding-while-dithering, technique has been designed for palette images
obtainedfromtruecolorimagesusingcolorquantizationanddithering.Inthistechnique, both the color quantization error and the error due to message
embedding are diffused through the image to avoid introducing artifactsinconsistentwiththeditheringalgorithm.
1 Introduction
The purpose of steganography is to hide messages in otherwise innocent lookingcarriers.Thepurposeistoachievesecurityandprivacyby maskingtheverypresenceofcommunication.Historically,thefirststeganographictechniquesincludedinvisiblewritingusingspecialinksorchemicals.Itwasalsofairlycommontohidemessagesintext.Byrecoveringthefirstlettersfromwordsorsentencesofsomeinnocentlookingtext,asecretmessagewascommunicated.Today,itseemsnaturaltousebinaryfileswith certain degree of irrelevancy and redundancy to hide data. Digital images,videos,andaudiotracksareidealforthispurpose.
Eachsteganographictechniqueconsistsofanembeddingalgorithmandadetector
function.Theembeddingalgorithmisusedtohidesecretmessagesinsideacover(or
carrier)document.Theembeddingprocessisusuallyprotectedbya keywordsothat
only those who posses the secret keyword can access the hidden message. Thedetectorfunctionisappliedto thecarrierandreturnsthehiddensecretmessage.For
securecovertcommunication,itisimportantthatbyinjectingasecretmessageintoa
carrierdocumentnodetectablechangesareintroduced.Themaingoalistonotraise
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suspicionandavoidintroducingstatisticallydetectablemodificationsintothecarrier
document.Theembeddedinformationisundetectableiftheimagewiththeembeddedmessageisconsistentwiththemodelofthesourcefromwhichthecarrierimagesare
drawn.Wepoint out that the ability todetect the presencedoes not automatically
imply the ability to read the hiddenmessage.We further note that undetectability
should not bemistaken for invisibility− a concept tied to human perception. Atpresent, the formal theoretical framework for steganography similar to Shannon
informationtheoryisstillmissing.Foracomprehensivetreatmentofthistopic,see
[1].
Theundetectabilityisdirectlyinfluencedbythesizeofthesecretmessageandthe
formatandcontentofthecarrierimage.Obviously,thelongerthemessage,thelarger
the modification of the carrier image and the higher the probability that the
modificationscan be statistically detected. The choice of the carrier image isalso
important.Naturalphotographswith 24bits perpixelprovidethe best environment
for message hiding. The redundancy of the data helps to conceal the presence ofsecretmessages.Imageformatsthatutilizecolorpalettesprovideefficientstoragefor
imageswithlimitednumberofcolors,suchascharts,computerart,orcolorquantized
truecolorimages.ThepaletteimageformatGIFisrecognizedbyallbrowsersandis
widelyusedovertheInternet.PostingaGIFfileonone'swebpagewillundoubtedly
raise less suspicion than sending an image in the BMP format. Despite their
usefulness and advantages, palette images provide a hostile environment for the
steganographer. The limited number ofpalette colors makes the process of secure
messagehidingadifficultchallenge.Themostcommonsteganographictechnique−theleastsignificantbitembedding(LSB)cannotbedirectlyappliedtopaletteimagesbecause too many new colors would be created. Most current steganographic
algorithmsfor paletteimagesintroduceeasilydetectableartifactsin thepaletteor in
theimagedata[8,9].
On the highest level, the typical palette image format consists of three parts: aheader,apalette,andimagedataorpointerstothepalette.Thepalettecontainsthe
RGB tripletsofall colors that occur inthe image. Secretmessagescan behidden
eitherinthepaletteitselforintheimagedata.Gifshuffle[10]isaprogramthatuses
the paletteorder tohideuptolog2(256!)=210bytesinthepalettebypermutingits
entries.While thismethod does not change the appearanceof the image, whichis
certainlyanadvantage,itssecurityisweakbecausemanyimageprocessingsoftware
productsorderthepaletteaccordingto luminance,frequencyofoccurrence,orsome
otherscalarfactor.Arandomlyorderedpaletteis suspicious,whichgoesagainstthe
basicrequirementofsecuresteganography.Also,displayingtheimageandresavingit
mayerasetheinformationbecausethepalettemaybereordered.Analternativeand
perhapsmore secure approach is to hide encrypted messages in the LSBs of the
palettecolors.Inordertomakethemessagereadablefromanimagewithareordered
palette, care needs to be taken during message embedding so that the message is
readableatthereceivingend.Thecommondisadvantageofalltechniquesthatembedmessagebitsintothepaletteisaratherlimitedcapacityindependentoftheimagesize.
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Practical methods should have capacity proportional to the image size, or the
numberofpixels.Manycurrentlyavailablesoftwaretools[3,4,7,10 −13]decreasethecolordepthoftheGIFimageto128,64,or32beforetheembeddingstarts.Thisway,
whentheLSBsofone,twoorthreecolorchannelsareperturbed,thetotalnumberof
newlycreatedcolorswillbeatmost256.Thus,itwillbepossibletoembedone,two,
or three bits per pixel without introducing visible artifacts into the carrier image.
However,aspointedoutbyJohnson[8,9],thenewpaletteswillhaveeasilydetectable
groupsofclosecolors.Itisthusrelativelyeasytodistinguishimageswithandwithout
secretmessages.Itappearsthatsecureschemesshouldnotmanipulatethepalettebut
ratherembedmessagebitsintheimagedata.In the next section,wediscussmethods that embedmessage bits asparities of
colors.InSect.3,wedefinetheenergyofdistortionsduetomessageembeddingand
introduce theconcept of optimal parity assignmentthat minimizes thisenergy.An
efficientalgorithmfortheoptimalparity ispresentedand theproofof optimality is
given.Thetechniqueisfurtherextendedtomultiplepixelembedding.Itisshownthattheoptimalparityassignmentisalsooptimalformultiple-pixelembedding.InSect.4,
westudyadaptivesteganographictechniques.Twomethodsare introducedandtheir
performance is tested oncomputer generated fractal images. A new technique for
paletteimagesobtainedthroughcolorquantizationandditheringoftrue-colorimages
isdescribedinSect.5.Inthisnewdithering-while-embeddingtechnique,theimage
modificationsduetomessageembeddingarediffusedthroughtheimageinthesame
wayasthequantizationerrorduringdithering.FinallyinSect.6,wesummarizethe
newtechniquesandconcludethepaperbyoutliningfutureresearchdirections.
2 Messagehidingusingtheparityofpalettecolors
Oneofthemostpopularmessagehidingschemesforpalette-basedimages(GIFfiles)hasbeenproposedbyMachado[11].In hermethodcalledEZStego, thepalette isfirst sorted by luminance. In the reordered palette, neighboringpalette entries aretypicallyneartoeachotherinthecolorspace,aswell.EZStegoembedsthemessageinabinaryformintotheLSBofrandomlychosenpointerstothepalettecolors.Onecansay thatthismethodconsists ofthree steps:parity assignment topalettecolors(ordering the palette), random, key-dependent selection of pixels, and embeddingmessage into color parities of the selected pixels. Message recovery is simplyachievedby selectingthe samepixelsandcollecting theLSBsof all indices totheordered palette. This algorithm is based on the premise that close colors in theluminance-orderedpalettearecloseinthecolorspace.However,sinceluminanceisalinearcombinationofthreecolors,occasionallycolorswithsimilarluminancevaluesmayberelativelyfarfromeachother.Toalleviate this problem, Fridrich [6]has proposed to hidemessage bits into the
parity bits of closest colors1
. For the color of each pixel, into which we embed
1 Using parityfor message embedding haspreviously been proposed byPetitcolas[1] and
Crandall[5].
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messagebits,theclosestcolorsinthepalettearesearchedtillapaletteentryisfound
withthedesiredparity bit.Theparity ofeach color couldbeassigned randomlyorsimply by calculating R+G+ B mod 2. Because the parity bits are randomly
distributed,wewillneverhavetodepartfromtheoriginalcolortoomuch.Thisway,
we avoid the problem of occasionally making large changes in color, whichwillcertainlycontributetotheundetectabilityofthemessage.Intheabsenceofarigorous
security definition for steganography, the following quantities were accepted as
measuresofsecurity:
1. Thedistance Dbetweentheoriginalandthestego-image
,,
1,
22 ∑ ==
N M
jiijd D
whered ij2=( Rij− Rij')
2+(Gij−Gij')
2+( Bij− Bij')
2forthe(i, j)-thpixeloftheoriginal
andthestego-image.
2. Themaximalcolorchange ij jid
,max .
Boththeaveragepowerperpixelandthemaximalcolorchangeforthenewtechnique
[6]havedecreased4−5timeswhencomparedtotheEZStego,whichisasignificantperformanceimprovement.
Inthenextsection,weinvestigatetheproblemofoptimalparityassignmentforthe
paletteinordertofurtherimprovetheschemedescribedinthissection.
3 Optimalparityassignment
Theparityassignment directlyinfluences theenergyof imagemodificationsdueto
message embedding. Obviously, if close colors are assigned opposite parities, the
energyofthemodificationswillbesmaller.Anaturalquestiontoaskiswhetheritis
possible to further improve the performance by using an optimized palette parity
assignment.Forapracticalmethod,whichdoesnothaveaccesstotheoriginalimage,
thepaletteparityassignmenthastobereconstructablefromthemodifiedimageatthe
receivingend.
Lettheimagepalettecontain N colorsc1,c2,…,c N withparitiesPi,Pi∈{0,1}.Theparityassignmentdeterminesanisolation siforthei-thcolor(siisthedistancefrom
colorci tothe closest colorwithdifferentparity).The colorsoccur inthe original
imagewithfrequencies p1,…, p N , p1+…+ p N=1.Providedthemessagecarryingpixelsareselectednon-adaptively,foramessageoflengthk ,approximatelykpipixels
ofcolorciwillcontainmessagebits.Theaveragesquareofthedistancebetweentheoriginalandthestego-imagecanbeexpressedas:
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∑==
N
i ii N s pk PPkE 1
2
1 2
1
),...,(2
1
.
Thequantity E doesnotdependonthemessagelengthandwillbecalledtheenergy
oftheparityassignment .Theoptimizationproblemistoassignparities P1,…,P N to
colors c1,…, c N so that E isminimal. The following algorithm always finds the
optimalparityassignmentthatminimizes E :
3.1 Algorithmforoptimalparityassignment
1. Calculatethedistancesbetweenallpairsofcolors d ij=ci− c j.ThedistancecanbecalculatedeitherintheRGBortheYUVspace.SetC =∅.
2. Orderthedistancesstartingfromthesmallesttothelargest,{d }=d i(1) j(1)≤d i(2)j(2)≤….
3. IterativelyrepeatstepNo.4untilC containsall N colors.
4. Choosethenextdistanced klintheorderedsequence{d }suchthateitherck∉C orcl∉C .Ifmorethanoned klisthesmallest,randomlychooseone.Ifthereisnosuchd klthismeansthatC containsall N colorsandwearedone.Ifboth ck∉C orcl∉C ,assigntwooppositeparitiestobothk and l.Ifck∉C andcl∈C ,setPk =
1−Pl.UpdateC =C ∪{ck }∪{cl}.
Itisclearthatonceaparityofacolorisdefined,itcannotbechangedlaterbythe
algorithm.Itisalsoclearthatattheendallcolorswillhaveassignedparities.What
needstobeprovedisthattheparityassignmenthastheminimalenergy E .Wepoint
outthattheminimalvalueof E canoccurformorethanoneparityassignment(see
Fig.1).
Fig. 1. Example of two different optimalparityassignments
Fig.2.
Each parity assignment induces a structure of anorientedgraphwith anarrow
pointingfromeachcolor(anode)toitsclosestcolorwithdifferentparity.
Propertiesofthegraph:Thereisexactlyonearrowgoingoutofeverynode.One
node may have more than one incoming arrow. Some nodes may not have anyincoming arrows (end nodes). Note that for an optimal parity assignment, when
followingasequenceofarrows,thedistancescanneverincreasebecauseonecould
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simplyflipthearrowofthelargerdistancebacktothepreviousnodeanddecreasethe
energy E (seeFig.2).
Proof of the optimality: Suppose that we have a parity assignment P that is
optimal.Wewillshowthatbyfollowingouralgorithm,itispossibletoreassigntheparitytoadifferentparityobtainablewithouralgorithmwhilepreservingtheenergy.
Letusassumethatwhilefollowingouralgorithmwefindadistanced ijwithPi=P j,
suchthateitherci∉C orc j∉C .Let usassumethatc j∉C .Wewillshowthatitispossibletochangetheparityofthiscolorandothercolorspointingtothiscolorwhile
the energy E stays the same.Let c1(1), c2
(1),…, c N (1)
(1) be the colors (nodes) with
arrowspointingtoc j.Whileflippingtheparityofc j,wealsofliptheparitiesofc1(1),
c2(1),…,c N (1)
(1).Thenwedothesamethingwithallnodespointingtooneofc1(1),c2
(1),
…,c N (1)(1),etc.Wehavetoshowthatwhileproceedingsinthiswayweneverruninto
aconflictofhavingtoflipthesamenodetoa0and1atthesametime.Thisisnot
possiblebecausesuchanodewouldhavetohavetwooutgoingarrows.Wecanend
upinanendnode,butwealsocanformacycleandgetbackto c jviaanodeck towhichc jpoints(seeFig.2).Ifd jk >d ij,wecouldcancelthearrowpointingfrom c jto
ck andreplaceitwithanarrowfromc jtoci decreasing theenergy by p j(d jk −d ij)>0,whichisacontradictionwithPbeingoptimal.Theotherinequality,d jk <d ijimplies
c j∈C ,whichcontradictsthe assumption.Therefore,d jk =d ijandtheenergy E staysunchangedbyreplacingthearrows.Inthecasethatthe"avalanche"ofparityflippingwouldalsofliptheparityof ci,weargueasfollows.Ifd il>d ijwecanreplacethe
arrowpointingfromcitoclwithanarrowfromcitoc janddecreasetheenergy.Ifd il<
d ijwecanfollowthearrowsonthebranchfrom cibacktoc jtoobtainc j∈C ,whichisagaincontradictionwithourassumption.Therefore,wemusthaved kl=d ijandwecan
replacethearrowfromcitoclwithanarrowfromcitoc jwhilepreserving E .
Fig.3.
Asa consequence, wehave shown thatwecan always reassign parities ofPina
mannercompatiblewithouralgorithmwhilepreservingtheenergy E .Thealgorithm
andourargumentsendwhenC ={c1,…,c N }.Thisconcludestheproof.
Note that the optimal parity assignment does not depend on the frequency of
occurrence ofpixels, p1,…, p N . Thissomewhatcontradictory andsurprisingresult
enables us to calculate the optimal parity assignment from the modified image
without accessing the original image. We just need to order the palette before
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applyingthealgorithm(onecanusethealphabeticalRGBorder,forexample).Ifany
randomdecisionsaremadeduringthealgorithmrun,weneedtoseedaPRNGwiththesameseed,aswell.Anotherpossibilitywouldbetoagreeonafixedorderinthe
sequence{d },the parity assignment forthe first pair,anda rule for assigning the
paritywhenbothnewnodesci∉C andc j∉C .Eitherway,theoptimalparitycanbeutilizedfordecreasingtheenergyofmodificationsinimages.
Numericalexperimentsindicatethatwhenusingtheoptimalparityasopposedto
theparity R+G+ B mod 2,theenergy E isdecreasedby 25−35%depending ontheimage.
3.2 Multiple-pixelembedding
It is possible to further decrease the energy of modifications due to message
embeddingbyusingclustersofqpixelsforonemessagebitratherthansinglepixels.TheimageisfirstdividedusingaPRNGintodisjointclustersofrandom qpixelsand
themessagebitisencodedasaparityofthesumofallqpixelparities.Thishasthe
benefitthatinordertochangetheparityofthewholesumonecanselectapixelwith
the smallest isolation among all q pixels. As a consequence, the energy of
modificationsdue tomessageembeddingmust decrease. Thepreviousmethod isa
specialcaseofthismultiplepixelencodingwithq=1.
Below,weshowthattheoptimalparityforthismethodisthesameasforthesingle
pixel embedding. The energy E of the parity assignment is defined in a similar
manner
∑ ==
N
ii
qi s pq E
1
)(
2
1)( ,
where pi(q)istheprobabilitythatamongrandomlychosen qpixelsintheimagetheonewith the smallest isolation is the i-th color. If pi
(q) does not depend onsi, the
optimal parity is again only a function of the palette and not of the image. To
calculatetheprobabilities pi(q),werearrangethecolors cisothattheirisolationsform
anon-decreasingsequence.Itcaneasilybeshownthat
.)()()(
q N
i j
q j
q N
i j
q j
qi p p p
−
= ∑∑ >≥
Becausetheprobabilities pi(q)donotdependontheisolations,si,theoptimalparityfor
singlepixelembeddingisalsooptimalformultiplepixelembedding.Theenergy E (q)
asafunctionofqisdepictedfortwotestimages"Fox"and"Mandrill"inFigs.4−7.Observethat evenwithq =2, the energy ofmodificationscoulddecreasebymore
thanathird.Forthetestimage"Fox",theenergywentdownto50%ofitsoriginalvalue for q = 3. This observation suggests that the multiple pixel embedding
techniqueisausefulandsignificantsecurityimprovement.
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Fig.4.Testimage"Fox"
Fig. 5. Energy of modifications as afunctionof the numberofpixelsqforthe
testimage"Fox"
Fig.6.Testimage"Mandrill"
Fig.7.Energyofmodificationsasafunctionofthenumberofpixelsqforthe
testimage"Mandrill"
Inthissection,wehaveshownthatanymethodinwhichpixelsareselectedina
random (non-adaptive) manner and in which the message bits are embedded by
changingtheparityofpixels(theanalogofLSBencodingforpaletteimages),cannotperform better than our method. This is because our method uses the best parity
assignmentpossible.Theresultisgeneralandholdsforbothsinglepixelembedding
andmultiple pixel embedding.Thenext section isdevotedto adaptivemethodsfor
message embedding toavoidareas of uniformcolor and avoidcreating detectable
artifactsinsingularimageswithlargeareasofuniformcolor.
4 Adaptivemethods
In this section, we explore the idea of an adaptive steganographic technique thatwould introduce less detectable artifacts into the carrier image by adapting the
message embedding technique to the content of the carrier image. Non-adaptive
steganographictechniquesaretechniquesinwhichthemodificationsduetomessageembedding are uncorrelated with image features. Examples are LSB encoding in
randomlyselectedpixels,messageembeddingbyrandomlymodulatingpixelvalues
orfrequencybinsinafixedband,etc.In adaptivesteganographythemodifications
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arecorrelatedwiththeimagecontent(features).Forsteganography,thiscouldmean
thatthepixelscarryingmessagebitsareselectedadaptivelyanddependontheimage.Forexample,wecouldavoidareasofuniformcolorandselectonlypixelswithlarge
localstandarddeviation.Thishowevercreatesaproblemwithmessagerecoveryifthe
originalunmodifiedimageisnotavailable.Wehavetobeabletoextractthesamesetofmessagecarryingpixelsatthereceivingendfromthemodifiedimage.
The capacity ofadaptive schemes is necessarily image dependent and, in some
cases, it isnoteven possibleto calculate thecapacitybefore theactualembedding
starts.But this isa pricewehave topay for increased security.Thereare several
differentwayshowa non-adaptiveschemecanbe turned intoanadaptiveone. For
example,themessagecarryingpartandthepartthatdeterminesthepixelselectiondo
notinteract.Forexample,onecancalculatethelocalstandarddeviation(STD)from
the7most significantbits and embedmessagebits intotheLSB.Thisapproach is
plausibleonlyforhighcolorimagesandcannotbeadoptedforpaletteimages.
Method 1. The imageis divided into disjoint blocks (for example 3×3 blocks)
completelycoveringtheimage.Atmostonebitwillbeassignedtoeachblock(either
theLSBofthemiddlepixelor itsparity, ortheparityof thewholeblock,etc.).A
thresholdforlocalSTDisselected.Apseudo-randomnon-intersectingwalkoverthe
blocks is generated from a secret key. If the local STD of a block is above the
threshold AND stays above the threshold aftermessage embedding, we select the
block for message embedding. If the STD fallsbelow the threshold aftermessage
embedding,wemake thechangeanywaybut donotincludethe block formessage
embedding, and continue message embedding with the samebit inthe next block.
Thisprocesswill guarantee thatatthereceiving end itis enough toregeneratethe
samerandomwalkovertheblocksandreadthemessagebitsonlyfromblockswhose
STDis above the threshold.Note thatthe localstandarddeviation canbereplaced
witha differentquantity, such asthe number of colors inthe block. Actually, our
experimentsshowthatthenumberofcolorsworksbetterthanthestandarddeviationforcomputergeneratedlow-colorimages.
TheadvantageofMethod1isthatanypixel(s)intheblockcanbemodified,which
will generally lead to smaller modifications especially for images with low color
depth.Thedisadvantageisthatitisnotpossibletosaywhetherornotamessageofa
givenlengthwillfitintotheimagebeforeoneactuallystartstheembeddingprocess.
Anotherdisadvantageissomewhatdecreasedcapacity.Atmostonebitisinsertedinto
eachblock,andonlyblockswithlocalSTDabovethe thresholdare considered for
embedding.Itis,however,onlynaturalthatmoresecureschemeswillhavesmaller
capacity,while"greedy"schemesemphasizingthecapacitywillofferlesssecurity.It
willbeuptotheendusertodecideaboutthepriorities.
We testedMethod 1 for several fractal GIF images2 shown in Figs. 8−10. The
imageinFig.8depictsaJuliasetgeneratedonacomputer.Juliasetsarefractalsets
2 Images provided courtesy of J. C. Sprott, Fractal Gallery,
http://sprott.physics.wisc.edu/fractals.htm.
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parametrized using complex numbers. The image is a bad carrier image for
steganographyforatleastthreereasons:
1. Thereare large areaswith flat color. Suchareas should beavoided otherwise
detectableartifactswillbecreated.2. The image has been computer generated and has a known complicated inner
structure common to all Julia sets. For example, the bands of close colors
gradually changingfromwhiteto dark redform lines ofconstantpotentialand
have toformsimplyconnectedsets.Thereforethe bandboundaries,too,should
beavoidedwhileembeddingamessage.
3. Thetitleoftheimagecontainsfontsandanysubtlechangetothosefontswillbe
easilydetected.
Fig. 8. Fractal carrier
image640×480,195colors
Fig.9.Fractal carrierimage,636×476,236colors
Fig. 10. Fractal carrier
image636×476,183colors
A non-adaptive technique, no matter how good, will always create some easily
detectableartifacts(seeFigs.9 −10).Ontheonehand,wearetemptedtosaythattheimageshouldnotbeusedforsecuresteganography.Ontheotherhand,weintuitively
feel that thoseareaswith complex structure can hold some additional informationwithout causing suspiciousartifacts.A smart adaptive techniqueshould be able to
recognizewhichportionsoftheimagecanbeusedfordatahiding.
A freeware software utility called MandelSteg [7] uses fractal images for
generatingcarrierimages.TheparametersoftheJuliasetformaportionofthesecret
key.Thealgorithmisnaïve,non-adaptive,andprovidesverypoorsecurity.First,the
fact that the softwarethatgenerates the images isavailable toanybody enablesan
efficient search for the parametersof the Juliasetby anybody skilled intheart of
fractals.Second,thefractalimageshavecomplicatedinnerstructurethatfollowsstrict
rules. Any non-adaptive technique must introduce severe and easily detectable
artifacts,suchasthosedepictedinFigs.11−12.
AversionofMethod1hasbeenusedwiththelocalstatisticscorrespondingtothe
numberofdifferentcolorsinapixel'sneighborhood.Weembedabitofinformation
wheneverthereareatleastthreedifferentcolorsinthe3×3neighborhood.Thisinfact
willguaranteethattherewillbenoartifactsinthepotentiallinesaroundtheJuliasetand noartifacts inthe fonts (white characters on uniform background).A detailed
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inspection of the carrier imagewith over 1000 embedded bits did not reveal any
suspiciousartifacts.
Fig. 11. Artifacts in
equipotentialbands
Fig.12.Artifactsinthefonts
Fig. 13. Fonts on a
complexbackground
Method2.Method1performssatisfactorilyevenfordifficultcarrierimages,such
astheimagesinFigs.8−10.However,thepricewepaidwasacapacitydecreasedbyafactorofmorethan9.Method2hasbeendesignedwiththeintenttoputonaverage
morebits perpixelwhileretainingthe adaptiveproperty.Themessageembedding
processstartswithpseudo-randomlyselectingthemessagecarryingpixels.Beforewe
explaintheselectionprocess,weintroducesomedefinitions.A2×2blockisgoodifithasatleastthreedifferentcolors.Inallothercases,theblockisbad.Apixelistermed
goodifallfour2×2squaresthatcontainthatpixelaregood.Themessagecarryingpixels are selectedpseudo-randomly from the set ofall good pixels in the image.
Then,allpalettecolorsareassignedtheoptimalparityusingthealgorithmfromSect.
3.Finally,wewalkthroughtheselectedpixelsandcomparetheparityofeachpixelto
themessagebit.Ifthereisamatch,wedonotmodifythepixelandmovetothenext
pixel.Ifthereisnomatch,wemodifythepixelcolorbysearchingthroughthepaletteforclosestneighborswiththecorrectparitysothatafterthechangeallfourblocks
containing the pixel P stay good. Then, we again move to the next pixel. The
embedding procedureguarantees thatthe setofgood blocks for theoriginalimageand for the modified image are identical. This enables the detection algorithm to
recoverthemessagefromcolorparitiesbygoingthroughthegoodpixelsinthesame
pseudo-randommannerasduringtheembedding.
The capacity of Method 1 and 2 is compared in Table 1. We ran a series of
experimentsfordifferentseedsforthePRNGthatwasusedtogeneratethepseudo-
random walk and calculated the standard deviation of the capacity. All three test
imagesshowninFigs.8−10wereusedforthisexperiment.Asexpected,Method2hassignificantlyhighercapacitythanMethod1.
Tofindouttheenergy ofmodificationsdue tomessageembedding,we used the
same three test images and for different seeds we calculated the average MSE
distortion per pixel. The resultsare showninTable2.Wehave alsoexperimented
withdifferentcombinationsof theblocksize(2×2and3×3)anddifferentnumberofcolors (2,3 or4)for the goodnesscriterion.Thecombination of2×2pixelsandatleastthreecolorsgaveusthebestresultswithnoperceptibleartifacts.
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Table1.ComparisonofcapacityforMethod1and2
Capacityasapercentageofthetotalnumberofpixels
Figure8 Figure9 Figure10
Method1 6.51~6.53% 3.16~3.18% 1.11~1.12%
Method22colors 55.64% 25.92% 10.37%
3colors 43.63% 16.94% 1.32%
Themean-square-errorbetweentheoriginalandthestego-imageforallthreefractal
testimageswithembeddeddifferentsizeofdataisillustratedinTables2−4.
Table2.MSEforFig.8anddifferentmessagelength
Sizeofembeddeddata 2371Bytes 1331Bytes 645Bytes 132Bytes
Method1 0.26±0.005 0.15±0.003 0.07±0.002 0.017±0.001
Method2 0.54±0.01 0.30±0.007 0.15±0.015 0.039±0.011
Table3.MSEforFig.9anddifferentmessagelength
Sizeofembeddeddata 1019Bytes 739Bytes 466Bytes 132Bytes
Method1 0.15±0.005 0.11±0.005 0.07±0.003 0.02±0.002
Method2 0.35±0.009 0.25±0.01 0.16±0.006 0.05±0.004
Table4.MSEforFig.8anddifferentmessagelength
Sizeofembeddeddata 376Bytes 285Bytes 192Bytes 132Bytes
Method1 0.05±0.004 0.04±0.003 0.03±0.002 0.02±0.002
Method2 0.40±0.042 0.29±0.02 0.20±0.024 0.15±0.02
Tables2−4showthattheforimagesinFigs.8and9theaveragepowerperpixelduetomessageembedding is about 4−5times bigger forMethod2thanforMethod1.ThiscanbeattributedtothefactthatinMethod1wecanselectthemessagecarrying
pixel as the one with the smallest isolation out ofnine pixels. Also, inMethod 2
occasionallylargemodificationsmayresultduetothefactthatalleight2×2squaresmust stay goodafterembedding.For image inFig.10, thedifference isevenmore
pronounced. Both methods can embed messages into computer generated fractal
imageswithout introducingany artifacts into regions ofuniform color, areaswith
equipotential linesaround theJuliasets, andaliased fontsonuniformbackground.
Method1providesbettersecuritybecauseit introducedsmallerpowerperpixeldue
tomessageembedding.Method2hashighercapacitybutmayoccasionallyintroduce
largechangesincolor.
5 Embeddingwhiledithering
Asthelaststeganographicmethodofthispaper,wedescribeatechniqueappropriate
for message hiding in palette images obtained from true-color images using color
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quantizationanddithering.Givenatruecolorimage,wefirstderivethecolorpalette
usingsomeofthestandardcolorquantizationalgorithms[2].Ifthetruecolorimageisnotknownandonlyitsquantizedformisavailable,wecouldincreasethecolordepth
using for example the method described in [14].We continue by calculating the
optimal parity assignment for the palette. Then we pseudo-randomly select themessagecarryingpixelsintheimage(inanon-adaptivemanner).Finally,weperform
the quantization and ditheringby scanning the imageby rows.For anon-message
carrying pixel, weperform the standardquantization anddithering step.Whenwe
come toamessagecarrying pixel,wequantize itscolor to theclosestpalettecolor
with the right parity. This way, both the quantization error and the error due to
message embedding will be scattered and diffused through the whole image.We
conjecturethattheartifactsintroducedbythismethodwillbelessdetectablebecause
theyshouldbeconsistentwiththeditheringmechanism.
Wehave tested the method on24bit scansof photographs. As expected, such
imagestypicallyprovideenoughtextureandcolorvariations,andevenwhenasmuchas50%ofallpixelsintheimagehavebeenusedforembedding,wecouldnotidentify
anyvisibleartifactsorsuspiciouspatterns.Themethodperformedsatisfactorilyeven
for"singular"images,suchasthecartoonoftheTweetyBirdshowninFig.14.The
imageisatruecolorcartoononabackgroundthatgraduallychangescolor.Wehave
againembeddedamessageoflengthequaltoonehalfofthenumberofallpixels.Fig.
15isaclose-upoftheoriginalTweety'seyeandbeak,andFigs.16and17showthe
same close-up for the non-adaptive naïve method with non-optimal palette,
respectively.Thenon-optimized,non-adaptivemethodperformspoorlyandonecan
identify a suspicious pattern in Tweety's eye. On the other hand, the edges and
contrastoftheoriginalpicturehasbeenmoreorlesspreserved.Thedithering-while-
embeddingmethoddoesnot introducesuspiciouspatternsbut theimageedges (see
theblacklinesaresomewhatblurredduetothediffusederror.ThecolorvariationsinTweety'sbeakhavealsobeenflattenedout.
6 Conclusionandfuturedirections
In this paper, we study non-adaptive and adaptive steganographic techniques for
images inpalette image formats.Wehave introducedthe conceptof optimalparity
assignment and designed an efficient algorithm that finds the optimal parity
assignment.Theoptimalparity is independent ofthe imagehistogramanddepends
only on the image palette. Thus, it can be used for increasing the security of
steganographictechniquesthatembedmessagebitsintotheparityofpalettecolors.
Wehaveshownthattheoptimalpaletteimprovestheaveragepowerperpixeldueto
messageembeddingby25−35%(formethodintroducedin[6]).Theoptimalparityisalsooptimalformultiplepixelembedding.
Wehavedevelopedtwonewmethodsforadaptivemessageembeddinginpalette
images.Thetechniquestendtoavoidareasofuniformcolorandembedmessagebits
into texture-rich portions of the carrier image. Both techniques utilize the optimal
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parityassignment.Thefirsttechniqueembedsonemessagebit intoa group of3×3pixels. The second technique has higher capacity, but provides less security whenmeasuredbytheaveragedistortionpowerperpixel.Bothtechniquesweretestedon
computer generated images with large areas of uniform color and with fonts on
uniformbackground.Noobviousartifactswereintroduced byeither technique.An
imagewithsimpleverticalbandsofthicknessofatleast3withdifferentcolorswould
beclassifiedbybothtechniquesasazerocapacityimage.Thisintuitivelycorresponds
to our feeling that such an image should not be used as a carrier image and the
algorithms work as we would expect. At this point, we stress that it is almost
impossible to design an algorithm that wouldworkwell on all low-color images,
especiallycomputergeneratedimagesorimageswithwell-definedinnerstructure.
Fig. 14. Test image TweetyBird
Fig.15.Original
Fig. 16. Non-adaptive non-
optimized
Fig. 17. Dithering-while-embedding
For example, an image with fonts of uniform color on a complex background,
rather thana uniformbackgroundasin Fig.3,willnot behandledby ouradaptive
algorithm correctly (seeFig. 13).Theborder pixelsof fontsmaybe changed.In a
situationlikethis,itbecomesincreasinglydifficulttoautomatizetheprocessofsecure
adaptiveselectionofpixels.Imageunderstandingandinterpretationofimagefeatures
comes into play.While a humancaneasilyrecognizethatapixel isactually adot
abovetheletter" i"andthusmustnotbechanged,itwouldbeveryhardtodesignan
algorithmthatwouldrecognizethisautomatically.
Thelasttechniquedescribed inthispaperhasbeendesignedforembeddinglarge
messagesintopaletteimagesobtainedfromtruecolorimagesusingcolorquantization
and dithering. The basic idea behind this embedding-while-dithering method is to
ditherboththecolorquantizationerrorandthe errordue tomessageembedding to
avoid introducing artifacts inconsistentwith theditheringalgorithm.We argue that
thestego-imagewillcorrespondtoanimageobtainedbyquantizingandditheringaslightly noisier version ofthe original image, thusmakingthe stego-imagefreeof
artifactsincompatiblewithdithering.
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Our future research effort will be directed towards a more formal approach to
adaptivemessageembedding includingestimatesfor capacity.Thedithering-while-embedding method could also be improved by making it adaptive to the image
content.
Acknowledgements
TheworkonthispaperwassupportedbyAirForceResearchLaboratory,AirForceMaterial Command, USAF, under a grant number F30602-98-C-0009. The U.S.Government is authorized to reproduce and distribute reprints for Governmentalpurposesnotwithstandinganycopyrightnotationthereon.Theviewsandconclusionscontainedhereinarethoseoftheauthorsandshouldnotbeinterpretedasnecessarilyrepresentingtheofficialpolicies,eitherexpressedorimplied,ofAirForceResearchLaboratory,ortheU.S.Government.
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