Calibration Revisited

Transcription

1 Jan Kodovský, Jessica Fridrich September 7, 2009 / ACM MM&Sec 09 1 / 16

2 What is Calibration? 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 Original image J 1 IDCT Crop DCT JPEG Reference image J 2 Calibrated feature = F(J 2 ) F(J 1 ) Non-calibrated feature = F(J 1 ) 2 / 16

3 Motivation How well does calibration approximate cover? Experiment: local histograms (average over 6,500 images) Relative frequency of occurence bpac nsf5 cover Value of the DCT coefficient (2,1) 3 / 16

4 Motivation How well does calibration approximate cover? Experiment: local histograms (average over 6,500 images) Relative frequency of occurence nsf5 1.0 bpac cover stego Value of the DCT coefficient (2,1) 3 / 16

5 Motivation How well does calibration approximate cover? Experiment: local histograms (average over 6,500 images) Relative frequency of occurence nsf5 1.0 bpac cover stego ref. stego Value of the DCT coefficient (2,1) 3 / 16

6 Motivation How well does calibration approximate cover? Experiment: local histograms (average over 6,500 images) Relative frequency of occurence nsf5 0.2 bpac (change rate 0.04) cover stego ref. stego Value of the DCT coefficient (2,1) 3 / 16

7 Motivation How well does calibration approximate cover? Experiment: local histograms (average over 6,500 images) Relative frequency of occurence nsf5 0.2 bpac (change rate 0.04) cover stego ref. stego Value of the DCT coefficient (2,1) 3 / 16

8 Motivation, cont d Detectability of the steganographic algorithm YASS [Pevný 2007] merged features (Pevný Feature Set) SVM machine with Gaussian kernel, 6500 images 1 YASS bpac PMD calibration P FA 4 / 16

9 Motivation, cont d Detectability of the steganographic algorithm YASS [Pevný 2007] merged features (Pevný Feature Set) SVM machine with Gaussian kernel, 6500 images 1 YASS bpac PMD no calibration calibration P FA 4 / 16

10 Challenges Challenges Goals How exactly does calibration affect detectability of steganographic algorithms? What is the real purpose of calibration? Does it make sense to calibrate all features? Create appropriate model for calibration Quantitative evaluation of the contribution of calibration to steganalysis performance 5 / 16

11 Notation Feature mapping... F : X F Reference transform... r : X X Reference-feature mapping... F r = F r : X F Space of images X Feature space F F x F(x) r F r(x) F r (x) 6 / 16

12 Notation Feature mapping... F : X F Reference transform... r : X X Reference-feature mapping... F r = F r : X F Space of images X Feature space F F x F(x) r F r(x) F r (x) 6 / 16

13 Basic Concept F(c) Feature Space F 0 F(s) F(c),F(s)... original features F r (c),f r (s)... reference features 7 / 16

14 Basic Concept F(c) Feature Space F 0 F(s) non-calibrated features F(c),F(s)... original features F r (c),f r (s)... reference features 7 / 16

15 Basic Concept F(c) F r (c) F r (s) Feature Space F 0 F(s) reference features F(c),F(s)... original features F r (c),f r (s)... reference features 7 / 16

16 Basic Concept F(c) F r (c) F r (s) Feature Space F 0 F(s) calibrated features F(c),F(s)... original features F r (c),f r (s)... reference features 7 / 16

17 Proposed Model Feature Space F F r (s) m q M rs m rs M e F r (c) m rc m e F(s) M c M rc F(c) M s 8 / 16

18 Proposed Model Feature Space F F r (s) m q M rs m rs M e F r (c) m rc m e F(s) M c M rc F(c) M s m e = median [F(s) F(c)], M e = median [ F(s) F(c) m e ] 8 / 16

19 Proposed Model Feature Space F F r (s) m q M rs m rs M e F r (c) m rc m e F(s) M c M rc F(c) M s m rs = median [F(rs) F(s)], M rs = median [ F(rs) F(s) m rs ] 8 / 16

20 Proposed Model Feature Space F F r (s) m q M rs m rs M e F r (c) m rc m e F(s) M c M rc F(c) M s m rc = median [F(rc) F(c)], M rc = median [ F(rc) F(c) m rc ] 8 / 16

21 Proposed Model Feature Space F F r (s) m q M rs m rs M e F r (c) m rc m e F(s) M c M rc F(c) M s m rc = median [F(rc) F(c)], M rc = median [ F(rc) F(c) m rc ] 8 / 16

22 Proposed Model Feature Space F F r (s) m q M rs m rs M e F r (c) m rc m e F(s) M c M rc F(c) M s m rc = median [F(rc) F(c)], M rc = median [ F(rc) F(c) m rc ] 8 / 16

23 Proposed Model Feature Space F m rc = median [F(rc) F(c)], M rc = median [ F(rc) F(c) m rc ] 8 / 16

24 Proposed Model Feature Space F m rc = median [F(rc) F(c)], M rc = median [ F(rc) F(c) m rc ] 8 / 16

25 Proposed Model Feature Space F m rc = median [F(rc) F(c)], M rc = median [ F(rc) F(c) m rc ] 8 / 16

26 Proposed Model Feature Space F m rc = median [F(rc) F(c)], M rc = median [ F(rc) F(c) m rc ] 8 / 16

27 Proposed Model Feature Space F F r (s) m q M rs m rs M e F r (c) m rc m e F(s) M c M rc F(c) M s m rc = median [F(rc) F(c)], M rc = median [ F(rc) F(c) m rc ] 8 / 16

28 Parallel Reference m rc m rc, M rc M rs Calibration can be seen as a constant feature-space shift Calibration causes failure of steganalysis m rc m rs F(c) F(s) Feature value 9 / 16

29 Parallel Reference m rc m rc, M rc M rs Calibration can be seen as a constant feature-space shift Calibration causes failure of steganalysis m rc m rs F(c) F(s) Feature value Experiments: observed often for YASS (robustness!) 9 / 16

30 Cover Estimate Both m rc and m rs are close to cover feature F(c) This stood behind the original idea of calibration Stego-image feature must differ from cover-image feature m rc m rs F(c) F(s) Feature value 10 / 16

31 Cover Estimate Both m rc and m rs are close to cover feature F(c) This stood behind the original idea of calibration Stego-image feature must differ from cover-image feature m rc m rs F(c) F(s) Feature value Experiments: easier to observe for larger payloads 10 / 16

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 m rc m rs F(c) F(s) Feature value Experiments: more frequent than cover estimate 11 / 16

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 m rc F(c) F(s) m rs Feature value Experiments: more frequent than cover estimate Different example: predictor in WS steganalysis 11 / 16

34 Divergent Reference m rc must be different from m rs This situation essentially covers some of the previous ones Works even when F(c) = F(s) m rc m rs F(c) F(s) Feature value 12 / 16

35 Divergent Reference m rc must be different from m rs This situation essentially covers some of the previous ones Works even when F(c) = F(s) m rc m rs F(c) F(s) Feature value Experiments: most frequent scenario Interesting example: histogram of zeros for JSteg 12 / 16

36 Lessons Learned Calibration does not have to approximate cover. Still, it might be benefitial to calibrate. 13 / 16

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

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

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

40 Different Point of View F r Cartesian calibration [F(x),F r(x)] Original calibration F cal (x) = F r(x) F(x) F 14 / 16

41 Different Point of View F r Cartesian calibration [F(x),F r(x)] Original calibration F cal (x) = F r(x) F(x) F How well does Cartesian calibration perform in practice? 14 / 16

42 Cartesian Calibration Improves Steganalysis P E P E Algorithm bpac F F r F [F r,f] Algorithm bpac F F r F [F r,f] nsf JPHS Jsteg YASS YASS YASS YASS Steghide YASS YASS YASS YASS MME Reported values of P E are medians over 5 runs P E = min 1 2 (P FA + P MD ) 1 PMD ROC curve P FA 15 / 16

43 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 16 / 16