A One-time Stegosystem and Applications to Efficient Covert Communication

We present the first information-theoretic steganographic protocol with an asymptotically optimal ratio of key length to message length that operates on arbitrary covertext distributions with constant min-entropy. Our results are also applicable to the computational setting: our stegosystem can be composed over a pseudorandom generator to send longer messages in a computationally secure fashion. In this respect our scheme offers a significant improvement in terms of the number of pseudorandom bits generated by the two parties in comparison to previous results known in the computational setting. Central to our approach for improving the overhead for general distributions is the use of combinatorial constructions that have been found to be useful in other contexts for derandomization: almost $t$-wise independent function families

Efficient Steganography with Provable Security Guarantees

We provide a new provably-secure steganographic encryption protocol that is proven secure in the complexity-theoretic framework of Hopper et al. The fundamental building block of our steganographic encryption protocol is a "one-time stegosystem" that allows two parties to transmit one-time steganographic messages of length shorter than the shared key with information-theoretic security guarantees. The employment of a pseudorandom number generator (PRNG) allows the 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. The advantage of our construction compared to that of Hopper et al. is that it avoids the use of a pseudorandom function family and instead relies (directly) on a PRNG in a way that provides a linear versus constant improvement in the number of applications of the underlying (say) one-way permutation per bit transmitted. This advantageous trade-o# is achieved by substituting the pseudorandom function family employed in the previous construction with an appropriate combinatorial construction that has been used extensively in derandomization, namely almost t-wise independent function families