Chair Professor ChinChen Chang n National Tsing Hua

基於龜殼魔術矩陣的隱寫技術及 其衍生的研究問題 Chair Professor Chin-Chen Chang (張真誠) n National Tsing Hua University n National Chung Cheng University n Feng Chia University http: //msn. iecs. fcu. edu. tw/~ccc

Introduction n Information Hiding system Cover image Stego image 10101 00101 11100 Secret message 2

Introduction (Cont. ) n Cover Carriers n n Image Video Sound Text 3

A Simple Steganography Scheme (120, 155, …, 80) (90, 135, …, 120) (100, 125, …, 150) … Original Image 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Index table (49, 117, …, 25) (50, 42, …, 98) (20, 65, …, 110) Codebook 4

Previous Work of Steganography on VQ To find the closest pairs 5

d(CW 0, CW 8) > TH d(CW 13, CW 14) > TH CW 0, CW 8, CW 13, CW 14 Unused CW 1 , CW 2 CW 4, CW 5 CW 6, CW 7 1 CW 11 , CW 3 CW 15, CW 10 CW 12, CW 9 0 6

Encode Index Table Original Image CW 0, CW 8, CW 13, CW 14 Unused Index Table

A secret message: 1 0 1 0 0 1 1 1 1 0 0 1 1 0 1 0 0 Index Table CW 1, CW 2, CW 4, CW 5 CW 6, CW 7 1 Secret bits CW 11, CW 3 CW 15, CW 10 CW 12, CW 9 0 0 1

A secret message: 1 0 1 0 0 1 1 1 1 0 0 1 1 0 1 0 0 Index Table CW 1, CW 2, CW 4, CW 5 CW 6, CW 7 1 Secret bits CW 11, CW 3 CW 15, CW 10 CW 12, CW 9 0 0 1

A secret message: 1 0 1 0 0 1 1 1 1 0 0 1 1 0 1 0 0 Index Table Secret bits 0 1

Kim et al. ’s Method ： 9 0 1 2 3 4 5 6 7 8 0 8 6 7 8 0 1 2 3 4 5 6 7 8 0 1 2 3 6 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 4 3 4 5 6 7 8 0 1 2 3 3 0 1 2 3 4 5 6 7 8 0 2 6 7 8 0 1 2 3 4 5 6 1 3 4 5 6 7 8 0 1 2 3 0 0 1 2 3 4 5 6 7 8 9 … 11

Kim et al. ’s Method (Embedding) Cover Image 5 8 8 3 4 8 7 6 8 6 7 7 8 3 1 2 6 3 5 6 8 2 1 5 6 5 4 7 3 5 2 8 6 5 4 3 2 1 5 1 1 2 5 1 3 4 1 6 8 2 3 3 1 6 4 5 8 6 7 8 0 1 2 3 4 5 6 1 8 7 5 3 2 6 3 7 3 4 5 6 7 8 0 1 2 3 9 0 1 2 3 4 5 6 7 8 0 6 0 1 2 3 4 5 6 7 8 0 Cover Image Stego Image ： 6 9 7 3 9 8 7 6 5 6 7 8 0 1 2 3 4 5 6 8 9 7 7 9 3 1 2 4 3 4 5 6 7 8 0 1 2 3 6 3 5 6 8 2 1 5 6 5 4 7 9 5 2 8 3 0 1 2 3 4 5 6 7 8 0 6 5 9 3 2 1 5 1 1 2 5 1 3 4 1 6 8 2 9 3 9 6 4 5 1 8 7 5 3 2 6 9 Stego Image 2 6 7 8 0 1 2 3 4 5 6 1 3 4 5 6 7 8 0 1 2 3 0 0 1 2 3 4 5 6 7 8 0… 0 1 2 3 4 5 6 7 8 9

Kim et al. ’s Method (Embedding) Stego Image 6 9 7 3 9 8 7 6 8 9 7 7 9 3 1 2 6 3 5 6 8 2 1 5 6 5 4 7 9 5 2 8 6 5 9 3 2 1 5 1 8 6 7 8 0 1 2 3 4 5 6 1 2 5 1 3 4 1 6 7 3 4 5 6 7 8 0 1 2 3 8 2 9 3 9 6 4 5 6 0 1 2 3 4 5 6 7 8 0 1 8 7 5 3 2 6 9 5 6 7 8 0 1 2 3 4 5 6 Stego Image ： 9 0 1 2 3 4 5 6 7 8 0 4 3 4 5 6 7 8 0 1 2 3 3 0 1 2 3 4 5 6 7 8 0 2 6 7 8 0 1 2 3 4 5 6 1 3 4 5 6 7 8 0 1 2 3 0 0 1 2 3 4 5 6 7 8 0… 0 1 2 3 4 5 6 7 8 9

Zhang and Wang’s Method (Embedding) Extracting function: p 2 255 : 11 10 9 8 7 6 5 4 3 2 1 0 0 : 2 0 3 1 4 2 0 1 : 3 1 4 2 0 3 1 2 : 4 2 0 3 1 4 2 3 : 0 3 1 4 2 0 3 4 : 1 4 2 0 3 1 4 0 : 2 0 3 1 4 2 0 1 : 3 1 4 2 0 3 1 … … … 2 0 3 1 4 2 0 0 1 2 3 4 5 6 7 8 9 10 11 … 255 Magic Matrix 8 7 9 4 79 54 55 11 20 21 12 24 12 10 10 9 Cover image 7 p 1 7 10 Secret data: 1000 1011… 10002 1 35 4 Stego image 14

Zhang and Wang’s Method (Extracting) p 2 7 7 10 4 Stego image 1 35 255 : 11 10 9 8 7 6 5 4 3 2 1 0 0 : 2 0 3 1 4 2 0 1 : 3 1 4 2 0 3 1 2 : 4 2 0 3 1 4 2 3 : 0 3 1 4 2 0 3 4 : 1 4 2 0 3 1 4 0 : 2 0 3 1 4 2 0 1 : 3 1 4 2 0 3 1 … … … 2 0 3 1 4 2 0 0 1 2 3 4 5 6 7 8 9 10 11 … 255 Extracted secret data: 10002 p 1 Magic Matrix 15

Sudoku n A logic-based number placement puzzle 16

Sudoku (Cont. ) n 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) 17

The Proposed Method 6 5 1 7 4 8 2 3 9 9 3 8 2 5 6 1 7 4 2 4 7 3 1 9 8 6 5 3 2 4 1 9 7 6 5 8 5 7 6 4 8 3 9 2 1 8 1 9 5 6 2 3 4 7 4 6 2 8 7 1 5 9 3 7 8 3 9 2 5 4 1 6 1 9 5 6 3 4 7 8 2 -1 5 4 0 6 3 7 1 2 8 8 2 7 1 4 5 0 6 3 1 3 6 2 0 8 7 5 4 2 1 3 0 8 6 5 4 7 4 6 5 3 7 2 8 1 0 7 0 8 4 5 1 2 3 6 3 5 1 7 6 0 4 8 2 6 7 2 8 1 4 3 0 5 0 8 4 5 2 3 6 7 1 Reference Matrix M 18

The Proposed Method (Embedding) (Cont. ) 8 7 11 12 79 54 55 11 20 21 12 24 12 10 10 9 Secret data: 011 001 10… 279 Cover Image 9 7 Stego Image d( , ) = d((8, 4) , (8, 7)) = d( , ) = d((9, 7) , (8, 7)) = d( , ) = d((6, 8) , (8, 7)) = min.

The Proposed Method (Embedding) (Cont. ) 8 7 11 12 79 54 55 11 20 21 12 24 12 10 10 9 Secret data: 011 001 10… 279 Cover Image d( , ) = 9 7 9 14 Stego Image min. 20

The Proposed Method (Extracting) (Cont. ) 9 7 9 14 Stego Image Extracted data: 279 = 011 0012 21

Proposed Scheme [1/8] The Core of our method… Turtle Shell Based Matrix 22

Proposed Scheme [2/8] 2( 3( 2 4 3 1 2 7 ( 5 ( 2 ( 0 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 2( 23

Proposed Scheme [3/8] … 255 9 8 7 Pixel b 6 5 4 3 2 1 0 2( 3( 2( 6 7 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 0 4 5 1 2 3 4 5 3 6 7 0 1 2 3 7 0 3 4 5 6 7 0 5 6 7 ( 5 ( 2 ( 0 0 2 6 2 4 3 1 2 7 1 2 3 4 5 6 7 0 1 2 3 4 5 6 Pixel a 7 8 9 … 255 24

Proposed Scheme [4/8] 6 7 0 1 2 3 4 5 6 7 4 3 44 8 4 5 6 7 0 1 2 3 4 5 9 7 1 2 3 4 5 6 7 0 5 4 5 6 7 0 1 2 3 4 5 4 2 3 4 5 6 7 0 1 2 3 3 7 0 1 2 3 4 5 6 7 0 2 5 6 7 0 1 2 3 4 5 6 7 0 1 0 0 1 2 3 4 5 6 Pixel a Pixel b 9 3 5 4 4 7 71 80 55 21 64 73 28 83 23 202 57 11 0 1 2 12 30 95 91 9 76 42 19 3 7 55 234 39 27 40 18 0 42 215 89 255 107 59 16 11 6 99 200 64 185 97 21 23 243 2 3 25 101 235 79 57 33 198 211 7 0 1 7 8 9 110 000 111 6 2 0 7 25

Proposed Scheme [5/8] 6 7 0 1 2 3 4 5 6 7 4 4 3 5 6 4 4 0 1 8 4 5 6 7 0 1 2 3 4 5 9 7 71 80 55 2 12 30 7 1 2 3 4 5 6 7 0 1 2 21 64 73 28 95 91 9 76 6 7 0 1 2 3 4 5 6 7 0 83 23 202 42 19 3 7 55 5 4 5 6 7 0 1 2 3 4 5 57 11 234 39 27 40 18 0 4 2 3 4 5 6 7 0 1 2 3 3 7 0 1 2 3 4 5 6 7 0 42 215 89 255 107 59 16 11 99 200 64 185 97 21 23 243 25 101 235 79 57 33 198 211 Pixel b 9 2 5 6 7 0 1 2 3 4 5 6 7 0 1 2 3 0 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 Pixel a 7 8 9 110 000 111 6 2 0 7 26

Proposed Scheme [6/8] 3 6 4 4 5 0 1 7 71 80 55 2 12 30 21 64 73 28 95 91 9 76 83 23 202 42 19 3 7 55 57 11 234 39 27 40 18 0 42 215 89 255 107 59 16 11 99 200 64 185 97 21 23 243 25 101 235 79 57 33 198 211 4 4 6 7 0 1 2 3 4 5 6 7 8 4 5 6 7 0 1 2 3 4 5 9 7 1 2 3 4 5 6 7 0 5 4 5 6 7 0 1 2 3 4 5 4 2 3 4 5 6 7 0 1 2 3 3 7 0 1 2 3 4 5 6 7 0 Pixel b 9 2 5 6 7 0 1 2 3 4 5 6 7 0 1 2 3 0 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 Pixel a 7 8 9 110 000 111 6 2 0 7 27

Proposed Scheme [7/8] 4 4 4 5 7 71 80 55 2 12 30 21 64 73 28 95 91 9 76 83 23 202 42 19 3 7 55 57 11 234 39 27 40 18 0 42 215 89 255 107 59 16 11 99 200 64 185 97 21 23 243 25 101 235 79 57 33 198 211 7 0 1 2 3 4 5 6 7 8 4 5 6 7 0 1 2 3 4 5 9 7 1 2 3 4 5 6 7 0 5 4 5 6 7 0 1 2 3 4 5 4 2 3 4 5 6 7 0 1 2 3 3 7 0 1 2 3 4 5 6 7 0 Pixel b 6 2 5 6 7 0 1 2 3 4 5 6 7 0 1 2 3 0 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 Pixel a 7 8 9 0 2 2 1 3 6 9 110 000 111 6 2 0 7 28

Proposed Scheme [8/8] 4 4 3 6 4 5 2 2 6 7 0 1 2 3 4 5 6 7 8 4 5 6 7 0 1 2 3 4 5 9 7 71 80 55 2 12 30 7 1 2 3 4 5 6 7 0 1 2 21 64 73 28 95 91 9 76 6 7 0 1 2 3 4 5 6 7 0 83 23 202 42 19 3 7 55 5 4 5 6 7 0 1 2 3 4 5 57 11 234 39 27 40 18 0 4 2 3 4 5 6 7 0 1 2 3 3 7 0 1 2 3 4 5 6 7 0 42 215 89 255 107 59 16 11 99 200 64 185 97 21 23 243 25 101 235 79 57 33 198 211 Pixel b 9 2 5 6 7 0 1 2 3 4 5 6 7 0 1 2 3 0 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 Pixel a 7 8 9 110 000 111 6 2 0 7 29

Experimental Results [1/3] 30

Experimental Results [2/3] Table I. Comparisons of PSNRs and ECs of the proposed scheme and reference-tablebased schemes Schemes Images Lena Airplane Boat Elaine House Peppers Baboon Man Average EMD [9] PSNR 52. 12 52. 11 52. 11 EC 1 1 1 1 1 EMD-2 [12] PSNR 50. 86 50. 79 50. 64 50. 67 50. 71 50. 78 50. 69 50. 82 50. 75 EC 1. 37 1. 37 Proposed PSNR 49. 42 49. 39 49. 40 49. 41 49. 40 49. 39 49. 42 49. 40 EC 1. 5 1. 5 PIXEL PAIR 3 4 SECRET 110 31

Experimental Results [3/3] Table II. Comparisons of PSNRs between the proposed scheme and various reference-tablebased schemes Schemes 1 bpp 1. 5 bpp EMD [9] 52. 11 n/a 52. 39 n/a 48. 99 44. 89 50. 68 48. 67 51. 08 47. 83 52. 39 49. 40 EMD-2 [12] Sudoku-S [10] Sudoku. SR [11] HP-PVD [13] Proposed 32

Conclusions & Future Directions [1/2] ■ Conclusions 1. Simple embedding & extracting 2. Goal: Design Philosophy: Embedding Capacity Image Quality 33

Conclusions & Future Directions [2/2] ■ Future directions 1. Reversability 2. Applications-Authentication & Watermarking 3. Optimal Substitution Table Problem (Dynamic Programming, Genetic Algorithm, PSO etc. ) 4. Vector Quantization (VQ) 5. Side Match VQ 6. Generalization: Small Turtle → Big Turtle 7. Formula Derivation f(p 1, p 2)=k 8. Performance Evaluation 9. Steganalysis 34

Questions ? Thank you! 35