本篇論文考慮在無線衰減通道具有相關性的情況下，使用向量量化技術之密鑰生成協定。在本篇論文中，我們利用兩位合法使用者之間的共同無線通道做為密鑰的產生來源。我們提出向量量化演算法以降低密鑰錯誤率 (KDP) 及提高密鑰亂度 (Key Entropy)。在傳統的密鑰生成協定中，絕大部分均考慮數值量化 (Scalar Quantization) 演算法以利於硬體實現，其缺點為較高的KDP以及當通道具有相關性時，具有較低的Key Entropy。有鑑於此，本篇論文提出兩種基於向量量化技術的密鑰產生演算法: 最低密鑰錯誤率 (MKDP) 演算法及最低二次失真 (MQD) 演算法。在這兩個方法中，分別將密鑰錯誤率及二次失真做為考慮基礎並使用Lloyd Algorithm找出最佳的量化器。MKDP演算法具有最低的密鑰錯誤率但同時其複雜度也較高；另一方面，MQD演算法複雜度較低但具有稍高的密鑰錯誤率。在我們提出的兩個演算法中，都會使用么正變換 (Unitary Transformation) 以避免通道向量落在量化間隔的邊界上並降低密鑰錯誤率。除此之外，我們亦將亂度限制 (Entropy Constraint) 加入我們的演算法內以保證密鑰有較高的不確定性。最後，電腦模擬顯示我們所提的演算法確實擁有較佳的效能。

This thesis examines the use of vector quantization to generate secret keys over correlated wireless fading channels. In channel-based secret key generation schemes, common randomness of the channel between two users are utilized to generate secret keys at the two terminals. These key generation schemes should be designed to ensure low key disagreement probability (KDP) among the two users and also high key entropy so that the generated keys cannot be easily inferred by the eavesdropper. Conventional channel-based secret key generation schemes utilize scalar quantization over individual channel observations, which is simple to implement but yields high KDP at low SNR and low key entropy when the channel is correlated. In this thesis, two vector quantization schemes are proposed to exploit the temporal correlation of channels: the minimum quadratic distortion (MQD) and the minimum key disagreement probability (MKDP) secret key generation schemes. In these schemes, the Lloyd-Max algorithm is used with the quadratic distortion and the KDP as their respective distortion measures to compute the quantizers. The MKDP scheme achieves low KDP but requires high complexity whereas the MQD yields low complexity but slightly higher KDP. The unitary transformation is performed on the channel vectors before quantization to avoid key disagreement caused by channel vectors lying on the boundary of quantization cells. Furthermore, to ensure high entropy of the secret keys, an entropy constraint is further incorporated into the objective of the quantization design. Computer simulations are provided to demonstrate the effectiveness of the proposed vector quantization schemes.

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