Data hiding based Hamming code Speaker: Su Guodong Date: 2019-01-31

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: 289-302. [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: 315-320. [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: 697-706.

Matrix coding-Embedding CodeWord (CW): 1010111 Modified CodeWord : 1000111 Secret message bits: S =1 0 1 z 001 010 011 100 101 110 111 ei 1000000 0100000 0010000 0001000 0000100 0000010 0000001

Matrix coding-Extraction Received Codeword (RCW): 1000111 Secret message bits: S =1 0 1

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

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:

Nearest Covering Code Example: C7 C3

Nearest Covering Code Example: C3:

Nearest Covering Code Example: Secret message bits: S =0 1 1 LSB Example: Decimal digit Secret message bits: S’ =3 Size: 1 7 pixels C3: S’ =3

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

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

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:

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

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

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

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

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

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:

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

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

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

Comparisons

Comparisons

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