1. Data hiding based Hamming code
Speaker: Su Guodong
Date:

2. Outline Matrix coding [1] Nearest covering code [2] Hamming+1 [3]
Comparisons
[1] Westfeld A., “F5—a steganographic algorithm,” International workshop on information hiding. Springer, Berlin, Heidelberg, 2001:
[2] Chang C. C., Chou Y. C., “Using nearest covering codes to embed secret information in grayscale images,” Proceedings of the 2nd international conference on Ubiquitous information management and communication. ACM, 2008:
[3]Zhang W., Wang S., Zhang X., “Improving embedding efficiency of covering codes for applications in steganography,” IEEE Communications Letters, 2007, 11(8).
[4] Kim C., Yang C. N., “Improving data hiding capacity based on hamming code,” Frontier and Innovation in Future Computing and Communications. Springer, Dordrecht, 2014:

3. Matrix coding-Embedding
CodeWord (CW):
Modified CodeWord :
Secret message bits: S =1 0 1 z
001
010
011
100
101
110
111 ei

4. Matrix coding-Extraction
Received Codeword (RCW):
Secret message bits: S =1 0 1

5. Matrix coding-Extraction
The 7-bit codeword can carry 3 secret bits by changing at most 1 bit
Embedding Rate:
Embedding efficiency:

6. Nearest Covering Code Classification rule:
First, a reference data prepared for secret data embedding is constructed by classifying all possible combinations of seven bits into eight classes C0, C1, ..., C7.
Classification rule:

7. Nearest Covering Code
Example: C7 C3

8. Nearest Covering Code
Example:
C3:

9. Nearest Covering Code Example: Secret message bits: S =0 1 1
LSB
Example:
Decimal digit
Secret message bits: S’ =3
Size: pixels
C3:
S’ =3

10. Nearest Covering Code Example: Secret message bits: S =0 1 1
LSB
Secret message bits: S =0 1 1
Secret message bits: S’ =3

11. Nearest Covering Code
The 7-bit Codeword can carry 3 secret bits by changing at most 1 bit

12. Hamming+1
It embeds k+1 bits into 2k pixel using at most change one bit.
(1,8,3): 8 pixels can carry 4 bits message by changing one bit at most.
LSB
Secret message bits:

13. Hamming+1----Example for embedding
Secret message bits:
LSB
0 change to 1 1

14. Hamming+1----Example for embedding
Secret message bits:
LSB

15. Hamming+1----Example for embedding
Secret message bits:

16. Hamming+1----Example for extraction
LSB
Secret message bits:

17. Hamming+1
The 8-bit Codeword can carry (3+1) secret bits by changing at most 1 bit

18. Hamming+3----Embedding
It embeds k+3 bits into 2k -1 pixels using at most change 2 bits.
(1,7,3): 7 pixels can carry 6 bits message by changing 2 bits at most.
LSB
Secret message bits:

19. Hamming+3--Embedding
Secret message bits:
2LSB
LSB

20. Hamming+3----Extraction
2LSB
LSB
Secret message bits:

21. Hamming+3
The 7-bit codeword can carry (3+3) secret bits by changing at most 1 bit

22. Comparisons

23. Comparisons

24. Thanks!