1. Model-based Steganography
Phil Sallee
University of California, Davis
IWDW October 20, Seoul, Korea

2. Outline Introduction Current methods
Model-based steganography framework
JPEG steganography example
Results
Conclusions
Future Work

3. Steganography + = Covered + Writing
Cryptography: Conceal message content
Steganography: Conceal communication + =

4. Steganography vs. Watermarking
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

5. Measurements of Interest
Capacity:
<message size> / <steganogram size>
Embedding Efficiency:
<message size> / <# changes to cover>

6. Current Steganography Methods
Coefficient Histogram
Maximum Capacity
Embedding efficiency
JSteg
13% 2 F5
1.5
Outguess
6.5% 1

7. 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?

8. 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

9. Model-Based Steganography: Encoding

10. Model-Based Steganography: Decoding

11. Capacity Maximum capacity = entropy of PXb |Xa:
Entropy codec designed to achieve the entropy limit

12. 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

13. 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

14. u = coefficient value p>1, s>0 are fit to each coefficient type
Model
u = coefficient value p>1, s>0 are fit to each coefficient type

15. Model CDF Cumulative density function easy to calculate:
Used to integrate density function for a given histogram bin

16. Fitting the Model Parameters
Parameters p, s fit by maximum likelihood:
where h is a coefficient histogram

17. Model Fit to Histogram

18. Embedding step size = 2 xb Î{0,1} xa = bin group
xb = offset (like LSB)
xb Î{0,1} xa

19. Embedding step size = 2 step size = 3 xb Î{0,1} xa = bin group
xb = offset (like LSB)
step size = 3
xa is lower precision
3 offsets per group
xb Î{0,1} xa
xb Î{0,1,2} xa

20. Embedding Efficiency Embedding rate = where p = P(xb = 0 | xa)
Change rate =
Efficiency =

21. Embedding Efficiency
Embedding efficiency >= 2!

22. Example
Each image is 47k bytes. Which contains a 6.5kb message?

23. Example original image: 47k steganogram: 47k message: 6.46k (13.7%)
embed. efficiency: 2.1

24. Results Image name File size (bytes) Message size (bytes) Capacity
Embedding Efficiency
barb
48,459
6,573
13.56%
2.06
boat
41,192
5,185
12.59%
2.03
bridge
55,698
7,022
12.61%
2.07
goldhill
48,169
6,607
13.72%
2.11
lena
37,678
4,707
12.49%
2.16
mandrill
78,316
10,902
13.92%

25. Histogram Comparison

26. JPEG Steganography Methods
Coefficient Histogram
Maximum Capacity
Embedding efficiency
JSteg
13% 2 F5
1.5
Outguess
6.5% 1
Model-based
>2

27. 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

28. Future Work
Use extra capacity to correct additional statistics: ‘blockiness’, wavelet statistics
Improve model:
Dependencies between coefficients
Embed in wavelet domain
JPEG2000, MP3, MPEG, …

29. Matlab code available: http://redwood.ucdavis.edu/phil