27-10-2012, 06:08 PM
A New Paradigm Hidden in Steganography
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INTRODUCTION
Steganography, which is Greek for \covered writing," is a
subset of the emerging discipline of information hiding [12,
1, 5, 18, 13]. It is the science of transmitting a message
between two parties (Alice and Bob) in such a manner that
an eavesdropper (Eve) will not be aware that the message
exists. The terms \information hiding" and \steganogra-
phy" are often, but incorrectly, used interchangeably. In-
formation hiding is the broad term for the scientic dis-
cipline which studies topics such as covert and subliminal
communication channels, detection of hidden information
(e.g., steganography), watermarking of digital objects, and
anonymity services. Unlike cryptography, which seeks to
hide the content of the message, with steganography we seek
to hide the existence of the message. Steganographically
hidden messages are inserted into legitimate and obvious
(with respect to Eve) communications between Alice and
Bob. Eve's steganographic challenge, therefore, is to detect
the message, not to understand it. Of course, steganogra-
phy and cryptography can be used in conjunction, so that
message content may be protected cryptographically, even
if the steganographic \shield" fails and the existence of the
message is discovered.
Paradigms old and new
The paradigm of cryptography (the \old" paradigm) is that
cryptography can be modeled, measured, and utilized by the
standards of information theory and noise. We have Shan-
non [21] to thank for this. Attempts have been made to
extend this paradigm to steganography [6, 16, 25]. We nd
that these extensions, although useful, do not capture all of
the essence of steganography. Note that the authors of [6,
16, 25] never claimed that their work did. We propose a
\new paradigm" for steganography, based upon (1) discon-
tinuous mathematical models, and (2) the lack of noise as
a detection deterrent. This is not to say that the present
steganographic models do not take, at least part of, this
thinking into account. However, we feel that it is impor-
tant to delineate these ideas as a new paradigm to force
ourselves to think of steganography in a dierent light than
that of cryptography. Perhaps by looking at steganography
in light of our new paradigms, the present steganographic
models can be \lled out" to capture more of the essence of
steganography
Terminology
We will use the standard terminology for steganography
as discussed at the First International Information Hiding
Workshop [19]. We assume that Alice wishes to send, via
steganographic transmission, a message to Bob. Alice starts
with a covermessage. The hidden message is called the em-
bedded message. A steganographic algorithm combines the
covermessage with the embedded message. The algorithm
may or may not use a steganographic key (stegokey), which
is similar to a cryptographic key in purpose and use | this
is illustrated by using a dotted line in gure 1. The output of
the steganographic algorithm is the stegomessage. The cov-
ermessage and stegomessage must be of the same datatype,
but the embedded message may be of another datatype.
We sometimes make the datatype explicit in our terminol-
ogy, e.g., \coverimage." Figure 1 illustrates the embedding
process. In steganography, we do not make the \strong"
assumption that Eve has knowledge of the steganographic
algorithm. This is why there may, or may not be, a ste-
gokey involved in the embedding and extraction of a hidden
message. Eve should not be able to determine from the
stegomessage that there is an embedded message in it. Of
course, in steganography we often make the assumption that
Eve does not have access to the covermessage. Thus, Eve
should not be able to tell if she is \observing" a legitimate
covermessage or a stegomessage. Both Bob and Eve receive
the stegomessage. Bob reverses the embedding process to
extract the embedded message. In gure 2, we illustrate the
extracting process.
KurakMcHugh
Method
In 1992 C. Kurak and J. McHugh presented [14] detailing
how one can hide an image inside of an image. The thrust
for writing that paper was to show that one should not be
too complacent about downgrading images from \private"
to \public." The paper simply and graphically demonstrates
that a public image that appears innocuous to a casual ob-
server may, in fact, be hiding an embedded private image.
We summarize the Kurak-McHugh method.
| Start with a bitmapped version of a greyscale image
that we wish to do the hiding in (the coverimage). Next,
we consider a bitmap of the image that we wish to hide.
The two images are merged into a bitmap (the stegoimage).
The merging is done in the following manner. The bitmaps
have one byte representing each pixel. Thus there are 256
levels of grey, ranging from 0 to 255 for each pixel. Replace
the n least signicant bits (LSB) of each pixel in the cov-
erimage, with the n most signicant bits (MSB) from the
corresponding pixel of the image to be embedded.
Covert Channels
We note that the existing paradigm for covert channels is
not appropriate for steganography. Steganography can be
thought of as a subliminal channel. Simmons was the rst
to use the term subliminal channel in a general sense in [22].
A subliminal channel is a secondary communication between
two parties Alice and Bob, such that the primary communi-
cation is publicly known, but the secondary communication
is meant to be hidden. A covert channel diers in that
there is communication between Alice and Bob that exists
outside of the system design. A covert channel is allowed
to exist if its information theoretical capacity is below an
agreed-upon upper bound. This does not, and should not,
work for steganography. Once Eve knows that there is hid-
den communication, the subliminal channel has been discov-
ered. There is no such thing as partially subliminal, which
is similar to the concept of being a little bit pregnant. The
paradigm of covert channels, the old paradigm, is similar to
that of cryptography, also the old paradigm. Steganogra-
phy (subliminal channels) must have a new paradigm that
does not include such distinctions as a little bit discovered
(non-hidden)! However, steganographic models do rely upon
the fact that one can be a little bit confused|through the
indeterminacy of what is a legitimate cover.
CONCLUSION
We have shown how two staples of cryptography: a contin-
uous information theoretic-based foundation, and the use
of noise, should not be staples for steganographic model-
ing. Steganographic models must contain some way of deal-
ing with (catastrophic) jumps from not knowing, to know-
ing, that there is hidden information. We have shown that
this type behavior is possible in other continuous physi-
cal/mathematical systems. Therefore, we feel it is imper-
ative to incorporate it into steganographic models. Adding
noise during the steganographic embedding phase can cause
the steganography to fail. The transition from a covermes-
sage to a stegomessage must be carefully done so that Eve
does not know that the covermessage has been tampered
with. In cryptography, one need not hide the fact that a
message has been encrypted. However, in steganography
one must hide the fact that a message has been embedded.
Since the philosophies of the two are so dierent, so should
the guiding paradigms be dierent