Abstract: In symmetrical polynomials of random key pre-distribution scheme, a safety mechanism was provided for the nodes communication, however, there are problems of t threshold properties. In order to well solve this problem, and to improve the safety threshold value of network and nodes ability of anti-trapping, this paper use common trivariate polynomial instead of binary symmetrical polynomial to build communication among nodes, and use one-way function to process the value of the sharing secret, enhancing the difficulty of cracking secret keys. Meanwhile, this scheme employs hexagon-based deployment mode,enhancing the safe connectivity rates of the network, meanwhile reducing the range that influenced by captured node. The analysis results show that this scheme has higher anti-destroying ability and security,also reducing the overhead of communication among nodes.

Key words: wireless sensor network(WSN), common trivariate polynomial, hexagon-based mode

摘要： 基于二元对称多项式的随机密钥预分配方案为节点的通信提供了一种安全机制，但这些方案都存在t门限性质问题。为了更好地解决此问题，提高网络的安全阈值及节点的抗俘获能力，采用同化三元多项式代替二元对称多项式来建立节点间通信，并对共享密钥使用单向hash函数进行处理，提高了密钥破解难度。同时采用六边形部署模型，提高网络的安全连通率，减少被捕获节点的影响范围。分析结果表明，该方案提高了网络的安全性及节点的抗毁性，降低了节点间的通信开销。

关键词: 无线传感器网络, 同化多项式, 六边形部署模型