Information Steganography Using Magic Matrix Chair Professor Chin-Chen Chang (張真誠) National Tsing Hua University National Chung Cheng University Feng Chia University http://msn.iecs.fcu.edu.tw/~ccc

Introduction 關帝詩竹 意君東謝不 名立獨青丹 淡葉孤嫌莫 零雕不久終

Introduction Information Hiding Hiding system Stego image Cover image 1 0 1 0 1 0 0 1 0 1 1 1 1 0 0 Secret message

Introduction (Cont.) Cover Carriers Image Video Sound Text

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

Previous Work of Steganography on VQ To find the closest pairs

d(CW0, CW8) > TH d(CW13, CW14) > TH Unused CW0, CW8, CW13, CW14

Encode Index Table CW0, CW8, CW13, CW14 Unused Index Table Original Image Index Table Unused CW0, CW8, CW13, CW14

A secret message: 1 0 1 0 1 0 0 1 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 Index Table Secret bits CW1, CW2, CW4, CW5 CW6, CW7 CW11, CW3 CW15, CW10 CW12, CW9 1

A secret message: 1 0 1 0 1 0 0 1 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 Index Table Secret bits CW1, CW2, CW4, CW5 CW6, CW7 CW11, CW3 CW15, CW10 CW12, CW9 1

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

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

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

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

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 … 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)

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

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

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

Conclusions 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.