Robust Undetectable Interference Watermarks

1. Robust Undetectable Interference Watermarks Ryszard Grząślewicz (WUT) Mirosław Kutyłowski (WUT) Jarosław Kutyłowski (HNI) Wojciech Pietkiewicz (WUT)

2. Introduction • Motivation • undetectable watermarks cannot be detected in an image • only the owner can prove his rights to an image using a secret private key • not suited for web crawlers • Key features of our scheme • watermarks encoded in spatial domain • resistant against attack preserving distance between points (filtering, rotation, JPEG compression) • resistance against some attacks changing distance between points • watermark can be reconstructed from a small part of image • original image not needed for reconstruction • large computational effort for reconstruction needed

3. Physical motivation • Interference – Young‘s experiment

4. Scheme overview

5. Construction of simple interference image 1 2 3 4 • Watermark image • all black with some white points • white points are light source • set of white points

6. Construction of simple interference image • Interference image • interference image is placed at distance on top of watermark image • each “light source” from influences each point of interference image • distance and determine strengthof influence • this is approximation of real physicalinterference image • drawback: visible pattern

7. Construction of encrypted interference image • Interference image • consider the influence of one point from • previously it influenced a point at distance with • a ring at distance consists of cells of size • intensity of each cell defined by value of hash function • the angle is taken modulo – repetition of the same sequence • key is needed for computation of values • interference image does not containvisible patterns

8. Scheme overview

9. Reconstruction of watermark • General idea • determine the intensity of each point of the watermark image • take the watermarked image (cover image + interference image) • generate interference image for point • compare them • if there is strong “similarity” – assign a high value Low similarity small pixel value High similarity large pixel value Example with simple interference image not with encrypted – usually the encrypted would be used watermarked image interference image for

10. Reconstruction of watermark • Idea (continued) • look for the highest valued points • check whether these points form a valid watermark • use equilateral triangles • certain number of triangles of specific edge length must be found to form a watermark • Properties • for the points actually in • there will be a large similarity between the watermarked image and the interference image • there are points to check • for each point operations are needed to compare the images • key is needed for reconstruction

11. Reconstruction of watermark • Additional operations • the reconstruction must be repeated for all rotations with degree • this yields resistance against rotations of the image • the scale factor of the image must be determined • take a small part of the image • there should be at least one “white point” from in this part • check different scale factors and perform reconstruction of this image part for it • determine scale factor with largest peak value – this peak corresponds to a white point from the watermark • perform full reconstruction with this scale factor

12. Experimental results • Evaluation against StirMark 3 • 77 of 89 tests passed • Cropping – all passed • Removing rows/columns – only lighter one passed • Flip – all passed • Scaling – all passed • Change aspect ratio – all passed • Rotation with cropping – for rotation smaller than 30% passed • Rotation with cropping and scalling – for rotation smaller than 30% passed • Shearing – only simple ones passed • Linear transformations – not passed • StirMark – not passed • Gaussian filtering – all passed • Sharpening – all passed • Median filtering – all passed • LRAttack – all passed • JPEG compression – all passed

13. Conclusions • Results • robustness against attacks basing on filtering and local editionsof image shown • robustness against some linear transformations (rotating, scaling) shown • Further work • methods for detection of general linear transformations needed • methods for detection of nonlinear transformations needed

14. Thank you for your attention!