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. Index Terms—Channel capacity, cryptography, fingerprinting, game theory, information hiding, network information theory,

Research on information embedding and particularly information hiding techniques has received considerable attention within the last years due to its potential application in multimedia security. Digital watermarking, which is an information hiding technique where the embedded information is robust against malicious or accidental attacks, might offer new possibilities to enforce the copyrights of multimedia data. In this article, the specific case of information embedding into independent identically distributed (IID) data and attacks by additive white Gaussian noise (AWGN) is considered. The original data is not available to the decoder. For Gaussian data, Costa proposed already in 1983 a scheme that theoretically achieves the capacity of this communication scenario. However, Costa's scheme is not practical. Thus, several research groups have proposed suboptimal practical communication schemes based on Costa's idea. The goal of this artical is to give a complete performance analysis of the scalar Costa scheme (SCS) which is a suboptimal technique using scalar embedding and reception functions. Information theoretic bounds and simulation results with state-of-the-art coding techniques are compared. Further, reception after amplitude scaling attacks and the invertibility of SCS embedding are investigated. Keywords Information embedding, communication with side-information, blind digital watermarking, scalar Costa scheme I.

Blind digital watermarking is the communication of information via multimedia host data, where the unmodified host data is not available to the watermark detector. Many watermarking schemes suffer considerably from the remaining host-signal interference. For the additive white Gaussian case, Costa showed theoretically that interference from the host can be eliminated. However, the proof involves a huge, unstructured, random codebook, which is not feasible in practical systems. We present a suboptimal, practical scheme that employs a lattice-structured codebook to reduce complexity. The performance of the proposed scheme is compared to the information-theoretic limit and similar recent proposals.

Using a theoretical approach based on random processes, signal processing, and information theory, we study the performance of digital watermarks subjected to an attack consisting of linear shift-invariant filtering and additive colored Gaussian noise. Watermarking is viewed as communication over a hostile channel, where the attack takes place. The attacker attempts to minimize the channel capacity under a constraint on the attack distortion (distortion of the attacked signal), and the owner attempts to maximize the capacity under a constraint on the embedding distortion (distortion of the watermarked signal). The distortion measure is frequency-weighted mean-squared error (MSE). In a conventional additive-noise channel, communication is most difficult when the noise is white and Gaussian, so we first investigate an effective white-noise attack based on this principle. We then consider the problem of resisting this attack and show that capacity is maximized when a power-spectrum condition (PSC) is fulfilled. The PSC states that the power spectrum of the watermark should be directly proportional to that of the original signal. However, unlike a conventional channel, the hostile attack channel adapts to the watermark, not vice versa. Hence, the effective white-noise attack is suboptimal. We derive the optimum attack, which minimizes the channel capacity for a given attack distortion. The attack can be roughly characterized by a rule-of-thumb: At low attack distortions, it adds noise, and at high attack distortions, it discards frequency components. Against the optimum attack, the PSC does not maximize capacity at all attack distortions. Also, there is no unique watermark power spectrum that maximizes capacity over the entire range of attack distortions. T...

An information-theoretic model for image watermarking and data hiding is presented in this paper. Recent theoretical results are used to characterize the fundamental capacity limits of image watermarking and data-hiding systems. Capacity is determined by the statistical model used for the host image, by the distortion constraints on the data hider and the attacker, and by the information available to the data hider, to the attacker, and to the decoder. We consider autoregressive, block-DCT and wavelet statistical models for images and compute datahiding capacity for compressed and uncompressed host-image sources. Closed-form expressions are obtained under sparse-model approximations. Models for geometric attacks and distortion measures that are invariant to such attacks are considered.

Recently it was shown that, in some situations, blind watermarking can perform as well as watermarking schemes with the host signal available to the decoder. In this paper, blind watermarking of colored Gaussian host signals in the presence of filtering and additive Gaussian noise attacks is discussed. Three suboptimal but practical schemes are compared with a scheme where the host signal is available at the decoder. The performance is analyzed theoretically and experimentally for image watermarking.

This tutorial paper reviews the theory and design of codes for hiding or embedding information in signals such as images, video, audio, graphics, and text. Such codes have also been called watermarking codes; they can be used in a variety of applications, including copyright protection for digital media, content authentication, media forensics, data binding, and covert communications. Some of these applications imply the presence of an adversary attempting to disrupt the transmission of information to the receiver; other applications involve a noisy, generally unknown, communication channel. Our focus is on the mathematical models, fundamental principles, and code design techniques that are applicable to data hiding. The approach draws from basic concepts in information theory, coding theory, game theory, and signal processing, and is illustrated with applications to the problem of hiding data in images. Keywords—Coding theory, data hiding, game theory, image processing, information theory, security, signal processing, watermarking. I.

In many blind watermarking proposals, the unwatermarked host data is viewed as unavoidable interference. Recently, however, it has been shown that blind watermarking corresponds to communication with side information (i.e., the host data) at the encoder. For a Gaussian host data and Gaussian channel, Costa showed that blind watermarking can theoretically eliminate all interference from the host data. Our previous work presented a practical blind watermarking scheme based on Costa's idea and called "scalar Costa scheme" (SCS). SCS watermarking was analyzed theoretically and initial experimental results were presented. This paper discusses further practical implications when implementing SCS. We focus on the following three topics: (A) high-rate watermarking, (B) low-rate watermarking, and (C) restrictions due to finite codeword lengths. For (A), coded modulation is applied for a rate of 1 watermark bit per host-data element, which is interesting for information-hiding applications. For (B), low rates can be achieved either by repeating watermark bits or by projecting them in a random direction in signal space (spread-transform SCS). We show that spread-transform SCS watermarking performs better than SCS watermarking with repetition coding. For (C), Gallager's random-coding exponent is used to analyze the influence of codeword length on SCS performance.

Steganography is the art of communicating a message by embedding it into multimedia data. It is desired to maximize the amount of hidden information (embedding rate) while preserving security against detection by unauthorized parties. An appropriate information-theoretic model for steganography has been proposed by Cachin. A steganographic system is perfectly secure when the statistics of the cover data and the stego data are identical, which means that the relative entropy between the cover data and the stego data is zero. For image data, another constraint is that the stego data must look like a "typical image." A tractable objective measure for this property is the (weighted) mean squared error between the cover image and the stego image (embedding distortion). Two different schemes are investigated. The first one is derived from a blind watermarking scheme. The second scheme is designed specifially for steganography such that perfect security is achieved, which means that the relative entropy between cover data and stego data tends to zero. In this case, a noiseless communication channel is assumed. Both schemes store the stego image in the popular JPEG format. The performance of the schemes is compared with respect to security, embedding distortion and embedding rate.

Information-theoretic analyses for data hiding prescribe embedding the hidden data in the choice of quantizer for the host data. In this paper, we consider a suboptimal implementation of this prescription, with a view to hiding high volumes of data in images with low perceptual degradation. Our two main findings are as follows: (a) In order to limit perceptual distortion while hiding large amounts of data, the hiding scheme must use perceptual criteria in addition to information-theoretic guidelines.