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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. The authors 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. They then construct a steganographic protocol, based on rejection sampling from the channel, that is provably secure and has nearly optimal bandwidth under these conditions.
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