1. Chair Professor Chin-Chen Chang Feng Chia University Aug. 2008
A High Payload Steganographic Scheme Based on (7, 4) Hamming Code for Digital Images
Chair Professor Chin-Chen Chang
Feng Chia University
Aug. 2008

2. Data Hiding Hiding system Stego image Cover image
Secret message

3. Cover Carriers
Image
Video
Sound
Text

4. VQ Encoding Index table Original Image Codebook … (120,155,…,80) 11 2 3 4 5 6 7 8 9 10 11 12 13 14 15
(90,135,…,120)
(100,125,…,150) …
Index table
Original Image
(49,117,…,25)
(50,42,…,98)
(20,65,…,110)
Codebook

5. Previous Work of Steganography on VQ
To find the closest pairs

6. d(CW0, CW8) > TH d(CW13, CW14) > TH Unused CW0, CW8, CW13, CW14

7. Encode Index Table CW0, CW8, CW13, CW14 Unused Index Table
Original Image
Index Table
Unused
CW0,
CW8,
CW13,
CW14

8. A secret message: 1 1 1 1 1 1 1 1
Index Table
Secret bits
CW1, CW2,
CW4, CW5
CW6, CW7
CW11, CW3
CW15, CW10
CW12, CW9 1

9. A secret message: 1 1 1 1 1 1 1 1
Index Table
Secret bits
CW1, CW2,
CW4, CW5
CW6, CW7
CW11, CW3
CW15, CW10
CW12, CW9 1

10. A secret message: 1 1 1 1 1 1 1 1
Index Table
Secret bits

11. Zhang and Wang’s Method (Embedding)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 … 5 1 2 3 4 1 2 3 4 1 7 10 4 … 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

12. 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 … 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 … 3 1 2 3 4 1 2 3 4 1 2 1 … 2 4 1 2 3 4 1 2 3 4 4
1 35 … 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
Extracted secret data: 10002
Magic Matrix

13. Sudoku
A logic-based number placement puzzle

14. Sudoku (Cont.) 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)

15. Data Hiding Using Sudoku
- 1
Reference Matrix M

16. Data Hiding Using Sudoku (Embedding) (Cont.)8 7 11 12 79 54 55 20 21 24 10 9
Secret data: …
279
Cover 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 9 7
Stego Image

17. Data Hiding Using Sudoku (Embedding) (Cont.)8 7 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
min. 9 7 14
Stego Image

18. Data Hiding Using Sudoku (Extracting) (Cont.)9 7 14
Stego Image
Extracted data: 279 =

19. Experimental Results

20. Experimental Results (Cont.)
The results of visual quality and Embedding capacity comparisons

21. (7, 4) Hamming Coding Encoding p1 p2 d1 p3 d2 d3 d4 Encoding
d1 d2 d3 d4
Encoding
Data:
d2  d3  d4 = p3
1  0  1 = 0
d1  d2  d4 = p1
1  1  1 = 1
d1  d3  d4 = p2
1  0  1 = 0
p1 p2 d1 p3 d2 d3 d4
Encoded data

22. (7, 4) Hamming Coding (Cont.)
Error Detection
Error bit
Received data:
Correcting
Corrected data:
Error Position
Parity check matrix H

23. Matrix Coding Method Embedding Secret data: 1 1 0 0… 11 10 9 6 3 4 12
Cover Image 10 9 6 3 4 12 11
( )T = (1 1 1)T
Stego Image
0 0 1 
Secret data: …
Parity check matrix H

24. Matrix Coding Method (Cont.)
Extracting 10 9 6 3 4 12 11
Stego Image
( )T = (1 1 0)T
Extracted secret data: …
■ 7 pixels embed 3 bits

25. “Hamming+1” Method Embedding Secret data: 1 1 0 0… 11 10 9 6 3 4 12
Cover Image
( ) mod 2= 1 or
( ) mod 2= 0 12 10 9 6 3 4 8 11
( )T = (1 1 1)T ? =
Stego Image
0 0 1 
Secret data: …
Parity check matrix H

26. “Hamming+1” Method (Cont.)
Extracting 12 10 9 6 3 4 11
Stego Image
( ) mod 2= 0
( )T = (1 1 0)T =
Extracted secret data: …
■ 8 pixels embed 4 bits

27. The Proposed Method G0000 (0000000) (0000001)
( ) :
( )
( )
( )
( )
( )
( )
( )
( )
( ), ( ), ( ), ( ),
( ), ( ), ( ), ( )
G0001
( ), ( ), ( ), ( ),
( ), ( ), ( ), ( )
G0010
( ), ( ), ( ), ( ),
( ), ( ), ( ), ( )
G1111
( ), ( ), ( ), ( ),
( ), ( ), ( ), ( )

28. The Proposed Method (Cont.)
( )T = (1 1 1)T = 710
( )T = (0 1 1)T = 310
( )T = (1 0 1)T = 510
( )T = (0 0 1)T = 110
( )T = (1 1 0)T = 610
( )T = (0 1 0)T = 210
( )T = (1 0 0)T = 410
( )T = (0 0 0)T = 010 H

29. The Proposed Method (Cont.)
Embedding
Secret data: … 7 10 9 6 3 4 12 8 11
G0001
( )T = (1 1 1)T = 710
( )T = (0 1 1)T = 310
( )T = (1 0 1)T = 510
( )T = (0 0 1)T = 110
( )T = (1 1 0)T = 610
( )T = (0 1 0)T = 210
( )T = (1 0 0)T = 410
( )T = (0 0 0)T = 010
Cover Image H 6 11 8 2 4 13
Stego Image

30. The Proposed Method (Cont.)
Extracting 6 11 8 2 4 13
Stego Image
( )T = (1 0 1)T H
Extracted secret: …

31. Experimental Results Each stego image (512512)
carried 262,143 secret bits
(i.e bpp)

32. Experimental Results (Cont.)

33. Conclusions
The proposed steganographic scheme achieves almost double payload (i.e. embedding payload P = 0.99 bpp) with a slightly lower visual quality of stego images (i.e. average PSNR value = 50dB) compared with the related works.
The proposed scheme is suitable for steganographic applications such as online content distribution systems.