Embedding Data in a Wet Digital Image Using Fully Exploiting Modification Directions Chair Professor Chin-Chen Chang Feng Chia University National Chung Cheng University National Tsing Hua University http://msn.iecs.fcu.edu.tw/~ccc 1

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

F(p1, p2) = (1*p1 + 2*p2) mod (2n+1) Magic Matrix F(p1, p2) = (1*p1 + 2*p2) mod (2n+1) p2 n=2, F(2, 3)=3 255 1 2 3 4 (p1', p2') = (2, 2) s=1 … … 4 3 4 1 2 3 3 1 2 3 4 1 2 4 1 2 3 4 1 2 3 4 1 2 1 2 3 4 … p1 1 2 3 4 255 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., 2006.

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

Data Hiding Using Sudoku (2/8) Property 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. Possible solutions: 6,670,903,752,021,072,936,960 (i.e. ≈ 6.671×1021)

Data hiding using Sudoku (3/8) Review Zhang and Wang’s method (Embedding) Extracting function: 8 7 9 4 79 54 55 11 20 21 12 24 10 Secret data: 1000 1011… p2 255 1 2 3 4 1 2 3 4 1 : : : : : : : : : : : : : 10002 1 35 … 11 2 3 4 1 2 3 4 1 2 3 2 … 10 1 2 3 4 1 2 3 4 1 Cover image … 9 3 4 1 2 3 4 1 2 3 4 3 … 8 1 2 3 4 1 2 3 4 1 2 1 … 7 4 1 2 3 4 1 2 3 4 4 … 6 2 3 4 1 2 3 4 1 2 3 2 7 10 4 … 5 1 2 3 4 1 2 3 4 1 … 4 3 4 1 2 3 4 1 2 3 4 3 … 3 1 2 3 4 1 2 3 4 1 2 1 … 2 4 1 2 3 4 1 2 3 4 4 … 1 2 3 4 1 2 3 4 1 2 3 2 … 1 2 3 4 1 2 3 4 1 Stego image 1 2 3 4 5 6 7 8 9 10 11 … 255 p1 Magic Matrix

Data hiding using Sudoku (4/8) Review Zhang and Wang’s method (Extracting) p2 7 10 4 255 1 2 3 4 1 2 3 4 1 : : : : : : : : : : : : : … 11 2 3 4 1 2 3 4 1 2 3 2 … 10 1 2 3 4 1 2 3 4 1 … 9 3 4 1 2 3 4 1 2 3 4 3 … 8 1 2 3 4 1 2 3 4 1 2 1 Stego image … 7 4 1 2 3 4 1 2 3 4 4 … 1 35 6 2 3 4 1 2 3 4 1 2 3 2 … 5 1 2 3 4 1 2 3 4 1 … 4 3 4 1 2 3 4 1 2 3 4 3 … Extracted secret data: 10002 3 1 2 3 4 1 2 3 4 1 2 1 … 2 4 1 2 3 4 1 2 3 4 4 … 1 2 3 4 1 2 3 4 1 2 3 2 … 1 2 3 4 1 2 3 4 1 p1 1 2 3 4 5 6 7 8 9 10 11 … 255 Magic Matrix

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

Data hiding using Sudoku (Embedding) (6/8) 7 11 12 79 54 55 20 21 24 10 9 Secret data: 011 001 10… 279 Cover Image 7 9 Stego Image min. 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=2.24

Data hiding using Sudoku (Embedding) (7/8) 11 12 79 54 55 20 21 24 10 9 Secret data: 011 001 10… 279 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=2.83 9 14 7 Stego Image min.

Data hiding using Sudoku (Extracting) (8/8) 9 7 14 Stego Image Extracted data: 279 = 011 0012

Magic Matrix t bits per pixel pair r = F(pi, pj) = ((t-1) × pi + t × pj ) mod t2 Duc, K., Chang, C. C., “A steganographic scheme by fully exploiting modification directions,” Technique Report of Feng-Chia University.

Wet Paper Coding Key 1 1 1 Fridrich, J. Goljan, M., Lisonek, P. and Soukal, D.,  “Writing on Wet Paper,” IEEE Transactions on Signal Processing, vol. 53, no. 10, pp. 3923- 3935, 2005   

The important area is marked as wet pixel Wet Paper Coding (2/2) The important area is marked as wet pixel 21 30 30 Cover Image × = ? Random Matrix LSB of Cover Image Secret Data 20 30 31 Stego-image

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

30 35 31 33 34 32 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

Proposed Scheme (1/6) Key Embeddable 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 S = 3, 1, 2, 3, 1, 0, 0

Proposed Scheme (2/6) (p1, p2) = (31, 35), n=2 S=3 x y

Proposed Scheme (3/6) (p1, p2) = (31, 32), n=2 S=1 y x

Proposed Scheme (4/6) (p1, p2) = (33, 32), n=2 S=2

Proposed Scheme (5/6) 33 34 32 35 31 Key 33 34 32 35 31 33 34 32 35 31

r = F(pi, pj) = ((t-1) × pi + t × pj ) mod t2 t=2 33 34 32 35 31 1 4 3 6 5 7 S = 3, 1, 2, 3, 1, 0, 0 2

Experimental Results (1/3) t= 2 (192 Kb) PSNR = 56.18 t = 3 (304 Kb) PSNR = 46.93 Cover Image t = 4 (384 Kb) PSNR = 44.96 t= 6 (496 Kb) PSNR = 38.72 t = 8 (576 Kb) PSNR = 34.58

Experimental Results (2/3)

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. 3923-3935, 2005.

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.