An analysis of steganographic systems subject to the following perfect undetectability condition is presented in this paper. Following embedding of the message into the covertext, the resulting stegotext is required to have exactly the same probability distribution as the covertext. Then no statistical test can reliably detect the presence of the hidden message. We refer to such steganographic schemes as perfectly secure. A few such schemes have been proposed in recent literature, but they have vanishing rate. We prove that communication performance can potentially be vastly improved; specifically, our basic setup assumes independent and identically distributed (i.i.d.) covertext, and we construct perfectly secure steganographic codes from public watermarking codes using binning methods and randomized permutations of the code. The permutation is a secret key shared between encoder and decoder. We derive (positive) capacity and random-coding exponents for perfectly secure steganographic systems. The error exponents provide estimates of the code length required to achieve a target low error probability. In some applications, steganographic communication may be disrupted by an active warden, modeled here by a compound discrete memoryless channel (DMC). The transmitter and warden are subject to distortion constraints. We address the potential loss in communication performance due to the perfect-security requirement. This loss is the same as the loss obtained under a weaker order-1 steganographic requirement that would just require matching of first-order marginals of the covertext and stegotext distributions. Furthermore, no loss occurs if the covertext distribution is uniform and the distortion metric is cyclically symmetric; steganographic capacity is then achieved by randomized linear codes. Our framework may also be useful for developing computationally secure steganographic systems that have near-optimal communication performance.

The purpose of image steganalysis is to detect the presence of hidden messages in cover photographic images. Supervised learning is an effective and universal approach to cope with the twin difficulties of unknown image statistics and unknown steganographic codes. A crucial part of the learning process is the selection of low-dimensional informative features. We investigate this problem from three angles and propose a three-level optimization of the classifier. First, we select a subband image representation that provides better discrimination ability than a conventional wavelet transform. Second, we analyze two types of features-empirical moments of probability density functions (PDFs) and empirical moments of characteristic functions of the PDFs-and compare their merits. Third, we address the problem of feature dimensionality reduction, which strongly impacts classification accuracy. Experiments show that our method outperforms previous steganalysis methods. For instance, when the probability of false alarm is fixed at 1%, the stegoimage detection probability of our algorithm exceeds that of its closest competitor by at least 15% and up to 50%

Capacity formulas and random-coding exponents are derived for a generalized family of Gel'fand-Pinsker coding problems. These exponents yield asymptotic upper bounds on the achievable log probability of error. In our model, information is to be reliably transmitted through a noisy channel with finite input and output alphabets and random state sequence, and the channel is selected by a hypothetical adversary. Partial information about the state sequence is available to the encoder, adversary, and decoder. The design of the transmitter is subject to a cost constraint. Two families of channels are considered: 1) compound discrete memoryless channels (CDMC), and 2) channels with arbitrary memory, subject to an additive cost constraint, or more generally, to a hard constraint on the conditional type of the channel output given the input. Both problems are closely connected. The random-coding exponent is achieved using a stacked binning scheme and a maximum penalized mutual information decoder, which may be thought of as an empirical generalized maximum a posteriori decoder. For channels with arbitrary memory, the random-coding exponents are larger than their CDMC counterparts. Applications of this study include watermarking, data hiding, communication in presence of partially known interferers, and problems such as broadcast channels, all of which involve the fundamental idea of binning

This paper presents a classifier built for differentiating digital photorealistic images from digital photographs. Results show that our 144-dimensional (144-D) feature vector extracted from characteristic functions of wavelet histograms is more efficient than Lyu and Farid's 216-D feature vector (S. Lyu and H. Farid), and Ng et al.'s 192-D feature vector (2005). Our classifier outperforms Lyu and Farid's state-of-art method while only requiring half of their feature extraction and testing time

Capacity and random-coding error exponent formulas are derived for a public fingerprinting (traitor tracing) game. The original media copy is available to the encoder, but not to the decoder. We derive the random-coding error exponent for a stacked binning scheme. The exponent is strictly positive at all rates below capacity. The converse part of the capacity proof is based on the Gel'fand-Pinsker technique

Capacity formulas and random-coding and sphere-packing exponents are derived for a generalized family of Gel'fand-Pinsker coding problems. Information is to be reliably transmitted through a noisy channel with random state sequence. Partial information about the state sequence is available to the encoder and decoder. Two families of channels are considered: (1) compound discrete memoryless channels (C-DMC); and (2) channels with arbitrary memory, subject to an additive cost constraint, or more generally to a constraint on the conditional type of the channel output given the input. Both problems are closely connected. For the C-DMC case, our random-coding and sphere-packing exponents coincide at high rates, thereby determining the reliability function of the channel family. The random-coding exponent is achieved using a 3D binning scheme and a maximum penalized mutual information decoder. In the case of arbitrary channels, with memory, a larger random-coding error exponent than in the C-DMC case is obtained. Applications of this study include watermarking, data hiding, communication in presence of partially known interferers, and problems such as broadcast channels, all of which involve the fundamental idea of binning.