UNIVERSAL COUNTER FORENSICS METHODS FOR FIRST ORDER STATISTICS

1. UNIVERSAL COUNTER FORENSICS METHODS FOR FIRST ORDER STATISTICS M. Barni, M. Fontani, B. Tondi, G. Di DomenicoDept. of Information Engineering, University of Siena (IT)

2. Outline • MultiMedia Forensics & Counter-Forensics • Universal counter-forensics • Proposed approach • Application to pixel domain • Application to DCT domain • Results and discussion

3. MM Forensics & Counter-Forensics • MM Forensics: • Goal: investigate the history of a MM content • Rapidly evolving field, but… • Countermeasures are evolving too! • Counter-Forensics: • Goal: edit a content without leaving traces (fingerprints) 01101101001100000011100001 project www.rewindproject.eu

4. Forensics & Counter-Forensics • MM Forensics is evolving rapidly… • Countermeasures are evolving too! • Counter-Forensics goal: allow to alter a content without leaving traces (fingerprints) [K07] M. Kirchner and R. Böhme, “Tamper hiding: Defeating image forensics,” in Information Hiding, ser. Lecture Notes in Computer Science, vol.4567. Springer,2007,pp. 326–341.

5. Universal Counter - Forensics • General idea: • Ifyouknowwhatstatisticisused by the analyst • just adapt the statistic of yourforgery to be veryclose to the statistic of “good” sequences • Any detector based on thatstatisticwill be fooled! • Game Theory: • This scenario can be seenas a game[B12] • Forensic Analyst vs. Attacker • Differentgames are possible: • The adversarydirectlyknow the statistic of the “untouchedsequences” • The adversaryonlyhas a training set of “untouchedsequences” [B12] M. Barni. A game theoretic approach to source identification with known statistics. In Proc. of ICASSP 2012, IEEE Int. Conference on Acoustics, Speech, and Signal Processing, 2012.

6. Outline of the scheme • Fool a detector = force it to misclassify • Approach: make the processed image statistic close to that of (an) untouched image • If it’s close enough… the detector must do a false-positive or a false-negative error • Assumptions: • Analyst’s detector relies only on first order statistics • Adversary has a database (DB) of histograms of untouched images • So the adversary: • Processes the image • Searches the DB for the nearest untouched histogram • Computes a transformation map from one histogram to the another • Applies the transformation, minimizing perceptual distortion

7. Practical applications • We show how the proposed method can be used for two different CF tasks: • Hiding traces left by processing operations in the histogram of pixel values • Hiding traces left by double JPEG compression in the histogram of quantized DCT coefficients • You will notice that switching between different domains do not change the scheme, but just the implementation of each “block”

8. Application #1Conceal traces in the image histogram • We propose a method to conceal traces left by any processing operation in the image histogram • Many detectors exist based on histogram analysis: • Detection of Contrast Enhancement (pixel histogram) [S08] • Detection of double JPEG compression (histograms of DCT coefficients) [B12] • We make no assumptions on the previous processing [S08] M. C. Stamm and K. J. R. Liu. Blind forensics of contrast enhancement in digital images. In Proc. of ICIP 2008, pages 3112–3115, 2008. [B12] T.Bianchi, A.Piva, "Image Forgery Localization via Block-Grained Analysis of JPEG Artifacts", IEEE Transactions on Information Forensics & Security, Volume: 7, Issue: 3 , Page(s): 1003 - 1017

9. Basic notation • Y and hY denote the processed image and its histogram • X and hX denote the untouched image and its histogram • Z and hZ denote the attacked image and its histogram • Γ denotes the set of histograms (in the database) respecting possible constraints imposed by the attacker (e.g: retaining a minimum contrast) • With ν* we always denote the normalized version of the h* histogram

10. Phase 1: histogram retrieval • Goal: search a database of untouched image histograms to find h* such that: • It has the most similar shape w.r.t. hY • It belongs to Γ • We propose to use the Chi-square distance, defined as • Therefore, the retrieved histogram is

11. Phase 2: histogram mapping • Goal: find the best mapping matrix that turns to • number of pixels to be moved from value to • A maximum distortion constraint is given, that avoid changes bigger than of the value of a pixel • We choose the Kullback-Leibler divergence to measure the statistical dissimilarity between the histograms, and yield the following optimization problem: Convex!  Mixed Integer Non Linear Problem 

12. Phase 3: pixel remapping • We have the mapping matrix, but which specific pixels should be changed? • Intuition: editing pixels in textured/high-variance regions causes smaller perceptual impact • We propose an iterative approach: for each couple (i,j) • Evaluate the SSIM map between Z and Y • Find pixels having value i, and: • scan these pixels by decreasing SSIM, change the first n(ij) to j • mark edited pixels as “unchangeable”, repeat 2. for (i, j+1) • If no more pixel of value i have to be remapped, repeat from 1., with (i+1,j) • Remarks • SSIM map evaluated iteratively, to take into account on-going modifications • Obtained image will have, by construction, the desired histogram Pixel Remapping DB

13. Advantage of iterative remapping • If SSIM map is not iteratively computed, visible artifact are likely to appear… With iterative update Without iterative update

14. Experimental validation • We use the proposed technique to hide traces left by: • Gamma-correction • Histogram Stretching (equalization) • Both these operators leave strong traces in image histogram Original GammaCorrected Equalized

15. Histogram Database Remapped image Case study Histogram from DB Processed image (gamma-correction) Original Image Resulting histogram Remapped histogram Best match Search

16. Before Counter-Forensics DB histogram After Counter-Forensics Dmax = 4

17. Histogram enhancement detection • Stamm’s detector [S08] • It detects the peak-and-gap behavior of the histogram • This is done by considering the contribution of high-frequencies in the Fourier transform of the histogram Original Gamma Corrected Equalized [S08] M. C. Stamm and K. J. R. Liu. Blind forensics of contrast enhancement in digital images. In Proc. of ICIP 2008, pages 3112–3115, 2008.

18. Dataset & Experiment setup • Database of untouched histograms from 25.000 JPEG images (MIRFLICKR dataset). Total weigth: ~10MB • Apply gamma-correction and histogram equalization to 1300 images from the UCID dataset • Each processed image is “attacked” with the proposed technique, using {2,4,6} as values for the Dmax constraint • We constrain the database search to histograms whose contrast is not smaller than that of the enhanced image (this is our Γ ) • We evaluate performance of Stamm detector in distinguishing: • Processed vs. untouched images • Processed&Attacked vs. untouched images • We evaluate the similarity between attacked and processed images using: • PSNR (“mathematical” metric) • Structural Similarity Index (“perceptual” metric) [W04]

19. Experimental results • Results in countering detection of gamma-correction Attacked – Processed distance

20. Experimental results • Results in countering detection of histogram equalization Attacked – Processed distance

21. Application #2Conceal traces in the image histogram • Method to conceal traces left by double compression in the histograms of quantized DCT coefficients • Huge number of detectors exploit double quantization, e.g.: • Estimation of previous compression [P08] • Forgery detection [H06] [P08]  T. Pevny and J. Fridrich, “Estimation of primary quantization matrix for steganalysis of double-compressed JPEG images,” Proceedings of SPIE, vol. 6819, pp. 681911–681911–13, 2008 [H06]  J. He, Z. Lin, L. Wang, and X. Tang, “Detecting doctored JPEG images via DCT coefficient analysis,” in Lecture Notes in Computer Science. Springer, 2006, pp. 423–435.

22. Double Quantization • DQ is a sequence of three steps: • quantization with step b • de-quantization with step b • quantization with step a Characteristic gaps

23. More on DQ… • Why is it interesting? • Allows forgery detection • Tells something about thehistory of the content(e.g. fake quality problem) • NOTICE: • Effect is visible when first quantization is stronger than the second • The behavior is observed in the histogram of quantized DCT coefficients • If JPEG compression has been carried, holes are always present in the histogram of de-quantized coefficients

24. More on DCT histograms… • Double JPEG compression leaves the trace in the histogram of each DCT coefficient • How is this histogram calculated? • Intuition: 8x8DCT Coeff.Analysis Block-wise DCT Image Single blocks

25. Perception in the DCT domain • Understand relationship between changes in the DCT domain and effects in the spatial domain • Just Noticeable Difference (JND) => minimum amount of change in a coefficient leading to a visible artifact • Watson defined JND for the DCT case, taking into account Human Visual System (HVS) properties: • More sensitive to low frequencies • Luminance masking: brighter blocks can be changed more • Contrast masking: more contrast allows more editing

26. What we want to do • In this case, traces are left in DCT histograms of quantized coefficients… • We must change these histograms, to make them similar to those of an singly-compressed image! • We need to revisit the previous application to adapt to the DCT domain • More histograms (64 instead of 1) • More variables (coefficients vary from -1024 to 1016) • Less intuitive remapping rules…

27. Histogram retrieval… revisited! • Need all DCT histograms of singly compressed images • Just take some JPEG images and extract them? NO! • DCT histograms depends on the undergone quantization • Search would be practically dominated by this fact • We need to simulate JPEG compressed images: • Take DCT histograms of never-compressed images • During search, quantize each of them with the same factor of the query histogram • Distances may be weighted, to give more importance to low frequency coeffs

28. Histogram mapping… revisited! • The problem is the very same, repeated 64 times • Problem: how to set the perceptual constraint (Dmax)? • Idea: make it depend on JNDs => allow at most the amount of change leading to a JND • Here we cannot exploit local information (luminance/contrast) • Notice: • we’re working on quantized coefficients! • Changes will be expanded after de-quantization! • => Watson’s matrix must be divided by the quantization step

29. Pixel mapping… revisited! • We have to move some DCT coefficients from a value to another… how do we choose them? • We exploit Watson model again • This time, we can exploit local information too • Algorithm: • Evaluate the JND for all blocks; • For each element n(ij) • Find coefficients having value i, and: • scan these coeffs by decreasing JND, change the first n(ij) to j • mark edited coeffsas “unchangeable”, repeat 2. for (i, j+1) • If no more pixel of value i have to be remapped, repeat from 2., with (i+1,j)

30. Does it work so smoothly? • No, it doesn’t • Artifacts show up, probably due to the high number of changed coefficients in high frequencies • Possible solutions • Consider the joint impact of changes in more than one frequency • Anything else? [open question!] • However, most detectors usually rely on low-frequency coefficients • We made some experiments remapping only the first 16 (in zig-zag ordering) coefficients

31. Experimental setup: detector • We implement a detector for double compression based on calibration • Calibration allows toestimate the originaldistribution of a quantizedsignal • Basic idea with JPEG: • Cut small number of rows/columns • Compute 8x8 DCT andhistograms Read from file Estimated

32. Experimental setup: method • 200 TIFF (never compressed) images • Experiment consists in evaluating detector performance before and after counter – attack • Detector evaluated in these tasks: • Discriminate single- vs. double- compressed images • Discriminate single- vs. attacked images • We do not want to cheat • i.e., we do not use threshold values from the first experiment to do classification in the second

33. Experimental results Mean SSIM: 0.968 Mean PSNR: 42.9 dB

34. Conclusions • Our universal CF methods allow to conceal traces left by any processing in the first-order statistic • Evaluation of the effectiveness should probably rely on statistic measures rather than on detectors • Future works: • Explore connections with Optimal Transportation theory • Explore the use on un-quantized DCT coefficients (conceal traces of single compression) • Develop an integrated method to re-compress an image without leaving traces • Explore the use of different objective function for the histogram mapping problem

35. Thank youQuestions? Acknowledgments This work has been supported by the REWIND project