Abstract:
In the last few years, we have seen many new and powerful steganog-
raphy and steganalysis techniques reported in the literature. In the fol-
lowing tutorial we go over some general concepts and ideas that apply
to steganography and steganalysis. We review and discuss the notions
of steganographic security and capacity. Some of the more recent im-
age steganography and steganalysis techniques are analyzed with this
perspective, and their contributions are highlighted.
presented by
Mehdi Kharrazi1, Husrev T. Sencar2, and Nasir Memon2 1Department of Electrical and Computer Engineering2Department of Computer and Information Science Polytechnic University, Brooklyn, NY 11201, USA
1. Introduction
Steganography refers to the science of invisible communication. Unlike
cryptography, where the goal is to secure communications from an eaves-
dropper, steganographic techniques strive to hide the very presence of the
message itself from an observer. The general idea of hiding some infor-
mation in digital content has a wider class of applications that go beyond
steganography, Fig. 1. The techniques involved in such applications are col-
lectively referred to as information hiding. For example, an image printed
on a document could be annotated by metadata that could lead a user
to its high resolution version. In general, metadata provides additional in-
formation about an image. Although metadata can also be stored in the
file header of a digital image, this approach has many limitations. Usually,
when a file is transformed to another format (e.g., from TIFF to JPEG or
to BMP), the metadata is lost. Similarly, cropping or any other form of
image manipulation destroys the metadata. Finally, metadata can only be
attached to an image as long as the image exists in the digital form and is
lost once the image is printed. Information hiding allows the metadata to
1
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travel with the image regardless of the file format and image state (digital
or analog).
A special case of information hiding is digital watermarking. Digital wa-
termarking is the process of embedding information into digital multimedia
content such that the information (the watermark) can later be extracted
or detected for a variety of purposes including copy prevention and control.
Digital watermarking has become an active and important area of research,
and development and commercialization of watermarking techniques is be-
ing deemed essential to help address some of the challenges faced by the
rapid proliferation of digital content. The key difference between informa-
tion hiding and watermarking is the absence of an active adversary. In wa-
termarking applications like copyright protection and authentication, there
is an active adversary that would attempt to remove, invalidate or forge wa-
termarks. In information hiding there is no such active adversary as there
is no value associated with the act of removing the information hidden in
the content. Nevertheless, information hiding techniques need to be robust
against accidental distortions.
Covert
Communication
Watermarking
Steganography
Information
Hiding
Fig. 1. Relationship of steganography to related fields.
Unlike information hiding and digital watermarking, the main goal of
steganography is to communicate securely in a completely undetectable
manner. Although steganography is an ancient art, first used against the
persian by the romans, it has evolved much trough the years.
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Image Steganography and Steganalysis: Concepts and Practice
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In the following tutorial we focus on some general concepts and ideas
that apply across the field of steganography. The rest of this tutorial is or-
ganized as follows: in section 2 we first define the problem which steganog-
raphy tries to address and introduce to the reader some terminologies com-
monly used in the field. In section 3 we go over different approaches in
defining security. In section 4, the notion of steganographic capacity is dis-
cussed, section 5 goes over some embedding techniques, and in sections 6
some steganalysis techniques are reviewed. We conclude in section 7.
2. General Concepts
In this section we go over the concepts and definitions used in the field
of steganography. We first start by going over the framework in which
steganography is usually presented and then go over some definitions.
The modern formulation of steganography is often given in terms of the
prisonerâ„¢s problem [1] where Alice and Bob are two inmates who wish to
communicate in order to hatch an escape plan. However, all communication
between them is examined by the warden, Wendy, who will put them in
solitary confinement at the slightest suspicion of covert communication.
Specifically, in the general model for steganography, illustrated in Fig. 2,
we have Alice wishing to send a secret message m to Bob. In order to do
so, she embeds m into a cover-object c, and obtains a stego-object s. The
stego-object s is then sent through the public channel. Thus we have the
following definitions:
Cover-object: refers to the object used as the carrier to embed messages
into. Many different objects have been employed to embed messages into
for example images, audio, and video as well as file structures, and html
pages to name a few.
Stego-object: refers to the object which is carrying a hidden message. so
given a cover object, and a messages the goal of the steganographer is to
produce a stego object which would carry the message.
In a pure steganography framework, the technique for embedding the
message is unknown to Wendy and shared as a secret between Alice and
Bob. However, it is generally considered that the algorithm in use is not
secret but only the key used by the algorithm is kept as a secret between
the two parties, this assumption is also known as Kerchoffâ„¢s principle in the
field of cryptography. The secret key, for example, can be a password used
to seed a pseudo-random number generator to select pixel locations in an
image cover-object for embedding the secret message (possibly encrypted).
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Wendy has no knowledge about the secret key that Alice and Bob share,
although she is aware of the algorithm that they could be employing for
embedding messages.
Wendy
Bob
Alice
Suppress
message
Embedding
Algorithm
Secret Message
Hidden message
Secret Key
Secret Key
Cover Message
Extracting
Algorithm
Is it Stego
Fig. 2. General model for steganography.
The warden Wendy who is free to examine all messages exchanged be-
tween Alice and Bob can be passive or active. A passive warden simply ex-
amines the message and tries to determine if it potentially contains a hidden
message. If it appears that it does, she suppresses the message and/or takes
appropriate action, else she lets the message through without any action.
An active warden, on the other hand, can alter messages deliberately, even
though she does not see any trace of a hidden message, in order to foil any
secret communication that can nevertheless be occurring between Alice and
Bob. The amount of change the warden is allowed to make depends on the
model being used and the cover-objects being employed. For example, with
images, it would make sense that the warden is allowed to make changes
as long as she does not alter significantly the subjective visual quality of a
suspected stego-image. In this tutorial we assume that no changes are made
to the stego-object by the warden Wendy.
Wendy should not be able to distinguish in any sense between cover-
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objects (objects not containing any secret message) and stego-objects (ob-
jects containing a secret message). In this context, steganalysis refers to the
body of techniques that aid Wendy in distinguishing between cover-objects
and stego-objects. It should be noted that Wendy has to make this distinc-
tion without any knowledge of the secret key which Alice and Bob may
be sharing and sometimes even without any knowledge of the specific algo-
rithm that they might be using for embedding the secret message. Hence
steganalysis is inherently a difficult problem. However, it should also be
noted that Wendy does not have to glean anything about the contents of
the secret message m. Just determining the existence of a hidden message
is enough. This fact makes her job a bit easier.
The development of techniques for steganography and the wide-spread
availability of tools for the same have led to an increased interest in ste-
ganalysis techniques. The last two years, for example, have seen many new
and powerful steganalysis techniques reported in the literature. Many of
such techniques are specific to different embedding methods and indeed
have shown to be quite effective in this regard. We will review these tech-
niques in the coming sections.
3. Steganographic Security
In steganography, unlike other forms of communications, oneâ„¢s awareness of
the underlying communication between the sender and receiver defeats the
whole purpose. Therefore, the first requirement of a steganographic system
is its undetectability. In other words, a steganographic system is considered
to be insecure, if the warden Wendy is able to differentiate between cover-
objects and stego-objects.
There have been various approaches in defining and evaluating the secu-
rity of a steganographic system. Zollner et al. [2] were among the first to ad-
dress the undetectability aspect of steganographical systems. They provide
an analysis to show that information theoretically secure steganography is
possible if embedding operation has a random nature and the embedded
message is independent from both the cover-object and stego-object. These
conditions, however, ensure undetectability against an attacker who knows
the stego-object but has no information available about the indeterminis-
tic embedding operation. That is, Wendy has no access to the statistics,
distribution, or conditional distribution of the cover-object.
On the other hand, [3,4] approached steganographic security from a
complexity theoretic point of view. Based on cryptographic principles, they
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propose the design of encryption-decryption functions for steganographic
embedding and detection. In this setting, the underlying distribution of the
cover-objects is known by the attacker, and undetectability is defined in a
conditional sense as the inability of a polynomial-time attacker (Wendy) to
distinguish the stego-object from a cover-object. This model assumes that
stego-object is a distorted version of the cover-object, however, it does not
attempt to probabilistically characterize the stego object.
In [5], Cachin defined the first steganographic security measure that
quantifies the information theoretic security of a stegosystem. His model
assigns probability distributions to cover-object and stego-object under
which they are produced. Then, the task of Wendy is to decide whether
the observed object is produced according to known cover-object distribu-
tion or not. In the best case scenario, Wendy also knows the distribution of
stego-object and makes a decision by performing a binary hypothesis test.
Consequently, the detectability of a stegosystem is based on relative entropy
between the probability distributions of the cover-object and stego-object,
denoted by Pc and Ps, respectively, i.e.,
D(Pc||Ps) =
Pc log
Pc
Ps
.
(1)
From this equation, we note that D(Pc||Ps) increases with the ratio Pc
Ps
which in turn means that the reliability of steganalysis detector will also
increase. Accordingly, a stego technique is said to be perfectly secure if
D(Pc||Ps)=0(Pc and Ps are equal), and -secure if the relative entropy
between Pc and Ps is at most , D(Pc||Ps) = . Perfectly secure algorithms
are shown to exist, although they are impractical [5]. However, it should
be noted that this definition of security is based on the assumption that
the cover-object and stego-object are independent, identically distributed
(i.i.d.) vectors of random variables.
Since Wendy uses hypothesis testing in distinguishing between stego-
objects and cover-objects, she will make two types of errors, namely, type-
I and type-II errors. A type-I error, with probability a occurs, when a
cover-object is mistaken for a stego-object (false alarm rate), and a type-
II error, with probability ÃƒÅ¸, occurs when a stego-object is mistaken for a
cover-object (miss rate). Thus bounds on these error probabilities can be
computed using relative entropy, thereby relating steganographic security
to detection error probabilities. Cachin [5] obtains these bounds utilizing
the facts that deterministic processing can not increase the relative entropy
between two distributions, say, Pc and Ps, and hypothesis testing is a form
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of processing by a binary function that yields a (P(detect message present
| message absent)) and ÃƒÅ¸ (P(detect message absent | message present)).
Then, the relative entropy between distributions Pc and Ps and binary
relative entropy of two distributions with parameters (a,1 - a) and (ÃƒÅ¸,
1 - ÃƒÅ¸) need to satisfy
d(a, ÃƒÅ¸) = D(Pc||Ps),
(2)
where d(a, ÃƒÅ¸) is expressed as
d(a, ÃƒÅ¸) = a log
a
1 - ÃƒÅ¸
+ (1 - a) log
1 - a
ÃƒÅ¸
.
(3)
Then, for an -secure stegosystem we have
d(a, ÃƒÅ¸) = .
(4)
Consequently, when the false alarm rate is set to zero (a = 0), the miss
rate is lower bounded as ÃƒÅ¸ = 2-. It should be noted that the probability
of detection error for Wendy is defined as
Pe = aP(message absent) + ÃƒÅ¸P(message present).
(5)
Based on above equations, for a perfectly secure stegosystem, a + ÃƒÅ¸ = 1,
and when a cover-object is equally likely to undergo embedding operation,
then Pe = 1
2
. Hence, Wendyâ„¢s decisions are unreliable.
As one can observe, there are several shortcomings in the above defi-
nition of security. While the -secure definition may work for random bit
streams (with no inherent statistical structure), for real-life cover-objects
such as audio, image, and video, it seems to fail. This is because, real-
life cover-objects have a rich statistical structure in terms of correlation,
higher-order dependence, etc. By exploiting these structures, it is possi-
ble to design good steganalysis detectors even if the first order probability
distribution is preserved (i.e., = 0) during the embedding process. If we
approximate the probability distribution functions using histograms, then,
examples such as [6] show that it is possible to design good steganalysis
detectors even if the histograms of the cover image is and the stego image
are the same.
Consider the following embedding example. Let X and Y be two binary
random variables such that P(X = 0) = P(Y = 0) = 1/2, and let them
represent the host and covert message, respectively. Let the embedding
function be given by the following:
Z = X + Y mod 2.
(6)
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We then observe that D(PZ||PX) = 0 but E(X - Z)2 = 1. Therefore the
non-zero mean squared error value may give away enough information to a
steganalysis detector even though D(.) = 0.
One attempt to overcome the limitations of i.i.d. cover-object model was
made by Wang et al. [7] where they extended Cachinâ„¢s results to multivari-
ate Gaussian case, assuming that cover-object and stego-object are vectors
of length N with distributions PcN and PsN , respectively. In the multivari-
ate case, similar to i.i.d. case, undetectability condition requires that the
distribution of cover-object is preserved after embedding. However, when
this is not possible, the degree of detectability of a stegosystem will depend
on the deviation from the underlying distribution and the covariance struc-
ture of the cover-object. If the cover-object is jointly Gaussian with zero
mean and covariance matrix RcN , among all distributions (with zero mean
and covariance matrix RsN ) the Gaussian distribution for the stego-object
minimizes the relative entropy. Then, the detectability of stegosystem can
be quantified based on the relative entropy as
D(PcN ||PsN ) =
1
2
(
tr( Ã‹â€ R) - log( Ã‹â€ R + IN )
)
Ã‹
1
4
tr( Ã‹â€ R2)
(7)
where tr(.) denotes the trace of a matrix, IN is the N Ãƒâ€” N identity matrix,
and Ã‹â€ R = RcN R-1
sN -IN . Consequently, Wendyâ„¢s detection error probability,
Pe can be lower bounded as [7]
Pe >
1
2
exp-
D(P
cN ''PsN )+D(P
sN ''PcN )
2
(8)
assuming both hypotheses are equally likely, i.e., Pe = 1
2
a + 1
2
ÃƒÅ¸.
Although [7] addressed the inherent limitation of the -secure notion
of Cachin, [5], by considering non-white cover-objects, due to analytical
tractability purposes they limited their analysis to cover-objects that are
generated by a Gaussian stationary process. However, as stated before, this
is not true for many real-life cover-objects. One approach to rectify this
problem is to probabilistically model the cover-objects or their transformed
versions or some perceptually significant features of the cover-object and
put a constraint that the relative entropy computed using the n-th order
joint probability distributions must be less than, say, n and then force
the embedding technique to preserve this constraint. But, it may then be
possible, at least in theory, to use (n + 1)th order statistics for successful
steganalysis. This line of thought clearly poses several interesting issues:
Â¢ Practicality of preserving nth order joint probability distribution
during embedding for medium to large values of n.
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Â¢ Behavior of n depends on the cover message as well as the embed-
ding algorithm. If it varies monotonically with n then, for a desired
target value, say, = *, it may be possible to pre-compute a value
of n = n* that achieves this target.
Of course, even if these nth order distributions are preserved, there is no
guarantee that embedding induced perceptual distortions will be accept-
able. If such distortions are significant, then it is not even necessary to use
a statistical detector for steganalysis!
Prob. of false alarm
Pure chance guess
45 o
Prob. of detection
Fig. 3. Detector ROC plane. (Figure taken from [8])
From a practical point of view, Katzenbeisser et al. [9] propose the idea
of using an indistinguishability test to define the security of a stegosys-
tem. In their model, Wendy has access to cover-object and stego-object
generation mechanisms and uses them consecutively to learn the statistical
features of both objects to distinguish between them, rather than assum-
ing their true probability distributions are available. In a similar manner,
Chandramouli et al. [8] propose an alternative measure for steganographic
security. Their definition is based on the false alarm probability (a), the
detection probability (1 - ÃƒÅ¸), and the steganalysis detectorâ„¢s receiver op-
erating characteristic (ROC) which is a plot of a versus 1 - ÃƒÅ¸. Points on
the ROC curve represent the achievable performance of the steganalysis de-
tector. The average error probability of steganalysis detection is as defined
in Eq. (5). Assuming P(message present)=P(message absent) and setting
a = 1 - ÃƒÅ¸, then Pe = 1/2 and ROC curve takes the form shown in Fig.
3. That is, the detector makes purely random guesses when it operates or
forced to operate on the 45 degree line in the ROC plane. Then, the stegano-
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graphic security can be defined in terms of the deviation of the steganalysis
detectorâ„¢s operation curve from the 45 degree ROC line. Correspondingly,
a stegosystem can be defined to be D-secure with respect to a steganalysis
detector D when |1 - ÃƒÅ¸D - aD| = D where 0 = D = 1 and D = 0 refers
to the perfect security condition, similar to the -security notion of Cachin
[5].
4. Steganographic Capacity
Steganographic capacity refers to the maximum amount (rate) of informa-
tion that can be embedded into a cover-object and then can be reliably
recovered from the stego-object (or a distorted version), under the con-
straints of undetectability, perceptual intactness and robustness, depending
on whether Wendy is active or passive. Compared to data hiding systems,
stegosystems have the added core requirement of undetectability. Therefore,
the steganographic embedding operation needs to preserve the statistical
properties of the cover-object, in addition to its perceptual quality. On the
other hand, if Wendy suspects of a covert communication but cannot re-
liably make a decision, she may choose to modify the stego-object before
delivering it. This setting of steganography very much resembles to data
hiding problem, and corresponding results on data hiding capacity can be
adapted to steganography [10].
As discussed in the previous section, the degree of undetectability of
a stegosystem is measured in terms of a distance between probability dis-
tributions PcN
and PsN , i.e., D(PcN ||PsN ) = where = 0 is the perfect
security condition. Let d(cN , sN ) be a perceptual distance measure defined
between cover-object cN and stego-object sN . When the warden is passive,
the steganographic capacity Cp of a perfectly secure stegosystem with em-
bedding distortion limited to P is defined, in terms of random vectors sN
and cN , as
Cp = {sup H(sN |cN ) : PcN = PsN and
1
N
E[d(cN , sN )] = P}
(9)
where E[.] denotes the expected value and supremum is taken over all
PsN |cN
for the given constraints. In [10], Moulin et al. discuss code gen-
eration (embedding) for a perfectly secure stegosystem with binary i.i.d.
cover-object and Hamming distortion measure, and provide capacity re-
sults. However, generalization of such techniques to real life cover-objects
is not possible due to two reasons. First is the simplistic i.i.d. assumption,
and second is the utilized distortion measure as there is no trivial relation
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between bit error rate and reconstruction quality.
In order to be able to design practical stegosystems, the perfect security
condition in Eq. (9) can be relaxed by replacing it with the -security notion.
One way to exploit this is by identifying the perceptually significant and
insignificant parts of the cover-object cN , and preserving the statistics of
the significant component while utilizing the insignificant component for
embedding. For this, let there be a function g(.) such that d(cN ,g(cN )) Ã‹ 0
and g(cN ) = g(sN ). Then, Eq. (9) can be modified as
Cp = {sup H(sN |cN ) : Pg(cN ) = Pg(sN ) and
1
N
E[(d(cN , sN )] = P} (10)
where D(PcN ||PsN ) = . This approach requires statistical modelling of the
cover-object or of some features of it, which will be modified during em-
bedding. For example, [11,12,13] observe the statistical regularity between
pairs of sample values in an image, and provide a framework for (-secure)
embedding in least significant bit (LSB) layer. Similarly, Sallee [14] models
AC components of DCT coefficients by Generalized Cauchy distribution and
uses this model for embedding. In the same manner, wavelet transformed
image coefficients can be marginally modelled by Generalized Laplacian
distribution [15]. This approach, in general, suffers due to the difficulty
in modelling the correlation structure via higher order joint distributions
which is needed to ensure -security.
In the presence of an active warden, the steganographic capacity can be
determined based on the solution of data hiding capacity with the inclusion
of undetectability or -security condition. Data hiding capacity has been
the subject of many research works, see, [16,17,18,19,20,21,22,23,24,25] and
references therein, where the problem is viewed as a channel communication
scenario with side information at the encoder. Accordingly, the solution
for the data hiding capacity requires consideration of an auxiliary random
variable u that serves as a random codebook shared by both embedder
and detector. Let the distorted stego-object be denoted by y, and assume
cover-object and stego-object are distorted by amounts P and D during
embedding operation and attack, respectively. Since undetectability is the
central issue in steganography, we consider the additional constraint of Pc =
Ps. Then, the steganographic capacity for the active warden case, Ca, is
derived, in terms of i.i.d. random variables c, u, s, and y, as
Ca = {sup I(u, y) - I(u, c) : Pc = Ps,E[(d(c, s)] = P, andE[(d(s, y)] = D}
(11)
where supremum is taken over all distributions Pu|c and all embedding func-
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tions under the given constraints. The computation of the steganographic
capacity of practical stegosystems, using Equations (9)-(11), still remains
to be an open problem due to lack of true statistical models and for reasons
of analytical tractability.
Chandramouli et al. [13], from a practical point of view, make an al-
ternative definition of steganographic capacity based on the -security no-
tion given in the previous section [8]. They define steganographic capacity
from a detection theoretic perspective, rather than information theoretic,
as the maximum message size that can be embedded so that a steganalysis
detector is only able to a make a perfectly random guess about the pres-
ence/absence of a covert message. This indicates that the steganographic
capacity in the presence of steganalysis varies with respect to the steganal-
ysis detector. Therefore, its formulation must involve parameters of the
embedding function as well as that of the steganalysis detector. Assuming
N is the number of message carrying symbols, and a(N)
D
and 1 - ÃƒÅ¸(N)
D
are
the corresponding false alarm and detection probabilities for a steganalysis
detector D, the steganographic capacity is defined as
N*
= {max N subject to |1 - ÃƒÅ¸(N)
D
- a(N)
D | = D} symbols.
(12)
Based on this definition, [13] provide an analysis on the capacity of LSB
steganography and investigate under what conditions an observer can dis-
tinguish between stego-images and cover-images.
5. Techniques for Image Steganography
Given the proliferation of digital images, and given the high degree of redun-
dancy present in a digital representation of an image (despite compression),
there has been an increased interest in using digital images as cover-objects
for the purpose of steganography. Therefore we have limited our discussion
to the case of images for the rest of this tutorial. We should also note that
there have been much more work on embedding techniques which make use
of the transform domain or more specifically JPEG images due to their
wide popularity. Thus to an attacker the fact that an image other that
that of JPEG format is being transferred between two entities could hint
of suspicious activity.
There have been a number of image steganography algorithm proposed,
these algorithm could be categorized in a number of ways:
Â¢ Spatial or Transform, depending on redundancies used from either
domain for the embedding process.
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Â¢ Model based or ad-hoc, if the algorithm models statistical proper-
ties before embedding and preserves them, or otherwise.
Â¢ Active or Passive Warden, based on whether the design of
embedder-detector pair takes into account the presence of an active
attacker.
In what follows we go over algorithm classified into 3 different sections,
based on the more important characteristics of each embedding technique.
Although some of the techniques which we will discuss below have been
successfully broken by steganalysis attacks, which we will go over in Section
6.
5.1. Spatial Domain Embedding
The best widely known steganography algorithm is based on modifying the
least significant bit layer of images, hence known as the LSB technique. This
technique makes use of the fact that the least significant bits in an image
could be thought of random noise and changes to them would not have
any effect on the image. This is evident by looking at Fig. 4. Although the
image seems unchanged visually after the LSBs are modified, the statistical
properties of the image changes significantly. We will discuss in the next
section of this tutorial how these statistical changes could be used to detect
stego images created using the LSB method.
In the LSB technique, the LSB of the pixels is replaced by the message to
be sent. The message bits are permuted before embedding, this has the effect
of distributing the bits evenly, thus on average only half of the LSBâ„¢s will be
modified. Popular steganographic tools based on LSB embedding [26,27,28],
vary in their approach for hiding information. Some algorithms change LSB
of pixels visited in a random walk, others modify pixels in certain areas of
images, or instead of just changing the last bit they increment or decrement
the pixel value [28].
Fridrich et al. [29] proposed another approach for embedding in spatial
domain. In their method, noise that statistically resemble common process-
ing distortion, e.g., scanner noise, or digital camera noise, is introduced to
pixels on a random walk. The noise is produced by a pseudo random noise
generator using a shared key. A parity function is designed to embed and
detect the message message signal modulated by the generated noise.
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Fig. 4. Bitplane decomposition of image Lena.
5.2. Transform Domain Embedding
Another category for embedding techniques for which a number of algo-
rithms have been proposed is the transform domain embedding category.
Most of the work in this category has been concentrated on making use of
redundancies in the DCT (discrete cosine transform) domain, which is used
in JPEG compression. But there has been other algorithms which make use
of other transform domains such as the frequency domain [30].
Embedding in DCT domain is simply done by altering the DCT coeffi-
cients, for example by changing the least significant bit of each coefficient.
One of the constraints of embedding in DCT domain is that many of the
64 coefficients are equal to zero, and changing two many zeros to non-zeros
values will have an effect on the compression rate. That is why the number
of bit one could embed in DCT domain, is less that the number of bits one
could embed by the LSB method. Also the embedding capacity becomes
dependent on the image type used in the case of DCT embedding, since de-
pending on the texture of image the number of non-zero DCT coefficients
will vary.
Although changing the DCT coefficients will cause unnoticeable visual
artifices, they do cause detectable statistical changes. In the next section,
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we will discuss techniques that exploit these statistical anomalies for ste-
ganalysis. In order to minimize statistical artifacts left after the embedding
process, different methods for altering the DCT coefficients have been pro-
posed, we will discuss two of the more interesting of these methods, namely
the F5 [31] and Outguess [32] algorithms.
F5 [31] embedding algorithm was proposed by Westfeld as the latest
in a series of algorithms, which embed messages by modifying the DCT
coefficients. For a review of jsteg, F3 and F4 algorithms that F5 is built on,
please refer to [31]. F5 has two important features, first it permutes the DCT
coefficients before embedding, and second it employs matrix embedding.
The first operation, namely permuting the DCT coefficients has the
effect of spreading the changed coefficients evenly over the entire image. The
importance of this operation becomes evident when a small message is used.
Letâ„¢s say we are embedding a message of size m, then if no permutation
is done and coefficients are selected in the order they appear, then only
the first m coefficients are used. Thus the first part of the image getâ„¢s fully
changed after embedding, and the rest of the image remains unchanged.
This could facilitate attacks on the algorithm since the amount of change
is not uniform over the entire image. On the other hand when permutation
is done, the message is spread uniformly over the image thus the distortion
effects of embedding is spread equally and uniformly over the entire image.
The second operation done by F5 is matrix embedding. The goal of
matrix embedding is to minimize the amount of change made to the DCT
coefficients. Westfeld [31], takes n DCT coefficients and hashes them to k
bits. If the hash value equals to the message bits then the next n coefficients
are chosen and so on. Otherwise one of the n coefficients is modified and the
hash is recalculated. The modifications are constrained by the fact that the
resulting n DCT coefficients should not have a hamming distance of more
than dmax from the original n DCT coefficients. This process is repeated
until the hash value matches the message bits. So then given an image, the
optimal values for k and n could be selected.
Outguess [32], which was proposed by Provos, is another embedding al-
gorithm which embeds messages in the DCT domain. Outguess goes about
the embedding process in two separate steps. First it identifies the redun-
dant DCT coefficients which have minimal effect on the cover image, and
then depending on the information obtained in the first steps, chooses bits
in which it would embed the message. We should note that at the time Out-
guess was proposed, one of its goals was to overcome steganalysis attacks
which look at changes in the DCT histograms after embedding. So Provos,
________________________________________
proposed a solution in which some of the DCT coefficients are left un-
changed in the embedding process, afterwards these remaining coefficients
are adjusted in order preserve the original histogram of DCT coefficients.
As we will see in the steganalysis section both F5 [31], and Outguess [32]
embedding techniques have been successfully attacked.
As mentioned before, another transform domain which has been used
for embedding is the frequency domain. Alturki et al. [30] propose quan-
tizing the coefficients in the frequency domain in order to embed messages.
They first decorrelate the image by scrambling the pixels randomly, which
in effect whitens the frequency domain of the image and increases the num-
ber of transform coefficients in the frequency domain thus increasing the
embedding capacity. As evident from Fig. 5, the result is a salt and pep-
per image where itâ„¢s probability distribution function resembles a gaussian
distribution. The frequency coefficients are then quantized to even or odd
multiples of the quantization step size to embed zeros or ones. Then the
inverse FFT of the signal is taken and descrambled. The resulting image
would be visually incomparable to the original image. But statistically the
image changes and as the authors show in their work, the result of the
embedding operation is the addition of a gaussian noise to the image.
5.3. Model Based Techniques
Unlike techniques discussed in the two previous subsections, model based
techniques try to model statistical properties of an image, and preserve
them in the embedding process. For example Sallee [14] proposes a method
which breaks down transformed image coefficients into two parts, and re-
places the perceptually insignificant component with the coded message
signal. Initially, the marginal statistics of quantized (non-zero) AC DCT
coefficients are modelled with a parametric density function. For this, a low
precision histogram of each frequency channel is obtained, and the model is
fit to each histogram by determining the corresponding model parameters.
Sallee defines the offset value of coefficient within a histogram bin as a sym-
bol and computes the corresponding symbol probabilities from the relative
frequencies of symbols (offset values of coefficients in all histogram bins).
In the heart of the embedding operation is a non-adaptive arithmetic
decoder which takes as input the message signal and decodes it with re-
spect to measured symbol probabilities. Then, the entropy decoded mes-
sage is embedded by specifying new bin offsets for each coefficient. In other
words, the coefficients in each histogram bin are modified with respect to
________________________________________
Image Steganography and Steganalysis: Concepts and Practice
17
a
b
c
d
Fig. 5. Frequency domain embedding. a) Original image, b) scrambled image, c) his-
togram of DFT coefficients, and d) histogram of DFT coefficients after quantization.
(Figure taken from [30])
embedding rule, while the global histogram and symbol probabilities are
preserved. Extraction, on the other hand, is similar to embedding. That
is, model parameters are determined to measure symbol probabilities and
to obtain the embedded symbol sequence (decoded message). (It should be
noted that the obtained model parameters and the symbol probabilities are
the same both at the embedder and detector). The embedded message is
extracted by entropy encoding the symbol sequence.
Another model based technique was proposed by Radhakrishnan et al.
[33], in which the message signal is processed so that it would exhibit the
properties of an arbitrary cover signal, they call this approach data masking.
As argued if Alice wants to send an encrypted message to Bob, the warden
Wendy would be able to detect such a message as an encrypted stream since
it would exhibit properties of randomness. In order for a secure channel to
achieve covertness, it is necessary to preprocess the encrypted stream at the
end points to remove randomness such that the resulting stream defeats
statistical tests for randomness and the stream is reversible at the other
end.
________________________________________
Encryption
Inverse
Wiener
Wiener
Decryption
Message
Key
Key
Message
Randomness
Test
Not Random
Alice
Bob
Fig. 6. Proposed System for Secure and Covert Communication.(Figure taken from
[33])
The authors propose Inverse Wiener filtering as a solution to remove
randomness from cipher streams as shown in Fig 6. Let us consider the ci-
pher stream as samples from a wide sense stationary (WSS) Process, E. We
would like to transform this input process with high degree of randomness
to another stationary process, A, with more correlation between samples
by using a linear filter, H. It is well known that the power spectrum of a
WSS input, A(w), to a linear time invariant system will have the output
with the power spectrum E(w) expressed as
E(w) = |H(w)|2A(w).
(13)
If E(w) is a white noise process, then H(w) is the whitening filter or Wiener
filter. Since the encrypted stream is random, its power spectral density is
flat and resembles the power spectral density of a white noise process.
Then, the desired Wiener filter can be obtained by spectral factorization of
(E(w)/A(w)) followed by selection of poles and zeros to obtain the mini-
mum phase solution for H(w). The authors discuss how the above method
could be used with audio as cover-object in [33], and more recently with
images as cover-object in [34].
6. Steganalysis
There are two approaches to the problem of steganalysis, one is to come
up with a steganalysis method specific to a particular steganographic al-
gorithm. The other is developing techniques which are independent of the
steganographic algorithm to be analyzed. Each of the two approaches has
itâ„¢s own advantages and disadvantages. A steganalysis technique specific
to an embedding method would give very good results when tested only
on that embedding method, and might fail on all other steganographic al-
________________________________________
gorithms. On the other hand, a steganalysis method which is independent
of the embedding algorithm might preform less accurately overall but still
provide acceptable results on new embedding algorithms. These two ap-
proaches will be discussed below and we will go over a few of the proposed
techniques for each approach.
Before we proceed, one should note that steganalysis algorithms in
essence are called successful if they can detect the presence of a message,
and the message itself does not have to be decoded. Indeed, the latter can
be very hard if the message is encrypted using strong cryptography. How-
ever, recently there have been methods proposed in the literature which in
addition to detecting the presence of a message are also able to estimate
the size of the embedded message with great accuracy. We consider these
aspects to be extraneous and only focus on the ability to detect the presence
of a message.
6.1. Technique Specific Steganalysis
We first look at steganalysis techniques that are designed with a particular
steganographic embedding algorithm in mind. As opposed to the previous
section, were the embedding algorithms were categorized depending on the
approach taken in the embedding process, here we categorize the stegano-
graphic algorithms depending on the type of image they operate on, which
includes Raw images (for example bmp format), Palette based images (for
example GIF images), and finally JPEG images.
6.1.1. Raw Images
Raw images are widely used with the simple LSB embedding method, where
the message is embedded in a subset of the LSB (least significant bit) plane
of the image, possibly after encryption. An early approach to LSB steganal-
ysis was presented in [11] by Westfeld et al. They note that LSB embedding
induces a partitioning of image pixels into Pairs of Values (PoVâ„¢s) that get
mapped to one another. For example the value 2 gets mapped to 3 on LSB
flipping and likewise 3 gets mapped to 2. So (2, 3) forms a PoV. Now LSB
embedding causes the frequency of individual elements of a PoV to flatten
out with respect to one another. So for example if an image has 50 pixels
that have a value 2 and 100 pixels that have a value 3, then after LSB
embedding of the entire LSB plane the expected frequencies of 2 and 3 are
75 and 75 respectively. This of course is when the entire LSB plane is mod-
ified. However, as long as the embedded message is large enough, there will
________________________________________
be a statistically discernible flattening of PoV distributions and this fact is
exploited by their steganalysis technique.
The length constraint, on the other hand, turns out to be the main
limitation of their technique. LSB embedding can only be reliably detected
when the message length becomes comparable with the number of pixels
in the image. In the case where message placement is known, shorter mes-
sages can be detected. But requiring knowledge of message placement is
too strong an assumption as one of the key factors playing in the favor of
Alice and Bob is the fact that the secret message is hidden in a location
unknown to Wendy.
A more direct approach for LSB steganalysis that analytically estimates
the length of an LSB embedded message in an image was proposed by
Dumitrescu et al. [12]. Their technique is based on an important statistical
identity related to certain sets of pixels in an image. This identity is very
sensitive to LSB embedding, and the change in the identity can quantify
the length of the embedded message. This technique is described in detail
below, where our description is adopted from [12].
Consider the partition of an image into pairs of horizontally adjacent
pixels. Let P be the set of all these pixel pairs. Define the subsets X, Y
and Z of P as follows:
Â¢ X is the set of pairs (u, v) P such that v is even and u<v, or v
is odd and u>v.
Â¢ Y is the set of pairs (u, v) P such that v is even and u>v, or v
is odd and u<v.
Â¢ Z is the subset of pairs (u, v) P such that u = v.
After having made the above definitions, the authors make the assumption
that statistically we will have
|X| = |Y |.
(14)
This assumption is true for natural images as the gradient of intensity
function in any direction is equally likely to be positive or negative.
Furthermore, they partition the set Y into two subsets W and V , with
W being the set of pairs in P of the form (2k, 2k + 1) or (2k + 1, 2k), and
V = Y - W. Then P = X W V Z. They call sets X, V , W and Z as
primary sets.
When LSB embedding is done pixel values get modified and so does the
membership of pixel pairs in the primary sets. More specifically, given a
pixel pair (u, v), they identify the following four situations:
________________________________________
21
00) both values u and v remain unmodified;
01) only v is modified;
10) only u is modified;
11) both u and v are modified.
The corresponding change of membership in the primary sets is shown in
Fig. 7.
V
W
Z
X
11,01
11,01
00,10
00,10
01,10
01,10
00,11
00,11
Fig. 7. State transition diagram for sets X, V, W, Z under LSB flipping.(Figure taken
from [12])
By some simple algebraic manipulations, the authors finally arrive at
the equation
0.5p2 + (2|X | - |P|)p + |Y |-|X | = 0.
(15)
where = |W| + |Z| = |W | + |Z |. The above equation allows one to
estimate p, i.e the length of the embedded message, based on X , Y , W ,
Z which can all be measured from the image being examined for possible
steganography. Of course it should be noted that we cannot have = 0,
the probability of which for natural images is very small.
In fact, the pairs based steganalysis described above was inspired by
an effectively identical technique, although from a very different approach,
called RS-Steganalysis by Fridrich et al. in [35] that had first provided re-
markable detection accuracy and message length estimation even for short
messages. However, RS-Steganalysis does not offer a direct analytical ex-
planation that can account for its success. It is based more on empirical
________________________________________
observations and their modelling. It is interesting to see that the Pairâ„¢s
based steganalysis technique essentially ends up with exactly the same ste-
ganalyzer as RS-Steganalysis.
Although the above techniques are for gray scale images, they are appli-
cable to color images by considering each color plane as a gray scale image.
A steganalysis technique that directly analyzes color images for LSB embed-
ding and yields high detection rates even for short messages was proposed
by Fridrich et al. [36]. They define pixels that are close in color intensity
to be pixels that have a difference of not more than one count in any of the
three color planes. They then show that the ratio of close colors to the
total number of unique colors increases significantly when a new message of
a selected length is embedded in a cover image as opposed to when the same
message is embedded in a stego-image (that is an image already carrying a
LSB encoded message). It is this difference that enables them to distinguish
cover-images from stego-images for the case of LSB steganography.
In contrast to the simple LSB method discussed, Hide [28] increments
or decrements the sample value in order to change the LSB value. Thus
the techniques previously discussed for LSB embedding with bit flipping do
not detect Hide. In order to detect embedded messages by Hide, Westfeld
[37] proposes a similar steganalysis attack as Fridrich et al. [36] were it
is argued that since the values are incremented or decremented, 26 neigh-
boring colors for each color value could be created, were as in a natural
image there are 4 to 5 neighboring colors on average. Thus by looking at
the neighborhood histogram representing the number of neighbors in one
axis and the frequency in the other one would be able to say if the image
carries a message. This is clearly seen in Fig 8.
6.1.2. Palette Based Images
Pallete based images, like GIF images, are another popular class of images
for which there have been a number of steganography methods proposed
[38,39,40]. Perhaps some of the earliest steganalysis work in this regard was
reported by Johnson et al. [41]. They mainly look at palette tables in GIF
images and anomalies caused therein by common stego-tools that perform
LSB embedding in GIF images. Since pixel values in a palette image are
represented by indices into a color look-up table which contains the actual
color RGB value, even minor modifications to these indices can result in
annoying artifacts. Visual inspection or simple statistics from such stego-
images can yield enough tell-tale evidence to discriminate between stego
________________________________________
23
0
5
10
15
20
25
0
5000
10000
15000
0
5
10
15
20
25
0
5000
10000
15000
Neighbours
Neighbours
Frequency
Frequency
Fig. 8. Neighborhood histogram of a cover image (top) and stego image with 40 KB
message embedded (bottom). (Figure taken from [37])
and cover-images.
In order to minimize the distortion caused by embedding, EzStego [38]
first sorts the color pallet so that the color differences between consecutive
colors is minimized. It then embeds the message bits in the LSB of the
color indices in the sorted pallet. Since pixels which can modified due to
the embedding process get mapped neighboring colors in the palette, which
are now similar, visual artifacts are minimal and hard to notice. To detect
EzStego, Fridrich [6] argues that a vector consisting of color pairs, obtained
after sorting the pallet, has considerable structure due to the fact there
a small number of colors in pallet images. But the embedding process will
disturb this structure, thus after the embedding the entropy of the color pair
vector will increase. The entropy would be maximal when the maximum
length message is embedded in to the GIF image. Another steganalysis
techniques for EzStego were proposed by Westfeld [11], but the technique
discussed above provides a much higher detection rate and a more accurate
estimate of the message lengths.
6.1.3. JPEG Images
JPEG images are the the third category of images which are used rou-
tinely as cover medium. Many steganalysis attacks have been proposed for
steganography algorithms [32,42,31] which employ this category of images.
Fridrich [6] has proposed attacks on the F5 and Outguess algorithms, both
of which were covered in the previous section. F5 [31] embeds bits in the
so that for a given message the
number of changes made to the cover image is minimized, at the same
time it spreads the message over the cover image. But F5 does alter the
histogram of DCT coefficients. Fridrich proposes a simple technique to es-
timate the original histogram so that the number of changes and length
of the embedded message could be estimated. The original histogram is
simply estimated by cropping the JPEG image by 4 columns and then re-
compressing the image using the same quantization table as used before.
As is evident in Fig 9, the resulting DCT coefficient histogram would be a
very good estimate of the original histogram.
Intuitively, effect of the cropping operation could be reasoned as fol-
lows. In a natural image, characteristics are expected to change smoothly
with respect to spatial coordinates. That is, image features computed in a
portion of image will not change significantly by a slight shift in the compu-
tation window. In the same manner, the statistics of the DCT coefficients
computed from a shifted partitioning of an image should remain roughly
unchanged. However, since in F5, DCT coefficients are tailored by the em-
bedder, cropping of the image (shift in the partitioning) will spoil the the
structure created by embedding process, thereby, the coefficient statistics
will vary and estimate the original structure.
-8
-6
-4
-2
0
2
4
6
8
0
500
1000
1500
2000
2500
3000
3500
4000
Value of the DCT coefficient (2,1)
Frequency of Occurence
cover image histogram
stego image histogram
estimated histogram
Fig. 9. The effect of F5 embedding on the histogram of the DCT coefficient (2,1).
(Figure taken from [6])
A second technique proposed by Fridrich [6] deals with the Outguess [32]
embedding program. Outguess first embeds information in LSB of the DCT
coefficients by making a random walk, leaving some coefficients unchanged.
Then it adjusts the remaining coefficient in order to preserve the origi-
nal histogram of DCT coefficients. Thus the previous steganalysis method
where the original histogram is estimated will not be effective. On the other
hand when embedding messages in a clean image, noise is introduced in the
DCT coefficient, therefore increasing the spatial discontinuities along the
8x8 JPEG blocks. Given a stego image if a message is embedded in the im-
age again there is partial cancellation of changes made to the LSBs of DCT
coefficients, thus the increase in discontinuities will be smaller. This increase
or lack of increase in the discontinuities is used to estimate the message size
which is being carried by a stego image. In a related work Wang et al. [43]
use a statistical approach and show how embedding in DCT domain effects
differently the distribution of neighboring pixels which are inside blocks or
across blocks. These differences could be used to distinguish between clean
and stego images.
6.2. Universal Steganalysis
The steganalysis techniques described above were all specific to a particular
embedding algorithm. A more general class of steganalysis techniques pio-
neered independently by Avcibas et al. [44,45,46] and Farid et al. [47,48],
are designed to work with any steganographic embedding algorithm, even
an unknown algorithm. Such techniques have subsequently been called Uni-
versal Steganalysis or Blind Steganalysis Techniques. Such approaches es-
sentially design a classifier based on a training set of cover-objects and
stego-objects obtained from a variety of different embedding algorithms.
Classification is done based on some inherent features of typical natural
images which can get violated when an image undergoes some embedding
process. Hence, designing a feature classification based universal steganal-
ysis technique consists of tackling two independent problems. The first is
to find and calculate features which are able to capture statistical changes
introduced in the image after the embedding process. The second is coming
up with a strong classification algorithm which is able to maximize the dis-
tinction captured by the features and achieve high classification accuracy.
Typically, a good feature should be accurate, monotonic, and consistent
in capturing statistical signatures left by the embedding process. Detection
accuracy can be interpreted as the ability of the measure to detect the
presence of a hidden message with minimum error on average. Similarly,
detection monotonicity signifies that the features should ideally be mono-
tonic in their relationship to the embedded message size. Finally, detection
consistency relates to the featureâ„¢s ability to provide consistently accurate
detection for a large set of steganography techniques and image types. This
implies that the feature should be independent on the type and variety of
images supplied to it.
In [46] Avcibas et al. develop a discriminator for cover images and stego
images, using an appropriate set of Image Quality Metrics (IQMâ„¢s). Objec-
tive image quality measures have been utilized in coding artifact evaluation,
performance prediction of vision algorithms, quality loss due to sensor in-
adequacy etc. In [46] they are used not as predictors of subjective image
quality or algorithmic performance, but specifically as a steganalysis tool,
that is, as features used in distinguishing cover-objects from stego-objects.
0.99
0.995
1
0
0.005
0.01
0.998
0.999
1
1.001
1.002
M5
M3
M
6
unmarked
marked
Fig. 10. Scatter plot of 3 image quality measures showing separation of marked and
unmarked images. (Figure takenh from [46])
To select quality metrics to be used for steganalysis, the authors use
Analysis of Variance (ANOVA) techniques. They arrive at a ranking of
IQMâ„¢s based on their F-scores in the ANOVA tests to identify the ones
that responded most consistently and strongly to message embedding. The
idea is to seek IQMâ„¢s that are sensitive specifically to steganography effects,
that is, those measures for which the variability in score data can be ex-
plained better because of some treatment rather then as random variations
due to the image set. The rationale of using several quality measures is
________________________________________
that different measures respond with differing sensitivities to artifacts and
distortions. For example, measures like mean-square-error respond more to
additive noise, whereas others such as spectral phase or mean square HVS-
weighted (Human Visual System) error are more sensitive to pure blur;
while the gradient measure reacts to distortions concentrated around edges
and textures. Similarly embedding techniques affect different aspects of im-
ages. Fig. 10 shows separation in the feature plane between stego images
and cover images, for 3 example quality metrics.
A second technique proposed by Avcibas et al. [44] looks at seventh
and eight bit planes of an image and calculates several binary similarity
measures. The approach is based on the fact that correlation between con-
tiguous bit-planes is effected after a message is embedded in the image.
The authors conjecture that correlation between the contiguous bit planes
decreases after a message is embedded in the image. In order to capture
the effect made by different embedding algorithms several features are cal-
culated. Using the obtained features a MMSE linear predictor is obtained
which is used to classify a given image as either a cover image or an image
containing hidden messages.
A different approach is taken by Farid et. al [47,48] for feature extrac-
tion from images. The authors argue that most of the specific steganaly-
sis techniques concentrate on first order statistics, i.e. histogram of DCT
coefficients, but simple counter measures could keep the first order statis-
tics intact thus making the steganalysis technique useless. So they propose
building a model for natural images by using higher order statistics and
then show that images with messages embedded in them deviate form this
model. Quadratic mirror filters (QMF) are used to decompose the image,
after which higher order statistics such as mean, variance, skewness, and
kurtosis are calculated for each subband. Additionally the same statistics
are calculated for the error obtained from an optimal linear predictor of
coefficient magnitudes of each subband, as the second part of the feature
set.
In all of the above methods, the calculated features are used to train a
classifier, which in turn is used to classify clean and stego images. Different
classifiers have been employed by different authors, Avcibas et al. use a
MMSE Linear predictor, where as Farid et al. [47,48] uses a Fisher linear
discriminant [49] and also a Support Vector Machine (SVM) [50] classifier.
SVM classifiers seem to have much better performance in terms of classifi-
cation accuracy compared to linear classifiers since they are able to classify
non-linearly separable features. All of the above authors have reported good
________________________________________
accuracy results in classifying images as clean or containing hidden mes-
sages after training with a classifier. Although, direct comparison might be
hard as is in many classification problems, due to the fact that the way
experiments are setup or conducted vary.
7. Conclusion
The past few years have seen an increasing interest in using images as
cover media for steganographic communication. There have been a multi-
tude of public domain tools, albeit many being ad-hoc and naive, available
for image based steganography. Given this fact, detection of covert commu-
nications that utilize images has become an important issue. In this tutorial
we have reviewed some fundamental notions related to steganography and
steganalysis.
Although we covered a number of security and capacity definitions, there
has been no work successfully formulating the relationship between the two
from the practical point of view. For example it is understood that as less
information is embedded in a cover-object the more secure the system will
be. But due to difficulties in statistical modelling of image features, the
security versus capacity trade-off has not been theoretically explored and
quantified within an analytical framework.
We also reviewed a number of embedding algorithms starting with the
earliest algorithm proposed which was the LSB technique. At some point
LSB seemed to be unbreakable but as natural images were better under-
stood and newer models were created LSB gave way to new and more
powerful algorithms which try to minimize changes to image statistics. But
with further improvement in understanding of the statistical regularities
and redundancies of natural images, most of these algorithms have also
been successfully steganalysed.
In term of steganalysis, as discussed earlier, there are two approaches,
technique specific or universal steganalysis. Although finding attacks spe-
cific to an embedding method are helpful in coming up with better em-
bedding methods, their practical usage seems to be limited. Since given
an image we may not know the embedding technique being used, or even
we might be unfamiliar with the embedding technique. Thus universal ste-
ganalysis techniques seem to be the real solution since they should be able
to detect stego images even when a new embedding technique is being em-
ployed.
for more please read
http://citeseerx.ist.psu.edu/viewdoc/dow...1&type=pdf
http://www.ims.nus.edu.sg/Programs/imgsc..._stego.pdf
http://www.ece.stevens-tech.edu/~mouli/lsbsteg.pdf