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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 ..."
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Cited by 30 (24 self)
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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.
Design of Adaptive Steganographic Schemes for Digital Images
 Proceedings of SPIE, Electronic Imaging, Media Watermarking, Security, and Forensics XIII
, 2011
"... Most steganographic schemes for real digital media embed messages by minimizing a suitably dened distortion function. In practice, this is often realized by syndrome codes which oer nearoptimal ratedistortion performance. However, the distortion functions are designed heuristically and the resulti ..."
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Cited by 18 (10 self)
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Most steganographic schemes for real digital media embed messages by minimizing a suitably dened distortion function. In practice, this is often realized by syndrome codes which oer nearoptimal ratedistortion performance. However, the distortion functions are designed heuristically and the resulting steganographic algorithms are thus suboptimal. In this paper, we present a practical framework for optimizing the parameters of additive distortion functions to minimize statistical detectability. We apply the framework to digital images in both spatial and DCT domain by rst dening a rich parametric model which assigns a cost of making a change at every cover element based on its neighborhood. Then, we present a practical method for optimizing the parameters with respect to a chosen detection metric and feature space. We show that the size of the margin between support vectors in softmargin SVMs leads to a fast detection metric and that methods minimizing the margin tend to be more secure w.r.t. blind steganalysis. The parameters obtained by the NelderMead simplexreection algorithm for spatial and DCTdomain images are presented and the new embedding methods are tested by blind steganalyzers utilizing various feature sets. Experimental results show that as few as 80 images are sucient for obtaining good candidates for parameters of the cost model, which allows us to speed up the parameter search.
Message in a bottle: Sailing past censorship
 In 29th Annual Computer Security Applications Conference – ACSAC 2013
, 2013
"... Exploiting recent advances in monitoring technology and the drop of its costs, authoritarian and oppressive regimes are tightening the grip around the virtual lives of their citizens. Meanwhile, the dissidents, oppressed by these regimes, are organizing online, cloaking their activity with anticens ..."
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Exploiting recent advances in monitoring technology and the drop of its costs, authoritarian and oppressive regimes are tightening the grip around the virtual lives of their citizens. Meanwhile, the dissidents, oppressed by these regimes, are organizing online, cloaking their activity with anticensorship systems that typically consist of a network of anonymizing proxies. The censors have become well aware of this, and they are systematically finding and blocking all the entry points to these networks. So far, they have been quite successful. We believe that, to achieve resilience to blocking, anticensorship systems must abandon the idea of having a limited number of entry points. Instead, they should establish first contact in an online location arbitrarily chosen by each of their users. To explore this idea, we have developed Message In A Bottle, a protocol where any blog post becomes a potential “drop point ” for hidden messages. We have developed and released a proofofconcept application using our system, and demonstrated its feasibility. To block this system, censors are left with a needleinahaystack problem: Unable to identify what bears hidden messages, they must block everything, effectively disconnecting their own network from a large part of the Internet. This, hopefully, is a cost too high to bear. 1
Estimating Steganographic Fisher Information in Real Images
"... Abstract. This paper is concerned with the estimation of steganographic capacity in digital images, using information theoretic bounds and very largescale experiments to approximate the distributions of genuine covers. The complete distribution cannot be estimated, but with carefullychosen algorith ..."
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Abstract. This paper is concerned with the estimation of steganographic capacity in digital images, using information theoretic bounds and very largescale experiments to approximate the distributions of genuine covers. The complete distribution cannot be estimated, but with carefullychosen algorithms and a large corpus we can make local approximations by considering groups of pixels. A simple estimator for the local quadratic term of KullbackLeibler divergence (Steganographic Fisher Information) is presented, validated on some synthetic images, and computed for a corpus of covers. The results are interesting not so much for their concrete capacity estimates but for the comparisons they provide between different embedding operations, between the information found in differentlysized andshaped pixel groups, and the results of DC normalization within pixel groups. This work suggests lessons for the future design of spatialdomain steganalysis, and also the optimization of embedding functions. 1
Moving Steganography and Steganalysis from the Laboratory into the Real World
"... There has been an explosion of academic literature on steganography and steganalysis in the past two decades. With a few exceptions, such papers address abstractions of the hiding and detection problems, which arguably have become disconnected from the real world. Most published results, including b ..."
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There has been an explosion of academic literature on steganography and steganalysis in the past two decades. With a few exceptions, such papers address abstractions of the hiding and detection problems, which arguably have become disconnected from the real world. Most published results, including by the authors of this paper, apply “in laboratory conditions ” and some are heavily hedged by assumptions and caveats; significant challenges remain unsolved in order to implement good steganography and steganalysis in practice. This position paper sets out some of the important questions which have been left unanswered, as well as highlighting some that have already been addressed successfully, for steganography and steganalysis to be used in the real world.
The square root law in stegosystems with imperfect information
 Proc. 12th Information Hiding Workshop
, 2010
"... Abstract. Theoretical results about the capacity of stegosystems typically assume that one or both of the adversaries has perfect knowledge of the cover source. Socalled perfect steganography is possible if the embedder has this perfect knowledge, and the Square Root Law of capacity applies when th ..."
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Abstract. Theoretical results about the capacity of stegosystems typically assume that one or both of the adversaries has perfect knowledge of the cover source. Socalled perfect steganography is possible if the embedder has this perfect knowledge, and the Square Root Law of capacity applies when the embedder has imperfect knowledge but the detector has perfect knowledge. The epistemology of stegosystems is underdeveloped and these assumptions are sometimes unstated. In this work we consider stegosystems where the detector has imperfect information about the cover source: once the problem is suitably formalized, we show a parallel to the Square Root Law. This answers a question raised by Böhme. 1
Reliable deniable communication: Hiding messages in noise,” http://personal.ie.cuhk.edu.hk/∼sjaggi/arxiv 01.pdf
, 2013
"... a message to a receiver Bob over a binary symmetric channel (BSC), while simultaneously ensuring that her transmission is deniable from an eavesdropper Willie. That is, if Willie listening to Alice’s transmissions over a “significantly noisier ” BSC than the one to Bob, he should be unable to estima ..."
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Cited by 4 (2 self)
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a message to a receiver Bob over a binary symmetric channel (BSC), while simultaneously ensuring that her transmission is deniable from an eavesdropper Willie. That is, if Willie listening to Alice’s transmissions over a “significantly noisier ” BSC than the one to Bob, he should be unable to estimate even whether Alice is transmitting. Even when Alice’s (potential) communication scheme is publicly known to Willie (with no common randomness between Alice and Bob), we prove that over n channel uses Alice can transmit a message of length O(√n) bits to Bob, deniably from Willie. We also prove informationtheoretically orderoptimality of our results. I.
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. The ..."
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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, information spectrum
An epistemological approach to steganography
 INFORMATION HIDING 2009
, 2009
"... Steganography has been studied extensively in the light of information, complexity, probability and signal processing theory. This paper adds epistemology to the list and argues that Simmon’s seminal prisoner’s problem has an empirical dimension, which cannot be ignored (or defined away) without sim ..."
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Cited by 2 (1 self)
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Steganography has been studied extensively in the light of information, complexity, probability and signal processing theory. This paper adds epistemology to the list and argues that Simmon’s seminal prisoner’s problem has an empirical dimension, which cannot be ignored (or defined away) without simplifying the problem substantially. An introduction to the epistemological perspective on steganography is given along with a structured discussion on how the novel perspective fits into the existing body of literature.
Perturbation Hiding and the Batch Steganography Problem
"... Abstract. The batch steganography problem is how best to split a steganographic payload between multiple covers. This paper makes some progress towards an informationtheoretic analysis of batch steganography by describing a novel mathematical abstraction we call perturbation hiding. As well as prov ..."
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Abstract. The batch steganography problem is how best to split a steganographic payload between multiple covers. This paper makes some progress towards an informationtheoretic analysis of batch steganography by describing a novel mathematical abstraction we call perturbation hiding. As well as providing a new challenge for information hiding research, it brings into focus the information asymmetry in steganalysis of multiple objects: Kerckhoffs ’ Principle must be interpreted carefully. Our main result is the solution of the perturbation hiding problem for a certain class of distributions, and the implication for batch steganographic embedding. However, numerical computations show that the result does not hold for all distributions, and we provide some additional asymptotic results to help explore the problem more widely. 1