Steganography is an art and science of hidden communication. Similarly as cryptography, steganography allows two trusted parties to exchange messages in secrecy, but as opposed to cryptography, steganography adds another layer of protection by hiding the mere fact that any communication takes place in a plausible cover traffic. Corresponding security goal is thus the statistical undetectability of cover and stego objects studied by steganalysis—a counterpart to steganography. Ultimately, a stegosystem is perfectly secure if no algorithm can distinguish its cover and stego objects.
This dissertation focuses on stegosystems which are not truly perfectly secure—they are imperfect. This is motivated by practice, where all stegosystems build for real digital media, such as digital images, are imperfect. Here, we present two systematic studies related to the secure payload loosely defined as the amount of payload, which can be communicated at a certain level of statistical detectability.
The first part of this dissertation describes a fundamental asymptotic relationship between the size of the cover object and the secure payload which is now recognized as the Square-root law (SRL). Contrary to our intuition, secure payload of imperfect stegosystems does not scale linearly but, instead, according to the square root of the cover size. This law, which was confirmed experimentally, is proved theoretically under very mild assumptions on the cover source and the embedding algorithm. For stegosystems subjected to the SRL, the amount of payload one is able to hide per square root of the cover size, called the root rate, leads to new definition of capacity of imperfect stegosystems.
The second part is devoted to a design of practical embedding algorithms by minimizing the statistical impact of embedding. By discovering the connection between steganography and statistical physics, the Gibbs construction provides a theoretical framework for implementing and designing such embedding algorithms. Moreover, we propose a general solution for implementing the embedding algorithms minimizing the sum of distortions over individual cover elements in practice. This solution, called the Syndrome-trellis code (STC), achieves near-optimal performance over wide class of distortion functions.
|Commitee:||Craver, Scott, Ker, Andrew, Sharma, Gaurav|
|School:||State University of New York at Binghamton|
|School Location:||United States -- New York|
|Source:||DAI-B 72/10, Dissertation Abstracts International|
|Keywords:||Asymptotic laws, Data hiding, Optimal constructions, Steganography|
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