本論文旨在提出應用於抗惡意干擾跳頻系統之實體層密鑰生成技術。跳頻是一種用於抵抗環境干擾及惡意攻擊的展頻無線通訊技術。然而，這項技術需要通訊兩端在通訊之初即享有共同的密鑰，以確保使用者間可以使用相同的跳頻序列。在我們所提出的技術中，通訊兩端的使用者可以藉由在前一時段收集到的共同無線通道資訊作為密鑰生成的來源，來決定下一個時段的跳頻序列。即使在受到惡意干擾下，每一個時段的密鑰生成速率仍必須足夠大，使得兩端使用者能夠正確判斷下一個時段的共同跳頻序列。在給定跳頻通道數目以及惡意攻擊者可同時攻擊的通道數目下，我們首先推導系統所需之最低需要的訓練訊號功率，以確保密鑰生成速率足以支應跳頻序列的持續生成。再進一步考量資訊的傳輸下，我們亦在訓練訊號以及資料傳輸訊號的功率間做最佳的功率分配。除以上的理論分析外，我們亦進一步納入實務上的考量，提出可實際運行的跳頻密鑰生成系統，並藉由模擬結果來展現我們提出的方法的效果。

This thesis proposes a jamming-resistant frequency hopping (FH) system that utilizes local channel observations for secret key generation (SKG). FH is a spread spectrum technique
used in both military and consumer wireless applications to avoid jamming attacks, but requires pre-shared secret keys among communicating terminals, say Alice and Bob, to ensure
that the same FH sequence is used at both sides. In our scheme, Alice and Bob utilize local observations of the channel between them as the source of common randomness to generate the shared secret key. By gathering multiple time slots into a frame, the sequence of channels
observed in each frame can be used to determine the FH sequence in the next frame. In this case, the key generation rate must be high enough to identify the FH sequence in the next frame and, thus, to sustain the operation over time. However, by further considering the data transmission, an interesting tradeoff exists between the power allocated for SKG and channel estimation in the training phase and that for communication in the data transmission
phase. Given the number of FH channels and the number of channels that the adversary can jam at once, we derive the minimum pilot signal power required for sustainability and also determine the optimal power allocation between pilot and data signals that maximizes the ergodic rate between the two users. We also propose a practical algorithm for this FH system to generate secret keys via vector quantizations. Simulations are provided to demonstrate the effectiveness of the proposed scheme.

Abstract i
Contents ii
1 Introduction 1
2 Proposed Secret Key Generation Scheme for Frequency Hopping 6
3 Theoretical Analysis of the Proposed SKG-Assisted Frequency Hopping
System 10
3.1 Minimum Required Pilot Signal Power for Sustainability . . . . . . . . . . . 10
3.2 Power Allocation Between Pilot and Data Transmissions . . . . . . . . . . . 12
3.3 Secret Key generation by Rate Limited Public Communication . . . . . . . . 14
3.4 Numerical Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4 Practical Approach to the Proposed SKG-Assisted Frequency Hopping
System 26
4.1 Secret Key Generation using Quantization . . . . . . . . . . . . . . . . . . . 26
4.2 Rendezvous Strategy for the Initialization of the FH System . . . . . . . . . 29
4.3 Jamming Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.4 Design of a Codebook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.5 Numerical Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
5 Conclusion 41
Appendices 42
A Proof in Chapter 3 43
A.1 Proof of secret key rate expression . . . . . . . . . . . . . . . . . . . . . . . . 43
A.2 Proof of the lower bound of ergodic rate . . . . . . . . . . . . . . . . . . . . 44

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