Randomness-optimal Steganography

Steganographic protocols enables one to “embed” covert messages into inconspicuous data over a public communication channel in such a way that no one, aside from the sender and the intended receiver can even detect the presence of the secret message. In this paper, we provide a new provably-secure, private-key steganographic encryption protocol. We prove the security of our protocol in the complexitytheoretic framework where security is quantified as the advantage (compared to a random guess) that the adversary has in distinguishing between innocent covertext and stegotext that embeds a message of his choice. The fundamental building block of our steganographic encryption protocol is a “one-time stegosystem” that allows two parties to transmit messages of length at most that of the shared key with information-theoretic security guarantees. The employment of a pseudorandom generator (PRG) permits secure transmission of longer messages in the same way that such a generator allows the use of one-time pad encryption for messages longer than the key in symmetric encryption. In this paper, we initiate the study of employing randomness extractors in a steganographic protocol construction to embed secret messages over the channel. To the best of our knowledge this is the first time randomness extractors have been applied in steganography.

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