A steganographer network corresponds to a graphic structure that the involved vertices (or called nodes) denote social entities such as the data encoders and data decoders, and the associated edges represent any real communicable channels or other social links that could be utilized for steganography. Unlike traditional steganographic algorithms, a steganographer network models steganographic communication by an abstract way such that the concerned underlying characteristics of steganography are quantized as analyzable parameters in the network. In this paper, we will analyze two problems in a steganographer network. The first problem is a passive attack to a steganographer network where a network monitor has collected a list of suspicious vertices corresponding to the data encoders or decoders. The network monitor expects to break (disconnect) the steganographic communication down between the suspicious vertices while keeping the cost as low as possible. The second one relates to determining a set of vertices corresponding to the data encoders (senders) such that all vertices can share a message by neighbors. We point that, the two problems are equivalent to the minimum cut problem and the minimum-weight dominating set problem.
In @math , a path between @math and @math implies that, @math can share a message with @math along the path. In @cite_6 , the authors present a communication strategy that aims to minimize the overall steganographic risk by determining a subtree supporting the required vertices. Mathematically, they use @math @math @math and @math @math @math to denote the encoder set and decoder set. For each @math , its individual decoder set is denoted by @math , meaning that, @math hopes to send a message to each of @math . Here, @math . The optimization task is to find such a subset of @math that it enables all @math to send a message to all decoders in @math , and the overall risk can be minimized. Namely, where @math denotes the risk over @math .
@cite_6
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Steganography aims to conceal the very fact that the communication takes place, by embedding a message into a digit object such as image without introducing noticeable artifacts. A number of steganographic systems have been developed in past years, most of which, however, are confined to the laboratory conditions where the real-world use of steganography are rarely concerned. In this paper, we introduce an alternative perspective to steganography. A graph-theoretic model to steganography on social networks is presented to analyze real-world steganographic scenarios. In the graph, steganographic participants are corresponding to the vertices with meaningless unique identifiers. Each edge allows the two vertices to communicate with each other by any steganographic algorithm. Meanwhile, the edges are associated with weights to quantize the corresponding communication risk (or say cost). The optimization task is to minimize the overall risk, which is modeled as additive over the social network. We analyze different scenarios on a social network, and provide the suited solutions to the corresponding optimization tasks. We prove that a multiplicative probabilistic graph is equivalent to an additive weighted graph. From the viewpoint of an attacker, he may hope to detect suspicious communication channels, the data encoder(s) and the data decoder(s). We present limited detection analysis to steganographic communication on a network.