DATA SECURITY An Information-Theoretic Model for Steganography full report
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02-03-2011, 09:21 AM

presented by:
L.Malavika Reddy
Y.Hannah Shobitha

Steganography is the art and science of communicating in such a way that the presence of a
message cannot be detected. It belongs to the field of information hiding, which has received
considerable attention recently. One may distinguish two general directions in information hiding, determined by the power of an adversary: protection only against the detection of a message by a passive adversary and hiding a message such that not even an active adversary can remove it.
An information-theoretic model for steganography with a passive adversary is proposed.
The adversary's task of distinguishing between an innocent cover message C and a modified message S containing a hidden information is interpreted as a hypothesis testing problem.The security of a steganographic system is quantified in terms of the relative entropy (or discrimination) between PC and PS, which gives quantitative bounds on the detection capability of any adversary. It is shown that secure steganographic schemes exist in this model provided the covertext distribution satisfies certain conditions. A universal stegosystem is presented in this model that needs no knowledge of the covertext distribution.
1 Introduction
Steganography’s goal is to conceal the presence of a secret message within an innocuous-looking communication.In other words, steganography consists of hiding a secret hiddentext message within a public covertext to obtain a stegotext in such a way that any observer (except, of cthese, the intended recipient) is unable to distinguish between a covertext with a hiddentext and one without. The model is perhaps best illustrated by Simmons”Prisoners' Problem". Alice and Bob are in jail,locked up in separate cells far apart from each other, and wish to devise an escape plan. Theyare allowed to communicate by means of sending authenticated messages via trusted ctheiers,provided they do not deal with escape plans. The ctheiers are agents of the warden Eve (the adversary) and will leak all communication to her. If Eve detects any sign of conspiracy, she will ution, except that it is generated from independently repeated experiments.
This paper views steganography as information hiding with a passive adversary thwart the escape plans by transferring both prisoners to high-security cells from which nobody has ever escaped. Alice and Bob are well aware of these facts, so that before getting locked up, they have shared a few secret codewords that they are now going to exploit for adding a hidden meaning to their seemingly innocent messages. Alice and Bob succeed if they can exchange information allowing them to coordinate their escape and Eve does not become suspicious.
Of cthese, Eve knows what a \legitimate" conversation among prisoners is like, and she
also knows about the tricks that prisoners apply to embed a hidden meaning in a seemingly
innocent message. Following the approach of information theory, we capture this knowledge
by a probabilistic model, and view Eve's task of detecting hidden messages as a problem of
hypothesis testing.
We consider only the scenario where Alice sends a message to Bob. Eve
models an innocent message from Alice as a covertext C with probability distribution PC. A
message with embedded hidden information is called stegotext and denoted by S.
In general, Eve might not know the process by which stegotext is generated; thus, Eve's
task would be to decide whether the observed message has been produced under the known
covertext distribution or under another distribution unknown to her. However, we adopt a
stronger model and assume that Eve has complete knowledge of the embedding and extraction
processes in a steganographic system, except for a short secret key K shared by Alice and Bob.
Upon observing the message sent by Alice, Eve has to decide whether it is covertext or
stegotext. This is the problem of choosing one of two different explanations for observed data,
known as ” hypothesis testing" in information theory Recall that Eve knows the probability distributions of covertext and stegotext, and draws her conclusion about the observed
message only from this knowledge. However, Eve does not know if Alice produced the message
according to Pcor PS, nor is she willing to assign any a priori probabilities to these two explanations.
We define the security of the steganographic system used by Alice and Bob (or stegosystem
for short) in terms of the relative entropy D(PC||PS) between PC and PS, which yields quantitative
bounds on Eve's detection performance. If the covertext and the stegotext distributions
are equal, D(PC||PS) = 0 and we have a perfectly secure stegosystem; Eve cannot distinguish
the two distributions and has no information at all about the presence of an embedded message.
This parallels Shannon's notion of perfect secrecy for cryptosystems .
Note how the model differs from the scenario sometimes considered for steganography, where
Alice uses a covertext that is known to Eve and modifies it for embedding hidden information.
Such schemes can only o_er protection against adversaries with limited capability of comparing
the modi_ed stegotext to the covertext. For instance, this applies to the popular use of
steganography on visual images, where a stegoimage may be perceptually indistinguishable from
the coverimage for humans, but not for an algorithm with access to the coverimage.
Limitations. How well the information-theoretic model covers real-world steganographic applications depends crucially on the assumption that there is a probabilistic model of the covertext.
Moreover, the users of a stegosystem need at least some knowledge about the covertext
distribution, as will become clear in the description of the stegosystems.
Probabilistic modeling of information is the subject of information theory, originating with
Shannon's pioneering work. Information theory is today regarded as the \right" approach
to quantifying information and to reasoning about the performance of communication channels.
This confidence in the theory stems from many practical coding schemes that have been built
according to the theory and perform well in real applications.
But the situation in steganography is more involved, since even a perfectly secure stegosystem
requires that the users and the adversary share the same probabilistic model of the covertext.
For instance, if the covertext distribution consists of uniformly random bits, then encrypting
a message under a one-time pad results in a perfectly secure stegosystem according to the
notion of security. But no reasonable warden would allow the prisoners to exchange randomlooking messages in the Prisoners' Problem, since the use of encryption is clearly forbidden! Thus, the validity of a formal treatment of steganography is determined by the accuracy of a probabilistic model for the real data. Assuming knowledge of the covertext distribution seems to render the model somewhat unrealistic for the practical purposes of steganography. But what are the alternatives? Should we rather study the perception and detection capabilities of the human cognition since most coverdata (images, text, and sound) is ultimately addressed to humans? Viewed in this way, steganography could fall entirely into the realms of image, language, and audio processing. However, it seems that an information-theoretic model, or any other formal approach, is more useful for deriving statements about the security of steganography schemes and a formal security notion is one of the main reasons for introducing a mathematical model of steganography.
So far most formal models of information hiding address the case of active adversaries. This problem is different from the one considered here since the existence of a hidden message is typically known publicly, as for example in copyright protection schemes. Information hiding with active adversaries can be divided into watermarking and fingerprinting. Watermarking supplies digital objects with an identification of origin; all objects are marked in the same way. Fingerprinting, conversely, attempts to identify individual copies of an object by means of embedding a unique marker in every copy that is distributed to a user. It is proposed a slightly different terminology and define watermarking in general as hiding covertext-dependent information, regardless of the adversary model. As most objects to be protected by watermarking consist of audio, image, or video data, these domains have received the most attention so far. A large number of hiding techniques and domain-specific models have been developed for robust, imperceptible information hiding
Ettinger models active adversaries with game-theoretic techniques: A general model for information hiding with active adversaries was formulated by Mittelholzer, but its hiding property also relies on the similarity of stegodata and coverdatain terms of a perceptually motivated distortion measure. Zollner use information theoretic methods to conclude that the embedding process in steganography must involve uncertainty. A complexity-theoretic model for steganography, which shares the focus on the indistinguishability of the stegotext from a given covertext distribution, has recently been proposed by Hopper, Langford, and van Ahn.
Another related work was by Maurer on unconditionally secure authentication in
cryptography, which demonstrates the generality of the hypothesis testing approach.
A large number of techniques for undetectable communication originate in the military
domain, where they have found many applications. This includes radar, spread-spectrum communication, and covert channels. It is likely that the model is also applicable to those areas.
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