1. Some Novel Steganographic Methods for Digital Images
Chin-Chen Chang
Chair Professor, Feng Chia University;
Honorary Professor, National Chung Cheng University
Hopewell Appointed Professor, National Tsing Hua University

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

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

4. Mielikainen’s Method Embedding
(gi, gi+1) = (8, 7) = ( , )
0  1 = 1
Secret data: (b1, b2) =
(0, 1)  (gi’, gi+1’) = (gi, gi+1) = (8, 7)
(0, 0)  (gi’, gi+1’) = (gi, gi+1-1) = (8, 6)
(1, 0)  (gi’, gi+1’) = (gi-1, gi+1) = (7, 7)
(1, 1)  (gi’, gi+1’) = (gi+1, gi+1) = (9, 7)
( , )
( , )
( , )
( , )
(gi, gi+1) = (8, 7) = ( , )
Extracting
0  1 = 1
Extracted secret data: 0 1

5. 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

6. 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

7. Sudoku
A logic-based number placement puzzle

8. 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)

9. Data Hiding Using Sudoku
- 1
Reference Matrix M

10. 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

11. 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

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

13. Data Hiding Using Sudoku Method (Experimental Results)

14. Data Hiding Using Sudoku Method (Experimental Results) (Cont.)

15. Data Hiding Using Sudoku Method (Experimental Results) (Cont.)
(b) Zhang and Wang’s method method
(a) Mielikainen’s method
(c) Data hiding using Sudoku

16. (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

17. (7, 4) Hamming Coding (Cont.)
Error Detection
Error bit
Received data:
Correcting
Corrected data:
Error Position
Parity check matrix H

18. 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

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

20. “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

21. “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: …
PS. 8 pixels embed 4 bits

22. Group of (7, 4) Hamming Codes
( )
( )
( ) :
( )
( )
( )
( )
( )
( )
( )
( )
( ), ( ), ( ), ( ),
( ), ( ), ( ), ( )
G0001
( ), ( ), ( ), ( ),
( ), ( ), ( ), ( )
G0010
( ), ( ), ( ), ( ),
( ), ( ), ( ), ( )
G1111
( ), ( ), ( ), ( ),
( ), ( ), ( ), ( )

23. Group of (7, 4) Hamming Codes (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

24. Group of (7, 4) Hamming Codes (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

25. Group of (7, 4) Hamming Codes (Cont.)
Extracting 6 11 8 2 4 13
Stego Image
( )T = (1 0 1)T H
Extracted secret: …

26. Group of (7, 4) Hamming Codes (Experimental Results)
Each stego image (512512)
carried 262,143 secret bits
(i.e bpp)

27. Group of (7, 4) Hamming Codes (Experimental Results) (Cont.)

28. Group of (7, 4) Hamming Codes (Experimental Results) (Cont.)
(b) The pixel histogram of the stego image generated by the “Hamming+1” scheme
(a) The pixel histogram of the stego image generated by the matrix coding scheme
(c) The pixel histogram of the stego image generated by the proposed scheme

29. Thank you very much for
your attention !!