Upper and Lower Bounds on Black-Box Steganography

TL;DR

This paper investigates the fundamental limits of black-box steganography, establishing exponential sample complexity lower bounds and introducing near-optimal stegosystems that match these bounds, even in high-entropy scenarios.

Contribution

It provides the first tight bounds on sample complexity for black-box steganography and introduces new stegosystems that approach these theoretical limits.

Findings

Sample complexity is exponential in the stegosystem rate.

First stegosystem matching the lower bound regardless of channel entropy.

High-entropy channels allow stateless near-optimal stegosystems.

Abstract

We study the limitations of steganography when the sender is not using any properties of the underlying channel beyond its entropy and the ability to sample from it. On the negative side, we show that the number of samples the sender must obtain from the channel is exponential in the rate of the stegosystem. On the positive side, we present the first secret-key stegosystem that essentially matches this lower bound regardless of the entropy of the underlying channel. Furthermore, for high-entropy channels, we present the first secret-key stegosystem that matches this lower bound statelessly (i.e., without requiring synchronized state between sender and receiver).