張真誠 逢甲大學 講座教授 中正大學榮譽教授、合聘教授 清華大學合聘教授 可逆與不可逆的信息偽裝術 張真誠 逢甲大學 講座教授 中正大學榮譽教授、合聘教授 清華大學合聘教授

Data Hiding Hiding system Stego image Cover image 1 0 1 0 1 0 0 1 0 1 1 1 1 0 0 Secret message

Zhang and Wang’s Method (Embedding) 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 … 5 1 2 3 4 1 2 3 4 1 7 10 4 … 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

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 … 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 … 3 1 2 3 4 1 2 3 4 1 2 1 … 2 4 1 2 3 4 1 2 3 4 4 1 35 … 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 Extracted secret data: 10002 Magic Matrix

Sudoku A logic-based number placement puzzle

Sudoku (Cont.) 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 - 1 Reference Matrix M

Data Hiding Using Sudoku (Embedding) (Cont.) 8 7 11 12 79 54 55 20 21 24 10 9 Secret data: 011 001 10… 279 Cover 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 9 7 Stego Image

Data Hiding Using Sudoku (Embedding) (Cont.) 8 7 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 min. 9 7 14 Stego Image

Data Hiding Using Sudoku (Extracting) (Cont.) 9 7 14 Stego Image Extracted data: 279 = 011 0012

Experimental Results

(7, 4) Hamming Coding Encoding p1 p2 d1 p3 d2 d3 d4 Encoding d1 d2 d3 d4 Encoding Data: 1 1 0 12 d2  d3  d4 = p3 1  0  1 = 0 d1  d2  d4 = p1 1  1  1 = 1 d1  d3  d4 = p2 1  0  1 = 0 1 0 1 0 1 0 1 p1 p2 d1 p3 d2 d3 d4 Encoded data

(7, 4) Hamming Coding (Cont.) Error Detection Error bit Received data: 1 0 1 0 1 1 1 Correcting Corrected data: 1 0 1 0 1 0 1 Error Position Parity check matrix H

Matrix Coding Method Embedding Secret data: 1 1 0 0… 11 10 9 6 3 4 12 00001011 00001010 00001001 00000110 00000011 00000100 00001100 00001010 00001001 00000110 00000011 00000100 00001100 00001011 Cover Image 10 9 6 3 4 12 11 (1010100)T = (1 1 1)T Stego Image 0 0 1  Secret data: 1 1 0 0… Parity check matrix H

Matrix Coding Method (Cont.) Extracting 10 9 6 3 4 12 11 00001010 00001001 00000110 00000011 00000100 00001100 00001011 Stego Image (0010100)T = (1 1 0)T Extracted secret data: 1 1 0 0… ■ 7 pixels embed 3 bits

Tian’s Method The embedding process Interger Average: 203 209 198 206 201 New Difference: (101b)2 = (1011)2 = (11)10 Difference: 5 = (101)2 Embed Payload b = 1

Tian’s Method (Cont.) Ex: How about embedding “0” Interger Average: 203 208 198 206 201 New Difference: (101b)2 = (1010)2 = (10)10 Difference: 5 = (101)2 Embed b = 0

Tian’s Method (Cont.) The extracting process Interger Average: 203 206 201 209 198 New Difference: (101)2 = (5)10 Difference: 11 = (1011)2 Extract b = 1

Design Philosophy Reversibility: One-to-One (208, 198) e.g. (206, 201) (209, 198) 2. Irreversibility: Many-to-One e.g. (8, 6) (8, 8) (8, 7) (7, 7) (9, 7) 1 8 4 7 1 2 3 6 9 2 2 2 2

Future Directions 1. Wet Paper Secret Message: 110110110011 Protected Region (Cover Image) (Stego Image)

Future Directions 2. Text Steganography 壞的毛病 壞毛病 山東的蘋果 山東蘋果 我的媽媽 我媽媽 壞的毛病 壞毛病 山東的蘋果 山東蘋果 我的媽媽 我媽媽 主要的問題 主要問題 另外的一件事 另外一件事 其他的問題 其他問題 北京的大學 北京大學 3. Video, Voice, 3D model…Steganograhpy