Block Structure in JPEG and Steganalysis CSM25 Secure Information Hiding Dr Hans Georg Schaathun University of Surrey Spring 2009 – Week 4 Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 1 / 41
Block Structure in JPEG and SteganalysisCSM25 Secure Information Hiding
Dr Hans Georg Schaathun
University of Surrey
Spring 2009 – Week 4
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 1 / 41
JPEG Histogramme
Outline
1 JPEG HistogrammeHistogrammeSteganalysis
2 Improvements – F3 & F4
3 JPEG Calibration
4 Blockiness as a Statistic
5 Conclusion
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 2 / 41
JPEG Histogramme Histogramme
Outline
1 JPEG HistogrammeHistogrammeSteganalysis
2 Improvements – F3 & F4
3 JPEG CalibrationThe ideaMatlab
4 Blockiness as a StatisticThe Blockiness AttackYASS
5 Conclusion
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 3 / 41
JPEG Histogramme Histogramme
The JPEG Coefficients
Recall that JPEG uses theblockwise DCT transform
8× 8 DCT coefficientsdifferent frequencies
The entries are quantised,called JPEG coefficients (integers)
DC – highest frequence coefficient(0, 0)
63 AC coefficients, (i , j) 6= (0, 0),0 ≤ i , j ≤ 7
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 4 / 41
JPEG Histogramme Histogramme
Histogramme
Different frequencies have different characteristicsDC coefficient stick out
We calculate the histogramme of the AC JPEG coefficientsh(x) is the number of coefficients equal to x
Frequency-wise histogrammehij(x) is the number of blocks where coefficient (i , j) is equal to x
DC histogramme h00(x)
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 5 / 41
JPEG Histogramme Histogramme
Histogramme
Different frequencies have different characteristicsDC coefficient stick out
We calculate the histogramme of the AC JPEG coefficientsh(x) is the number of coefficients equal to x
Frequency-wise histogrammehij(x) is the number of blocks where coefficient (i , j) is equal to x
DC histogramme h00(x)
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 5 / 41
JPEG Histogramme Histogramme
Extracting AC coefficients
Consider N ×M matrix, AIf B is a boolean (logical) N ×M matrix,
then A(B) is a vector consisting of all elements from Acorresponding to a 1 (true) in B
Suppose we run (where A is N ×M DCT image)1 B = logical(ones(8,8)) % Make 8x8 matrix of ones2 B(1,1) = 0 % DC coefficient : zero3 BB = repmat ( B, N/8, M/8 ) % Concatenate block
for full image4 X = A(B) % Vector of AC coefficients
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 6 / 41
JPEG Histogramme Histogramme
HistogrammeMatlab
We have discussed histogrammes beforeEssentially you need two functions
hist to extract frequenciesbar or stem to make the plot
Refer to help filesand to exercise sheet
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 7 / 41
JPEG Histogramme Steganalysis
Outline
1 JPEG HistogrammeHistogrammeSteganalysis
2 Improvements – F3 & F4
3 JPEG CalibrationThe ideaMatlab
4 Blockiness as a StatisticThe Blockiness AttackYASS
5 Conclusion
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 8 / 41
JPEG Histogramme Steganalysis
JSteg Histogramme
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Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 9 / 41
JPEG Histogramme Steganalysis
Histogramme analysis
1 Pairs of valuesGeneralised χ2 works
2 SymmetryEmbedding exchange +2 ↔ +3 and −2 ↔ −1.The DCT histogramme is expected to be symmetricOutguess/JSteg destroy the symmetry.
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 10 / 41
JPEG Histogramme Steganalysis
Symmetry analysis
J2i =
(1− q
2
)I2i +
q2
I2i+1,
J2i+i =q2
I2i +
(1− q
2
)I2i+1
Writing
a =1− q/21− q
and b =q/2
1− q,
we get
I2i = aJ2i − bJ2i+1,
I2i+1 = −bJ2i + aJ2i+1.
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 11 / 41
JPEG Histogramme Steganalysis
Symmetry analysis (II)
∑i>0
I2i =∑i<0
I2i , and∑i<0
I2i+1 =∑i>0
I2i+1.
In other words ∑i>0
I2i +∑i<0
I2i+1 =∑i<0
I2i +∑i>0
I2i+1.
Substitute for I2i and J2i+1
One equation in one unknown : q
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 12 / 41
JPEG Histogramme Steganalysis
ExerciseSymmetry analysis
∑i>0
I2i +∑i<0
I2i+1 =∑i<0
I2i +∑i>0
I2i+1.
Substitute for I2i and I2i+1get equation in J2i and J2i+1.
Solve for J1, write as equation inJ1 (left hand side)∆i = J2i − J2i+1 (i > 0), and ∆i = J2i+1 − J2i (i < 0).
Solve for qCan you implement the resulting expression for p in Matlab?
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 13 / 41
Improvements – F3 & F4
Outline
1 JPEG Histogramme
2 Improvements – F3 & F4
3 JPEG Calibration
4 Blockiness as a Statistic
5 Conclusion
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 14 / 41
Improvements – F3 & F4
Improvements at a glance
F3 – F4 changes the embeddingbetter histogramme – maintain symmetry
Statistics-aware embeddingOutguess 0.2 uses unused capacitydummy changes are used to even out the statistics
Matrix coding/wet paper codingF5 minimises distortion using coding theoryfewer bit-flips per message bittechniques from coding for restricted memory
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 15 / 41
Improvements – F3 & F4
Bitflips in F3
Avoid pairs of values.Always decrease absolute value when changingZeros are ignored.Zero created: reembed in new coefficient
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Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 16 / 41
Improvements – F3 & F4
The problem of F3
ReembeddingZero created by message zeroesZeros are reembeddedExtra zeros embedded ⇒ overweight of even coefficients.
Typical JPEG. Typical F3.
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 17 / 41
Improvements – F3 & F4
F4 : evening out even values
Swap interpretation for negative coefficients+1 causes reembedding of zero-1 causes reembedding of one
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Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 18 / 41
Improvements – F3 & F4
F4 histogramme
What does the histogramme look like after F4 embedding?Maginitudes have generally been decreased.Effect similar to reduced quality factor.F4 (and F5) can be broken
Suggested Reading
Jessica Fridrich, Miroslav Goljan, Dorin Hogea: ‘Steganalysis of JPEGImages: Breaking the F5 Algorithm’. http://www.ws.binghamton.edu/fridrich/Research/F5.pdf
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 19 / 41
Improvements – F3 & F4
F4 histogramme
What does the histogramme look like after F4 embedding?Maginitudes have generally been decreased.Effect similar to reduced quality factor.F4 (and F5) can be broken
Suggested Reading
Jessica Fridrich, Miroslav Goljan, Dorin Hogea: ‘Steganalysis of JPEGImages: Breaking the F5 Algorithm’. http://www.ws.binghamton.edu/fridrich/Research/F5.pdf
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 19 / 41
Improvements – F3 & F4
F4 histogramme
What does the histogramme look like after F4 embedding?Maginitudes have generally been decreased.Effect similar to reduced quality factor.F4 (and F5) can be broken
Suggested Reading
Jessica Fridrich, Miroslav Goljan, Dorin Hogea: ‘Steganalysis of JPEGImages: Breaking the F5 Algorithm’. http://www.ws.binghamton.edu/fridrich/Research/F5.pdf
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 19 / 41
Improvements – F3 & F4
F4 histogramme
What does the histogramme look like after F4 embedding?Maginitudes have generally been decreased.Effect similar to reduced quality factor.F4 (and F5) can be broken
Suggested Reading
Jessica Fridrich, Miroslav Goljan, Dorin Hogea: ‘Steganalysis of JPEGImages: Breaking the F5 Algorithm’. http://www.ws.binghamton.edu/fridrich/Research/F5.pdf
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 19 / 41
Improvements – F3 & F4
F5 : Matrix embedding
Embedding as F4. . . extra Matrix Coding layer
n coefficients represent k bits
Flip fewer k/2 bits on average.See Week 7 for details
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 20 / 41
Improvements – F3 & F4
Statistics-aware embeddingOutguess 0.2
Modify unused coefficientsMimick original statisticTune for every statistic used in known analysis techniques
OutGuess 0.2Embedding as OutGuess 0.1.Modify selected unused coefficients to correct histogram
Flexible – adapt to any modelIf you know attacker’s model
... you mimick it.
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 21 / 41
Improvements – F3 & F4
Statistics-aware embeddingOutguess 0.2
Modify unused coefficientsMimick original statisticTune for every statistic used in known analysis techniques
OutGuess 0.2Embedding as OutGuess 0.1.Modify selected unused coefficients to correct histogram
Flexible – adapt to any modelIf you know attacker’s model
... you mimick it.
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 21 / 41
Improvements – F3 & F4
Statistics-aware embeddingOutguess 0.2
Modify unused coefficientsMimick original statisticTune for every statistic used in known analysis techniques
OutGuess 0.2Embedding as OutGuess 0.1.Modify selected unused coefficients to correct histogram
Flexible – adapt to any modelIf you know attacker’s model
... you mimick it.
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 21 / 41
Improvements – F3 & F4
Statistics-aware embeddingOutguess 0.2
Modify unused coefficientsMimick original statisticTune for every statistic used in known analysis techniques
OutGuess 0.2Embedding as OutGuess 0.1.Modify selected unused coefficients to correct histogram
Flexible – adapt to any modelIf you know attacker’s model
... you mimick it.
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 21 / 41
Improvements – F3 & F4
Statistics-aware embeddingOutguess 0.2
Modify unused coefficientsMimick original statisticTune for every statistic used in known analysis techniques
OutGuess 0.2Embedding as OutGuess 0.1.Modify selected unused coefficients to correct histogram
Flexible – adapt to any modelIf you know attacker’s model
... you mimick it.
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 21 / 41
Improvements – F3 & F4
Statistics-aware embeddingOutguess 0.2
Modify unused coefficientsMimick original statisticTune for every statistic used in known analysis techniques
OutGuess 0.2Embedding as OutGuess 0.1.Modify selected unused coefficients to correct histogram
Flexible – adapt to any modelIf you know attacker’s model
... you mimick it.
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 21 / 41
Improvements – F3 & F4
Statistics-aware embeddingOutguess 0.2
Modify unused coefficientsMimick original statisticTune for every statistic used in known analysis techniques
OutGuess 0.2Embedding as OutGuess 0.1.Modify selected unused coefficients to correct histogram
Flexible – adapt to any modelIf you know attacker’s model
... you mimick it.
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 21 / 41
Improvements – F3 & F4
Statistics-aware embeddingOutguess 0.2
Modify unused coefficientsMimick original statisticTune for every statistic used in known analysis techniques
OutGuess 0.2Embedding as OutGuess 0.1.Modify selected unused coefficients to correct histogram
Flexible – adapt to any modelIf you know attacker’s model
... you mimick it.
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 21 / 41
Improvements – F3 & F4
Statistics-aware embeddingOutguess 0.2
Modify unused coefficientsMimick original statisticTune for every statistic used in known analysis techniques
OutGuess 0.2Embedding as OutGuess 0.1.Modify selected unused coefficients to correct histogram
Flexible – adapt to any modelIf you know attacker’s model
... you mimick it.
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 21 / 41
Improvements – F3 & F4
Combinations
Statistics-aware Matrix CodingMore advanced code allows a choice of coefficient to modifyUse choice to mimick original statistical distribution
Known as Wet Paper CodesBased on Dirty Paper Codes by Costa 1983.
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 22 / 41
JPEG Calibration
Outline
1 JPEG Histogramme
2 Improvements – F3 & F4
3 JPEG CalibrationThe ideaMatlab
4 Blockiness as a Statistic
5 Conclusion
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 23 / 41
JPEG Calibration The idea
Outline
1 JPEG HistogrammeHistogrammeSteganalysis
2 Improvements – F3 & F4
3 JPEG CalibrationThe ideaMatlab
4 Blockiness as a StatisticThe Blockiness AttackYASS
5 Conclusion
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 24 / 41
JPEG Calibration The idea
The calibrated image
JPEG has a block-structureSteganography in JPEG follows the block-structureWhat happens if we de- and re-compress the image
with different block structure?
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 25 / 41
JPEG Calibration The idea
The calibrated image
JPEG has a block-structureSteganography in JPEG follows the block-structureWhat happens if we de- and re-compress the image
with different block structure?
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 25 / 41
JPEG Calibration The idea
The calibrated image
JPEG has a block-structureSteganography in JPEG follows the block-structureWhat happens if we de- and re-compress the image
with different block structure?
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 25 / 41
JPEG Calibration The idea
The calibrated image
JPEG has a block-structureSteganography in JPEG follows the block-structureWhat happens if we de- and re-compress the image
with different block structure?
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Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 25 / 41
JPEG Calibration The idea
The calibrated image
JPEG has a block-structureSteganography in JPEG follows the block-structureWhat happens if we de- and re-compress the image
with different block structure?
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Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 25 / 41
JPEG Calibration The idea
Histogramme comparison
1 Decompress the image2 Crop 4 pixels; either
4 rows at top and bottom4 columns left and right4 pixels on each edge
3 Recompress using same quality factor and quantisation matrixcalled calibrated image
4 Compare histogramme of original and calibrated images5 What do you see?
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 26 / 41
JPEG Calibration The idea
Effect of calibration
Original and Calibrated image have similar statisticsMost JPEG stego-systems
change the statistics in 8× 8 grid... but the calibrated image hardly change
Statistical difference between an image and its calibration... tends to indicate a steganogram
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 27 / 41
JPEG Calibration Matlab
Outline
1 JPEG HistogrammeHistogrammeSteganalysis
2 Improvements – F3 & F4
3 JPEG CalibrationThe ideaMatlab
4 Blockiness as a StatisticThe Blockiness AttackYASS
5 Conclusion
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 28 / 41
JPEG Calibration Matlab
JPEG ToolboxDecompression
Dequantisation» Xy2 = dequantize ( Xy, Q ) ;
Inverse transform» Xy3 = ibdct ( Xy2 ) ;
Normalisation» Xy4 = uint8( Xy3 + 128 ) ;
Did it work?» imshow ( Xy4 )
Note, we have only used grayscale information.
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 29 / 41
JPEG Calibration Matlab
JPEG ToolboxRecompression
New range» Xy3 = double( Xy4 - 128 ) ;
Inverse transform» Xy2 = bdct ( Xy3 ) ;
Quantisation» Xy = quantize ( Xy2, Q ) ;
Reinsertion» im.coef_arrays{im.comp_info(1).component_id} =Xy ;
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 30 / 41
Blockiness as a Statistic
Outline
1 JPEG Histogramme
2 Improvements – F3 & F4
3 JPEG Calibration
4 Blockiness as a StatisticThe Blockiness AttackYASS
5 Conclusion
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 31 / 41
Blockiness as a Statistic The Blockiness Attack
Outline
1 JPEG HistogrammeHistogrammeSteganalysis
2 Improvements – F3 & F4
3 JPEG CalibrationThe ideaMatlab
4 Blockiness as a StatisticThe Blockiness AttackYASS
5 Conclusion
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 32 / 41
Blockiness as a Statistic The Blockiness Attack
The Blockiness Statistic
Compare each edge pixelwith its neighbourAdd all the differences
B =
M/8−1∑i=1
N∑j=1
|g8i,j − g8i+1,j |
+M∑
i=1
N/8−1∑j=1
|gi,8j − gi,8j+1
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 33 / 41
Blockiness as a Statistic The Blockiness Attack
Information on Blockiness
Blockiness increases linearly in the number of modifiedcoefficients
Empirically confirmed
Calibration is used for comparison
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 34 / 41
Blockiness as a Statistic The Blockiness Attack
Comparing slides
Suspicious image (to be classified) [S]Calibrated image [S0]Suspicious image with maximum capacity embedding on top [S1]
Sample the statistic forembedded messagesof different lengths qDistance between thecurves indicatessteganogramMessage length can beestimated
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 35 / 41
Blockiness as a Statistic The Blockiness Attack
The message estimate
q =s0 − ss0 − s1
where s0, s, and s1 are the average slopes of S0, S, and S1respectively
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 36 / 41
Blockiness as a Statistic The Blockiness Attack
Acknowledgment
Figures in this section are from
Suggested Reading
MSc dissertation 2007: Statistical Steganalysis by Marios Leivaditis
Core Reading
Fridrich, J., Goljan, M. and Hogea, D. (December 6, 2002) «Attackingthe OutGuess», Proc. of the ACM Workshop on Multimedia andSecurity 2002
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 37 / 41
Blockiness as a Statistic YASS
Outline
1 JPEG HistogrammeHistogrammeSteganalysis
2 Improvements – F3 & F4
3 JPEG CalibrationThe ideaMatlab
4 Blockiness as a StatisticThe Blockiness AttackYASS
5 Conclusion
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 38 / 41
Blockiness as a Statistic YASS
YASS – Yet Another Steganographic SchemeSolanki, Sarkar, and Manjunath IH’07
Simple idea – do not use the 8× 8 grid for embedding10× 10 macro-blocks
Pseudo-random 8× 8 subblock in each macro-block... DCT-transform the subblock... embed in DCT coefficients... reconvert
Embedding creates some blockiness,but analyst does not know where to expect it
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 39 / 41
Conclusion
Outline
1 JPEG Histogramme
2 Improvements – F3 & F4
3 JPEG Calibration
4 Blockiness as a Statistic
5 Conclusion
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 40 / 41
Conclusion
Conclusion
Main challenge in stegananalysiswhat is the expected statistics for a normal image?a.k.a. baseline value
Calibrated image offers a solutionNormally very similar statistics,. . . because neighbour blocks are similar (visually)
Data embedding change blocks independentlyChanges block structure and block statistics,. . . but the calibrated image is not changed in the same way
We can use the calibrated image to estimate statistics in theoriginal coverimage.
Dr Hans Georg Schaathun Block Structure in JPEG and Steganalysis Spring 2009 – Week 4 41 / 41