1 濕影像的資訊隱藏技術 Chair Professor Chin-Chen Chang Feng Chia University National Chung Cheng University National Tsing Hua University 1

2 Secrets Sender Receiver Internet Data Embedding ‧ Steganography - prison problem ‧ Reversible data hiding - Medical image - Military image -Quality and capacity Secrets

… …… 255 p2p2 p1p Magic Matrix Zhang, X. P. and Wang, S. Z., “Efficient Steganographic Embedding by Exploiting Modification Direction,” IEEE communications letters, vol. 10, no. 11, pp. 1-3, Nov., n=2, F(2, 3)=3 s=1 (p 1 ', p 2 ') = (2, 2) F(p 1, p 2 ) = (1*p 1 + 2*p 2 ) mod (2n+1)

4 Data Hiding Using Sudoku (1/8)  Spatial domain data embedding  Sudoku  A logic-based number placement puzzle

5 Data Hiding Using Sudoku (2/8)  Property Possible solutions: 6,670,903,752,021,072,936,960 (i.e. ≈ 6.671×10 21 ) A Sudoku grid contains nine 3 × 3 matrices, each contains different digits from 1 to 9. Each row and each column of a Sudoku grid also contain different digits from 1 to 9.

6 1 2 Data hiding using Sudoku (3/8) Review Zhang and Wang’s method (Embedding) Extracting function: … : … … … … … … … … … … … … :::::::::::: Magic Matrix Cover image Secret data: … Stego image p1p1 p2p2

… : … … … … … … … … … … … … :::::::::::: Magic Matrix Stego image Extracted secret data: p1p1 p2p2 Data hiding using Sudoku (4/8) Review Zhang and Wang’s method (Extracting)

8 Data hiding using Sudoku (5/8) - 1 Reference Matrix M

9 Data hiding using Sudoku (Embedding) (6/8) Cover Image Secret data: … d(, ) = ((8-8) 2 +(4-7) 2 ) 1/2 =3 d(, ) = ((9-8) 2 +(7-7) 2 ) 1/2 =1 d(, ) = ((6-8) 2 +(8-7) 2 ) 1/2 = Stego Image min.

10 Data hiding using Sudoku (Embedding) (7/8) Cover Image d(, ) = ((11-11) 2 +(15-12) 2 ) 1/2 =3 d(, ) = ((15-11) 2 +(12-12) 2 ) 1/2 =4 d(, ) = ((9-11) 2 +(14-12) 2 ) 1/2 = Stego Image min Secret data: …

11 Data hiding using Sudoku (Extracting) (8/8) Stego Image Extracted data: 27 9 =

12 Magic Matrix Duc, K., Chang, C. C., “A steganographic scheme by fully exploiting modification directions,” Technique Report of Feng-Chia University. r = F(p i, p j ) = ((t-1) × p i + t × p j ) mod t 2 t bits per pixel pair

13 Color retinal imageSegmented image

14 Wet Paper Coding Key Fridrich, J. Goljan, M., Lisonek, P. and Soukal, D., “Writing on Wet Paper,” IEEE Transactions on Signal Processing, vol. 53, no. 10, pp , 2005

15 Wet Paper Coding (2/2) Random Matrix LSB of Cover Image Secret Data 2130 Cover Image ×= ? The important area is marked as wet pixel Stego-image

16 Wet Paper Coding with XOR Operation Key Eight groups {31}, {35, 31, 32}, {34, 35, 33}, {32}, {33}, {35, 35}, {33, 33, 34}, {32, 32} At least one dry pixel Secrets: LSB(35) ⊕ LSB( 31) ⊕ LSB(32) 1 {35, 31, 33} LSB(31) 0 {30} Stego-pixels

Secret Extracting LSB(30) = 0 LSB(35) ⊕ LSB(31) ⊕ LSB(33) =1 LSB(34) ⊕ LSB(35) ⊕ LSB(33) = 0 LSB(33) = 1 LSB(32) = 0 LSB(35) ⊕ LSB(34) = 1 LSB(33) ⊕ LSB(33) ⊕ LSB(35)= 1 LSB(32) ⊕ LSB(33) = 1

18 Proposed Scheme (1/6) Key S = 3, 1, 2, 3, 1, 0, 0 Three types: - Restricted Pairs of Wet Pixels (RPW) - Non-restricted Pairs of Wet Pixels (NRPW) - Pairs of Dry Pixels (DP) Embeddable

19 35 (p 1, p 2 ) = (31, 35), n=2 Proposed Scheme (2/6) S=3 (p 1 ', p 2 ') = (33, 35) x y

20 Proposed Scheme (3/6) S=1 (p 1 ', p 2 ') = (31, 31) y x 32 (p 1, p 2 ) = (31, 32), n=2

21 32 (p 1, p 2 ) = (33, 32), n=2 Proposed Scheme (4/6) S=2 (p 1 ', p 2 ') = (34, 32)

Proposed Scheme (5/6) Key

S = 3, 1, 2, 3, 1, 0, r = F(p i, p j ) = ((t-1) × p i + t × p j ) mod t 2 t=2

24 Experimental Results (1/3) t= 2 (192 Kb) PSNR = t = 3 (304 Kb) PSNR = t = 4 (384 Kb) PSNR = t= 6 (496 Kb) PSNR = t = 8 (576 Kb) PSNR = Cover Image

25 Experimental Results (2/3)

26 Experimental Results (3/3) [3] Fridrich, J., Goljan, M., Lisonek, P. and Soukal, D., “Writing on wet paper,” IEEE Transactions on Signal Processing, vol. 53, no. 10, pp , 2005.

27 Conclusions  A novel steganographic technique with the fully exploiting modification (FEM) is proposed for digital images.  The experiments confirm that our proposed scheme can achieve the goals of high capacity and good visual quality.