Using Kolmogorov Complexity for Understanding Some Limitations on Steganography

TL;DR

This paper explores the limitations of perfect steganography systems by applying Kolmogorov complexity, showing that for sources with maximal complexity, high-speed perfect stegosystems cannot exist.

Contribution

It introduces a complexity-based framework to identify sources where perfect steganography cannot achieve high transmission speeds.

Findings

Perfect stegosystems do not exist for sources with maximal Kolmogorov complexity.

High-speed perfect stegosystems require complexity comparable to the source.

Certain sources inherently limit steganographic capacity due to their complexity.

Abstract

Recently perfectly secure steganographic systems have been described for a wide class of sources of covertexts. The speed of transmission of secret information for these stegosystems is proportional to the length of the covertext. In this work we show that there are sources of covertexts for which such stegosystems do not exist. The key observation is that if the set of possible covertexts has a maximal Kolmogorov complexity, then a high-speed perfect stegosystem has to have complexity of the same order.