1,281 research outputs found
Perfectly Secure Steganography: Capacity, Error Exponents, and Code Constructions
An analysis of steganographic systems subject to the following perfect
undetectability condition is presented in this paper. Following embedding of
the message into the covertext, the resulting stegotext is required to have
exactly the same probability distribution as the covertext. Then no statistical
test can reliably detect the presence of the hidden message. We refer to such
steganographic schemes as perfectly secure. A few such schemes have been
proposed in recent literature, but they have vanishing rate. We prove that
communication performance can potentially be vastly improved; specifically, our
basic setup assumes independently and identically distributed (i.i.d.)
covertext, and we construct perfectly secure steganographic codes from public
watermarking codes using binning methods and randomized permutations of the
code. The permutation is a secret key shared between encoder and decoder. We
derive (positive) capacity and random-coding exponents for perfectly-secure
steganographic systems. The error exponents provide estimates of the code
length required to achieve a target low error probability. We address the
potential loss in communication performance due to the perfect-security
requirement. This loss is the same as the loss obtained under a weaker order-1
steganographic requirement that would just require matching of first-order
marginals of the covertext and stegotext distributions. Furthermore, no loss
occurs if the covertext distribution is uniform and the distortion metric is
cyclically symmetric; steganographic capacity is then achieved by randomized
linear codes. Our framework may also be useful for developing computationally
secure steganographic systems that have near-optimal communication performance.Comment: To appear in IEEE Trans. on Information Theory, June 2008; ignore
Version 2 as the file was corrupte
Capacity and Random-Coding Exponents for Channel Coding with Side Information
Capacity formulas and random-coding exponents are derived for a generalized
family of Gel'fand-Pinsker coding problems. These exponents yield asymptotic
upper bounds on the achievable log probability of error. In our model,
information is to be reliably transmitted through a noisy channel with finite
input and output alphabets and random state sequence, and the channel is
selected by a hypothetical adversary. Partial information about the state
sequence is available to the encoder, adversary, and decoder. The design of the
transmitter is subject to a cost constraint. Two families of channels are
considered: 1) compound discrete memoryless channels (CDMC), and 2) channels
with arbitrary memory, subject to an additive cost constraint, or more
generally to a hard constraint on the conditional type of the channel output
given the input. Both problems are closely connected. The random-coding
exponent is achieved using a stacked binning scheme and a maximum penalized
mutual information decoder, which may be thought of as an empirical generalized
Maximum a Posteriori decoder. For channels with arbitrary memory, the
random-coding exponents are larger than their CDMC counterparts. Applications
of this study include watermarking, data hiding, communication in presence of
partially known interferers, and problems such as broadcast channels, all of
which involve the fundamental idea of binning.Comment: to appear in IEEE Transactions on Information Theory, without
Appendices G and
On the Saddle-point Solution and the Large-Coalition Asymptotics of Fingerprinting Games
We study a fingerprinting game in which the number of colluders and the
collusion channel are unknown. The encoder embeds fingerprints into a host
sequence and provides the decoder with the capability to trace back pirated
copies to the colluders.
Fingerprinting capacity has recently been derived as the limit value of a
sequence of maximin games with mutual information as their payoff functions.
However, these games generally do not admit saddle-point solutions and are very
hard to solve numerically. Here under the so-called Boneh-Shaw marking
assumption, we reformulate the capacity as the value of a single two-person
zero-sum game, and show that it is achieved by a saddle-point solution.
If the maximal coalition size is k and the fingerprinting alphabet is binary,
we show that capacity decays quadratically with k. Furthermore, we prove
rigorously that the asymptotic capacity is 1/(k^2 2ln2) and we confirm our
earlier conjecture that Tardos' choice of the arcsine distribution
asymptotically maximizes the mutual information payoff function while the
interleaving attack minimizes it. Along with the asymptotic behavior, numerical
solutions to the game for small k are also presented.Comment: submitted to IEEE Trans. on Information Forensics and Securit
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