Key-Efficient Steganography

Abstract

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 length at most that of the shared key with information-theoretic security guarantees; employing a pseudorandom generator (PRG) then permits secure transmission of longer messages in a striaghtforward manner.

The advantage of our construction in comparison with previous work is key-length efficiency: in the information-theoretic setting our protocol embeds a n bit message using a shared secret key of length (1 + o(1))n while achieving security $2^{-n/\log^{O(1)}n}$: this gives a rate of key length over message length that converges to 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 key-length efficient steganographic system. 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.