using high-dimensional image models to perform highly...

Using High-Dimensional Image Models to Perform

Highly Undetectable Steganography

Tomá² Pevný1, Tomá² Filler2, Patrick Bas3

1CTU, Prague, Czech Republic2 SUNY, Binghamton, USA

3Lagis, Lille, France

29th June 2010

T. Pevný, T. Filler, P. Bas | HuGO � Highly Undetectable steGO 1/20

Outline

1 Motivation

2 Minimizing the distortion function

3 Designing the distortion function

4 Experimental veri�cation

5 Conclusion


Outline

1 Motivation




5 Conclusion


Steganography

Practical steganography for digital media

modi�es the cover objects to convey the message.

makes changes as undetectable as possible.

Distortion function

any function D : X ×X → [0,∞].

correlates with detectability.

is minimized during embedding.


Additive distortion function

D(x ,y) =n

∑i=1

ρi |xi − yi |

|xi − yi | ≤ 1,

ρi cost of changing one pixel (embedding impact)

Aditivity implies that embedding changes do not interact.


Separational principle

Theorema

If we want to communicate m bits in n elements (pixels), than the

minimal expected distortion is

Dmin(m,n,ρ) =n

∑i=1

piρi ,

where pi is the probability of changing the ith pixel,

pi =e−λρi

1+ e−λρi

.

The parameter λ is obtained by solving ∑ni=1H(pi ) = m.

aJ. Fridrich and T. Filler, Practical Methods for Minimizing Embedding Impact in

Steganography, 2007


Corollary of the theorem

Corrolary

Design of the steganographic algorithm boils down to

the design of an additive distortion function D, orthe setting embedding costs ρi .

Allows to compare additive distortion functions.

Practical algorithms approaching the distortion bound existsa.

aT. Filler, J. Fridrich, and J. Judas, Minimizing embedding impact in steganography

using Trellis-Coded Quantization, 2010


Outline

1 Motivation




5 Conclusion


Designing the distortion function

Distortion function

D(x,y) = ‖f (x)− f (y)‖=d

∑j=1

wj |fj(x)− fj(y)|

d � number of features

Additive approximation

D ′(x,y) =n

∑i=1

D(x,yix)|xi − yi |

n � number of pixels


Model Correction

+1

-1

+1

-1

+1

-1

+1

-1

no change change pixel

Compensates the suboptimality caused by approximating D(x ,y) byD ′(x ,y).


Outline

1 Motivation




5 Conclusion


Features of the model

d3

d2

d1

Distortion function

D(x,y) =T

∑d1,d2,d3=−T

wd1,d2,d3

∣∣fd1,d2,d3(x)− fd1,d2,d3(y)∣∣f →d1,d2,d3 � # of di�erences (d1,d2,d3) between neighboring pixels


Setting the weights

−60

6

−60

6

0

5 · 10−2

0.1

d2d1

Mean of CX,→d1d2

feature

00

0

0.5

1

d2d1

w(d1, d2) =[√

d21 + d2

2 + σ]−γ


Outline

1 Motivation




5 Conclusion


Detectability by Spam

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.1

0.3

0.5

noModelCorrect.

withModelCorrect.

HuGO

ternary LSB match.

simulatedSTC h = 10

Relative payload (bpp)

Err

or

PE

�xed size 512×512

images

PE = min1

2

(PFp +PFn

)SVMs with Gaussian

kernel.


Detectability by feature sets

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.1

0.3

0.5 WAMSPAM 1st

SPAM 2nd

CDF

ternary LSB matching

HuGO

Relative payload (bpp)

Err

or

PE


HuGO, where did you hide the message?

Fig: 0.25 bits per pixel Fig: 0.50 bits per pixel


Outline

1 Motivation




5 Conclusion


Conclusion

We presented a methodology to design a steganographic

algorithm by applying state of the art principles:

separate distortion function from codinguse of high-dimensional model (107 features).

The practical realization, HuGO allows the embedder to hide

7× longer message than LSB matching at the same level of

security.


Do you want be the BOSS?

B O S SBreak Our Steganographic SystemBreak Our Steganographic System

Steganalytic challenge is coming up in June 2010!

1000 images, 500 with a hidden message

Guess which ones!

http://boss.gipsa-lab.grenoble-inp.fr


http://boss.gipsa-lab.grenoble-inp.fr

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