Abstract: The intrinsically secure communications graph, iS-graph, is a random graph which describes the connections that can be securely established over a wireless network by exploiting the physical properties of the wireless medium. Secrecy capacity of iS-graph can be increased by reducing the SINR (signal to interference plus noise ratio) of the eavesdroppers by adding controlled interference. Inspired by recent results on information-theoretic security, this paper considers the transmission of secret messages over wireless networks in which the legitimate communication nodes are aided by cooperative jamming nodes, and proposes a secure communication graph model with jamming, namely jS-graph, on the basis of iS-graph. This paper aims to characterize the security properties of the jS-graph in the protocol model and the threshold model, proposes jamming strategies to handle unknown eavesdropper locations. The results show that, with the aid of jamming, the secure communication graph can lead to significant secrecy gains compared to its counterpart iS-graph without the aid of jamming. These results help clarify how the presence of eavesdroppers and the cooperative jamming can influence secure connectivity in wireless networks.

Key words: jamming, secrecy graph, stochastic geometry, wireless networks

摘要： 安全通信图即iS-graph是描述随机无线网络中安全链路的一种随机图，图中的安全链路利用无线媒介的物理特性建立。iS-graph的安全容量可通过增加可控干扰以降低窃听者的信道质量来实现。受信息论安全启发，研究了无线网络上机密信息的传输，并在iS-graph的基础上提出了一种干扰协助的安全通信图模型jS-graph。该模型中合法节点在协作干扰节点的帮助下实现安全通信。描述了jS-graph在协议模型和阈值模型中的安全属性，并提出了窃听者位置未知情况下的干扰策略。结果表明，与无协作干扰的iS-graph相比，jS-graph能取得显著的安全增益，结果有助于分析窃听者和协作干扰对无线网络安全性的影响。

关键词: 干扰, 安全图, 随机几何, 无线网络