Computer Science Department
School of Computer Science, Carnegie Mellon University
Toward a Theory of Steganography
Nicholas J. Hopper
This thesis initiates the study of steganography from a cryptographic point of view. We give a precise model of a communication channel and a rigorous definition of steganographic security, and prove that relative to a channel oracle, secure steganography exists if and only if one-way functions exist. We give tightly matching upper and lower bounds on the maximum rate of any secure stegosystem. We introduce the concept of steganographic key exchange and public-key steganography, and show that provably secure protocols for these objectives exist under a variety of standard number-theoretic assumptions. We consider several notions of active attacks against steganography, show how to achieve each under standard assumptions, and consider the relationships between these notions. Finally, we extend the concept of steganograpy as covert communication to include the more general concept of covert computation.