Calibration Revisited Jan Kodovsk, Jessica Fridrich September 7, - - PowerPoint PPT Presentation

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Calibration Revisited Jan Kodovsk, Jessica Fridrich September 7, - - PowerPoint PPT Presentation

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Calibration Revisited Jan Kodovsk, Jessica Fridrich September 7, 2009 / ACM MM&Sec 09 Calibration Revisited 1 / 16 What is Calibration? 2002 - Calibration introduced (attack on F5) Part of feature extraction procedure for blind

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SLIDE 1

Calibration Revisited

Jan Kodovský, Jessica Fridrich September 7, 2009 / ACM MM&Sec ’09

1 / 16 Calibration Revisited

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SLIDE 2

What is Calibration?

2002 - Calibration introduced (attack on F5) Part of feature extraction procedure for blind steganalysis Idea: estimate cover image statistics from the stego image

JPEG Spatial Spatial JPEG

Crop Original image

J1

Reference image

J2

IDCT DCT

Calibrated feature = F(J2)−F(J1) Non-calibrated feature = F(J1)

2 / 16 Calibration Revisited

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SLIDE 3

Motivation

How well does calibration approximate cover? Experiment: local histograms (average over 6,500 images)

−4 −2 2 4 0.1 0.2 0.3 0.4 Value of the DCT coefficient (2,1) Relative frequency of occurence 1.0 bpac cover nsF5

3 / 16 Calibration Revisited

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SLIDE 4

Motivation

How well does calibration approximate cover? Experiment: local histograms (average over 6,500 images)

−4 −2 2 4 0.1 0.2 0.3 0.4 Value of the DCT coefficient (2,1) Relative frequency of occurence 1.0 bpac cover stego nsF5

3 / 16 Calibration Revisited

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SLIDE 5

Motivation

How well does calibration approximate cover? Experiment: local histograms (average over 6,500 images)

−4 −2 2 4 0.1 0.2 0.3 0.4 Value of the DCT coefficient (2,1) Relative frequency of occurence 1.0 bpac cover stego

  • ref. stego

nsF5

3 / 16 Calibration Revisited

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SLIDE 6

Motivation

How well does calibration approximate cover? Experiment: local histograms (average over 6,500 images)

−4 −2 2 4 0.1 0.2 0.3 0.4 Value of the DCT coefficient (2,1) Relative frequency of occurence 0.2 bpac (change rate 0.04) cover stego

  • ref. stego

nsF5

3 / 16 Calibration Revisited

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SLIDE 7

Motivation

How well does calibration approximate cover? Experiment: local histograms (average over 6,500 images)

−4 −2 2 4 0.1 0.2 0.3 0.4 Value of the DCT coefficient (2,1) Relative frequency of occurence 0.2 bpac (change rate 0.04) cover stego

  • ref. stego

nsF5

3 / 16 Calibration Revisited

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SLIDE 8

Motivation, cont’d

Detectability of the steganographic algorithm YASS [Pevný 2007] - 274 merged features (Pevný Feature Set) SVM machine with Gaussian kernel, 6500 images

0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1 PF A 1 − PMD YASS - 0.11 bpac calibration

4 / 16 Calibration Revisited

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SLIDE 9

Motivation, cont’d

Detectability of the steganographic algorithm YASS [Pevný 2007] - 274 merged features (Pevný Feature Set) SVM machine with Gaussian kernel, 6500 images

0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1 PF A 1 − PMD YASS - 0.11 bpac no calibration calibration

4 / 16 Calibration Revisited

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SLIDE 10

Challenges Challenges

How exactly does calibration affect detectability of steganographic algorithms? What is the real purpose of calibration? Does it make sense to calibrate all features?

Goals

Create appropriate model for calibration Quantitative evaluation of the contribution of calibration to steganalysis performance

5 / 16 Calibration Revisited

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SLIDE 11

Notation

Feature mapping . . . F : X → F Reference transform . . . r : X → X Reference-feature mapping . . . Fr = F ◦ r : X → F

Space of images X Feature space F

x F(x) r(x) F

r(x)

r F F

6 / 16 Calibration Revisited

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SLIDE 12

Notation

Feature mapping . . . F : X → F Reference transform . . . r : X → X Reference-feature mapping . . . Fr = F ◦ r : X → F

Space of images X Feature space F

x F(x) r(x) F

r(x)

r F F

6 / 16 Calibration Revisited

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SLIDE 13

Basic Concept

F(c) F(s)

Feature Space F

F(c), F(s) . . . original features Fr(c), Fr(s) . . . reference features

7 / 16 Calibration Revisited

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SLIDE 14

Basic Concept

F(c) F(s)

Feature Space F

non-calibrated features

F(c), F(s) . . . original features Fr(c), Fr(s) . . . reference features

7 / 16 Calibration Revisited

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SLIDE 15

Basic Concept

F(c) F(s)

Feature Space F

reference features Fr(c) Fr(s)

F(c), F(s) . . . original features Fr(c), Fr(s) . . . reference features

7 / 16 Calibration Revisited

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SLIDE 16

Basic Concept

F(c) F(s)

Feature Space F

calibrated features Fr(c) Fr(s)

F(c), F(s) . . . original features Fr(c), Fr(s) . . . reference features

7 / 16 Calibration Revisited

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SLIDE 17

Proposed Model

Mc Ms F(c) Mrc F(s) Me me Fr(c) Mrs mrc Feature Space F Fr(s) mq mrs

8 / 16 Calibration Revisited

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SLIDE 18

Proposed Model

Mc Ms F(c) Mrc F(s) Me me Fr(c) Mrs mrc Feature Space F Fr(s) mq mrs

me = median [F(s) − F(c)] , Me = median [F(s) − F(c) − me]

8 / 16 Calibration Revisited

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SLIDE 19

Proposed Model

Mc Ms F(c) Mrc F(s) Me me Fr(c) Mrs mrc Feature Space F Fr(s) mq mrs

mrs = median [F(rs) − F(s)] , Mrs = median [F(rs) − F(s) − mrs]

8 / 16 Calibration Revisited

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SLIDE 20

Proposed Model

Mc Ms F(c) Mrc F(s) Me me Fr(c) Mrs mrc Feature Space F Fr(s) mq mrs

mrc = median [F(rc) − F(c)] , Mrc = median [F(rc) − F(c) − mrc]

8 / 16 Calibration Revisited

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SLIDE 21

Proposed Model

Mc Ms F(c) Mrc F(s) Me me Fr(c) Mrs mrc Feature Space F Fr(s) mq mrs

mrc = median [F(rc) − F(c)] , Mrc = median [F(rc) − F(c) − mrc]

8 / 16 Calibration Revisited

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SLIDE 22

Proposed Model

Mc Ms F(c) Mrc F(s) Me me Fr(c) Mrs mrc Feature Space F Fr(s) mq mrs

mrc = median [F(rc) − F(c)] , Mrc = median [F(rc) − F(c) − mrc]

8 / 16 Calibration Revisited

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SLIDE 23

Proposed Model

Feature Space F

mrc = median [F(rc) − F(c)] , Mrc = median [F(rc) − F(c) − mrc]

8 / 16 Calibration Revisited

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SLIDE 24

Proposed Model

Feature Space F

mrc = median [F(rc) − F(c)] , Mrc = median [F(rc) − F(c) − mrc]

8 / 16 Calibration Revisited

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SLIDE 25

Proposed Model

Feature Space F

mrc = median [F(rc) − F(c)] , Mrc = median [F(rc) − F(c) − mrc]

8 / 16 Calibration Revisited

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SLIDE 26

Proposed Model

Feature Space F

mrc = median [F(rc) − F(c)] , Mrc = median [F(rc) − F(c) − mrc]

8 / 16 Calibration Revisited

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SLIDE 27

Proposed Model

Mc Ms F(c) Mrc F(s) Me me Fr(c) Mrs mrc Feature Space F Fr(s) mq mrs

mrc = median [F(rc) − F(c)] , Mrc = median [F(rc) − F(c) − mrc]

8 / 16 Calibration Revisited

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SLIDE 28

Parallel Reference

mrc ≈ mrc, Mrc ≈ Mrs Calibration can be seen as a constant feature-space shift Calibration causes failure of steganalysis

F(c) F(s) mrs mrc

Feature value

9 / 16 Calibration Revisited

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SLIDE 29

Parallel Reference

mrc ≈ mrc, Mrc ≈ Mrs Calibration can be seen as a constant feature-space shift Calibration causes failure of steganalysis

F(c) F(s) mrs mrc

Feature value Experiments: observed often for YASS (robustness!)

9 / 16 Calibration Revisited

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SLIDE 30

Cover Estimate

Both mrc and mrs are close to cover feature F(c) This stood behind the original idea of calibration Stego-image feature must differ from cover-image feature

F(c) F(s)

mrc mrs

Feature value

10 / 16 Calibration Revisited

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SLIDE 31

Cover Estimate

Both mrc and mrs are close to cover feature F(c) This stood behind the original idea of calibration Stego-image feature must differ from cover-image feature

F(c) F(s)

mrc mrs

Feature value Experiments: easier to observe for larger payloads

10 / 16 Calibration Revisited

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SLIDE 32

Eraser

Reference cover and stego features are close to each other Mapping r erases embedding changes F(c) → F(s) must be consistent in terms of direction

F(c) F(s)

mrc mrs

Feature value Experiments: more frequent than cover estimate

11 / 16 Calibration Revisited

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SLIDE 33

Eraser

Reference cover and stego features are close to each other Mapping r erases embedding changes F(c) → F(s) must be consistent in terms of direction

F(c) F(s)

mrc mrs

Feature value Experiments: more frequent than cover estimate Different example: predictor in WS steganalysis

11 / 16 Calibration Revisited

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SLIDE 34

Divergent Reference

mrc must be different from mrs This situation essentially covers some of the previous ones Works even when F(c) = F(s)

F(c) F(s)

mrc mrs

Feature value

12 / 16 Calibration Revisited

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SLIDE 35

Divergent Reference

mrc must be different from mrs This situation essentially covers some of the previous ones Works even when F(c) = F(s)

F(c) F(s)

mrc mrs

Feature value Experiments: most frequent scenario Interesting example: histogram of zeros for JSteg

12 / 16 Calibration Revisited

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SLIDE 36

Lessons Learned

Calibration does not have to approximate cover. Still, it might be benefitial to calibrate.

13 / 16 Calibration Revisited

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SLIDE 37

Lessons Learned

Calibration does not have to approximate cover. Still, it might be benefitial to calibrate. Several different mechanisms may be responsible for a positive effect of calibration.

13 / 16 Calibration Revisited

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SLIDE 38

Lessons Learned

Calibration does not have to approximate cover. Still, it might be benefitial to calibrate. Several different mechanisms may be responsible for a positive effect of calibration. Calibration may have a catastrophically negative effect on steganalysis as well (parallel reference).

13 / 16 Calibration Revisited

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SLIDE 39

Lessons Learned

Calibration does not have to approximate cover. Still, it might be benefitial to calibrate. Several different mechanisms may be responsible for a positive effect of calibration. Calibration may have a catastrophically negative effect on steganalysis as well (parallel reference). How to prevent steganalysis from such failures?

13 / 16 Calibration Revisited

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SLIDE 40

Different Point of View

Fr

[F(x), Fr(x)] Fcal(x) = Fr(x) − F(x)

F

Cartesian calibration Original calibration

14 / 16 Calibration Revisited

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SLIDE 41

Different Point of View

Fr

[F(x), Fr(x)] Fcal(x) = Fr(x) − F(x)

F

Cartesian calibration Original calibration

How well does Cartesian calibration perform in practice?

14 / 16 Calibration Revisited

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SLIDE 42

Cartesian Calibration Improves Steganalysis

PE PE Algorithm bpac F Fr − F [Fr, F] Algorithm bpac F Fr − F [Fr, F] nsF5 0.05 0.361 0.360 0.331 JPHS 0.05 0.306 0.100 0.094 0.10 0.202 0.218 0.177 0.10 0.160 0.066 0.054 0.15 0.100 0.094 0.077 0.15 0.076 0.034 0.022 0.20 0.048 0.040 0.036 0.20 0.039 0.014 0.006 Jsteg 0.02 0.097 0.132 0.083 YASS 1 0.110 0.133 0.317 0.113 0.03 0.042 0.051 0.032 YASS 2 0.051 0.179 0.347 0.164 0.04 0.022 0.021 0.018 YASS 3 0.187 0.102 0.121 0.082 0.05 0.015 0.013 0.010 YASS 4 0.118 0.120 0.303 0.109 Steghide 0.02 0.114 0.127 0.083 YASS 5 0.159 0.075 0.241 0.064 0.03 0.055 0.056 0.043 YASS 6 0.032 0.269 0.342 0.258 0.04 0.031 0.031 0.024 YASS 7 0.078 0.244 0.298 0.225 0.05 0.021 0.015 0.011 YASS 8 0.138 0.211 0.251 0.180 MME3 0.05 0.309 0.310 0.277 0.10 0.187 0.207 0.165 Reported values of PE are medians over 5 runs. 0.15 0.130 0.149 0.107 0.20 0.023 0.017 0.012 PFA 1 − PMD

PE = min 1

2 (PFA + PMD)

ROC curve 15 / 16 Calibration Revisited

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SLIDE 43

Calibration Revisited

Shed more light on how, why, and when calibration works Introduced a new framework capable of both quantitatively and qualitatively capture behaviour of calibration in the feature space Supported our findings experimentally Proposed an improved way of calibration

Extractor of Cartesian-calibrated 274 merged features available http://dde.binghamton.edu/ccmerged

16 / 16 Calibration Revisited