The Cut and Dominating Set Problem in A Steganographer Network

TL;DR

This paper models steganographic communication networks using graph theory, analyzing problems related to network disruption and message sharing, by linking them to well-known graph problems like minimum cut and dominating set.

Contribution

It introduces a novel graph-based framework for analyzing steganographer networks and establishes equivalences to classic graph problems for network security and communication.

Findings

Passive attack problem reduces to minimum cut problem.

Vertex set selection problem reduces to minimum-weight dominating set.

Provides a new analytical approach for steganographic network security.

Abstract

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.