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A Generalization of LSB Matching

A Generalization of LSB Matching. Source: IEEE Signal Processing Letters , vol. 16, pp. 69-72, 2009 Authors: Xiaolong Li, Bin Yang, Daofang Cheng, and Tieyong Zeng Speaker: Chia-Chun Wu ( 吳佳駿 ) Date: 2009/9/23. Outlines. Introduction Related works The proposed scheme Experimental results

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A Generalization of LSB Matching

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  1. A Generalization of LSB Matching Source: IEEE Signal Processing Letters, vol. 16, pp. 69-72, 2009 Authors: Xiaolong Li, Bin Yang, Daofang Cheng, and Tieyong Zeng Speaker: Chia-Chun Wu (吳佳駿) Date: 2009/9/23

  2. Outlines • Introduction • Related works • The proposed scheme • Experimental results • Conclusion

  3. Introduction • Traditional data hiding Interceptor Sender Secret data: 0110… Secret data: 0110… Public channel (Ex: Internet) Receiver Stego-image Cover image

  4. Related works • LSB replacement • LSB matching • LSB matching revisited

  5. LSB replacement & LSB matching Secret bit: “0” or “1” Expected Number of Modifications Per Pixel (ENMPP) Cover pixel Stego-pixel Cover pixel Stego-pixel 150 (10010110) “0” 150 (10010110) 150 (10010110) “0” 151 (10010111) “1” +1 150 (10010110) 151 (10010111) “1” “0” 150 (10010110) -1 151 (10010111) 149 (10010101) 151 (10010111) “1” LSBreplacement LSBmatching [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

  6. LSB matching revisited Secret bits: “00”,“01”,“10”or “11” (x1, x2)=(6, 7)=(0110,0111)2 Stego-pixels Cover pixels LSB(1+1)=0 (0110,0111) (y1, y2)=(6, 7) “00” “0” LSB(1+0)=1 (0110,0110) (y1, y2)=(6, 6) “01” LSB(1+1)=0 “0” (y1, y2)=(7, 7) (0111,0111) “10” “1” LSB(0+1)=1 (y1, y2)=(5, 7) (0101,0111) “11” “1” [5]J.M,“LSBmatching revisited,” IEEE Signal Processing Letters, vol. 13, pp.285-287, 2006

  7. Generalized LSB matching(n=2) • Outline of G-LSB-M Cover image: Stego-image: ={0, 1, 2, …, 2n-1) Secret message:

  8. Example of G-LSB-M n=2 Example: (x1, x2)=(4, 8) Secret bits: “00”,“01”,“11”or “10”

  9. Generalized LSB matching(n=3) n=3

  10. Example of G-LSB-M n=3, Example: (x1, x2, x3)=(4, 8, 7) Secret bits: “001”,“010”,“011”,“100”,“000”,“111”,“110”or “101”

  11. ENMPP of G-LSB-M Expected Number of Modifications Per Pixel (ENMPP)

  12. 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

  13. The lower bound of ENMPP (2/2)

  14. Experimental results 1. change the color images to gray-scale 2. re-sample them with the size from 400 x 400 to 800 x 800 • Steganalysis: 5000 images with the size 800×800

  15. 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

  16. 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

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