Information-theoretic analysis of information hiding

An information–theoretic analysis of information hiding is presented in this paper, forming the theoretical basis for design of information–hiding systems. Information hiding is an emerging research area which encompasses applications such as copyright protection for digital media, watermarking, fingerprinting, and steganography. In these applications, information is hidden within a host data set and is to be reliably communicated to a receiver. The host data set is purposely corrupted, but in a covert way, designed to be imperceptible to a casual analysis. Next, an attacker may seek to destroy this hidden information, and for this purpose, introduce additional distortion to the data set. Cryptographic keys may be available to the information hider and to the decoder. We formalize these notions and evaluate the hiding capacity, which upper–bounds the rates of reliable transmission and quantifies the fundamental tradeoff between three quantities: the achievable information–hiding rates and the allowed distortion levels for the information hider and the attacker. The hiding capacity is the value of a game between the information hider and the attacker. The optimal attack strategy is the solution of a particular rate-distortion problem, and the optimal hiding strategy is the solution to a channel coding problem. Explicit formulas for capacity are given in several cases, including the important special case of small distortions. In some cases, including the one above, the hiding capacity is the same whether or not the decoder knows the host data set. It is shown that existing information–hiding systems in the literature operate far below capacity.