This work concerns the definition of conditional mutual information in the framework of Algorithmic Information Theory (AIT), which is of use when no probabilistic model of the data is available, or hard to devise. We introduce a practical way to construct a conditional mutual information quantity which respects the chain rule and the data processing inequalityThe proposed implementation, named SALZA, allows to accomplish various information-theoretic tasks on sequences. The algorithmic model of the data used in this work is that of the well-known Lempel-Ziv primitive: we assume new data is to be expressed in terms of references to prior data.SALZA enables a flexible specification of prior data and extracts information quantities based on the significance of the references to these prior data. The tool readily implements the computation of an information measure based on LZ77 and a universal classifier based on the Ziv-Merhav relative coder for the universal clustering of sequences.Illustration of the proposed implementation is provided on clustering and causality inference examples.

In the above paper [1, p. 1215], it was assumed that [1, eq. (8)] was a convex optimization problem. However,$C(X)$(see [1, eq. (6)]) is in general not convex, since it is an absolute value of the difference between two convex functions. Indeed, the proposed cost function is non-convex. By using the subgradient method with the chosen steps, however, we can get a quite good solution (probably a local minimum) that has a sufficiently low cost function value. This makes the proposed algorithm work sufficiently well, as demonstrated by the experimental results.

Median filtering enjoys its popularity as a widely adopted image denoising and smoothing tool. It is also used by anti-forensic researchers in helping disguise traces of other image processing operations, e.g., image resampling and JPEG compression. This paper proposes an image variational deconvolution framework for both quality enhancement and anti-forensics of median filtered (MF) images. The proposed optimization-based framework consists of a convolution term, a fidelity term with respect to the MF image, and a prior term. The first term is for the approximation of the median filtering process, using a convolution kernel. The second fidelity term keeps the processed image to some extent still close to the MF image, retaining some denoising or other image processing artifact hiding effects. Using the generalized Gaussian as the distribution model, the last image prior term regularizes the pixel value derivative of the obtained image so that its distribution resembles the original one. Our method can serve as an MF image quality enhancement technique, whose efficacy is validated by experiments conducted on MF images which have been previously “salt & pepper” noised. Using another parameter setting and with an additional pixel value perturbation procedure, the proposed method outperforms the state-of-the-art median filtering anti-forensics, with a better forensic undetectability against existing detectors as well as a higher visual quality of the processed image. Furthermore, the feasibility of concealing image resampling traces and JPEG blocking artifacts is demonstrated by experiments, using the proposed median filtering anti-forensic method.

This paper proposes a JPEG anti-forensic method, which aims at removing from a given image the footprints left by JPEG compression, in both the spatial domain and DCT domain. With reasonable loss of image quality, the proposed method can defeat existing forensic detectors that attempt to identify traces of the image JPEG compression history or JPEG anti-forensic processing. In our framework, first because of a total variation-based deblocking operation, the partly recovered DCT information is thereafter used to build an adaptive local dithering signal model, which is able to bring the DCT histogram of the processed image close to that of the original one. Then, a perceptual DCT histogram smoothing is carried out by solving a simplified assignment problem, where the cost function is established as the total perceptual quality loss due to the DCT coefficient modification. The second-round deblocking and de-calibration operations successfully bring the image statistics that are used by the JPEG forensic detectors to the normal status. Experimental results show that the proposed method outperforms the state-of-the-art methods in a better tradeoff between the JPEG forensic undetectability and the visual quality of processed images. Moreover, the application of the proposed anti-forensic method in disguising double JPEG compression artifacts is proven to be feasible by experiments.

This paper studies the impact of secure watermark embedding in digital images by proposing a practical implementation of secure spread-spectrum watermarking using distortion optimization. Because strong security properties (key-security and subspace-security) can be achieved using natural watermarking (NW) since this particular embedding lets the distribution of the host and watermarked signals unchanged, we use elements of transportation theory to minimize the global distortion. Next, we apply this new modulation, called transportation NW (TNW), to design a secure watermarking scheme for grayscale images. The TNW uses a multiresolution image decomposition combined with a multiplicative embedding which is taken into account at the distribution level. We show that the distortion solely relies on the variance of the wavelet subbands used during the embedding. In order to maximize a target robustness after JPEG compression, we select different combinations of subbands offering the lowest Bit Error Rates for a target PSNR ranging from 35 to 55 dB and we propose an algorithm to select them. The use of transportation theory also provides an average PSNR gain of 3.6 dB on PSNR with respect to the previous embedding for a set of 2000 images.

International audience

This paper proposes an anti-forensic method that disguises the footprints left by JPEG compression, whose objective is to fool existing JPEG forensic detectors while keeping a high visual quality of the processed image. First we examine the reliability of existing detectors and point out the potential vulnerability of the quantization table estimation based detector. Then we construct a new, non-parametric method to DCT histogram smoothing without any histogram statistical model. Finally JPEG forensic detectors are fooled by optimizing an objective function considering both the anti-forensic terms and a natural image statistical model. We show that compared to the state-of-the-art methods the proposed JPEG anti-forensic method is able to achieve a higher image visual quality while being undetectable under existing detectors.

This paper presents a study of the embedding of Tardos binary fingerprinting codes with watermarking techniques. By taking into account the security of the embedding scheme, we present a new approach for colluding strategies which relies on the possible estimation error rate of the code symbols (denoted$\epsilon$). We derive a new attack strategy called “$\epsilon$-Worst Case Attack” and show its efficiency using the computation of achievable rates for simple decoding. Then we consider the interplay between security and robustness regarding the accusation performances of the fingerprinting scheme and show that 1) for the same accusation rate secure schemes can afford to be less robust than insecure ones, and 2) that secure schemes enable to cast the Worst Case Attack into an interleaving attack. Additionally, we use the security analysis of the watermarking scheme to derive from$\epsilon$a security attack for a fingerprinting scheme based on Tardos codes and a new scheme called stochastic spread-spectrum watermarking. We compare a removal attack against an AWGN robustness attack and we show that for the same distortion, the combination of a fingerprinting attack and a security attack easily outperform classical attacks even with a small number of observations.

The paper proposes a new approach for evaluating the security levels of digital watermarking schemes, which is more in line with the formulation proposed in cryptography. We first exhibit the class of equivalent decoding keys. These are the keys allowing a reliable decoding of contents watermarked with the secret key. Then, we evaluate the probability that the adversary picks an equivalent key. The smaller this probability, the higher the key length. This concept is illustrated on two main families of watermarking schemes: DC-QIM (Distortion Compensation Quantization Index Modulation) and SS (Spread Spectrum). The trade-off robustness-security is again verified and gives some counter-intuitive results: For instance, the security of SS is a decreasing function of the length of the secret vector at a fixed Document to Watermark power ratio. Additionally, under the Known Message Attack, the practical key length of the watermarking scheme rapidly decreases to 0 bits per symbol.

This article is a theoretical study on binary Tardos' fingerprinting codes embedded using watermarking schemes. Our approach is derived from and encompasses both security and robustness constraints. We assume here that the coalition has estimated the symbols of the fingerprinting code by the way of a security attack, the quality of the estimation relying on the security of the watermarking scheme. Taking into account the fact that the coalition can perform estimation errors, we update the Worst Case Attack, which minimises the mutual information between the sequence of one colluder and the pirated sequence forged by the coalition. After comparing the achievable rates of the previous and proposed Worst Case Attack according to the estimation error, we conclude this analysis by comparing the robustness of no-secure embedding schemes versus secure ones. We show that, for low probabilities of error during the decoding stage (e.g. highly robust watermarking schemes), security enables to increase the achievable rate of the fingerprinting scheme.

Abstract — It has recently been discovered that using pseudorandom sequences as carriers in spread-spectrum techniques for data-hiding is not at all a sufficient condition for ensuring datahiding security. Using proper and realistic a priori hypothesis on the messages distribution, it is possible to accurately estimate the secret carriers by casting this estimation problem into a Blind Source Separation problem. After reviewing relevant works on spread-spectrum security for watermarking, we further develop on this topic to introduce the concept of security classes which broaden previous notions in watermarking security and fills the gap with steganography security as defined by Cachin. We define four security classes, namely, by order of creasing security: insecurity, key-security, subspace-security and stego-security. To illustrate these views, we present two new modulations for truly secure watermarking in the Watermark-Only-Attack (WOA) framework. The first one is called Natural Watermarking and can be made either stego-secure or subspace-secure. The second is called Circular Watermarking and is key-secure. We show that Circular Watermarking has robustness comparable to that of the insecure classical spread spectrum. We shall also propose information leakage measures to highlight the security level of our new spread-spectrum modulations. Index Terms — Spread spectrum watermarking, security. EDICS Category: WAT-SSPM

State-of-the-art blind and robust 3D watermarking schemes already withstand combinations of a wide variety of attacks (e.g. noise addition, simplification, smoothing, ...) except cropping. This attack is however very common and should be dealt with in a copyright protection framework. In this paper, we propose a technique which enables to extend the robustness of such schemes to cropping. Our algorithm proceeds by the automatic detection of robust shape feature points which are then used for the embedding of a watermark in a local neighborhood. We show that robustness against cropping and other common attacks is achieved provided that at least one feature point as well as its corresponding local neighborhood are retrieved.

This article proposes a theory of watermarking security based on a cryptanalysis point of view. The main idea is that information about the secret key leaks from the observations, for instance watermarked pieces of content, available to the opponent. Tools from information theory (Shannon's mutual information and Fisher's information matrix) can measure this leakage of information. The security level is then defined as the number of observations the attacker needs to successfully estimate the secret key. This theory is applied to two common watermarking methods: the substitutive scheme and the spread spectrum based techniques. Their security levels are calculated against three kinds of attack

Spectral decomposition of mesh geometry has first been introduced by Taubin for geometry processing purposes. It has been extended to address transmission issues by Kami & Gotsman. Such decompositions give rise to pseudofrequential information of the geometry defined over the mesh connectivity. For large meshes a piecewise decomposition has to be applied in order to restrict the complexity of the transform. In this paper, we propose to introduce overlap for its spectral representation. We show visual gains obtained in compression and progressive transmission of mesh geometry.

The Certimark Consortium consists of 15 partners from European industry and academia. The consortium has been developing a benchmark suite that will enable its users to evaluate digital watermarking technologies. Here, we present the basic architecture of the benchmark suite and its underlying rationale. We also provide an outlook on future plans for making the benchmark suite available outside the consortium and for its further development.