在無線感知網路上的金鑰部署中(Key Management)，隨機預先佈署機制(Random key pre-distribution scheme)一直是具有良好適應性及彈性的方法。在這篇論文中，我提出的方法是基於組合數學中鴿籠原理(Pigeon-hole principle)以及組合(Combination)本身去設計一個金鑰管理機制。一開始我先挑選一個較小的金鑰池(Key Pool)，接著隨機從此金鑰池中去挑選不同的組合的金鑰部署到每一個節點中；部署這些節點後，每個節點會與鄰近節點利用所設計的金鑰溝通協定(Key agreement protocol)去產生一把新的金鑰。
安全性方面，它能保證在整個網路中每一對節點之間都能分享不同的金鑰，由於每對節點之間建立的金鑰是全相異的，所以攻擊者無法藉由被捕獲的節點中的資訊去攻擊剩下未被捕獲的節點。至於網路連通性，我的方法保證每一個節點在其發射區域中都能達到完整的連通性，它和鄰近節點皆能產生新的金鑰。在過去的文獻中，每個節點必須儲存大量金鑰來維持高度連通。然而，我的方法能減低記憶體需求量卻能同時維持高連通性。另外，我的策略提高最大可部署的節點數量來提供了更大的彈性。同時，我也提供了一個新的機率模型去計算在Path-Key建置階段中所建立的路徑平均長度。最後，我們藉由模擬去驗證連通性的估計值和計算路徑長度機率模型的正確性。

Random key pre-distribution scheme is a flexible key management scheme for wireless sensor networks. Over the past years, numerous studies have been proposed to address this problem. However, most of them may suffer some drawbacks. The major drawback is that each sensor node demands large storage to maintain high connectivity. Another drawback is that attacks from compromised nodes can not be completely eliminated.
In this thesis, we propose a new pair-wise key establishment scheme based on the combination of a small key pool and the pigeon-hole principle. We ensure that the pair-wise key for each pair of sensor nodes is different from the others. Therefore, attacks from compromised nodes will never occur in our scheme. We also reduce the storage and maintain high connectivity simultaneously. Most significantly, we achieve the merit of fully connectivity which means that each node can build all secure relations with its neighbors. Moreover, we design a probability model to analyze the average length of paths which was built in path-key establishment phase.
Comparing to other schemes, our scheme is energy-efficient in contrast to the previous works, including computation overhead and communication overhead. Finally, simulations on connectivity and average length of path built in path-key phase are also conducted.

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