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

Calibration Revisited Jan Kodovský, 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 steganalysis Idea: estimate cover image statistics from the stego image Spatial Spatial JPEG JPEG Original IDCT DCT Reference image Crop image J 1 J 2 Calibrated feature = F ( J 2 ) − F ( J 1 ) Non-calibrated feature = F ( J 1 ) Calibration Revisited 2 / 16

Motivation How well does calibration approximate cover? Experiment: local histograms (average over 6,500 images) 1.0 bpac 0 . 4 Relative frequency of occurence cover nsF5 0 . 3 0 . 2 0 . 1 0 − 4 − 2 0 2 4 Value of the DCT coefficient (2,1) Calibration Revisited 3 / 16

Motivation How well does calibration approximate cover? Experiment: local histograms (average over 6,500 images) 1.0 bpac 0 . 4 Relative frequency of occurence cover nsF5 stego 0 . 3 0 . 2 0 . 1 0 − 4 − 2 0 2 4 Value of the DCT coefficient (2,1) Calibration Revisited 3 / 16

Motivation How well does calibration approximate cover? Experiment: local histograms (average over 6,500 images) 1.0 bpac 0 . 4 Relative frequency of occurence cover nsF5 stego ref. stego 0 . 3 0 . 2 0 . 1 0 − 4 − 2 0 2 4 Value of the DCT coefficient (2,1) Calibration Revisited 3 / 16

Motivation How well does calibration approximate cover? Experiment: local histograms (average over 6,500 images) 0.2 bpac (change rate 0.04) 0 . 4 Relative frequency of occurence cover nsF5 stego ref. stego 0 . 3 0 . 2 0 . 1 0 − 4 − 2 0 2 4 Value of the DCT coefficient (2,1) Calibration Revisited 3 / 16

Motivation How well does calibration approximate cover? Experiment: local histograms (average over 6,500 images) 0.2 bpac (change rate 0.04) 0 . 4 Relative frequency of occurence cover nsF5 stego ref. stego 0 . 3 0 . 2 0 . 1 0 − 4 − 2 0 2 4 Value of the DCT coefficient (2,1) Calibration Revisited 3 / 16

Motivation, cont’d Detectability of the steganographic algorithm YASS [Pevný 2007] - 274 merged features (Pevný Feature Set) SVM machine with Gaussian kernel, 6500 images YASS - 0.11 bpac 1 0 . 8 1 − P MD 0 . 6 0 . 4 0 . 2 calibration 0 0 0 . 2 0 . 4 0 . 6 0 . 8 1 P F A Calibration Revisited 4 / 16

Motivation, cont’d Detectability of the steganographic algorithm YASS [Pevný 2007] - 274 merged features (Pevný Feature Set) SVM machine with Gaussian kernel, 6500 images YASS - 0.11 bpac 1 0 . 8 1 − P MD 0 . 6 0 . 4 0 . 2 no calibration calibration 0 0 0 . 2 0 . 4 0 . 6 0 . 8 1 P F A Calibration Revisited 4 / 16

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 Calibration Revisited 5 / 16

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 ) Calibration Revisited 6 / 16

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 ) Calibration Revisited 6 / 16

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

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

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

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

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

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

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

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

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

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

Proposed Model Feature Space F = median [ F ( rc ) − F ( c )] , m rc M rc = median [ � F ( rc ) − F ( c ) − m rc � ] Calibration Revisited 8 / 16

Proposed Model Feature Space F = median [ F ( rc ) − F ( c )] , m rc M rc = median [ � F ( rc ) − F ( c ) − m rc � ] Calibration Revisited 8 / 16

Proposed Model Feature Space F = median [ F ( rc ) − F ( c )] , m rc M rc = median [ � F ( rc ) − F ( c ) − m rc � ] Calibration Revisited 8 / 16

Proposed Model Feature Space F = median [ F ( rc ) − F ( c )] , m rc M rc = median [ � F ( rc ) − F ( c ) − m rc � ] Calibration Revisited 8 / 16

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

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 Calibration Revisited 9 / 16

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!) Calibration Revisited 9 / 16

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 rs m rc F ( c ) F ( s ) Feature value Calibration Revisited 10 / 16

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 rs m rc F ( c ) F ( s ) Feature value Experiments: easier to observe for larger payloads Calibration Revisited 10 / 16

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 Calibration Revisited 11 / 16

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 ) Feature value m rs Experiments: more frequent than cover estimate Different example: predictor in WS steganalysis Calibration Revisited 11 / 16

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 Calibration Revisited 12 / 16

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 Calibration Revisited 12 / 16

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

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 Revisited 13 / 16

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). Calibration Revisited 13 / 16