1. Information Steganography Using Magic Matrix
Chair Professor Chin-Chen Chang (張真誠)
National Tsing Hua University
National Chung Cheng University
Feng Chia University

2. Introduction Information Hiding Hiding system Stego image Cover image
Secret message

3. Introduction (Cont.)
Cover Carriers
Image
Video
Sound
Text

4. A Simple Steganography Scheme
(120,155,…,80) 1 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. Kim et al.’s Method ： 9 1 2 3 4 5 6 7 8 …

12. Kim et al.’s Method (Embedding)5 8 3 4 7 6 1 2 ： 9 1 2 3 4 5 6 7 8
Cover Image
Cover Image 6 9 7 3 8 1 2 5 4 …
Stego Image
Stego Image

13. Kim et al.’s Method (Embedding)6 9 7 3 8 1 2 5 4 ： 9 1 2 3 4 5 6 7 8
Stego Image
Stego Image …

14. 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 … 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

15. 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

16. Sudoku
A logic-based number placement puzzle

17. 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)

18. The Proposed Method - 1 Reference Matrix M 6 5 1 7 4 8 2 3 9 5 4 6 3 76 3 7 1 2 8
Reference Matrix M

19. The Proposed Method (Embedding) (Cont.)8 7 11 12 79 54 55 20 21 24 10 9
Secret data: …
279
Cover Image 9 7
Stego Image
d( , ) = d((8,4) , (8,7)) =
d( , ) = d((9,7) , (8,7)) =
d( , ) = d((6,8) , (8,7)) =
min.

20. The Proposed Method (Embedding) (Cont.)8 7 11 12 79 54 55 20 21 24 10 9
Secret data: …
279
min.
Cover Image
d( , ) = |11-11|+|15-12|=3
d( , ) = |15-11|+|12-12|=4
d( , ) = |9-11|+|14-12|=4 9 7 11 15
Stego Image

21. The Proposed Method (Extracting) (Cont.)9 7 11 15
Stego Image
Extracted data: 279 =

23. Conclusions
Based on the property of magic matrix, the embedding and the extracting are very simple.
Higher embedding capacity always result in lower stego image quality.