濕影像的資訊隱藏技術

1. 濕影像的資訊隱藏技術 Chair Professor Chin-Chen Chang Feng Chia University National Chung Cheng University National Tsing Hua University http://msn.iecs.fcu.edu.tw/~ccc 1

2. Data Embedding Secrets Secrets Internet Sender ‧Steganography - prison problem ‧Reversible data hiding - Medical image - Militaryimage -Quality and capacity Receiver

3. Magic Matrix (p1', p2') = (2, 2) F(p1, p2) = (1*p1 + 2*p2) mod (2n+1) p2 n=2, F(2, 3)=3 255 0 1 2 3 4 0 s=1 … … 4 3 4 0 1 2 3 3 1 2 3 4 0 1 2 4 0 1 2 3 4 1 2 3 4 0 1 2 0 0 1 2 3 4 … 0 p1 0 1 2 3 4 255 Zhang, X. P. and Wang, S. Z., “Efficient Steganographic Embedding by Exploiting Modification Direction,” IEEE communications letters, vol. 10, no. 11, pp. 1-3, Nov., 2006.

4. Data Hiding Using Sudoku (1/8) Spatial domain data embedding Sudoku A logic-based number placement puzzle

5. Data Hiding Using Sudoku (2/8) Property • A Sudoku grid contains nine 3 × 3 matrices, each contains different digits from 1 to 9. • Each row and each column of a Sudoku grid also contain different digits from 1 to 9. Possible solutions: 6,670,903,752,021,072,936,960 (i.e. ≈ 6.671×1021)

6. Data hiding using Sudoku (3/8)Review Zhang and Wang’s method (Embedding) Extracting function: Secret data:1000 1011… p2 255 0 1 2 3 4 0 1 2 3 4 0 1 10002 1 35 : : : : : : : : : : : : : … 11 2 3 4 0 1 2 3 4 0 1 2 3 2 … 10 0 1 2 3 4 0 1 2 3 4 0 1 0 Cover image … 9 3 4 0 1 2 3 4 0 1 2 3 4 3 … 8 1 2 3 4 0 1 2 3 4 0 1 2 1 … 2 7 4 0 1 2 3 4 0 1 3 4 0 4 … 6 2 3 4 0 1 2 3 4 0 1 2 3 2 … 5 0 1 2 3 4 0 1 2 3 4 0 1 0 … 4 3 4 0 1 2 3 4 0 2 3 4 3 1 … 3 1 2 3 4 0 1 2 3 4 0 1 2 1 … 2 4 0 1 2 3 4 0 1 2 3 4 0 4 … 1 2 3 4 0 1 2 3 4 0 1 2 3 2 … 0 0 1 2 3 4 0 1 2 3 4 0 1 0 Stego image p1 0 1 2 3 4 5 6 7 8 9 10 11 … 255 Magic Matrix

7. Data hiding using Sudoku (4/8)Review Zhang and Wang’s method (Extracting) 135 Extracted secret data: 10002 p2 255 0 1 2 3 4 0 1 2 3 4 0 1 : : : : : : : : : : : : : … 11 2 3 4 0 1 2 3 4 0 1 2 3 2 … 10 0 1 2 3 4 0 1 2 3 4 0 1 0 … 9 3 4 0 1 2 3 4 0 1 2 3 4 3 … 8 1 2 3 4 0 1 2 3 4 0 1 2 1 Stego image … 7 4 0 1 2 3 4 0 1 2 3 4 0 4 … 6 2 3 4 0 1 2 3 4 0 1 2 3 2 … 5 0 1 2 3 4 0 1 2 3 4 0 1 0 … 4 3 4 0 1 2 3 4 0 1 2 3 4 3 … 3 1 2 3 4 0 1 2 3 4 0 1 2 1 … 2 4 0 1 2 3 4 0 1 2 3 4 0 4 … 1 2 3 4 0 1 2 3 4 0 1 2 3 2 … 0 0 1 2 3 4 0 1 2 3 4 0 1 0 p1 0 1 2 3 4 5 6 7 8 9 10 11 … 255 Magic Matrix

8. Data hiding using Sudoku (5/8) - 1 Reference Matrix M

9. Data hiding using Sudoku (Embedding) (6/8) 279 min. d( , ) = ((8-8)2+(4-7)2)1/2=3 d( , ) = ((9-8)2+(7-7)2)1/2=1 d( , ) = ((6-8)2+(8-7)2)1/2=2.24 9 7 Stego Image Secret data:011 001 10… Cover Image

10. Data hiding using Sudoku (Embedding) (7/8) 279 d( , ) = ((11-11)2+(15-12)2)1/2=3 d( , ) = ((15-11)2+(12-12)2)1/2=4 d( , ) = ((9-11)2+(14-12)2)1/2=2.83 min. 9 7 9 14 Stego Image Secret data:011 001 10… Cover Image

11. Data hiding using Sudoku (Extracting) (8/8) Stego Image Extracted data: 279 = 011 0012

12. Magic Matrix tbits per pixel pair r = F(pi, pj) = ((t-1) × pi + t× pj ) mod t2 Duc, K., Chang, C. C., “A steganographic scheme by fully exploiting modification directions,” Technique Report of Feng-Chia University.

13. Color retinal image Segmented image

14. Wet Paper Coding 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 Key Fridrich, J. Goljan, M., Lisonek, P. and Soukal, D.,  “Writing on Wet Paper,” IEEE Transactions on Signal Processing, vol. 53, no. 10, pp. 3923- 3935, 2005

15. Wet Paper Coding (2/2) ? × = 20 30 31 Stego-image The important area is marked as wet pixel 21 30 30 Cover Image Random Matrix LSB of Cover Image Secret Data

16. Wet Paper Coding with XOR Operation 30 35 31 33 34 35 33 33 32 35 34 33 33 35 32 33 Stego-pixels 0 LSB(31) {30} 1 LSB(35) ⊕LSB(31) ⊕ LSB(32) {35, 31, 33} Key Eight groups {31}, {35, 31, 32}, {34, 35, 33}, {32}, {33}, {35, 35}, {33, 33, 34}, {32, 32} Secrets: 0 1 0 1 0 1 1 1 At least one dry pixel

17. 30 35 31 33 34 35 33 33 32 35 34 33 33 35 32 33 Secret Extracting LSB(30) = 0 LSB(35) ⊕LSB(31) ⊕ LSB(33) =1 LSB(34) ⊕LSB(35) ⊕LSB(33) = 0 LSB(33) =1 LSB(32) = 0 LSB(35) ⊕LSB(34) = 1 LSB(33) ⊕LSB(33) ⊕LSB(35)= 1 LSB(32) ⊕LSB(33) = 1

18. Proposed Scheme (1/6) Key • Three types: • Restricted Pairs of Wet Pixels (RPW) • - Non-restricted Pairs of Wet Pixels (NRPW) • - Pairs of Dry Pixels (DP) Embeddable S = 3, 1, 2, 3, 1, 0, 0

19. Proposed Scheme (2/6) y x (p1, p2) = (31, 35), n=2 S=3 (p1', p2') = (33, 35)

20. Proposed Scheme (3/6) x y (p1, p2) = (31, 32), n=2 S=1 (p1', p2') = (31, 31)

21. Proposed Scheme (4/6) (p1, p2) = (33, 32), n=2 S=2 (p1', p2') = (34, 32)

22. Proposed Scheme (5/6) Key 33 35 31 31 33 35 31 31 33 35 31 31 34 35 34 32 34 35 34 32 34 35 34 32 33 35 35 33 33 35 35 33 33 35 35 33 33 34 32 32 33 34 32 32 33 34 32 32

23. 33 35 31 31 34 35 34 32 33 35 35 33 33 34 32 32 r = F(pi, pj) = ((t-1) × pi + t× pj ) mod t2t=2 4 1 5 3 6 7 S = 3, 1, 2, 3, 1, 0, 0 2

24. Experimental Results (1/3) t = 3 (304 Kb) PSNR = 46.93 t= 2 (192 Kb) PSNR = 56.18 Cover Image t = 8 (576 Kb) PSNR = 34.58 t = 4 (384 Kb) PSNR = 44.96 t= 6 (496 Kb) PSNR = 38.72

25. Experimental Results (2/3)

26. Experimental Results (3/3) [3] Fridrich, J., Goljan, M., Lisonek, P. and Soukal, D., “Writing on wet paper,” IEEE Transactions on Signal Processing, vol. 53, no. 10, pp. 3923-3935, 2005.

27. Conclusions A novel steganographic technique with the fully exploiting modification (FEM) is proposed for digital images. The experiments confirm that our proposed scheme can achieve the goals of high capacity and good visual quality.