Randomness Efficient Steganography (original) (raw)

Steganographic protocols enable 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 secure in the framework of Hopper et al [2]. We first present a "one-time stegosystem" that allows two parties to transmit messages of fixed length (depending on the length of the shared key) with information-theoretic security guarantees. Employing 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 long messages in a symmetric encryption framework. The advantage of our construction, compared to all previous work is randomness efficiency: in the information theoretic setting our protocol embeds a message of length n bits using a shared secret key of length (1 + o(1))n bits while achieving security 2 −n/ polylog n ; simply put this gives a rate of key over message that is 1 as n → ∞ (the previous best result [5] achieved a constant rate > 1 regardless of the security offered). In this sense, our protocol is the first truly randomness efficient steganographic system and breaks through a natural barrier imposed by bounded-round rejecting sampling. Furthermore, in our protocol, we can permit a portion of the shared secret key to be public while retaining precisely n private key bits. In this setting, by separating the public and the private randomness of the shared key, we achieve security of 2 −n. Our result comes as an effect of a novel application of randomness extractors to stegosystem design. Definition 2. The min-entropy of a random variable X, taking values in a set V , is the quantity H ∞ (X) min v∈V (− log Pr[X = v]). Statistical Distance We use statistical distance to measure the distance between two random variables. Shoup [14] presents a detailed discussion on statistical distance and its properties.