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