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,

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We describe a new watermarking system based on the principles of informed coding and informed embedding. This system is capable of embedding 1380 bits of information in images with dimensions 240 × 368 pixels. Experiments on 2000 images indicate the watermarks are robust to significant valumetric distortions, including additive noise, low pass filtering, changes in contrast, and lossy compression. Our system encodes watermark messages with a modified trellis code in which a given message may be represented by a variety of different signals, with the embedded signal selected according to the cover image. The signal is embedded by an iterative method that seeks to ensure the message will not be confused with other messages, even after addition of noise. Fidelity is improved by the incorporation of perceptual shaping into the embedding process. We show that each of these three components improves performance substantially.

Inspired by a recently proposed constructive framework for the distributed source coding problem, 1 we propose a powerful constructive approach to the watermarking problem, emphasizing the dual roles of "source codes" and "channel codes." In our framework, we explore various source and channel codes to achieve watermarks that are robust to attackers in terms of maximizing the distortion between the corrupted coded-source signal and the original signal while holding the distortion between the coded-source signal and the original signal constant. We solve the resulting combinatorial optimization problem using an original technique based on robust optimization and convex programming. Keywords: Data Hiding, Digital Watermarking, Multimedia, Convex Optimization, Robustness 1. INTRODUCTION Digital watermarking (data hiding) is an emerging research area that has received a considerable amount of attention in recent years. The basic idea behind digital watermarking is to embed information...

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.

El ectronic watermarking can be traced back as far as 1954. Thel ast 10 years has seen considerabl interest in digital watermarking, due in l rge part to concerns aboutil4 al piracy of copyrighted content. In this paper, we consider the fol wing questions: Is the interest warranted? What are the commercial appl ications of the technol ogy? What scientific progress has been made in thel ast 10 years? What are the most exciting areas for research? And where might the next 10 years take us? In our opinion, the interest in watermarking is appropriate. However, we expect that copyright appl1 ationswil be overshadowed by appl1 ations such as broadcast monitoring, authentication, and tracking content distributed within corporations. We further see a variety of appl ications emerging that add val ue to media, such as annotation andl inking content to the Web. Thesel atter appl ications may turn out to be the most compel9 g. Considerabl progress has been made toward enabl g these appl1 ations -- perceptual model5 g, security threats and countermeasures, and the devel pment of a bag of tricks for e#cientimpl51p tations. Further progress is needed in methods for handl g geometric and temporal distortions. We expect other exciting devel opments to arise from research in informed watermarking.

Informed coding is the practice of representing watermark messages with patterns that are dependent on the cover Works. This requires the use of a dirty-paper code, in which each message is represented by a large number of alternative vectors. Most previous dirty-paper codes are based on lattice codes, in which each code vector, or pattern, is a point in a regular lattice. While such codes are very efficient to implement, they suffer from inherent weakness against valumetric scaling, such as changes in audio volume or image brightness. In the present paper, we present an alternative to lattice codes that is inherently robust to valumetric scaling. This code is based on a trellis that has been modified so that each bit value may be coded by traversing several alternative arcs. A Viterbi decoder is used in the detector to identify the path with the highest correlation to the input Work. Since relative correlation values are unaffected by valumetric scaling, the same message will be detected no matter how the input has been scaled. 1.

Quanitization index modulation (QIM) is a computationally efficient method of watermarking with side information. This paper proposes two improvements to the original algorithm. First, the fixed quantization step size is replaced with an adaptive step size that is determined using Watson’s perceptual model. Experimental results on a database of 1000 images illustrate significant improvements in both fidelity and robustness to additive white Gaussian noise. Second, modifying the Watson model such that it scales linearly with valumetric (amplitude) scaling, results in a QIM algorithm that is invariant to valumetric scaling. Experimental results compare this algorithm with both the original QIM and an adaptive QIM and demonstrate superior performance. 1.

We consider a data hiding channel in this paper that is not perfectly known by the encoder and the decoder. The imperfect knowledge could be due to the channel estimation error, time-varying active adversary etc. A mathematical model for this scenario is proposed. Many important attacks such as scaling, geometrical transformations etc. fall under the proposed mathematical model. Minimal assumptions are made regarding the probability distributions of the data-hiding channel. Lower and upper bounds on the data hiding capacity are derived. It is shown that the popular additive Gaussian noise channel model may not su#ce in real-world scenarios; the capacity estimates using the additive Gaussian channel model tend to either over- or under-estimate the capacity under di#erent scenarios. Asymptotic value of the capacity as the signal to noise ratio becomes arbitrarily large is also given. Many existing data hiding capacity estimates are observed to be a special case of the formulas derived in this paper. We also observe that the proposed mathematical model can be applied to real-life applications such as data hiding in image/video. Theoretical results are further explained using numerical values.

Abstract. Watermarking systems can employ either informed detection, where the original cover work is required, or blind detection, where it is not required. While early systems used informed detection, recent work has focused on blind detection, because it is considered more challenging and general. Further, recent work on “dirty-paper watermarking” has suggested that informed detection provides no benefits over blind detection. This paper discusses the dirty-paper assumptions and questions whether they apply to real-world watermarking. We discuss three basic ways in which an informed video-watermark detector, developed at Sarnoff, uses the original work: canceling interference between the cover work and the watermark, canceling subsequent distortions, and tailoring the watermark to the perceptual characteristics of the source. Of these, only the first is addressed by theoretical work on dirty-paper watermarking. Whether the other two can be accomplished equally well with blind watermarking is an open question. 1