Optimization
problems in adaptive steganography
(Strategic adaptive steganography)
subject sept 2014 - fin
2017
Encadrants : Marc Chaumont
marc.chaumont@lirmm.fr
(pdf)
(slides)
Laboratoire d'Informatique, de
Robotique et de Microélectronique de Montpellier
Team: ICAR
Keywords: Game Theory,
Optimization, Probabilistic models, Security,
Steganography/Steganalysis.
Steganography is the art and
science of hiding a message in any media, in such a way that no one can
suspect
the existence of the message. Steganalysis
is the art and science of detecting the presence of a hidden message
i.e.
detecting the existence of a secret channel. The
study of modern
steganography /
steganalysis began in
the early 2000s.
Correcting codes are
used to hide information,
i.e., a secret message,
in an image, and to extract
hidden
information from
the modified
image. (F5-Hamming [Westfeld2001_F5], Modified Matrix
Encoding: MME [Kim2007_MME],
FastBCH [Zhang2009_BCH], [Sachnev2009_BCH], Reed-Solomon (RS)
[Fontaine2009_BCH]
…). Moreover, recently,
it is accepted that some parts of the
image are more susceptible
to detection,
i.e. more “sensitive”
than others [Fridrich2007_Embedding].
The
“sensitivity” is modeled with a detectability
value attributed to each
pixel of the image.
The message
embedding, through
the use of correcting
codes [Filler2011_STC], is
then carried out with the
constraint
of minimizing the sum of the detectability
of
the modified pixels. These detectability
values
can be binary,
as the algorithms based on the wet
paper codes [Fridrich2005],
or be in a real interval [Pevny_HUGO_2010], [Filler_MOD2011], [Kouider2012_ASO].
When the values of detectability
are
in a real interval,
algorithms are
named adaptive
algorithms [HUGO_2010],
[Filler_MOD2011], [Kouider2012_ASO].
Adaptive steganography is
known as an interesting
problem of
steganography/steganalysis. Currently, the
only existing code
is STC [Filler2011_STC]. Furthermore, the recent
proposals [Pevny_HUGO_2010], [Filler_MOD2011], [Kouider2012_ASO] deal with the definition
of the detectability values.
Adaptive
steganography is interesting because the embedding
is done by optimizing a cost function, i.e., (the detectability)
[Filler2011_STC]. By
cons, the embedding
does not take into account the strategy of the steganalyser. In order
to take
into account the steganalyser, the steganography may model this two
player
game, with game theory. Game theory is a good method to model a
situation with
two (or more) opponents (players) who can vary their strategies and
make some
assumptions about the behavior of opponents. In general, each player
wants to
maximize their gain or minimize their loss in a competitive
environment. The
Nash equilibrium [vanDamme1991_Nash]
is
the stable situations in this environment: none of the players would
benefit
from changing her strategy.
In steganography and
steganalysis, the different participants of the game are Nature, the
Steganograph (Alice), The Judge, and the Steganalyser (Eve)
[Ettinger1998_SGE].
The authors of In [Schottle_GTA_2012] develop the first rigorous method
based
on Game theory to adapt the embedding in an adaptive steganography
context. An
optimal game strategy is developed with strong hypothesis on the model
as the
use of a LSB (Least Significant Bit) embedding, a 2 pixels image, or
the embedding
of one and only one bit, etc.
Thesis:
The topics
include but are not
limited to probabilistic modeling, game theory, steganography /
steganalysis.
In this thesis,
the PhD
student will identify and analyze
the
links between the
detectability
map, the cost function, and the strategies in
a game theory context. He
will then propose
different
models of steganography,
strategies, security functions, values
of detectability, etc,
based on
Game Theory. Those strategies
will be evaluated, on different type of covers.
Références :
[Westfeld2001_F5]
Westfeld, A.: F5–A Steganographic Algorithm: High Capacity Despite
Better
Ste-ganalysis. In: Information Hiding - 4th International Workshop.
vol. 2137,
pp. 289–302. Springer-Verlag, New York, Pittsburgh, PA (April 25-27
2001)
[Kim2007_MME]
Y. Kim, Z. Duric, D. Richards: “Modified matrix encoding technique for
minimal
distortion steganography”. In: Camenisch, J.L., Collberg, C.S.,
Johnson, N.F.,
Sallee, P. (eds.) IH 2006. LNCS, vol. 4437, pp. 314–327 (2007).
[Zhang2009_BCH]
R. Zhang, V. Sanchev, H. J. Kim: “Fast BCH Syndrome Coding for
Steganography”.
In: Katzenbeisser, S. and Sadeghi, A.-R (Ed.) Information Hiding 2009,
IH’2009,
LNCS 5806, pp. 48-58, 2009, Springer-Verlag Berlin Heidelberg 2009.
[Sachnev2009_BCH]
V. Sachnev, H.J. Kim and R. Zhang: “Security Less Detectable JPEG
Steganography
Method Based on Heuristic Optimization and BCH Syndrome Coding”, The
11th ACM
Workshop on Multimedia and Security, MM&Sec’09, September 7–8,
2009,
Princeton, New Jersey, USA.
[Fontaine_2009_RS]
C. Fontaine and F. Galand: “How Reed-Solomon Codes Can Improve
Steganographic
Schemes”, Hindawi Publishing Corporation EURASIP Journal on Information
Security Volume 2009, Article ID 274845, 10 pages
doi:10.1155/2009/274845.
[Pevny_HUGO_2010]
“Using
High-Dimensional Image Models to Perform Highly Undetectable
Steganography”, T.
Pevny, T. Filler and P. Bas, 12th
Information Hiding Conference, June 28 - 30, 2010, Calgary, Alberta,
Canada. Code
source : Break Our
Steganography System, 2010,
http://boss.gipsa-lab.grenoble-inp.fr/BOSSRank/.
[Filler_MOD2011]
T. Filler and J. Fridrich, “Design of Adaptive Steganographic Schemes
for
Digital Images,” in Media Watermarking, Security, and Forensics XIII,
part of
IS&T SPIE Electronic Imaging Symposium, San Francisco, CA,
January 23-26
2011, vol. 7880, paper. 13, pp. F 1–14.
[Fridrich2007_Embedding]
Jessica J. Fridrich and Tomas Filler, “Practical Methods for Minimizing
Embedding Impact in Steganography,” in Security, Steganography, and
Watermarking of Multimedia Contents IX, part of IS&T SPIE
Electronic
Imaging Symposium, San Jose, CA, January 29-February 1 2007, vol. 6505,
pp.
02–03. Principle of minimizing the
embedding impact
was proposed in 2007 [Fridrich2007]. It is based on the adaptivity of
the embedding
operation by the use of a detectability map.
[Filler2011_STC]
T. Filler, J. Judas, and J. Fridrich, “Minimizing Additive Distortion
in
Steganography using Syndrome-Trellis Codes” IEEE Trans. on
Info. Forensics and
Security,
vol. 6(1), pp. 920–935, 2011.
[Ettinger1998_SGE]
Ettinger, J. Mark , « Steganalysis and Game
Equilibria », In :
PetitColas, F.A.P.(ed) LNCS, vol.1525, pp319- 328. Springer, Heidelberg
(1998).
[Schottle2012_GTA]
P. Schöttle and R. Böhme, “A
Game-Theoretic Approach to Content-Adaptive Steganography,”
in
Information Hiding, Berkeley, California, May
15-18, 2012, vol. 6958 of Lecture Notes in Computer
Science,
IH’2012, Springer.
[vanDamme1991_Nash]
Eric Van Damme « Stability and
Perfection of Nash Equilibria, » Springer-Verlag,
1991 - 339 pages
[Kouider2012_ASO]
S. Kouider and M. Chaumont and W. Puech, "Technical Points About
Adaptive
Steganography by Oracle (ASO)", EUSIPCO'2012, 20th European Signal
Processing Conference 2012, Bucharest, Romania, August 27 - 31, 2012. http://www.lirmm.fr/~chaumont/Publications.html
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