Perfectly Secure Steganography: Capacity, Error Exponents, and Code Constructions

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 independently 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. 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.Comment: To appear in IEEE Trans. on Information Theory, June 2008; ignore Version 2 as the file was corrupte

Perfectly Secure Steganography: Capacity, Error Exponents, and Code Constructions

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 independently 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. 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.Comment: To appear in IEEE Trans. on Information Theory, June 2008; ignore Version 2 as the file was corrupte

Watermarking for multimedia security using complex wavelets

This paper investigates the application of complex wavelet transforms to the field of digital data hiding. Complex wavelets offer improved directional selectivity and shift invariance over their discretely sampled counterparts allowing for better adaptation of watermark distortions to the host media. Two methods of deriving visual models for the watermarking system are adapted to the complex wavelet transforms and their performances are compared. To produce improved capacity a spread transform embedding algorithm is devised, this combines the robustness of spread spectrum methods with the high capacity of quantization based methods. Using established information theoretic methods, limits of watermark capacity are derived that demonstrate the superiority of complex wavelets over discretely sampled wavelets. Finally results for the algorithm against commonly used attacks demonstrate its robustness and the improved performance offered by complex wavelet transforms

Information theoretic analysis of watermarking systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2001.Includes bibliographical references (p. 185-193).This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Watermarking models a copyright protection mechanism where an original data sequence is modified before distribution to the public in order to embed some extra information. The embedding should be transparent (i.e., the modified data should be similar to the original data) and robust (i.e., the information should be recoverable even if the data is modified further). In this thesis, we describe the information-theoretic capacity of such a system as a function of the statistics of the data to be watermarked and the desired level of transparency and robustness. That is, we view watermarking from a communication perspective and describe the maximum bit-rate that can be reliably transmitted from encoder to decoder. We make the conservative assumption that there is a malicious attacker who knows how the watermarking system works and who attempts to design a forgery that is similar to the original data but that does not contain the watermark. Conversely, the watermarking system must meet its performance criteria for any feasible attacker and would like to force the attacker to effectively destroy the data in order to remove the watermark. Watermarking can thus be viewed as a dynamic game between these two players who are trying to minimize and maximize, respectively, the amount of information that can be reliably embedded. We compute the capacity for several scenarios, focusing largely on Gaussian data and a squared difference similarity measure.(cont.) In contrast to many suggested watermarking techniques that view the original data as interference, we find that the capacity increases with the uncertainty in the original data. Indeed, we find that out of all distributions with the same variance, a Gaussian distribution on the original data results in the highest capacity. Furthermore, for Gaussian data, the capacity increases with its variance. One surprising result is that with Gaussian data the capacity does not increase if the original data can be used to decode the watermark. This is reminiscent of a similar model, Costa's "writing on dirty paper", in which the attacker simply adds independent Gaussian noise. Unlike with a more sophisticated attacker, we show that the capacity does not change for Costa's model if the original data is not Gaussian.by Aaron Seth Cohen.Ph.D

Wide spread spectrum watermarking with side information and interference cancellation

Nowadays, a popular method used for additive watermarking is wide spread spectrum. It consists in adding a spread signal into the host document. This signal is obtained by the sum of a set of carrier vectors, which are modulated by the bits to be embedded. To extract these embedded bits, weighted correlations between the watermarked document and the carriers are computed. Unfortunately, even without any attack, the obtained set of bits can be corrupted due to the interference with the host signal (host interference) and also due to the interference with the others carriers (inter-symbols interference (ISI) due to the non-orthogonality of the carriers). Some recent watermarking algorithms deal with host interference using side informed methods, but inter-symbols interference problem is still open. In this paper, we deal with interference cancellation methods, and we propose to consider ISI as side information and to integrate it into the host signal. This leads to a great improvement of extraction performance in term of signal-to-noise ratio and/or watermark robustness.Comment: 12 pages, 8 figure