Modelbased Steganography

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Model-based Steganography

• Phil Sallee

University of California, Davis
IWDW 2003
October 20, 2003
Seoul, Korea
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Outline

• Introduction
• Current methods
• Model-based steganography framework
• JPEG steganography example
• Results
• Conclusions
• Future Work

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Steganography

• Covered Writing
• Cryptography Conceal message content
• Steganography Conceal communication

10110101101010101010010100010110110110101010010101
10101010111100001010101001011101011010110101001010
01000010011101010011110110111101110111010001


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Steganography vs. Watermarking

• Steganography
• Emphasis on avoiding detection
• Largest hidden message possible
• Usually fragile
• Watermarking
• Emphasis on avoiding distortion of cover
• As robust as possible
• Usually small hidden message

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Measurements of Interest

• Capacity
• ltmessage sizegt / ltsteganogram sizegt
• Embedding Efficiency
• ltmessage sizegt / lt changes to covergt

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Current Steganography Methods
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Can we do better?

• What is the maximum capacity achievable before
  risking detection?
• How can we achieve this maximum capacity?
• At what embedding efficiency can we obtain this
  maximum capacity?

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Model-based Steganography

• Cover x is an instance of a random variable X
  distributed according to model PX
• x ( xa , xb )
• Choose x0 (xa , x0b ) to encode a message M
  while maintaining model statistics PX

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Model-Based Steganography Encoding
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Model-Based Steganography Decoding
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Capacity

• Maximum capacity entropy of PXb Xa
• Entropy codec designed to achieve the entropy
  limit

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Steganalysis

• Determine likelihood that xb is drawn from PXb
  Xa(xb xa).
• Compute expected message length
• Decode message
• Longer than expected message indicates a
  violation of the statistical model

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An example JPEG Steganography

• Model marginal statistics of DCT coefficients
• Achieve maximum capacity without altering
  marginal statistics
• Measure capacity, embedding rate achievable
• Compare results to current JPEG steganography
  methods F5 and Outguess

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Model
u coefficient valuepgt1, sgt0 are fit to each
coefficient type
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Model CDF

• Cumulative density function easy to calculate
• Used to integrate density function for a given
  histogram bin

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Fitting the Model Parameters

• Parameters p, s fit by maximum likelihood
• where h is a coefficient histogram

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Model Fit to Histogram
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Embedding

• step size 2
• xa bin group
• xb offset (like LSB)

xb Î0,1
xa
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Embedding

• step size 2
• xa bin group
• xb offset (like LSB)
• step size 3
• xa is lower precision
• 3 offsets per group

xb Î0,1
xa
xb Î0,1,2
xa
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Embedding Efficiency

• Embedding rate where p P(xb 0 xa)
• Change rate
• Efficiency

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Embedding Efficiency

• Embedding efficiency gt 2!

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Example
Each image is 47k bytes. Which contains a 6.5kb
message?
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Example
original image 47k
steganogram 47k message 6.46k (13.7) embed.
efficiency 2.1
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Results
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Histogram Comparison
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JPEG Steganography Methods
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Conclusions

• Presented a unifying framework for steganography
  and steganalysis
• Proposed method maximizes capacity while
  preserving a given set of statistics
• Steganographic security is based on a statistical
  model of the cover media

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Future Work

• Use extra capacity to correct additional
  statistics blockiness, wavelet statistics
• Improve model
• Dependencies between coefficients
• Embed in wavelet domain
• JPEG2000, MP3, MPEG,

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• Matlab code available http//redwood.ucdavis.edu/
  phil
• Email sallee_at_cs.ucdavis.edu