EFFICIENT IMAGE STEGANOGRAPHY APPROACHES BASED ON …

EFFICIENT IMAGE STEGANOGRAPHY APPROACHES

BASED ON MIX COLUMN TRANSFORM TECHNIQUE

BY

WAFAA MUSTAFA ABDUALLAH

A thesis submitted in fulfillment of the requirement for the

degree of Doctor of Philosophy in Information and

Communication Technology

Kulliyyah of Information and

Communication Technology

International Islamic University Malaysia

MAY 2015

ii

ABSTRACT

Steganography is the science of hiding a secret message in cover media, without any

perceptual distortion of the cover media. Using steganography, information can be

hidden in the carrier items such as images, videos, sounds files, text files, while

performing data transmission. In image steganography field, it is a major concern of

the researchers how to improve the capacity of hidden data into host image without

causing any statistically significant modification. In this work, a novel orientation for

data hiding within transform domain of the color images is presented, which is

represented with two schemes: Data Hiding Approach based on Mix Column

Transform (DHAMCT) and Enhanced Data Hiding Approach based on Mix Column

Transform (EDHAMCT). The novelty of these schemes comes from the use of Mix

Column Transform (MCT) technique in image data hiding which is an essential step

of Advanced Encryption Standard (AES) algorithm. These proposed schemes can hide

large amount of information without affecting the imperceptibility aspect of the stego-

image and at the same time, they increase the security level of the system by using

some novel method for embedding based on a distinct type of transform - called Mix

Column Transform. The proposed schemes are based on dividing an image into

blocks, then applying the proposed transform on these blocks and hiding the secret

message within those. The results and comparisons have proven the ability of the

proposed schemes in balancing among the three critical properties for any

steganography system: embedding capacity, security, and imperceptibility.

iii

خلاصة البحثABSTRACT IN ARABIC

دون اي تشويه غطاء لنقل البيانات في رسالة سريةعلم اخفاء المعلومات هو علم اخفاء . باستخدام اخفاء المعلومات فانه من الممكن ان يتم اخفاء المعلومات في انواع لغطاءادراكي ل

مختلفة من النواقل مثل الصور ومقاطع الفيديو والملفات الصوتية والملفات النصية اثناء اداء عملية نقل المعلومات. في مجال اخفاء المعلومات بالصور, فان مسألة تحسين سعة البيانات

صورة المضيفة دون التسبب في اي تغيير احصائي واضح للصورة المضيفة يعتبر المخبأة في المصدر قلق رئيسي لمعظم الباحثين في هذا المجال.توجه جديد لإخفاء البيانات ضمن مجال التحويل للصور الملونة تم تقديمه في هذا العمل متمثلا بطريقتين: نهج اخفاء البيانات على

و تحسين نهج اخفاء البيانات على اساس مزيج تحويل العمود. اساس مزيج تحويل العمود حداثة هاتين الطريقتين تاتي من استخدام تقنية مزيج تحويل العمود في مجال اخفاء البيانات بالصور في حين انها تمثل خطوة اساسية من خطوات خوارزمية التشفير المتقدم . ان هاتين

ء كمية كبيرة من المعلومات بدون التأثير على دقة الصورة الطريقتين المقترحتين بامكانهما اخفاالمخفية وفي الوقت نفسه، فانها تزيد من المستوى الأمني للنظام باستخدام بعض الطرق الجديدة المبنية على اساس نوع مميز من التحويل يدعى مزيج تحويل العمود.اساس الطرق

ومن ثم تطبيق التحويل المقترح على هذه المقترحة يعتمد على تقسيم الصورة الى مجاميع، المجاميع ليتم اخفاء الرسالة السرية فيها. وقد اثبتت النتائج والمقارنات قدرة الطرق المقترحة على تحقيق التوازن بين الخصائص الثلاثة الهامة لأي نظام اخفاء البيانات: سعة التضمين،

الأمنية، والدقة.

iv

APPROVAL PAGE

The dissertation of Wafaa Mustafa Abduallah has been approved by the following:

________________________

Al-Sakib Khan Pathan

Supervisor

________________________

Abdul Monem S. Rahma

Co Supervisor

________________________

Internal Examiner

________________________

External Examiner

________________________

External Examiner

_________________________

Chairman

v

DECLARATION

I hereby declare that this research is the result of my own investigations, except where

otherwise stated. I also declare that it has not been previously or concurrently

submitted as a whole or in part for any other degrees at IIUM or any other institutions.

Wafaa Mustafa Abduallah

Signature………………………… Date…………………………

vi

INTERNATIONAL ISLAMIC UNIVERSITY MALAYSIA

DECLARATION OF COPYRIGHT AND AFFIRMATION OF

FAIR USE OF UNPUBLISHED RESEARCH

Copyright © 2014 by Wafaa Mustafa Abduallah. All rights reserved.

EFFICIENT IMAGE STEGANOGRAPHY APPROACHES

BASED ON MIX COLUMN TRANSFORM TECHNIQUE

I hereby affirm that the International Islamic University Malaysia (IIUM) holds all

rights in the copyright of this work and henceforth any reproduction or use in any

form or by means whatsoever is prohibited without the written consent of IIUM. No

part of this unpublished research may be reproduced, stored in a retrieval system, or

transmitted, in any form or by means, electronic, mechanical, photocopying,

recording or otherwise without prior written permission of the copyright holder.

Affirmed by Wafaa Mustafa Abduallah

…………………… ……………………

Signature Date

vii

DEDICATION

I'd like to dedicate this work to:

The memory of my dear and lovely father…

My mother's tears of sadness and her endless tiredness…

My beloved brother and sisters…

All my friends and relatives…

Anyone get benefit from this thesis…

viii

ACKNOWLEDGEMENTS

First of all, thanks to Allah for giving me the strength and confidence to complete this

work and realize my goals.

I would like to express my sincere gratitude to my supervisor, Dr. Al-Sakib

Khan Pathan, for his valuable guidance, In addition to the enthusiastic encouragement

and support he rendered to me in each stage of my research.

I am very grateful to my co-supervisor Prof. Abdul Monem S. Rahma

(University of Technology, Baghdad, Iraq) for his valuable suggestions and

comments.

My sincere gratefulness is to my brother and teacher (Dr. Subhi R. M.

Zeebaree) for his helpful discussions and continuous support during the progress of

the work.

My special thanks to my beloved family for their support, encouragement and

love throughout my life. I am indebted to my dear mother, my lovely brother (Dakhaz)

and my sisters. I couldn’t reach what I have achieved in my life without their

sacrifices.

I would like to thank all my relatives and friends for their continuous support.

Finally, I am thankful to all who taught me, helped me, and criticized me

during achieving this work.

ix

TABLE OF CONTENTS

Abstract .................................................................................................................... ii Abstract in Arabic .................................................................................................... iii Approval Page .......................................................................................................... iv

Declaration ............................................................................................................... v Copyright Page ......................................................................................................... vi

Dedication ................................................................................................................ vii Acknowledgements .................................................................................................. viii

List of Tables ........................................................................................................... xi List of Figures .......................................................................................................... xiii List of Abbreviations ............................................................................................... xv

CHAPTER ONE: INTRODUCTION ................................................................. 1 1.1 Introduction............................................................................................. 1 1.2 Steganography ........................................................................................ 2

1.2.1 Steganography Requirements ....................................................... 4

1.2.2 Steganalysis ................................................................................... 6 1.2.3 Steganography Applications ......................................................... 10

1.3 Problem Statements ................................................................................ 11 1.4 Objectives ............................................................................................... 13

1.5 Contributions to the Field ....................................................................... 14 1.6 Limitation of the study............................................................................ 15

1.7 Outline of the Thesis ............................................................................... 15

CHAPTER TWO: LITERATURE REVIEW .................................................... 17 2.1 Review of the Past Works....................................................................... 17 2.2 Spatial Domain Techniques .................................................................... 17

2.2.1 The Least Significant Bit .............................................................. 17 A. The Least Significant Bit Replacement: .................................. 18

B. The Least Significant Bit Matching: ........................................ 21 2.2.2 Optimal Pixel Adjustment ............................................................. 23 2.2.3 Pixel Value Differencing: ............................................................. 25

2.2.4 Other Schemes Based On Spatial Domain: ................................... 28 2.3 Transform Domain Techniques: ............................................................. 31

2.3.1 Discrete Cosine Transform: .......................................................... 31 2.3.2 Fourier Transform: ........................................................................ 37

2.3.3 Wavelet Transform: ...................................................................... 40 2.3.4 Contourlet Transform .................................................................... 47 2.3.5 Other Types of Transform Methods .............................................. 51 2.3.6 Combination of Transform Methods ............................................. 53

2.4 Gaps in the Previous Methods ................................................................ 55

CHAPTER THREE: MATHEMATICAL BACKGROUND BEHIND

THE PROPOSED SCHEMES .............................................................................. 57 3.1 Introduction............................................................................................. 57 3.2 Finite Fields ............................................................................................ 57

x

3.3 Arithmetic with Polynomials .................................................................. 58 3.4 Irreducible Polynomials .......................................................................... 65 3.5 Mix Column Transform .......................................................................... 66

3.6 Huffman Coding ..................................................................................... 69

CHAPTER FOUR: RESEARCH METHODOLOGY ...................................... 76 4.1 Introduction............................................................................................. 76 4.2 The Elaboration of the Proposed Mechanism ......................................... 76

4.2.1 Text Coding................................................................................... 77 4.2.2 Cover Image Preprocessing Stage................................................. 78 4.2.3 Embedding Stage .......................................................................... 79 4.2.4 Extraction Stage ............................................................................ 86

4.3 Illustrative Examples .............................................................................. 89 4.3.1 Example of DHAMCT Approach ................................................. 89 4.3.2 Example of EDHAMCT Approach............................................... 93

4.4 Security Improvement ............................................................................ 97 4.4.1 Cover Selection Mechanism ......................................................... 98 4.4.2 Secret Key Sharing........................................................................ 98

CHAPTER FIVE: EXPERIMENTAL RESULTS ............................................ 100 5.1 Introduction............................................................................................. 100

5.2 Research Environment ............................................................................ 100 5.3 Selected Requirements ........................................................................... 102 5.4 Implemented Results .............................................................................. 102

5.4.1 Implemented Results Using DHAMCT Approach ....................... 103 5.4.2 Implemented Results Using EDHAMCT Approach ..................... 108

5.5 Analysis of Implemented Results ........................................................... 119 5.5.1 Analysis of Implemented Results related to the

Imperceptibility and Capacity ...................................................... 119 5.5.2 Analysis of Implemented Results Related to Security .................. 121 5.5.3 Analysis of Robustness against Well-Known Steganalysis

Attacks .......................................................................................... 122

5.6 Comparison with Other Works ............................................................... 123 5.6.1 Comparison in Terms of Imperceptibility and Capacity ............... 123 5.6.2 Comparison in Terms of Security ................................................. 128

CHAPTER SIX: CONCLUSIONS AND FUTURE DIRECTIONS ................ 131

REFERENCES ....................................................................................................... 134

APPENDIX A EXAMPLE CALCULATION FOR DHAMCT APPROACH ... 144 APPENDIX B EXAMPLE CALCULATION FOR EDHAMCT

APPROACH ................................................................................ 149 APPENDIX C EXAMPLE CALCULATION FOR FINDING INVERSE

MATRIX...................................................................................... 154 APPENDIX D IMPLEMENTED RESULTS OF EDHAMCT APPROACH

USING (3 AND 4) LSB .............................................................. 164 APPENDIX E PUBLICATIONS DURING PHD RESEARCH ......................... 184

xi

LIST OF TABLES

Table No. Page No.

2.1 Gaps in the Previous Studies 56

3.1 Elements of 𝐺𝐹(23) 59

3.2 Addition in 𝐺𝐹(2) 60

3.3 Multiplication in 𝐺𝐹(2) 60

3.4 Using Primitive Polynomial (11) 61

3.5 Using Primitive Polynomial (13) 62

3.6 Polynomial Arithmetic Modulo(𝑥3 + 𝑥 + 1)(Stallings, 2003) 63

3.7 List of Irreducible Polynomials (Ruskey, n.d.). 65

3.8 Occurrence of letters with their frequency as generated by the U.S.

Supreme Court in a set of opinions (Wayner, 2009). 71

3.9 The codes as formed from Table 3.8 (Wayner, 2009). 71

4.1 The Results of multiplying (16×18) in GF using different Irreducible

Polynomials (I.P.) 99

5.1 Results of preprocessing stage for the standard images. 102

5.2 Maximum embedding capacity for DHAMCT Approach 103

5.3 Partial embedding rates for DHAMCT Approach 104

5.4 The Transform and Inverse Matrices that are used in the experiments

of 5.5 and 5.6 109

5.5 Maximum embedding capacity for EDHAMCT Approach using (2

LSB) 110

5.6 Partial embedding rates for EDHAMCT Approach using (2 LSB) 114

5.7 Results of the Proposed approach as Comparative with other

methods based spatial domain 125

5.8 Average PSNR values of the Proposed approach as Comparative

with Reference (Sajedi & Jamzad, 2010) 126

xii

5.9 Results of the Proposed approach as Comparative with Reference

(Lin, 2012) 126

5.10 Comparison of the proposed approach with DWT and IWT 127

5.11 Experimental Results of detecting hidden data using HUGO, WOW

and the proposed steganographic approaches with different

embedding rates. 129

xiii

LIST OF FIGURES

Figure No. Page No.

1.1 The illustration of prisoners' problem 4

1.2 Confusion matrix 10

2.1 The flowchart of the proposed information embedding (Sun et al.,

2012). 20

2.2 The steps of data hiding procedure (Sabeti et al., 2013). 22

2.3 The process of data embedding (Pandian & Thangavel, 2012) 24

2.4 A clarification of the data hiding process introduced by (Wu & Tsai,

2003) 26

2.5 Embedding steps of PVD presented by (Luo et al., 2011) 27

2.6 The steps of embedding procedure (Yu et al., 2007) 30

2.7 The block diagram of the encoding stage (Amiruzzaman et al., 2009) 32

2.8 The proposed data embedding phase (Wang et al., 2013) 36

2.9 The conceptual model of the optimized algorithm (Khashandarag et

al., 2011) 38

2.10 The flowchart of hiding process proposed by (Shejul & Kulkarni,

2010) 43

2.11 Embedding steps for the scheme presented by (Raja et al., 2008) 45

2.12 The block diagram for the proposed system used by (Mohan &

Anurenjan, 2011) 50

3.1 Summary of the axioms that define the field (Stallings, 2003). 58

3.2 Multiplication of (5) by (6) in GF(23) using 𝑚(𝑥)=11 61

4.1 General Structure for applying the proposed approaches. 77

4.2 Determination of the Inverse of Galois Field matrix. 81

4.3 The explanation of the reserved bits for security purpose. 82

4.4 The Embedding Process. 83

xiv

4.5 The flowchart of Embedding Steps_ Part1 84

4.6 The flowchart of the Embedding Steps _ Part2 85

4.7 The Extraction Process. 86

4.8 The flowchart of Extraction Steps_ Part1 87

4.9 The flowchart of Extraction Steps _ Part2 88

5.1 Sample of the secret message. 101

5.2 Test images used for the proposed approaches. 101

5.3 PSNR values vs. Different Embedding Rates using DHAMCT

approach 105

5.4 MSSIM values VS. Different Embedding Rates using DHAMCT

approach 105

5.5 Embedding Consumed time versus different Embedding Rates using

DHAMCT approach 106

5.6 Results of using Maximum embedding capacity with DHAMCT

Approach 107

5.7 Results of applying Maximum embedding capacity with EDHAMCT

Approach using (2 LSB) and Block order=2 111

5.8 PSNR Values VS. Block Orders with Maximum embedding capacity

for EDHAMCT approach using (2 LSB) 112

5.9 MSSIM VS. Block Order with Maximum embedding capacity for

EDHAMCT approach using (2 LSB) 112

5.10 Embedding Consumed Time VS. Block Order with Maximum

embedding capacity for EDHAMCT approach using (2 LSB) 113

5.11 PSNR Values VS. Embedding rates for different Block Orders with

Partial embedding rates for EDHAMCT Approach using (2 LSB) 117

5.12 MSSIM VS. Embedding rates for different Block Orders with Partial

embedding rates for EDHAMCT Approach using (2 LSB) 118

5.13 Embedding Duration Time VS. Embedding rates for different Block

Orders with Partial embedding rates for EDHAMCT Approach using

(2 LSB) 118

5.14 The cover and payload images that are depended by Reference (Raja

et al., 2008) 127

xv

LIST OF ABBREVIATIONS

DSP Digital Signal Processing

PSNR Peak Signal to Noise Ratio

dB Decibel

MSE Mean Square Error

MSSIM Mean Structural Similarity

RGB Red-Green-Blue

LDA Linear Discriminant Analysis

FLD Fisher Linear Discriminant

NDA Nonlinear Discriminant Analysis

SVM Support Vector Machines

TP True positive

FN False negative

TN True negative

FP False positive

DICOM Digital Imaging and Communications In Medicine

JPEG Joint Photographic Experts Group

MCT Mix Column Transform

DHAMCT Data Hiding Approach based Mix Column Transform

EDHAMCT Enhanced Data Hiding Approach based Mix Column Transform

LSB Least Significant Bit

ENMPP Expected Number of Modifications Per Pixel

WAM Wavelet Absolute Moment

G-LSB-M Generalized LSB Matching

SDCS Sum And Difference Covering Set

CBL Complexity Based LSB Matching

OPA Optimal Pixel Adjustment

MM Matrix embedding

PVD Pixel Value Differencing

DES Data Encryption Standard

HUGO High Undetectable steGO

SPAM Subtractive Pixel Adjacency Matrix

WOW Wavelet Obtained Weights

DCT Discrete Cosine Transform

DWT Discrete Wavelet Transform

AC Alternative Current coefficients

DC Direct Current coefficients

SIS Statistically Invisible Steganography

ME Matrix Encoding

BPP Bit Per Pixel

DFT Discrete Fourier Transform

APM Adaptive Phase Modulation

LZW Lempel–Ziv–Welch

LFSR Linear Feedback Shift Register

IDFT Inverse Discrete Fourier Transform

SI Secret Information

CSFH Coefficients Selection and Frequency hopping

PN Pseudo random Number

FFT Fast Fourier Transform

FRFT Fractional Fourier Transform

xvi

WFRFT Weighted Fractional Fourier Transform

IWT Integer Wavelet Transform

GA Genetic Algorithm

OPAP optimal pixel adjustment process

YCbCr Luminance; Chroma Blue; Chroma Red

HVS Human Visual System

MRT Magnetic Resonance Tomography

DHT Discrete Hadamard Transform

SVD Singular Value Decomposition

RC4 Ron's Code Cryptographic algorithm

SV Singular Values

GF Galois Field

XOR exclusive-OR

AES Advanced Encryption standard

TXL Text Length

BR Block Order

TMB Total number of Blocks

TIS Transformed Image Size

UP Unused Pixels

KeyLen Key Length

SC Security Code

STM Standard Transform Matrix

RTM Random Transform Matrix

AP Approach

TXLBin Text Length in Binary

IMC Image Block

TXLC Text Length for each Channel

TXC Text Counter

IMS Image Size

PX Counter for Pixels

SB Secret Bits

CSB Coded Secret Bit

Bbit B-channel in bits

BbitLen Length of Bbit vector

CB Check Bit

SBC Secret Bit Counter

SBV Secret Bit Vector

I.P. Irreducible Polynomial

PC Personal Computer

CPU Central Processing Unit

GHz Gigahertz

GB Giga Byte

TB Tera Byte

Ver. Version

IPVD improved version of PVD

TIFF Tagged Image File Format

NRCS Natural Resources Conservation Service

UCID Uncompressed Color Image Database

RBF Radial Basis Function

1

CHAPTER ONE

INTRODUCTION

1.1 INTRODUCTION

Internet has become significantly important in today’s life. It is generally used for data

transfer though currently what concerns its users the most is the security of the data

transferred via the Internet. In fact, for many government organizations, business

industries, and individuals, it has become increasingly important to secure the

information exchanged in bulk while making use of cyber space (El-Alfy & Al-Sadi,

2012). The reason why questions of cybersecurity or those of online privacy have

brought the issue of secret writing into limelight is the fact that the social, economic

and professional lives of the masses today are heavily dependent on emailing, net

posting, electronic banking, e-commerce, etc. (Conway, 2003).

Steganography does the wonder of hiding the presence of the secret

information. This is unlike cryptography, where alterations are made to the message,

thus rendering it unreadable to an adversary or a third party (El-Alfy & Al-Sadi,

2012). Hence, it can be said that “Steganography and cryptography are cousins in the

spy craft family”. A message is scrambled by cryptography which makes it

unintelligible. Steganography, on the other hand, makes a message invisible (i.e., that

is the objective) by hiding it. The encrypted text may cause doubt in the mind of the

recipient but the invisibility of text created by steganography never creates any doubt

(Johnson & Jajodia, 1998).

In steganography, the secret message is concealed using a cover medium (i.e.,

carrier) before it is transmitted on a public communication channel. It therefore,

impedes the unauthorized access to the message and protects its confidentiality.

2

Before the application of steganography for increasing the security level and reduction

in the amount of data to be embedded, the secret message can be encrypted or

compressed. As a result, this may minimize the perceived artifacts in the carrier image

(note: the carrier object can be text, video, or audio too) (El-Alfy & Al-Sadi, 2012).

In this thesis, distinct image steganography techniques are proposed for

providing acceptable level of security with relatively high embedding rate to be used

for any secret communication. The efficiency of the schemes are proven by evaluating

the quality of the image after embedding the secret information as well as by assessing

the level of security through applying one of the most powerful steganalysis

techniques.

1.2 STEGANOGRAPHY

In the field of information security, steganography is a considerably important

domain. This makes one recall one’s childhood when one would allow the paper to

dry after writing on it with lemon juice. This in fact resulted in the disappearance of

the written text. On heating the paper, the text would reappear magically on a piece of

paper which was apparently blank. This may be taken as an illustration of

steganography. Precisely, steganography is the science of secret writing or writing the

messages within other messages for the purpose of secrecy (Conway, 2003). Hence,

Steganography is basically used for secrecy when it comes to communication between

two parties. In the actual phenomenon, a carrier file contains the secret information in

a way that any change to the appearance of the carrier file is not identified by naked

eye. Originally, the etymology of the word ‘steganography’ comes from two Greek

words: ‘steganos’ meaning ‘covered’ and ‘graptos’ which connotes ‘writing’.

Steganography, in various forms, has been in use for thousands of years. In ancient

3

Greece, the heads of message bearers would be shaved for the messages to be written

on them. The hair would be allowed to grow up once the message would be written

after which the message would be taken by the messenger whose head was once again

shaved by the recipient of the message (Cole & Krutz, 2003; Swain & Lenka, 2012).

The same way of delivering secret messages was used during World War II.

Steganography has become digital with the advent of computer power, the Internet

with emerging Digital Signal Processing (DSP), coding theory, and information

theory. An atmosphere of corporate vigilance is created in the digital world by the

virtue of steganography. Since then, various interesting applications have

mushroomed up and the development is ongoing (Swain & Lenka, 2012).

Simmons (1984) described the first mode of steganography regarding it as

prisoners' problem. Alice and Bob were the two prisoners taken up by Simmons as

they wished to craft an escape plan. The communication between the two prisoners

was done through a warden named Wendy who would keep an eye on the entire

communication. Alice and Bob were to be put into isolation cells if they were ever

suspected by Wendy for plotting an escape plan in the course of their communication.

In this connection, cryptography was of no use to the two prisoners as any encrypted

message could create suspicion in the warden’s mind. In order to deceive the warden

thus, Alice and Bob had to make their messages innocuous looking called (covers).

This way, all that the warden could see were only the messages that were

unremarkable in their content (Böhme, 2010; Blasco et al., 2012). It was thus

imperative for the prisoners to frame their messages using inconspicuous cover text

(Böhme, 2010).

Both the parties were therefore bound to communicate in a way that would not

arouse suspicion in Wendy’s mind. A subliminal channel had to be set up for this.

4

This could be done by hiding meaningful information into some harmless message.

For instance, Bob could send a picture to Alice as explained in Figure 1.1. Without

drawing Wendy’s attention, the colors would transmit information (Katzenbeisser &

Petitolas, 2004).

Figure 1.1 The illustration of prisoners' problem

1.2.1 Steganography Requirements

In order to evaluate the performance of a steganographic technique, there are three

common requirements: security, capacity, and imperceptibility (Böhme, 2010; Li et

al., 2011).

Security: Steganography is susceptible to various active and passive attacks. A

steganography is considered secure under a certain steganalytic system if the presence

of a secret message is estimated with a probability not greater than ‘random guessing’.

Otherwise, it is considered insecure.

Capacity: In any steganographic technique, capacity is a critical part. Within a

steganographic technique, the hiding capacity should be at the highest possible level.

This may be given with absolute measurement such as, the size of secret message, or

5

with a value that is relative (e.g., data embedding rate, for instance, bits per pixel, bits

per non-zero discrete cosine transform coefficient, or the ratio of the secret message to

the cover-medium, etc.).

Imperceptibility (quality of the image): There should not be any visual artifacts in

stego-images. The higher the fidelity of the stego-image is, the better it is within the

same level of security and capacity. Consequently, if the resultant stego-image is

considerably innocuous, one may assume that the requirement of imperceptibility is

fulfilled well for a possessor which does not have the original cover-image for

comparison.

Peak Signal-to-Noise-Ratio (PSNR) is the measurement used primarily for testing the

image quality of any steganographic technique. This is what is commonly used in

image-processing research. The PSNR is estimated in decibel (dB) and is defined as

(Yu et al., 2007):

PSNR = 10 × log10(2552

MSEavg) … (1.1)

MSE =1

hw∑ ∑ (xij − yij)

2wj=1

hi=1 … (1.2)

Where, the width and height of the images are respectively denoted by 𝑤and ℎ. The

value of pixel [i, j], in the original and the processed images, is denoted by xij and yij

respectively.

MSEavg =MSER+MSEG+ MSEB

3 … (1.3)

Where, (MSER, MSEG, and MSEB) are Mean Square Errors in the three channels; Red,

Green, and Blue respectively.

Mean Structural Similarity (MSSIM) is yet another measure for assessing

image quality (Wang et al., 2004). So, the perceived visual quality of an image is

approximated more through this measure than PSNR or any other measure. Values are

6

taken in [0, 1] in MSSIM index which increases with an increase in quality. As far as

color images are concerned, MSSIM is extended using the simplest way. This is

achieved through calculating the MSSIM index of each RGB channel after which the

average is taken (Roussos & Maragos, 2007).

𝑆𝑆𝐼𝑀(𝑥, 𝑦) =(2𝜇𝑥𝜇𝑦+𝑐1)(2𝜎𝑥𝑦+𝑐2)

(𝜇𝑥2+𝜇𝑦

2+𝑐1)(𝜎𝑥2+𝜎𝑦

2+𝑐2) … (1.4)

𝑀𝑆𝑆𝐼𝑀(𝑥, 𝑦) = ∑ 𝑆𝑆𝐼𝑀(𝑥, 𝑦)𝑀𝑗=1 … (1.5)

Where, 𝜇𝑥 is the average of x, 𝜇𝑦 is the average of y, 𝜎𝑥2 is the variance of x, 𝜎𝑦

2 is the

variance of y, 𝜎𝑥𝑦 is the covariance of x and y,

𝑐1 = (𝑘1𝐿)𝟐, 𝑐2 = (𝑘2𝐿)𝟐 are two variables used to stabilize the division with weak

denominator,

𝐿is the dynamic range of the pixel values (typically this is 2𝑁𝑜 𝑜𝑓 𝑏𝑖𝑡𝑠 𝑝𝑒𝑟 𝑝𝑖𝑥𝑒𝑙-1 ), and

the default values for 𝑘1 and 𝑘2 are 0.01 and 0.03 respectively. M is the number of

local windows in the image (Wang et al., 2004).

The difference between MSSIM and other related techniques such as MSE,

and PSNR is the ability of these techniques in estimating perceived errors while

MSSIM technique can consider image distortion (perceived change) in structural

information. The idea of Structural information comes from the strong inter-

dependencies for the pixels that are spatially close. The values of dependencies

represent significant information regarding object structure in the visual landscape.

1.2.2 Steganalysis

Contrary to steganography, steganalysis is both an art and science of identifying if a

given medium carries a concealed message in it with a probability of recovering that

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message. The fact that steganography is used for hiding the message is similar to

cryptanalysis applied to cryptography (Farid, 2002).

Steganalysis can be defined as the science and/or art in which secret messages

are detected and often decoded as these are hidden within stego-files. Steganography

is however considered broken if only the secret message has been detected within a

stego-file. Steganalysis research is simulated due to the increasing number of

steganography (or, steganographic) techniques. Consequently, there has been a rise in

the significance of detection techniques that are reliable (Fridrich et al., 2001). In the

stego-files, most of the steganographic systems actually leave some traces behind.

This is what renders such files detectable albeit such traces are not discernible by

naked human eye. With modifications to some parts of a cover-file, changes can be

made to that file to a certain extent. This can therefore be taken as a sign of a

concealed message inside this stego-file (Provos & Honeyman, 2003). A simple

comparison between a stego-file and its corresponding cover may nevertheless expose

the presence of a secret message. With an aim to avoid such a comparison, the cover-

files should either be destroyed or not made available publicly. However, the absence

of cover-files signifies a form of steganalysis that is the weakest (stego only attack)

(Artz, 2001).

Steganalysis methods are generally classified into two kinds depending on the

applicability: specific and universal. The former is meant to break a particular

steganographic algorithm while, the latter aims at frustrating all the steganographic

algorithms. Generally, the greater detection accuracy is achieved through specific

approaches than the universal ones on account of the prior knowledge of the former in

terms of how the particular target method operates. Nevertheless, on account of the

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fact that they can work independently of the embedding technique and even generalize

to unidentified algorithms is what makes the universal approaches more appealing.

One may consider steganalysis as a task of recognizing patterns where it

functions to determine which class is the clean medium that does not contain hidden

message and the stego-medium that contain hidden message. Generally, the precept of

designing a steganalysis algorithm entails the identification and extraction of features

that are specifically sensitive to data hiding; that is, the features that may capture the

differences arising from embedding. This implies that the features obtained from clean

medium are distinguishable from the ones coming from stego-medium (Shi et al.,

2005).

In general, a larger difference means a better choice of features. After feature

extraction is considered, one designs a classifier with an aim to differentiate the clean

medium (non-marked) and stego-medium (marked) through training the features. On

the whole, it is the feature extraction and classifier design on which the performance

of a steganalysis system depends on heavily. Each single medium typically generates

N-dimensional vector of features and hence, in the N-dimensional space, each

medium is denoted as a point by a feature vector. It is considered that; for the greater

efficacy of the feature vector, N should be as big as possible. Recent studies (Wang &

Moulin, 2007) have however shown that a very large value of N is not essential.

Rather, one such N may produce high computational costs that negatively affect the

detection accuracy.

For creating a classifier, the extracted feature vectors from a training set of

medium, whether with or without hidden data, are put into a machine learning

algorithm. This is done in the hope that the two kinds of media can be distinguished.

So far, both Linear Discriminant Analysis (LDA), for instance Fisher Linear