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.

[1]  Christian Cachin,et al.  An information-theoretic model for steganography , 1998, Inf. Comput..

[2]  Shirley Dex,et al.  JR 旅客販売総合システム(マルス)における運用及び管理について , 1991 .

[3]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[4]  John Langford,et al.  Provably Secure Steganography , 2002, IEEE Transactions on Computers.

[5]  Moni Naor,et al.  Small-bias probability spaces: efficient constructions and applications , 1990, STOC '90.

[6]  Hannes Federrath,et al.  Modeling the Security of Steganographic Systems , 1998, Information Hiding.

[7]  Nicholas Hopper,et al.  Public-Key Steganography , 2003, EUROCRYPT.

[8]  Thomas Mittelholzer,et al.  An Information-Theoretic Approach to Steganography and Watermarking , 1999, Information Hiding.

[9]  Silvio Micali,et al.  How to construct random functions , 1986, JACM.

[10]  Moni Naor,et al.  Number-theoretic constructions of efficient pseudo-random functions , 2004, JACM.

[11]  Noga Alon,et al.  Simple construction of almost k-wise independent random variables , 1990, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science.

[12]  Aggelos Kiayias,et al.  Efficient Steganography with Provable Security Guarantees , 2005, Information Hiding.

[13]  G. David Forney,et al.  Concatenated codes , 2009, Scholarpedia.

[14]  Noga Alon,et al.  Simple Construction of Almost k-wise Independent Random Variables , 1992, Random Struct. Algorithms.

[15]  Gustavus J. Simmons,et al.  The Prisoners' Problem and the Subliminal Channel , 1983, CRYPTO.

[16]  Nesir Rasool Mahmood,et al.  Public Key Steganography , 2014 .