A Generalization of LSB Matching

Source: IEEE Signal Processing Letters, vol. 16, pp. 69-72, 2009Authors: Xiaolong Li, Bin Yang, Daofang Cheng, and Tieyong Zeng

Speaker: Chia-Chun Wu (吳佳駿 )

Date: 2009/9/23

1

Outlines

•Introduction•Related works•The proposed scheme•Experimental results•Conclusion

2

3

Introduction Traditional data hiding

Cover image

Secret data: 0110…

Public channel(Ex: Internet)

Stego-image

SenderSender InterceptorInterceptor

ReceiverReceiver

Secret data: 0110…

Related works

•LSB replacement•LSB matching•LSB matching revisited

4

LSB replacement & LSB matching

Cover pixel

150 (10010110)

151 (10010111)

Stego-pixel

150 (10010110)

151 (10010111)

150 (10010110)

151 (10010111)

“0”

“1”

“0”

“1”

Cover pixel

150 (10010110)

Stego-pixel

150 (10010110)

151 (10010111)

“0”

+1

149 (10010101)

-1

LSB replacement LSB matching

Expected Number of Modifications Per Pixel (ENMPP)

5

ENMPP=1/2=0.5 ENMPP=1/2=0.5

“1”

[4] T. Sharp, “An implementation of key-based digital signal steganography, in Proc. 4th Int. Workshop Information Hiding, 2001, vol. 2137, Springer LNCS, pp. 13–26

Secret bit: “0” or “1”

LSB matching revisited

[5] J. M, “LSB matching revisited,” IEEE Signal Processing Letters, vol. 13, pp.285-287, 2006

Cover pixels

(0110,0111)

Secret bits: “00”, “01”, “10” or “11”

Stego-pixels

“0”

LSB(1+1)=0“00” (y1, y2)=(6,

7)

(0110,0110) “0”

LSB(1+0)=1“01” (y1, y2)=(6,

6)

(0111,0111) “1”

LSB(1+1)=0“10” (y1, y2)=(7,

7)

(0101,0111) “1”

LSB(0+1)=1“11” (y1, y2)=(5,

7)

y1-x1 y2-x2

0 0

0 -1

+1 0

-1 0

ENMPP=3/8=0.375

6

(x1, x2)=(6, 7)=(0110,0111)2

11 2 i

ii y

yLSBw

ii yLSBw

Generalized LSB matching (n=2)•Outline of G-LSB-M

Cover image:

Stego-image:

Secret message: ={0, 1, 2, …, 2n-1)

7

Example of G-LSB-Mn=2 Example: (x1, x2)=(4, 8)

2 22{0,1,2,3} {00,01,10,11}w

1 2 0,2( , )x x x I

1 2 2( , )y y y I

21 2( ) ( 2 )mod 4extf y y y

1 2 1 2 1 2{( , ), ( 1, ), ( , 1)}xA x x x x x x

21 2 1 2( , ) { ( , ) : ( 2 )emb xf x w y y y A y y

x1 x2

(x1+2x2

) (x1+2x2) mod 4

4 8 20 0

5 (+1)

8 21 1

3 (-1) 8 19 3

4 7 (-1)

18 2

4 9 (+1)

22 2

ENMPP=3/8=0.375

8

Secret bits: “00”, “01”, “11” or “10”

mod4 }w

Generalized LSB matching (n=3)n=3

3 22{0,1,2,3,4,5,6,7} {000,001,010,011,100,101,110,111}w

1 2 3 0,3( , , )x x x x I

1 2 3 3( , , )y y y y I

31 2 3( , ) { : ( 2 3 )mod8 }emb xf x w y A x x x w

31 2 3( ) ( 2 3 )mod8extf y y y y

1 2 3 1 2 3 1 2 3

1 2 3 1 2 3 1 2 3

{( , , ), ( 1, , ), ( , 1, ),

( , , 1), ( 1, , 1), ( 1, , 1)}xA x x x x x x x x x

x x x x x x x x x

9

Example of G-LSB-Mn=3, Example: (x1, x2, x3)=(4, 8, 7)

x1 x2 x3 (x1+2x2+3x3) (x1+2x2+3x3) mod

8

4 8 7 41 1

5 (+1) 8 7 42 2

4 9 (+1) 7 43 3

4 8 8 (+1) 44 4

3 (-1) 8 7 40 0

4 7 (-1) 7 39 7

4 8 6 (-1) 38 6

5 (+1) 8 8 (+1) 45 5

3 (-1) 8 6 (-1) 37 5

ENMPP=8/24=0.333 < 0.375

10

Secret bits: “001”, “010”, “011”, “100”, “000”, “111”, “110” or “101”

ENMPP of G-LSB-M

11

Expected Number of Modifications Per Pixel (ENMPP)

The lower bound of ENMPP (1/2)

Theorem Example

• For any integer n>0, let kn be the unique integer determined by

• Lower bound

• n=3, k3=2

1

0 0

2 2 2n nk k

i n i

i i

n n

i i

1 1

0 0

2 2 2

2

n nk ki n i

ni i

n n

n ni k

i i

n

20 1 2

0

3 3 32 2 2 2

0 1 2

1 6 12 19

i

i

n

i

10 1

0

3 32 2 2

0 1

1 6 7

i

i

n

i

1 13

0 0

3 32 2 2 2

10.333

24 3

i i

i i

n

ii i

12

The lower bound of ENMPP (2/2)

13

2271.0lim n

n

Experimental results

•Steganalysis: 5000 images with the size 800×800

14

1. change the color images to gray-scale2. re-sample them with the size from 400 x 400 to 800 x 800

Conclusion•Generalized LSB matching (G-LSB-M)

scheme can reduce the embedding noise while the payload hold

•Each cover pixel changes at most by 1 in the embedding process

•Investigate the lower bound of ENMPP for G-LSB-M scheme

15

Comment

•They need to specially consider the boundary pixels with value 0 or 255: once a pixel value changes from 0 to 1 or from 255 to 256 in the embedding process, they must adjust the cover pixel value from 0 to 1 or from 255 to 254 and restart the embedding operation

16