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Issue No. 05 - May (2009 vol. 58)
ISSN: 0018-9340
pp: 662-676
Nicholas Hopper , University of Minnesota, Minneapolis
Luis von Ahn , Carnegie Mellon University, Pittsburgh
John Langford , Yahoo! Research, New York
Steganography is the problem of hiding secret messages in "innocent-looking” public communication so that the presence of the secret messages cannot be detected. This paper introduces a cryptographic formalization of steganographic security in terms of computational indistinguishability from a channel, an indexed family of probability distributions on cover messages. We use cryptographic and complexity-theoretic proof techniques to show that the existence of one-way functions and the ability to sample from the channel are necessary conditions for secure steganography. We then construct a steganographic protocol, based on rejection sampling from the channel, that is provably secure and has nearly optimal bandwidth under these conditions. This is the first known example of a general provably secure steganographic protocol. We also give the first formalization of "robust” steganography, where an adversary attempts to remove any hidden messages without unduly disrupting the cover channel. We give a necessary condition on the amount of disruption the adversary is allowed in terms of a worst case measure of mutual information. We give a construction that is provably secure and computationally efficient and has nearly optimal bandwidth, assuming repeatable access to the channel distribution.
Steganography, covert channels, provable security.

N. Hopper, J. Langford and L. von Ahn, "Provably Secure Steganography," in IEEE Transactions on Computers, vol. 58, no. , pp. 662-676, 2008.
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