Watermarking models a copyright protection mechanism where an original source sequence or "covertext" is modified before distribution to the public in order to embed some extra information. The embedding should be transparent (i.e., the modified data sequence or "stegotext" should be similar to the covertext) and robust (i.e., the extra information should be recoverable even if the stegotext is modified further, possibly by a malicious "attacker"). We compute the coding capacity of the watermarking game for a Gaussian covertext and squared-error distortions. Both the public version of the game (covertext known to neither attacker nor decoder) and the private version of the game (covertext unknown to attacker but known to decoder) are treated. While the capacity of the former cannot, of course, exceed the capacity of the latter, we show that the two are, in fact, identical. These capacities depend critically on whether the distortion constraints are required to be met in expectation or with probability one. In the former case the coding capacity is zero, whereas in the latter it coincides with the value of related zero-sum dynamic mutual informations games of complete and perfect information. # Parts of this work were presented at the 2000 Conference on Information Sciences and Systems (CISS '00), Princeton University, Princeton, NJ, March 15--17, 2000, and at the 2000 IEEE International Symposium on Information Theory (ISIT '00), Sorrento, Italy, June 25--30, 2000.

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.

Digital fingerprinting is a technique for identifying users who might try to use multimedia content for unintended purposes, such as redistribution. These fingerprints are typically embedded into the content using watermarking techniques that are designed to be robust to a variety of attacks. A cost-e#ective attack against such digital fingerprints is collusion, where several di#erently marked copies of the same content are combined to disrupt the underlying fingerprints. In this paper, we investigate the problem of designing fingerprints that can withstand collusion and allow for the identification of colluders. We begin by introducing the collusion problem for additive embedding. We then study the e#ect that averaging collusion has upon orthogonal modulation. We introduce an e#cient detection algorithm for identifying the fingerprints associated with K colluders that requires log(n/K)) correlations for a group of n users. We next develop a fingerprinting scheme based upon code modulation that does not require as many basis signals as orthogonal modulation. We propose a new class of codes, called anti-collusion codes (ACC), which have the property that the composition of any subset of K or fewer codevectors is unique. Using this property, we can therefore identify groups of K or fewer colluders. We present a construction of binary-valued ACC under the logical AND operation that uses the theory of combinatorial designs and is suitable for both the on-o# keying and antipodal form of binary code modulation. In order to accommodate n users, our code construction requires only # n) orthogonal signals for a given number of colluders. We introduce four di#erent detection strategies that can be used with our ACC for identifying a suspect set of colluders. We demonstrate th...

Steganography is used to hide the occurrence of communication. Recent suggestions in US newspapers indicate that terrorists use steganography to communicate in secret with their accomplices. In particular, images on the Internet were mentioned as the communication medium. While the newspaper articles sounded very dire, none substantiated these rumors. To determine whether there is steganographic content on the Internet, this paper presents a detection framework that includes tools to retrieve images from the world wide web and automatically detect whether they might contain steganographic content. To ascertain that hidden messages exist in images, the detection framework includes a distributed computing framework for launching dictionary attacks hosted on a cluster of loosely coupled workstations. We have analyzed two million images downloaded from eBay auctions and one million images obtained from a USENET archive but have not been able to find a single hidden message.

A considerable amount of attention has been lately payed to a number of data hiding methods based in quantization, seeking to achieve in practice the results predicted by Costa for a channel with side information at the encoder. With the objective of filling a gap in the literature, this paper supplies a fair comparison between significant representatives of both this family of methods and the former spread-spectrum approaches that make use of near-optimal ML decoding; the comparison is based on measuring their probabilities of decoding error in the presence of channel distortions. Accurate analytical expressions and tight bounds for the probability of decoding error are given and validated by means of Monte Carlo simulations. For Dithered Modulation (DM) a novel technique that allows to obtain tighter bounds to the probability of error is presented. Within the new framework, the strong points and weaknesses of both methods are distinctly displayed. This comparative study allows us to propose a new technique named "Quantized Projection" (QP), which by adequately combining elements of those previous approaches, produces gains in performance.

Quantization index modulation (QIM) methods, a class of digital watermarking and information embedding methods, achievevery efficient trade-offs among the amount of embedded information (rate), the amount of embedding-induced distortion to the host signal, and the robustness to intentional and unintentional attacks. For example, we show that against independent additive Gaussian attacks, which are good models for at least some types of uninformed and unintentional attacks, QIM methods exist that achieve the best possible rate-distortion-robustness trade-offs (i.e., capacity) asymptotically at high rates and achieve performance within a few dB of capacity at all finite rates. Furthermore, low-complexity realizations of QIM methods, such as so-called dither modulation, have also been shown to achieve favorable rate-distortion-robustness trade-offs. We further develop preprocessing and postprocessing techniques that enable QIM to fully achieve capacity, not only against Gaussian attacks but also ag...

This article discusses existing steganographic systems and presents recent research in detecting them via statistical steganalysis. Other surveys focus on the general usage of information hiding and watermarking or else provide an overview of detection algorithms

We derive capacity formulas and strategies for transmission over the the channel Y = X + S + N , 1 n EkXk 2 PX , where the interference S is a (strong) stochastic process or an arbitrarily varying sequence, known causally or with nite anticipation at the transmitter but not at the receiver. In the causal side information case, we show that strategies associated with entropy constrained quantizers provide lower and upper bounds on the capacity. At high SNR conditions, i.e., if N is weak relative to the power constraint PX , these bounds coincide, the optimum strategies take the form of scalar lattice translations, and the capacity loss due to not having S at the receiver is shown to be exactly the \shaping gain" 0.254 bit. We also extend these ideas to any SNR and to non-causal side information, by incorporating \MMSE weighting", and by using k- dimensional lattices. For Gaussian N , the capacity loss of this scheme is upper bounded by 0:5 log(2eG k ), where G k is the normalize...

Copyright notification and enforcement, authentication, covert communication, and hybrid transmission are examples of emerging multimedia applications for digital watermarking methods, methods for embedding one signal (e.g., the digital watermark) within another “host ” signal to form a third, “composite ” signal. The embedding is designed to achieve efficient trade-offs among the three conflicting goals of maximizing information-embedding rate, minimizing distortion between the host signal and composite signal, and maximizing the robustness of the embedding. Quantization indexmodulation (QIM) methods are a class of watermarking methods that achieve provably good rate-distortion-robustness performance. Indeed, QIM methods exist that achieve performance within a few dB of capacity in the case of a (possibly colored) Gaussian host signal and an additive (possibly colored) Gaussian noise channel. Also, QIM methods can achieve capacity with a type of postprocessing called distortion compensation. This capacity is independent of host signal statistics, and thus, contrary to popular belief, the information-embedding capacity when the host signal is not available at the decoder is the same as the case when the host signal is available at the decoder. A low-complexity realization of QIM called dither modulation has previously been proven to be better than both linear methods of spread spectrum and nonlinear methods of low-bit(s) modulation against square-error distortionconstrained intentional attacks. We introduce a new form of dither modulation called spread-transform dither modulation that retains these favorable performance characteristics while achieving better performance against other attacks such as JPEG compression.

In this paper, we show that the communication channel known as writing in memory with defective cells [1][2] is a relevant information-theoretical model for a specific case of passive warden steganography when the sender embeds a secret message into a subset C of the cover object X without sharing C with the recipient. The set C, also called the selection channel, could be arbitrary, determined by the sender from the cover object using a deterministic, pseudo-random, or a truly random process. We call this steganography “writing on wet paper ” and realize it using a simple variable-rate random linear code that gives the sender a convenient flexibility and control over the embedding process and is thus suitable for practical implementation. The importance of the wet paper scenario for covert communication is discussed within the context of adaptive steganography and perturbed quantization steganography [3]. Heuristic arguments supported by tests using blind steganalysis [4] indicate that the wet paper steganography provides improved steganographic security and is less vulnerable to steganalytic attacks compared to existing methods with shared selection channels.