Results 1 
8 of
8
The Square Root Law of Steganographic Capacity for Markov Covers
"... It is a wellestablished result that steganographic capacity of perfectly secure stegosystems grows linearly with the number of cover elements—secure steganography has a positive rate. In practice, however, neither the Warden nor the Steganographer has perfect knowledge of the cover source and thus ..."
Abstract

Cited by 21 (19 self)
 Add to MetaCart
It is a wellestablished result that steganographic capacity of perfectly secure stegosystems grows linearly with the number of cover elements—secure steganography has a positive rate. In practice, however, neither the Warden nor the Steganographer has perfect knowledge of the cover source and thus it is unlikely that perfectly secure stegosystems for complex covers, such as digital media, will ever be constructed. This justifies study of secure capacity of imperfect stegosystems. Recent theoretical results from batch steganography, supported by experiments with blind steganalyzers, point to an emerging paradigm: whether steganography is performed in a large batch of cover objects or a single large object, there is a wide range of practical situations in which secure capacity rate is vanishing. In particular, the absolute size of secure payload appears to only grow with the square root of the cover size. In this paper, we study the square root law of steganographic capacity and give a formal proof of this law for imperfect stegosystems, assuming that the cover source is a stationary Markov chain and the embedding changes are mutually independent.
Perfectly Secure Steganography: Capacity, Error Exponents, and Code Constructions
, 2007
"... 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 statisti ..."
Abstract

Cited by 16 (0 self)
 Add to MetaCart
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 randomcoding exponents for perfectlysecure 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, modelled here by a compound discrete memoryless channel. The transmitter and warden are subject to distortion constraints. We address the potential loss in communication performance due to the perfectsecurity requirement. This loss is the same as the loss obtained under a weaker order1 steganographic requirement that would just require matching of firstorder
On joint coding for watermarking and encryption
 IEEE Trans. Inform. Theory
, 2006
"... In continuation to earlier works where the problem of joint information embedding and lossless compression (of the composite signal) was studied in the absence [8] and in the presence [9] of attacks, here we consider the additional ingredient of protecting the secrecy of the watermark against an una ..."
Abstract

Cited by 11 (2 self)
 Add to MetaCart
In continuation to earlier works where the problem of joint information embedding and lossless compression (of the composite signal) was studied in the absence [8] and in the presence [9] of attacks, here we consider the additional ingredient of protecting the secrecy of the watermark against an unauthorized party, which has no access to a secret key shared by the legitimate parties. In other words, we study the problem of joint coding for three objectives: information embedding, compression, and encryption. Our main result is a coding theorem that provides a single–letter characterization of the best achievable tradeoffs among the following parameters: the distortion between the composite signal and the covertext, the distortion in reconstructing the watermark by the legitimate receiver, the compressibility of the composite signal (with and without the key), and the equivocation of the watermark, as well as its reconstructed version, given the composite signal. In the attack–free case, if the key is independent of the covertext, this coding theorem gives rise to a threefold separation principle that tells that asymptotically, for long block codes, no optimality is lost by first applying a rate– distortion code to the watermark source, then encrypting the compressed codeword, and finally, embedding it into the covertext using the embedding scheme of [8]. In the more general case, however, this separation principle is no longer valid, as the key plays an additional role of side information used by the embedding unit.
Steganalysis of spread spectrum data hiding exploiting cover memory
 in Security, Steganography, and Watermarking of Multimedia Contents VII
, 2005
"... In this paper we study steganalysis, the detection of hidden data. Specifically we focus on detecting data hidden in grayscale images with spread spectrum hiding. To accomplish this we use a statistical model of images and estimate the detectability of a few basic spread spectrum methods. To verify ..."
Abstract

Cited by 10 (0 self)
 Add to MetaCart
In this paper we study steganalysis, the detection of hidden data. Specifically we focus on detecting data hidden in grayscale images with spread spectrum hiding. To accomplish this we use a statistical model of images and estimate the detectability of a few basic spread spectrum methods. To verify the results of these findings, we create a tool to discriminate between natural “cover ” images and “stego ” images (containing hidden data) taken from a diverse database. Existing steganalysis schemes that exploit the spatial memory found in natural images are particularly effective. Motivated by this, we include interpixel dependencies in our model of image pixel probabilities and use an appropriate statistical measure for the security of a steganography system subject to optimal hypothesis testing. Using this analysis as a guide, we design a tool for detecting hiding on various spread spectrum methods. Depending on the method and power of the hidden message, we correctly detect the presences of hidden data in about 95 % of images.
Determining achievable rates for secure, zero divergence, steganography
 in Proceedings of ICIP
, 2006
"... In steganography (the hiding of data into innocuous covers for secret communication) it is difficult to estimate how much data can be hidden while still remaining undetectable. To measure the inherent detectability of steganography, Cachin [1] suggested the csecure measure, where c is the Kullback ..."
Abstract

Cited by 8 (3 self)
 Add to MetaCart
In steganography (the hiding of data into innocuous covers for secret communication) it is difficult to estimate how much data can be hidden while still remaining undetectable. To measure the inherent detectability of steganography, Cachin [1] suggested the csecure measure, where c is the Kullback Leibler (KL) divergence between the cover distribution and the distribution after hiding. At zero divergence, an optimal statistical detector can do no better than guessing; the data is undetectable. The hider's key question then is, what hiding rate can be used while maintaining zero divergence? Though work has been done on the theoretical capacity of steganography, it is often difficult to use these results in practice. We therefore examine the limits of a practical scheme known to allow embedding with zerodivergence. This scheme is independent of the embedding algorithm and therefore can be generically applied to find an achievable secure hiding rate for arbitrary cover distributions. Index Terms Steganography, steganalysis 1.
Capacity of steganographic channels
 Proceedings 7th ACM Workshop on Multimedia and Security
, 2005
"... Abstract — This work investigates a central problem in steganography, that is: How much data can safely be hidden without being detected? To answer this question a formal definition of steganographic capacity is presented. Once this has been defined a general formula for the capacity is developed. T ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Abstract — This work investigates a central problem in steganography, that is: How much data can safely be hidden without being detected? To answer this question a formal definition of steganographic capacity is presented. Once this has been defined a general formula for the capacity is developed. The formula is applicable to a very broad spectrum of channels due to the use of an informationspectrum approach. This approach allows for the analysis of arbitrary steganalyzers as well as nonstationary, nonergodic encoder and attack channels. After the general formula is presented, various simplifications are applied to gain insight into example hiding and detection methodologies. Finally, the context and applications of the work are summarized in a general discussion. Index Terms — Steganographic capacity, stegochannel, steganalysis, steganography, information theory, informa
DETECTION AND INFORMATIONTHEORETIC ANALYSIS OF STEGANOGRAPHY AND FINGERPRINTING
, 2006
"... The proliferation of multimedia and the advent of the Internet and other public networks have created many new applications of information hiding in multimedia security and forensics. This dissertation focuses on two of these application scenarios: steganography (and its counter problem, steganalysi ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
The proliferation of multimedia and the advent of the Internet and other public networks have created many new applications of information hiding in multimedia security and forensics. This dissertation focuses on two of these application scenarios: steganography (and its counter problem, steganalysis), and fingerprinting. First, from a detectiontheoretic perspective, we quantify the detectability of commonly used informationhiding techniques such as spread spectrum and distortioncompensated quantization index modulation, and also the detectability of blockbased steganography. We devise a practical steganalysis method that exploits the peculiar block structure of blockDCT image steganography. To cope with the twin difficulties of unknown image statistics and unknown steganographic codes, we explore image steganalysis based on supervised learning and build an optimized classifier that outperforms previously proposed image steganalysis methods. Then, from an informationtheoretic perspective, we derive the capacity and randomcoding error exponent of perfectly secure steganography and public fingerprinting. For both games, a randomized stackedbinning scheme and a matched maximum penalized mutual information decoder are used to achieve capacity and to realize a randomcoding error exponent that is strictly positive at all rates below capacity.
The Square Root Law of Steganographic Capacity for Markov Covers
"... It is a wellestablished result that steganographic capacity of perfectly secure stegosystems grows linearly with the number of cover elements—secure steganography has a positive rate. In practice, however, neither the Warden nor the Steganographer has perfect knowledge of the cover source and thus ..."
Abstract
 Add to MetaCart
It is a wellestablished result that steganographic capacity of perfectly secure stegosystems grows linearly with the number of cover elements—secure steganography has a positive rate. In practice, however, neither the Warden nor the Steganographer has perfect knowledge of the cover source and thus it is unlikely that perfectly secure stegosystems for complex covers, such as digital media, will ever be constructed. This justifies study of secure capacity of imperfect stegosystems. Recent theoretical results from batch steganography, supported by experiments with blind steganalyzers, point to an emerging paradigm: whether steganography is performed in a large batch of cover objects or a single large object, there is a wide range of practical situations in which secure capacity rate is vanishing. In particular, the absolute size of secure payload appears to only grow with the square root of the cover size. In this paper, we study the square root law of steganographic capacity and give a formal proof of this law for imperfect stegosystems, assuming that the cover source is a stationary Markov chain and the embedding changes are mutually independent.