1. A Quadratic-Residue-based Fragile Watermarking Scheme
Chair Professor Chin-Chen Chang
Feng Chia University
National Chung Cheng University
National Tsing Hua University

2. Outline Introduction The proposed scheme Experimental results
Conclusions

3. The Fields of Image Authentication
Media communications
Embedding
Verifying
Authentication code

4. (Tampered areas located Image)
Introduction
Authentication bits:
(Cover Image)
(Watermarked Image)
(Tampered Image)
(Tampered areas located Image)
(Restored Image)

5. Requirements Effectiveness:
Differentiation:
Security:
Recoverability:
Provide a high probability of tamper detection
Can distinguish between an innocent adjustment and replacing or adding features on purpose
Only a selected group of people having a secret key can perform the detection
Can recover back to the correct image from the modification

6. The Proposed Method Three techniques are employed Watermark Generating
Watermark Embedding
Tamper Detecting and Recovering

7. The Proposed Scheme . Embedding Processes … . . .
1. Divide the image into non-overlapping 1x3 blocks 50 60 61
175 30
150 …
100 95
203 90 93 .
. . .

8. The Proposed Scheme 2. Generate authentication bits:
Y = (PM)2e-1 mod N
N = r × s = 13x19 = 247 < 255 (grey-level)
PM = the decimal value of the first pixel’s high nibble
e-1(a randomly chosen modifier)
= the inverse of e mod (r × s), where
Case 1 a: the first element satisfied and
Case 2 b: the first element satisfied and
Case 3 c: the first element satisfied and
Case 4 d: the first element satisfied and

9. The Proposed Scheme Ex: 28 90 93 PM = 1
PM = 1
R = {2 mod r | 1 ≤  ≤ r – 1} = {1, 3, 4, 9, 10, 12}
S = {2 mod s | 1 ≤  ≤ s – 1} = {1, 4, 5, 6, 7, 9, 11, 16, 17}
a = 4, b = 3, c = 5, d = 2
If e = c = 5, then e-1 = 99
Y = (PM)2e-1 mod N = (1)2 × 99 mod 247=99

10. The Proposed Scheme 3. Embed authentication bits into cover pixels28 90 93 28 86 83
(binary representation)
Y = 99

11. The Proposed Scheme Verifying Processes PM = 1 Y = 99 0110 0011
1. Extract PM and the embedded Y 28 86 83
(binary representation)
PM = 1
Y = 99

12. The Proposed Scheme 2. Compute , where t = 0
e = 5 (e = c, c is selected by a pseudo-random number
generator with private key K )
N = 247

13. The Proposed Scheme = 1 PM = 1 3. Verify 12 mod 247 = 12 mod 247
 pass (Otherwise, mark this block as tampered block)

14. The Proposed Scheme
Recovering Processes n1 n2 n3
P(n1,n2,n3)

15. Recovering Processes . … . . . x1 = P(61, 175, 203) = 6150 60 61
175 30
150 …
100 95
203 x1 x2 x3 .
. . .
x1 = P(61, 175, 203) = 61
x2 = P(175, 30, 61) = 144
x3 = P(30, 150, 144) = 36

16. Experimental Results
Original Images (512 X 512)

17. Experimental Results
Modified Images (512 X 512)

18. Experimental Results

19. Experimental Results

20. 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   

21. 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

22. 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}

23. 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

24. Conclusions
Simple
Efficient
Good stego image quality

25. Thanks for your listening~