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Page 1: From Blind to Quantitative Steganalysis - Department of

From Blind to Quantitative Steganalysis

Tomá² Pevný1, Jessica Fridrich2, Andrew D. Ker3

1GIPSA-Lab, INPG, France2Binghamton University, SUNY, USA

3University of Oxford, UK

19th January 2009

T. Pevný, J. Fridrich, A. Ker | From Blind to Quantitative Steganalysis 1/23

Page 2: From Blind to Quantitative Steganalysis - Department of

Outline

1 Motivation

2 Methodology

3 ExperimentsGeneral resultsDetailed results for Jsteg and nsF5Comparison to previous art

4 Conclusion and Future directions

T. Pevný, J. Fridrich, A. Ker | From Blind to Quantitative Steganalysis 2/23

Page 3: From Blind to Quantitative Steganalysis - Department of

Outline

1 Motivation

2 Methodology

3 ExperimentsGeneral resultsDetailed results for Jsteg and nsF5Comparison to previous art

4 Conclusion and Future directions

T. Pevný, J. Fridrich, A. Ker | From Blind to Quantitative Steganalysis 3/23

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Steganalysis � Quantitative Steganalysis

Steganalysis

Steganalysis detects presence of secret message.

Steganalyzer is a binary detector (classi�er).

Quantitative steganalysis

Quantitative steganalysis estimates number of embeddingchanges (length of message).

Quantitative steganalyzer is an estimator.

T. Pevný, J. Fridrich, A. Ker | From Blind to Quantitative Steganalysis 4/23

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Time for Change

Advantages of Quantitative Steganalysis

provide the steganalyst with further information (estimate ofmessage length).

useful for forensic analysis (message is encrypted).

important in pooled steganalysis.a

allow a �ner control of false positive and false negative rate intargeted blind steganalysis.

alleviate problems with dependence of the steganalyzer onmessage length in the training set.b

aA. D. Ker, Batch Steganography and Pooled Steganalysis, 2006.bCancelli et al., A Comparative Study of �1 Steganalyzers, 2008.

T. Pevný, J. Fridrich, A. Ker | From Blind to Quantitative Steganalysis 5/23

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Outline

1 Motivation

2 Methodology

3 ExperimentsGeneral resultsDetailed results for Jsteg and nsF5Comparison to previous art

4 Conclusion and Future directions

T. Pevný, J. Fridrich, A. Ker | From Blind to Quantitative Steganalysis 6/23

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Methodology

Assumption

Steganographic features used in blind steganalysis react

predictably to the number of embedding changes.

Identify relationship between feature vector and change rate

First two most signi�cant components of merged features of nsF5 identi�ed by Partial Least Square.

1st component of PLS

2ndcomponentof

PLS

0

0.1

0.2

0.3

0.4

0.5

0.6

change

rate

Figure: 3 most important components in linear partial least square of nsF5.

T. Pevný, J. Fridrich, A. Ker | From Blind to Quantitative Steganalysis 7/23

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Quantitative Steganalysis by Regression

Problem

We seek a function ψ :X 7! [0;1] revealing relationshipbetween location of feature vector and change rate

(X is the feature space).

Function ψ is learned from a set of examplesf(x1;y1); : : : ;(xl ;yl )g ;

xi 2X features of stego image with change rate yi :

Construction of a quantitative steganalyzer is a regressionproblem, for which many tools are available.

This work utilizes

linear ordinary least-square regression,support vector regression.

T. Pevný, J. Fridrich, A. Ker | From Blind to Quantitative Steganalysis 8/23

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Advantages over Prior Art

Prior art

Quantitative steganalyzers are built from heuristic principles andalways rely on full knowledge of embedding algorithm.

Advantages of proposed method

Cookie cutter approach:

1 Find feature set detecting the stego algorithm.2 Create set of training examples (xi ;yi ).3 Use regression to learn dependence between features and

change rate.

The knowledge of embedding mechanism is not needed.

T. Pevný, J. Fridrich, A. Ker | From Blind to Quantitative Steganalysis 9/23

Page 10: From Blind to Quantitative Steganalysis - Department of

Outline

1 Motivation

2 Methodology

3 ExperimentsGeneral resultsDetailed results for Jsteg and nsF5Comparison to previous art

4 Conclusion and Future directions

T. Pevný, J. Fridrich, A. Ker | From Blind to Quantitative Steganalysis 10/23

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Experimental Settings

Quantitative steganalyzers for 8 steganographic methods:JP Hide&Seek, Jsteg, MBS1, MMx, F5 with removedshrinkage (nsF5), OutGuess, Perturbed Quantization (PQ),and Steghide.

Quantitative steganalyzers were constructed by

linear ordinary least-square regression (OLS)support vector regression (SVR).

Single-compressed JPEGs with quality factor 80, all createdfrom 9163 raw images evenly divided into training/testing set.

Random payload between zero and maximum for given imageand algorithm was embedded into images.

274 �calibrated merged features� augmented by number ofnon-zero DCTs.

T. Pevný, J. Fridrich, A. Ker | From Blind to Quantitative Steganalysis 11/23

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Outline

1 Motivation

2 Methodology

3 ExperimentsGeneral resultsDetailed results for Jsteg and nsF5Comparison to previous art

4 Conclusion and Future directions

T. Pevný, J. Fridrich, A. Ker | From Blind to Quantitative Steganalysis 12/23

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Detection Accuracy of MB1 and MMx

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

estimated

change

rate

true change rate

MB1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0 0.05 0.1 0.15 0.2 0.25 0.3estimated

change

rate

true change rate

MMx

Figure: Estimated versus true relative change rate of SVR quantitativesteganalyzers of MB1 and MMx.

T. Pevný, J. Fridrich, A. Ker | From Blind to Quantitative Steganalysis 13/23

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Experimental Results

OLS SVR

Algorithm MAE Bias MAE Bias

JP Hide&Seek 7:91 �10�03 �1:70 �10�04 5:24 �10�03 2:41 �10�04

Jsteg 8:38 �10�03 �5:29 �10�04 1:9 �10�03 2:5 �10�04

nsF5 8:39 �10�03 �5:29 �10�04 4:82 �10�03 �2:51 �10�04

MB1 9:07 �10�03 3:86 �10�05 6:63 �10�03 �1:63 �10�04

MMX 3:25 �10�03 1:58 �10�04 2:70 �10�03 1:08 �10�04

Steghide 3:23 �10�03 2:60 �10�04 2:04 �10�03 1:80 �10�04

PQ 5:69 �10�02 �2:89 �10�03 4:83 �10�02 �3:78 �10�02

OutGuess 2:53 �10�03 1:51 �10�04 2:48 �10�03 3:67 �10�04

Table: Median absolute error (MAE) and bias measured on testing images withrandom payload.

T. Pevný, J. Fridrich, A. Ker | From Blind to Quantitative Steganalysis 14/23

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Outline

1 Motivation

2 Methodology

3 ExperimentsGeneral resultsDetailed results for Jsteg and nsF5Comparison to previous art

4 Conclusion and Future directions

T. Pevný, J. Fridrich, A. Ker | From Blind to Quantitative Steganalysis 15/23

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Compound Error

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0 0.1 0.2 0.3 0.4 0.5

meanabsolute

error

relative number of embedding changes

nsF5Jsteg

-0.002

-0.001

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0 0.1 0.2 0.3 0.4 0.5bias

relative number of embedding changes

nsF5Jsteg

Figure: Median absolute error (MAE) and bias of SVR based estimators ofnsF5 and Jsteg on 21 di�erent �xed embedding change rates.

T. Pevný, J. Fridrich, A. Ker | From Blind to Quantitative Steganalysis 16/23

Page 17: From Blind to Quantitative Steganalysis - Department of

Outline

1 Motivation

2 Methodology

3 ExperimentsGeneral resultsDetailed results for Jsteg and nsF5Comparison to previous art

4 Conclusion and Future directions

T. Pevný, J. Fridrich, A. Ker | From Blind to Quantitative Steganalysis 17/23

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Comparison to Previous Art

0

0.005

0.01

0.015

0.02

0.025

0.03

0 0.1 0.2 0.3 0.4 0.5

meanabsolute

error

relative number of embedding changes

JPairsWBSVR

-0.01

-0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

0 0.1 0.2 0.3 0.4 0.5

bias

relative number of embedding changes

JPairsWBSVR

Figure: Comparison of accuracy of SVR, Jpairs, and Weightednon-steganographic Borders attack (WB) at 21 di�erent �xedembedding change rates on 4563 images from testing set.

T. Pevný, J. Fridrich, A. Ker | From Blind to Quantitative Steganalysis 18/23

Page 19: From Blind to Quantitative Steganalysis - Department of

Outline

1 Motivation

2 Methodology

3 ExperimentsGeneral resultsDetailed results for Jsteg and nsF5Comparison to previous art

4 Conclusion and Future directions

T. Pevný, J. Fridrich, A. Ker | From Blind to Quantitative Steganalysis 19/23

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Conclusion

Conclusion

A solid method to construct quantitative steganalyzer fromfeatures was presented.

Regression is used to learn dependence between features forblind steganalysis and embedding change rate.

Method was demonstrated on 8 JPEG stego-schemes.

For Jsteg, accuracy is at least as good as best targeted attacks.

Distributions of within image and between image error wereestimated � same as of quantitative steganalyzers of LSBreplacement.

T. Pevný, J. Fridrich, A. Ker | From Blind to Quantitative Steganalysis 20/23

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Future Directions

Future directions

Combine existing LSB quant. steganalyzers to improveaccuracy.

Improve control of false positive/false negative rate in targetedblind steganalysis.

Quantitative steganalysis of �1, YASS?

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Within and Between Image Error of Jsteg

Jsteg

Shapiro- Between Within Flips

β Wilk IQR IQR IQR

p > 0:1 �Q(Zcov ) �Q(Zpos ) �Q(Z�ip)

0 � 3.63 0.00 0.00

0.025 90.2% 3.23 1.52 0.28

0.05 89.9% 3.02 1.91 0.39

0.125 90.2% 2.79 2.57 0.59

0.25 89.8% 2.87 3.25 0.78

0.375 90.3% 3.69 3.56 0.87

T. Pevný, J. Fridrich, A. Ker | From Blind to Quantitative Steganalysis 22/23

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Within and Between Image Error of nsF5

nsF5

Shapiro- Between Within Flips

β Wilk IQR IQR IQR

p > 0:1 �Q(Zcov ) �Q(Zpos ) �Q(Z�ip)

0 � 7.74 0.00 0.00

0.025 93.9% 6.99 2.81 0.29

0.05 93.9% 6.79 3.52 0.41

0.125 93.7% 6.93 4.78 0.62

0.25 94.2% 8.31 6.77 0.81

0.375 94.2% 10.63 8.47 0.91

T. Pevný, J. Fridrich, A. Ker | From Blind to Quantitative Steganalysis 23/23


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