### PowerPoint

```1
Matrix Embedding Steganography
Using Linear Block Code
Speaker:陳奕君
Presentation Date:2014/3/26
Outline
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Linear block code
Construct the matrix
Error correction
(7,4) Standard array
Steganography process
Reference
Linear block code
3
Construct the matrix (1/3)

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A： X4⊕X5⊕X6⊕X7 = 0
B： X2⊕X3⊕X6⊕X7 = 0
C： X1⊕X3⊕X5⊕X7 = 0
0
0
1
4
0
1
0
0
1
1
1
0
0
1
0
1
1 1
1 1
0 1
1
2
3
0
4 = 0
5
0
6
7

（systematic form）之HS
0 1 1 1 1 0 0
HS = 1 0 1 1 0 1 0 =
1 1 0 1 0 0 1

Construct the matrix (2/3)
0 1
HS = 1 0
1 1
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1
1
0
1 1 0 0
1 0 1 0 =
1 0 0 1

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HS =
GS =
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1
GS =    = 0
0
0
5
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
1
1
1
1
0
1
Construct the matrix (3/3)
1
G= 0
1
1
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1
1
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1 0 0 1 0 1 1
H= 0 1 0 1 1 1 0
0 0 1 0 1 1 1
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(7,4)標準陣列（Standard Array），4-bit訊息序列 u 有十六種型態
（0000,0001,0010, ……, 1111），碼字c = u
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0000000 1010001 1110010 0100011 0110100 1100101 1000110 0010111 1101000 0111001 0011010 1001011 1011100 0001101 0101110 1111111

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0000000 1010001 1110010 0100011 0110100 1100101 1000110 0010111 1101000 0111001 0011010 1001011 1011100 0001101 0101110 1111111
1000000 0010001 0110010 1100011 1110100 0100101 0000110 1010111 0101000 1111001 1011010 0001011 0011100 1001101 1101110 0111111
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0000001 1010000 1110011 0100010 0110101 1100100 10000111 0010110 1101001 0111000 0011011 1001010 1011101 0001100 0101111 1111110
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Error correction (1/2)
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（binary symmetric channel）中傳輸，而接收到的是一個 r ∈ 2 的向量，可

s = r = (c + e) = 0 + e
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Error correction (2/2)
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1)
2)
3)
4)

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000
100
010
001
110
011
111
101
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0000000
1000000
0100000
0010000
0001000
0000100
0000010
0000001
(7,4) Standard array
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Steganography process
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1 1 0 1 0 0 0
1 0 0 1 0 1 1
0
0
0
1
1
1
0
G=
H= 0 1 0 1 1 1 0
1 1 1 0 0 1 0
0 0 1 0 1 1 1
1 0 1 0 0 0 1

m = 101

110 ⊕ 101 = 011

v ′。 v ⊕ e = v ′ → 1011001 ⊕ 0000100 = 1011101 完成藏密。

v ′ ∙  = m → 1011101 ∙  = 101
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+ parity:3) 的掩護序列更改 1 bit 。
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Reference
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Linear block code ─ http://cnx.org/content/m18174/1.3/
Shu Lin and Daniel J. Costello,
“Error Control Coding – Fundamentals and Applications,”
Second Edition, 2004. (歐亞書局代理)
Todd K. Moon, “Error Correction Coding – Mathematical
Methods and Algorithms” 2005. (全華科技圖書代理)
```