Constructing Perfect Steganographic Systems

TL;DR

This paper introduces perfectly secure steganographic systems for finite-memory sources that do not require keys and can approach the Shannon entropy limit, while also discussing computational limitations of such systems.

Contribution

It presents keyless, perfectly secure steganographic systems for finite-memory sources with near-optimal transmission rates, and analyzes fundamental computational constraints.

Findings

Steganographic systems achieve perfect security with no keys.

Transmission speed can approach Shannon entropy limit.

Certain sources impose exponential complexity on efficient stegosystems.

Abstract

We propose steganographic systems for the case when covertexts (containers) are generated by a finite-memory source with possibly unknown statistics. The probability distributions of covertexts with and without hidden information are the same; this means that the proposed stegosystems are perfectly secure, i.e. an observer cannot determine whether hidden information is being transmitted. The speed of transmission of hidden information can be made arbitrary close to the theoretical limit - the Shannon entropy of the source of covertexts. An interesting feature of the suggested stegosystems is that they do not require any (secret or public) key. At the same time, we outline some principled computational limitations on steganography. We show that there are such sources of covertexts, that any stegosystem that has linear (in the length of the covertext) speed of transmission of hidden text must have an exponential Kolmogorov complexity. This shows, in particular, that some assumptions on the sources of covertext are necessary.