Steganalysis An Overview from Statistical Mechanical perspective

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Steganalysis- An Overviewfrom Statistical
Mechanical perspective

• Aruna Ambalavanan
• Feb 10 2005

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Plan of the Talk

• Growth of Steganography and Steganalysis
• Problem Formulation
• Relevance of the problem to Statistical Physics
• Probability models used
• Conclusions

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Data hiding Detection/Estimation Comparison
on growth

• Data hiding Immense Growth
• Hiding in all possible cover mediums
• Hiding in all possible domains
• Recent innovation -DNA based data hiding
• Detection/ Estimation Still novice

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Steganalysis

• Passive steganalysis
• detect the presence or absence of a message
• Active Steganalysis
• Estimate the message length and location
• Estimate the Secret Key in embedding
• Extract the message

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Research Focus

• Bayesian Estimation of the original image
• - Original Image
• - Degraded Image
• O - Square Lattice
• How to model the prior
• What is the likelihood function

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Statistical Mechanics

• Ising Model
• N dimensional lattice
• Associated with each lattice site is a spin
  variable that is either 1 or 1
• Set of these spin variables specifies the
  configuration of the system
• Energy of the system specified by the
  configuration of the spin variables is defined to
  be
• Here and represent the correlation
  and the external force respectively

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Energy expression relates image model how?

• Interaction correlation between pixels
• External force amount of degradation
• Therefore the problem is to find these 2
  parameters

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MRF , Gibbs - equivalence

• Using the bayes formula and the assumption that
  the a priori probability is a MRF the a
  posteriori distribution is found to follow the
  Gibbs distribution (Hammersley Clifford theorem)
• For a specified U(f) the Gibbs distribution is
  given by
• where the summation is taken over all possible
  configurations of the lattice

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Prior and Degradation model

• The following prior model is assumed
• The degraded image is obtained by flipping the
  intensity of every pixel with a probability p

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Degradation Model

• Parameter for the degradation process is found to
  be related to the flipping probability by
• The degradation model is assumed to be

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A posteriori Probability

• A posteriori probability distribution for an
  Ising model with nearest neighbor interactions is
• where

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Parameter Estimation

• Evidence Prdegradedparameters
• The task is to find the parameters that would
  maximize the evidence
• The configuration of the image that corresponds
  to these parameters is the original image

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Parameter Estimation

• The conditions for extremum involve marginal
  probability distribution.
• Given the size of the image it is hard to
  calculate these distribution without
  approximating techniques. Therefore Bethe
  Approximation is used
• In this approximation method we approximate the
  marginal probabilities as messages between
  neighboring pixels
• Refer 1 for details on the approximation
  technique

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Belief Propagation (BP) Messages

• Given the intensity of the current pixel the
  probability that the neighboring pixel is of the
  same intensity is termed as a message
• This message depends on the parameters of the
  model
• Therefore an algorithm is devised which would
  compute the intensity of every pixel by
  propagating this message throughout the entire
  image
• An analytical expression for this message
  depending on the parameters is derived in 1

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Image Restoration

• Initialize the parameters to 1
• Compute the message between the neighboring
  pixels with the current value of the parameters
  and the observed intensity of the pixel under
  consideration
• Compute the difference between the messages in
  the previous iteration and the current one
• If the difference is greater than a threshold
  value go to step 2 after incrementing the
  parameters by 0.1, else stop the iteration
• With the computed parameter values and the
  messages between the neighboring pixels the
  intensity of every pixel is determined

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Conclusions

• Results indicate that the embedded message could
  be extracted when the pixels are more correlated
  and the whole image has some structure
• As the LSB plane is more or less random the
  extraction procedure does not perform well.

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DNA Steganography- a digression

• DNA Steganography
• The idea of DNA Computing can also be used in
  the field of security for data transmission. The
  idea is very simple.
• Ø      First convert the alphabets into
  combination of four nucleotides.
• Ø      Create a strand of DNA based on that code
• Ø      This piece of DNA is placed in the middle
  plus short marker sequences at the ends of the
  message.
• Ø      The encoded piece of DNA is then placed
  into a piece of human DNA and is then mixed with
  other DNA strands.
• Ø      The mixture is then dried on to paper that
  can be cutup into microdots with each dot
  containing billions of strands of DNA.
• Ø      The key to decrypting the message lies in
  knowing which markers on each end of the DNA are
  the correct ones.