Optimal Design of Linear Network Coding for information theoretically secure unicast
Optimal Design of Linear Network Coding for information theoretically secure unicast
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DOI：
10.1109/infcom.2011.5935296
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发表时间：
2011-04
期刊：
影响因子：
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通讯作者：
Jin Wang;Jianping Wang;K. Lu;Y. Qian;Bin Xiao;Naijie Gu
中科院分区：
文献类型：
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作者：
Jin Wang;Jianping Wang;K. Lu;Y. Qian;Bin Xiao;Naijie Gu
本文在信息理论安全（ITS）的要求下，研究了安全单播抗被动攻击的线性网络编码（LNC）的优化设计问题。我们的最佳LNC设计的目标包括（1）满足ITS的要求，（2）最大化单播流的传输速率，（3）最小化额外的随机符号的数量。首先将ITS要求下的安全传输速率最大化问题转化为一个有约束的最大网络流问题，并设计了一个有效的算法来求解最优传输拓扑。基于传输拓扑，我们设计了一个确定性的LNC，它满足上述目标，并提供了一个建设性的上限的有限域的大小。此外，我们还研究了随机LNC的潜势，并给出了随机LNC信息理论安全概率的下界。
In this paper, we study the optimal design of linear network coding (LNC) for secure unicast against passive attacks, under the requirement of information theoretical security (ITS). The objectives of our optimal LNC design include (1) satisfying the ITS requirement, (2) maximizing the transmission rate of a unicast stream, and (3) minimizing the number of additional random symbols. We first formulate the problem that maximizes the secure transmission rate under the requirement of ITS, which is then transformed to a constrained maximum network flow problem.We devise an efficient algorithm that can find the optimal transmission topology. Based on the transmission topology, we then design a deterministic LNC which satisfies the aforementioned objectives and provide a constructive upper bound of the size of the finite field. In addition, we also study the potential of random LNC and derive the low bound of the probability that a random LNC is information theoretically secure.