Introduction Feature Correction Method (FCM) Experimental results On Completeness of Feature Spaces in Blind Steganalysis Jan Kodovsk´ y Jessica Fridrich September 23 / MM&SEC 2008 Kodovsk´ y, Fridrich On Completeness of Feature Spaces
Introduction Feature Spaces in Blind Steganalysis Feature Correction Method (FCM) Motivation Experimental results Proposed Approach Feature Spaces in Blind Steganalysis In blind steganalysis, the feature set plays the role of a low-dimensional image model . Good low-dimensional models are used for Steganalysis Benchmarking Design of steganographic schemes (blind steganalyzer used as an oracle) For these applications, it is important that the features completely describe natural images e.g., if a stego method preserves the whole feature vector, it should be undetectable using other features. Kodovsk´ y, Fridrich On Completeness of Feature Spaces
Introduction Feature Spaces in Blind Steganalysis Feature Correction Method (FCM) Motivation Experimental results Proposed Approach Motivation Notation: . . . X original space of images, e.g., X = { 0 , . . . , 255 } N × N . . . F low-dimensional feature space f . . . feature map, f : X → F Our goals: Decide whether or not a given feature space F completely describes cover images Ability to refute completeness experimentally Kodovsk´ y, Fridrich On Completeness of Feature Spaces
Introduction Feature Spaces in Blind Steganalysis Feature Correction Method (FCM) Motivation Experimental results Proposed Approach Motivation Space of images X Feature space F c f ( c ) ∼ P f ( c ) f ( s ) ∼ P f ( s ) s c ∼ P c P f ( c ) P f ( s ) s ∼ P s σ decide cover decide stego Kodovsk´ y, Fridrich On Completeness of Feature Spaces
Introduction Feature Spaces in Blind Steganalysis Feature Correction Method (FCM) Motivation Experimental results Proposed Approach Motivation Space of images X Feature space F c f ( c ) ∼ P f ( c ) f ( s ) ∼ P f ( s ) s c ∼ P c P f ( c ) P f ( s ) s ∼ P s σ decide cover decide stego What if P f ( c ) = P f ( s ) ? ⇒ undetectability within the given feature space Kodovsk´ y, Fridrich On Completeness of Feature Spaces
Introduction Feature Spaces in Blind Steganalysis Feature Correction Method (FCM) Motivation Experimental results Proposed Approach Motivation Two possibilities: P c = P s in the original space X perfect steganography (unlikely) P c � = P s in the original space X feature space F is not a complete descriptor of cover images there exists a different feature space F ′ in which P f ′ ( c ) � = P f ′ ( s ) (at least in theory) Kodovsk´ y, Fridrich On Completeness of Feature Spaces
Introduction Feature Spaces in Blind Steganalysis Feature Correction Method (FCM) Motivation Experimental results Proposed Approach Proposed Approach Given the feature space F , we construct a steganographic method that approximately preserves the feature vector ⇒ P f ( c ) ≈ P f ( s ) Feature Correction Method (FCM) If we find a different space F ′ in which the proposed method is detectable ⇒ feature space F is not a complete descriptor of cover images Kodovsk´ y, Fridrich On Completeness of Feature Spaces
Introduction Feature Correction Method (FCM) Feature Correction Method (FCM) Merged Features Experimental results Differential Feature Computation Feature Correction Method (FCM) FCM approximately preserves the entire feature vector . Embedding procedure Split the set of all DCT coefficients D into D e ∪ D c . Embed payload in non-zero coefficients from D e by modifying them by ± 1 while choosing the direction that perturbs the feature vector the least (requires WPCs). Use DCTs from D c to reduce the final distortion even more, using changes by ± 1 and ± 2 . Kodovsk´ y, Fridrich On Completeness of Feature Spaces
Introduction Feature Correction Method (FCM) Feature Correction Method (FCM) Merged Features Experimental results Differential Feature Computation Feature Correction Method (FCM) How to measure distance in feature space? n ( x i − y i ) 2 � → d ( x , y ) = , var i . . . variance of i -th var i feature on covers i = 1 How to split D into D e and D c ? → Experimentally Is it computationally realisable? → Differential feature computation Kodovsk´ y, Fridrich On Completeness of Feature Spaces
Introduction Feature Correction Method (FCM) Feature Correction Method (FCM) Merged Features Experimental results Differential Feature Computation Feature Set Used in Experiments 274 Merged extended DCT and Markov features Global histograms (11) 5 local AC histograms (5 × 11) 11 dual histograms (11 × 9) 193 extended DCT features Variation (1) Blockiness (2) Co-occurence matrix (25) Markov features (81) + calibration (Pevn´ y et al., SPIE 2007) Kodovsk´ y, Fridrich On Completeness of Feature Spaces
Introduction Feature Correction Method (FCM) Feature Correction Method (FCM) Merged Features Experimental results Differential Feature Computation Differential Feature Computation Calculation of feature vector is O ( N ) , where N is number of DCT coefficients We need to update feature vector after every DCT flip Recalculating every time → O ( N 2 ) . . . . . . infeasible Solution: differential feature computation → O ( N ) Example (global DCT histogram): modify DCT coefficient value from d to d + 1: h [ d ] ← h [ d ] − 1 h [ d + 1 ] ← h [ d + 1 ] + 1 Kodovsk´ y, Fridrich On Completeness of Feature Spaces
Introduction Feature Correction Method (FCM) Feature Correction Method (FCM) Merged Features Experimental results Differential Feature Computation Differential Feature Computation Higher order statistics, Markov features: 0 1 0 0 0 0 0 0 -1 1 0 0 0 0 2 0 -1 0 0 1 0 0 0 0 0 -1 1 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 1 1 0 0 0 92 -5 1 0 -1 0 0 0 89 -3 -1 0 1 -1 0 0 0 0 0 2 2 -1 0 0 0 0 0 3 -1 0 -1 0 1 0 0 0 0 0 -1 0 -1 1 0 0 0 0 2 2 1 -1 0 -1 0 0 0 0 0 1 1 0 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 0 0 0 87 -1 2 0 1 0 0 0 83 -1 0 1 0 0 -1 0 0 0 0 4 -2 0 -1 0 0 0 0 -2 -2 2 1 0 1 0 0 0 0 0 -2 1 1 0 0 0 0 0 -1 2 0 0 0 1 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 -1 0 0 Kodovsk´ y, Fridrich On Completeness of Feature Spaces
Introduction Evaluating Security Feature Correction Method (FCM) Experimental Results Experimental results Evaluating Security Blind steganalyzer (Pevn´ y et al., SPIE 2007) SVM machine with Gaussian kernel 6000 images, single compressed 75 % JPEGs, smaller side 512 pixels, grayscale 3500 training and 2500 testing images P FA Detection error (0,1) (1,1) P MD P E = min 1 2 ( P FA + P MD ) P D P FA (0,0) (1,0) Kodovsk´ y, Fridrich On Completeness of Feature Spaces
Introduction Evaluating Security Feature Correction Method (FCM) Experimental Results Experimental results Experimental Results Distortion reduction (0 . 10 bpac, avg. over 6,000 images) 100 % 80 % Distortion reduction 60 % 40 % 20 % 0 % 0 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 |D c | / |D| Kodovsk´ y, Fridrich On Completeness of Feature Spaces
Introduction Evaluating Security Feature Correction Method (FCM) Experimental Results Experimental results Experimental Results Detection error P E (payload 0 . 10 bpac) 0.45 FCM 0.40 Detection error P E 0.35 0.30 nsF5 0.25 0.20 0 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 |D c | / |D| Kodovsk´ y, Fridrich On Completeness of Feature Spaces
Introduction Evaluating Security Feature Correction Method (FCM) Experimental Results Experimental results Experimental Results Character of corrections in D c (payload 0 . 10 bpac) 700 Changes by 1 to zero 600 Changes by 1 from zero Changes by 2 to zero Number of changes changes 500 Changes by 2 from zero by 1 400 300 200 changes by 2 100 0 0 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 |D c | / |D| Kodovsk´ y, Fridrich On Completeness of Feature Spaces
Introduction Evaluating Security Feature Correction Method (FCM) Experimental Results Experimental results Experimental Results Comparison with nsF5 and MMx (for |D c | / |D| = 0 . 10) 0.50 FCM nsF5 MMx 0.40 Detection error P E 0.30 0.20 0.10 diff 0 0 0.05 0.10 0.15 0.20 Payload (in bpac) Kodovsk´ y, Fridrich On Completeness of Feature Spaces
Introduction Evaluating Security Feature Correction Method (FCM) Experimental Results Experimental results Experimental Results Comparison with nsF5 and MMx (for |D c | / |D| = 0 . 10) 0.50 FCM nsF5 MMx 0.40 Detection error P E cropping 0.30 by 4 × 4 0.20 different calibration 0.10 cropping 0 0 0.05 0.10 0.15 0.20 by 2 × 4 Payload (in bpac) Kodovsk´ y, Fridrich On Completeness of Feature Spaces
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