本論文旨在在分散式系統中使用者們可以藉由共同的通道技術經由所提出的向量量化技術產生密鑰以達到資訊保密的效果。 根據之前所提出的向量量化技術，額外在上層加上量化器選擇與取樣選擇的功能，以進一步地降低使用者間密鑰生成不同的機率，其中，在量化器選擇與取樣選擇中，最主要的設計概念在於使得所估測的通道向量最遠離所產生的量化器的邊界。除此之外，在設計向量量化技術的同時，加入了叢集式密鑰映射函數的設計，使得在給定竊聽者的觀察下，進一步提升了條件熵 。其中，條件熵主要是在反映著在給定竊聽者的觀察下，所產生密鑰的隨機性的程度。映射函數是將多個量化的區間形成一個叢集，如此一個量化器中將會有多個叢集，並且重複使用相同的密鑰在不同的叢集之間，使得竊聽者不能清楚解析叢集內的區間，僅能辨別叢集與叢集的差別。藉由向量量化的設計並且於設計中加入叢集式密鑰映射函數，故產生了叢集式向量量化器。其概念相似於在通道編碼中的自然隨意分群法。最後，藉由模擬結果，來展現我們所提出的方法的效果。

In this work, vector quantization schemes were proposed for the generation of shared secret keys between two terminals, called Alice and Bob, using their local channel measurements. Building upon our proposed vector quantization schemes, quantizer, sample and rotation selection schemes are further proposed on top of the conventional secret key generation procedure to reduce the key disagreement probability (KDP). The key idea is to choose from a bank of quantizers the one whose boundaries are farthest away from the locally observed channel vector. Moreover, a clustered key mapping function was proposed for the quantizer design to further increase the conditional key entropy at the eavesdropper. The conditional key entropy provided a measure of the randomness of the secret key at the eavesdropper given its observation. The mapping effectively groups together multiple quantization regions into one cluster, so that the regions within the cluster are not distinguishable by the eavesdropper, and reuse the same set of secret keys among different clusters. The resulting quantizer is thus called a clustered vector quantizer. The idea is similar to the concept of random binning in the channel coding literature. The effectiveness of the proposed schemes were demonstrated through computer simulations.

Abstract i
Contents ii
1 Introduction 1
1.1 Motivation and Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 System Model 8
3 Secret Key Generation Procedure with Clustered Vector Quantization 12
4 Clustered Vector Quantizer Design 17
4.1 Entropy-Constrained Fine Quantizer Design . . . . . . . . . . . . . . . . . . 18
4.1.1 Entropy-Constrained Minimum Quadratic Distortion (EC-MQD) Fine
Quantizer Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.1.2 Entropy-Constrained Minimum Key Disagreement Probability (ECMKDP)
Fine Quantizer Design . . . . . . . . . . . . . . . . . . . . . 23
4.2 Clustered Key Mapping Design . . . . . . . . . . . . . . . . . . . . . . . . . 26
5 Simulation Results and Performance Comparison 30
6 Conclusion 38

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