Information-theoretic analysis of information hiding

Abstract

Abstract-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, steganography, and data embedding. 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 intentionally 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. Side information (in the form of cryptographic keys and/or information about the host signal) 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. The hiding capacity is derived by extending the Gel'fand-Pinsker theory of communication with side information at the encoder. The extensions include the presence of distortion constraints, side information at the decoder, and unknown communication channel. Explicit formulas for capacity are given in several cases, including Bernoulli and Gaussian problems, as well as the important special case of small distortions. In some cases, including the last two above, the hiding capacity is the same whether or not the decoder knows the host data set. It is shown that many existing information-hiding systems in the literature operate far below capacity.

Towards geometrically robust data-hiding with structured codebooks

“…O'Sullivan, Moulin and Ettinger were among the first who recognized this game [1]. In the extended version of the previous paper [2], Moulin and O'Sullivan have considered two possible set-ups. In the first set-up they assumed the availability of host at both encoder and decoder, i.e., the so-called private game and in the second one they considered a case, where the host is available only at the encoder, i.e., public game.…”

Reducing Host Interference from Spread Spectrum Watermarking

“…Hence, even for situations where the watermark channel does not introduce any attack, correct detection of hidden information is limited. The host interference is an inherent noise in SSW algorithms and is the main reason for the relatively low embedding rate in SSW [7].…”

Watermarking via optimization algorithms for quantizing randomized semi-global image statistics

“…On the other hand, the former can be modeled as an information-theoretic problem of communications with transmitter side information. Recently, extensive research has been carried out on the data embedding problem and fundamental performance limits have been studied thoroughly, see for instance [2][3][4][5][6] and references therein. 2 Comparatively, research work in security-based watermarking is much more limited to the best of our knowledge.…”

“…Recently, extensive research has been carried out on the data embedding problem and fundamental performance limits have been studied thoroughly, see for instance [2][3][4][5][6] and references therein. 2 Comparatively, research work in security-based watermarking is much more limited to the best of our knowledge. Ideally, one needs to show that to break a proposed secure watermarking system within perceptual constraints is equivalent to solving a hard problem in the presence of a resource-bounded adversary (by using tools from complexity theory); this is our ultimate goal.…”

“…Although our scheme is specifically designed for verification purposes, it can be extended to the decoding problem with little effort, see[1] 2. Note that, in most of these works, there are significant restrictions on the attack channel, e.g., often memoryless or block-wise memoryless attacks are considered.…”