1. Embedding Data in a Wet Digital Image Using Fully Exploiting Modification Directions
Chair Professor Chin-Chen Chang
Feng Chia University
National Chung Cheng University
National Tsing Hua University 1

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

3. F(p1, p2) = (1*p1 + 2*p2) mod (2n+1)
Magic Matrix
F(p1, p2) = (1*p1 + 2*p2) mod (2n+1) p2
n=2, F(2, 3)=3
255 1 2 3 4
(p1', p2') = (2, 2)
s=1 … … 4 3 4 1 2 3 3 1 2 3 4 1 2 4 1 2 3 4 1 2 3 4 1 2 1 2 3 4 … p1 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: 8 7 9 4 79 54 55 11 20 21 12 24 10
Secret data: … p2
255 1 2 3 4 1 2 3 4 1 : : : : : : : : : : : : :
10002
1 35 … 11 2 3 4 1 2 3 4 1 2 3 2 … 10 1 2 3 4 1 2 3 4 1
Cover image … 9 3 4 1 2 3 4 1 2 3 4 3 … 8 1 2 3 4 1 2 3 4 1 2 1 … 7 4 1 2 3 4 1 2 3 4 4 … 6 2 3 4 1 2 3 4 1 2 3 2 7 10 4 … 5 1 2 3 4 1 2 3 4 1 … 4 3 4 1 2 3 4 1 2 3 4 3 … 3 1 2 3 4 1 2 3 4 1 2 1 … 2 4 1 2 3 4 1 2 3 4 4 … 1 2 3 4 1 2 3 4 1 2 3 2 … 1 2 3 4 1 2 3 4 1
Stego image 1 2 3 4 5 6 7 8 9 10 11 …
255 p1
Magic Matrix

7. Data hiding using Sudoku (4/8) Review Zhang and Wang’s method (Extracting)p2 7 10 4
255 1 2 3 4 1 2 3 4 1 : : : : : : : : : : : : : … 11 2 3 4 1 2 3 4 1 2 3 2 … 10 1 2 3 4 1 2 3 4 1 … 9 3 4 1 2 3 4 1 2 3 4 3 … 8 1 2 3 4 1 2 3 4 1 2 1
Stego image … 7 4 1 2 3 4 1 2 3 4 4 …
1 35 6 2 3 4 1 2 3 4 1 2 3 2 … 5 1 2 3 4 1 2 3 4 1 … 4 3 4 1 2 3 4 1 2 3 4 3 …
Extracted secret data: 10002 3 1 2 3 4 1 2 3 4 1 2 1 … 2 4 1 2 3 4 1 2 3 4 4 … 1 2 3 4 1 2 3 4 1 2 3 2 … 1 2 3 4 1 2 3 4 1 p1 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)7 11 12 79 54 55 20 21 24 10 9
Secret data: …
279
Cover Image 7 9
Stego Image
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

10. Data hiding using Sudoku (Embedding) (7/8)11 12 79 54 55 20 21 24 10 9
Secret data: …
279
Cover Image
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 9 14 7
Stego Image
min.

11. Data hiding using Sudoku (Extracting) (8/8)9 7 14
Stego Image
Extracted data: 279 =

12. Magic Matrix t bits 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. Wet Paper Coding
Key 1 1 1
Fridrich, J. Goljan, M., Lisonek, P. and Soukal, D.,  “Writing on Wet Paper,” IEEE Transactions on Signal Processing, vol. 53, no. 10, pp ,   

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

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

16. 30 35 31 33 34 32
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

17. Proposed Scheme (1/6) Key Embeddable S = 3, 1, 2, 3, 1, 0, 0
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

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

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

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

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

22. r = F(pi, pj) = ((t-1) × pi + t × pj ) mod t2 t=233 34 32 35 31 1 4
3 6 5 7
S = 3, 1, 2, 3, 1, 0, 0 2

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

24. Experimental Results (2/3)

25. 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 , 2005.

26. 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.