Information Steganography Using Magic Matrix Chair Professor ChinChen

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Information Steganography Using Magic Matrix Chair Professor Chin-Chen Chang (張真誠) n National Tsing Hua

Information Steganography Using Magic Matrix 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

Introduction n Information Hiding system Cover image Stego image 10101 00101 11100 Secret message 3

Introduction (Cont. ) n Cover Carriers n n Image Video Sound Text 4

Introduction (Cont. ) n Cover Carriers n n Image Video Sound Text 4

A Simple Steganography Scheme (120, 155, …, 80) (90, 135, …, 120) (100, 125,

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 5

Previous Work of Steganography on VQ To find the closest pairs 6

Previous Work of Steganography on VQ To find the closest pairs 6

d(CW 0, CW 8) > TH d(CW 13, CW 14) > TH CW 0,

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 7

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

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

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

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

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

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 … 12

Kim et al. ’s Method (Embedding) Cover Image 5 8 8 3 4 8

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

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

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 15

Zhang and Wang’s Method (Extracting) p 2 7 7 10 4 Stego image 1

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 16

Sudoku n A logic-based number placement puzzle 17

Sudoku n A logic-based number placement puzzle 17

Sudoku (Cont. ) n Property • A Sudoku grid contains nine 3 × 3

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) 18

The Proposed Method 6 5 1 7 4 8 2 3 9 9 3

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 19

The Proposed Method (Embedding) (Cont. ) 8 7 11 12 79 54 55 11

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

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. 21

The Proposed Method (Extracting) (Cont. ) 9 7 9 14 Stego Image Extracted data:

The Proposed Method (Extracting) (Cont. ) 9 7 9 14 Stego Image Extracted data: 279 = 011 0012 22

Conclusions n n Based on the property of magic matrix, the embedding and the

Conclusions n n Based on the property of magic matrix, the embedding and the extracting are very simple. Higher embedding capacity always result in lower stego image quality. 24