Feature-Based Steganalysis for JPEG images and its applications for future design of steganographic schemes. - Jessica Fridrich

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Feature-Based Steganalysis for JPEG images and
its applications for future design of
steganographic schemes.
- Jessica Fridrich

• Submitted by
• 
  Praveena Gummadi
• 
  Vandana Vasudeva

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Contents

1. Abstract
2. Previous work
3. Proposed Research
4. Experimental results
5. Conclusion
6. Comments
7. Acknowledgements

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Abstract

• The goal of forensic steganalysis is to detect
  the presence of embedded data and to eventually
  extract the secret message. In the given paper a
  new feature based steganalytic method for JPEG
  images was introduced. The detection method is a
  linear classifier trained on feature vectors
  corresponding to cover and stego images. The
  features are calculated as an L1 norm of
  difference between a specific macroscopic
  functional calculated from stego image and same
  functional obtained from a decompressed, cropped,
  and recompressed stego image. The functionals are
  built from marginal and joint statistics of DCT
  coefficients. Because the features are calculated
  directly from DCT coefficients, conclusions can
  be drawn about the impact of embedding
  modifications on detectability.
• Three different steganographic examples are
  tested and compared. The experimental results
  reveal new facts about current steganographic
  methods for JPEGs and new design principles for
  more secure JPEG steganography.

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Previous work on Steganalytic methods

• Chi-square attack by Westfield original
  version could detect sequentially embedded
  message and was based on first order statistics.
• Based on distinguishing statistic steganalyst
  first inspects the embedding algorithm and then
  identifies a quantity (distinguishing statistics)
  that changes predictably with the length of
  embedded message. For JPEG images the calibration
  is done by decompressing the stego image,
  cropping up a few pixels in each direction and
  recompressing using same quantisation table. The
  DS calculated from this image is used as an
  estimate for the same quantity from the cover
  image. Using this calibration a highly accurate
  and reliable estimation of the embedded message
  length can be constructed for many schemes.
• Blind Classifiers by Memon and Farid A blind
  detector learns what a typical unmodified image
  looks like in a multidimensional feature space
  and a classifier is then trained to learn the
  difference between cover and stego image
  features.
• Introduction of blind detectors prompted further
  research in steganography and Tzscoppe
  constructed a JPEG steganographic scheme HPDM
  (histogram preserving data mapping) which was
  undetectable using Farids scheme but is easily
  detectable using single scalar feature-calibrated
  spatial blockiness in DCT domain rather than from
  a wavelet decomposition.

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Proposed Research

• The paper combined the concept of calibration
  with the feature based classification to devise a
  blind detector specific to JPEG images.
• Calibrated Features
• Two types of features were used in analysis
  first order features second order features. All
  features were constructed in the following
  manner.
• A vector functional F is applied to the stego
  JPEG image J1. This functional could be global
  DCT coefficient histogram, a cocurrence matrix,
  spatial blockiness. The stego image J1 is
  decompressed to the spatial domain, cropped by 4
  pixels in each direction and then recompressed
  with the same quantisation as J1 to obtain J2.
  The same vector functional F is then applied to
  J2. The final feature f is obtained as an L1 norm
  of the difference
• f
  F(J1) F(J2)

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• Basic logic behind this choice for features is
  the following
• The cropping and recompression produces a
  calibrated image with most macroscopic features
  similar to the original cover image because the
  cropped stego image is perceptually similar to
  the cover image and thus its DCT coefficients
  have approx the same statistical properties as
  the cover image.
• Cropping by 4 pixels is important because 8 x 8
  grid of recompression does not see the previous
  JPEG compression and thus the obtained DCT
  coefficients are not influenced by previous
  quantisation in DCT domain.
• We can think the cropped/recompressed image as
  an approximation to the cover image or as side
  information.

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• First order Features
• The simplest first order statistic of DCT
  coefficients is their histogram. Suppose the
  stego JPEG file is represented with a DCT
  coefficient array dk(i,j) and quatisation matrix
  Q(i,j) and global histogram of all 64k DCT
  coefficients will be denoted as Hr where
  rL,..,R Lmin k, i, j dk(i,j) and Rmax k, i,
  j dk(i,j)
• For a fixed DCT mode (i,j) let hr ij ,denote the
  individual histogram of values dk(i,j). To
  provide additional first order macroscopic
  statistics to our set of functionals, we use dual
  histogram given as
• Where delta(u,v) 1 if uv and 0 otherwise.
• The above g value is the number of times the
  value d occurs as (i,j)-th DCT coefficient over
  all total B blocks in JPEG image.

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Second order Features

• If the corresponding DCT coefficients from
  different blocks were independent then any
  embedding scheme that preserves the first order
  statistics the histogram would be undetectable
  by Cachins definition of steganographic
  security. Thus we use the features that capture
  inter-block dependencies as they would be likely
  violated by most steganographic algorithms.
• Let Ir and Ic denote the vectors of block indices
  while scanning the image by rows and columns
  resp. The first functional capturing inter-block
  dependencies is the variation V defined as
• Embedding changes also increase the
  discontinuities along the 8 x 8 block boundaries,
  thus two blockiness measures Ba , a1,2are
  included to our set of functionals. The
  blockiness is calculated from decompressed JPEG
  image and represents an integral measure of
  inter-block dependency over all DCT modes over
  the whole image.

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• In the expression above M and N are image
  dimensions, x ij are grayscale values of the
  decompressed JPEG image.
• The final three functionals are calculated from
  the co-occurrence matrix C of neighboring DCT
  coefficients which is a DxD matrix, DR-L1 and
  matrix C describes the probability distribution
  of pairs of neighboring DCT coefficients and is
  defined as
• Let C(J1) and C(J2) b e the co-occurrence
  matrices for JPEG images J1 and J2 resp. Due to
  approx symmetry of Cst around (s, t)(0,0), the
  differences Cst(J1) Cst(J2) for (s, t)
  belonging to (0,1),(1,0),(-1,0),(0,-1) are
  strongly positively correlated and same is true
  for the group (s, t) belonging to
  (1,1),(-1,1),(1,-1),(-1,-1).

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• The co-occurrence matrix for the embedded image
  can be obtained as a convolution CP (q), where P
  is the probability distribution of the embedding
  distortion which depend on the relative message
  length, and values of CP (q) will spread out and
  following three quantities were taken as our
  features

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• The final set of 23 functionals used in this
  paper is summarized as in table below

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Experiment

• The paper used the Greenspun image database
  consisting of 1814 images of size 780x540. All
  these images were converted to grayscale, the
  black border frame was cropped away and images
  were compressed using 80quality JPEG. The paper
  selected three different steganographic
  algorithms namely F5 algorithm, Outguess 0.2, and
  Model based Steganography without and with
  deblocking MB1 and MB2 for JPEG images.
• Each technique was analyzed separately. For a
  fixed relative message length expressed in bits
  per non-zero DCT coefficients of the cover image,
  a training database of embedded image was
  created. The Fisher Linear Discriminant
  Classifier was trained on 1314 cover and stego
  images. The generalized Eigen vector obtained
  form this training was then used to calculate the
  ROC curve for the remaining 500 cover and stego
  images. The detection performance was evaluated
  using detection reliability P defined as
• P
  2A-1,
• Where A is the area under ROC (Receiver
  Operating Characteristic Curve) also called as
  accuracy. The accuracy was scaled to obtain P 1
  for a perfect detection and P 0 when ROC
  coincides with diagonal line (where reliability
  of detection is 0). The detection reliability of
  all the three methods is shown in table 2 as

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• Table 2.
• Detection reliability p for F5 algorithm with
  matrix embedding (1,k,2k -1), F5 turned off
  matrix embedding, Outguess 0.2, Model based
  steganography without and with deblocking (MB1
  andMB2) for different embedded rates.

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Figure 1.Capacity for the tested techniques
expressed in bits per non-zero DCT coefficients.

• .

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Figure 2. ROC curves for embedding
capacities and methods from table 2.
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Table 3.Detection reliability for individual
features for all three embedding algorithms for
fully embedded images.
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Conclusion

• From table 2 we can see that Outguess algorithm
  is the most detectable and also it provides the
  smallest capacity. The detection reliability is
  relatively high even for embedding rates as small
  as 0.05 bpc and this method becomes highly
  detectable for messages above 0.1 bpc.
• F5 algorithm performs better than outguess on
  turning off the matrix embedding since matrix
  embedding decreases the detectability of short
  messages as it improves the efficiency.
• From table 3 it can be seen that both MB1 and MB2
  methods clearly have the best performance of all
  three tested algorithms. MB1 preserves not only
  the global histogram but all marginal statistics
  (histograms) for each individual DCT mode. MB2
  algorithm has same embedded mechanism as MB1 but
  reserves one half of the capacity for
  modifications that bring the blockiness of the
  stego image to its original value.

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Comments

• Looking at the results in table 1 and table 2
  there is no doubt that the model based
  Steganography MB1 and MB2 is by far the most
  secure method out of three tested paradigms. MB1
  and MB2 not only preserve the global histogram
  but also all histograms of individual DCT
  coefficients and hence all dual histograms are
  also preserved. MB2 also preserves one second
  order functional, L1 blockiness. Thus, we
  conclude that the more statistical measures an
  embedding method preserves, the more difficult it
  is to detect it.
• One surprising fact revealed is that preserving a
  specific functional does not mean that the
  calibrated feature will be preserved. Preserving
  the blockiness along the original 8x8 grid does
  not mean that the blockiness along the shifted
  grid will also be preserved . This is because the
  embedding and deblocking changes are likely to
  introduce distortion into the middle of the
  blocks and thus disturb the blockiness feature,
  which is the difference between the blockiness
  along the solid and dashed lines as seen in the
  figure 3 below

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Figure 3
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• Its further pointed out that the features derived
  from the co-occurrence matrix are very
  influential for all three schemes esp. for Model
  based steganographic methods.
• MB2 method is the currently the only JPEG
  steganographic method that takes into account the
  inter-blocking dependencies between the DCT
  coefficients which is the probability
  distribution of coefficient pairs from
  neighboring blocks.

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Acknowledgements

• Information Hiding 6th International Workshop,
  IH 2004, Toronto, Canada, May 23-25 2004, Revised
  Selected Papers
• By Jessica Fridrich
• Published by Springer, 2004
• Determining the stego algorithm for JPEG
  imagesPevny, T.   Fridrich, J.   Dept. of
  Computer Science, State Univ. of New York
  Binghamton, NY

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• Thank You!