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研究生： 陳知余
Chen, Chih-Yu
論文名稱： 認證式差分相移量子金鑰分配系統之設計
Design of Authenticated Differential Phase Shift Quantum Key Distributions
指導教授： 黃宗立
Hwang, Tzone-Lih
學位類別： 碩士
Master
系所名稱： 電機資訊學院 - 資訊工程學系
Department of Computer Science and Information Engineering
論文出版年： 2022
畢業學年度： 110
語文別： 英文
論文頁數： 60
中文關鍵詞： 量子密碼學 、量子金鑰分配 、差分相移 、安全性
外文關鍵詞： Quantum cryptography, Quantum key distribution, Differential phase shift, Security
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    • 量子金鑰分配是量子密碼學中一項重要的主題。量子金鑰分配的目的是要在兩個或更多的參與者中基於量子力學去分配對稱式的密鑰。在2002年，Kyo Inoue、Edo Waks、Yoshihisa Yamamoto提出了第一個差分相移量子金鑰分配的協定。在協定中，一個光子被分割成三個相似的脈衝並且使用相鄰脈衝間的相位差來攜帶資訊。接收者可以藉由偵測干涉的脈衝來取得傳送者傳送的資訊，最後他們可以分享一把會議金鑰。在這之後，許多差分相移量子金鑰分配協定陸續被提出。
    然而，在所有差分相移量子金鑰分配協定中存在三個主要的問題。首先，所有協定都使用了馬赫-曾德爾干涉儀來偵測收到的脈衝，但因為前後兩端兩個以上脈衝的偵測結果是不確定的，並且與傳送者的相位調變無關，所以它們必須被捨棄。接著，由於這些偵測結果的不確定性，理想的傳統認證通道對於兩位參與者的討論是必要的。最後一個問題是由於現存的差分相移量子金鑰分配協定都是設計給兩方，對於兩個彼此互不認識的遠端參與者來說，要提前建立量子通道或預先分享密鑰是很困難的。
    為了解決上述問題，本論文首先提出了改進的偵測方法以使得每個偵測結果具有確定性。所有的偵測結果都會和傳送者的相位調變有關，而且偵測脈衝的利用率比以往的協定都來得更高。其次，根據這項改進，我們提出了第一個兩方的認證式差分相移量子金鑰分配協定，此協定使用預先分配的密鑰取代理想傳統認證通道以實現認證性。此外，我們提出了中介認證式差分相移量子金鑰分配協定。藉由有能力產生單光子之不誠實第三方的幫助，可以降低傳送者的能力負擔。最後，我們在多方的認證式差分相移量子金鑰分配協定中引入了半誠實的第三方來幫助沒有預先分享密鑰的參與者能夠間接地認證彼此並且分享對話金鑰。

    Quantum key distribution (QKD) is an important topic in quantum cryptography. The quantum key distribution aims to distribute symmetric secret keys among two or more participants based on quantum mechanics. In 2002, Kyo Inoue, Edo Waks, and Yoshihisa Yamamoto proposed the first differential phase shift quantum key distribution (DPS-QKD) scheme. This scheme splits a photon into three identical pulses and applies the phase difference between adjacent pulses for carrying the information. The receiver detects the interfered pulses to obtain the information sent by the sender, and in consequence they can share a session key. After that, various DPS-QKD schemes have been proposed.
    However, three problems exist in these DPS-QKD schemes. First, every existing scheme applies the Mach-Zehnder interferometer to detect the incoming pulses; however, the detection result of two or more end pulses must be discarded because it is uncertain and independent to the sender's phase modulation. Secondly, the ideal authenticated classical channel is essential for the communication of participants owing to the uncertainty of detecting result. Lastly, because all of existing DPS-QKD protocols are designed for two participants, it is hard for both remote participants who do not know each other before to establish a quantum channel or pre-share a secret key as a prerequisite.
    This thesis proposes an improved detecting method to solve the problems mentioned above by first making every detecting result certain. Every detecting result will depend on the modulation of the sender and the utilization ratio of pulse detection is better than previous DPS-QKD schemes. Second, based on this improvement, we propose the first 2-party authenticated DPS-QKD scheme with the assumption of pre-shared keys instead of an ideal authenticated classical channel for mutual authentication. Furthermore, the mediated authenticated DPS-QKD is proposed to reduce the sender's burden with the help of an untrusted third party who is capable of preparing the single photons. Finally, semi-honest third parties are introduced in multi-party authenticated DPS-QKD schemes to help those participants who do not pre-share secret keys authenticate each other and share the session key indirectly.

    中文摘要 i Abstract ii 誌謝 iv Contents v List of Tables vii List of Figures viii Chapter 1 Introduction 1 Chapter 2 Preliminaries 3 2.1 Properties of Single Photon 3 2.2 Pauli Operators 4 2.3 Entanglement 5 2.4 Review of Inoue et al.'s DPS-QKD 6 Chapter 3 Proposed DPS-QKD with an Improved Detecting method 8 3.1 Description of Proposed Scheme 8 3.2 Security Analysis 10 3.2.1 Trojan-horse Attack 10 3.2.2 Intercept-and-Resend Attack 11 3.2.3 Unconditional Security Proof 12 3.2.3.1 Entanglement Distillation Protocol 12 3.2.3.2 Estimation of the Phase Error Rate 14 3.3 Comparison 17 Chapter 4 Proposed 2-Party Authenticated DPS-QKD 18 4.1 Description of Proposed Scheme 18 4.2 Security Analysis 20 4.2.1 Trojan-horse Attack 21 4.2.2 Intercept-and-Resend Attack 21 4.2.3 Unconditional Security Proof 22 4.2.3.1 Entanglement Distillation Protocol 22 4.2.3.2 Estimation of the Phase Error Rate 23 4.3 Comparison 26 Chapter 5 Proposed Mediated Authenticated DPS-QKD 27 5.1 Description of Proposed Scheme 27 5.2 Security Analysis 29 5.2.1 Trojan-horse Attack 29 5.2.2 Unconditional Security Proof 31 5.2.2.1 Entanglement Distillation Protocol 31 5.2.2.2 Estimation of the Phase Error Rate 32 Chapter 6 Proposed 3-Party Authenticated DPS-QKD 34 6.1 Description of Proposed Scheme 35 6.2 Security Analysis 37 6.2.1 Trojan-horse Attack 37 6.2.2 Unconditional Security Proof 38 6.2.2.1 Entanglement Distillation Protocol 38 6.2.2.2 Estimation of the Phase Error Rate 39 Chapter 7 Proposed 4-Party Authenticated DPS-QKD 41 7.1 Description of Proposed Scheme 42 7.2 Security Analysis 45 7.2.1 Trojan-horse Attack 45 7.2.2 Unconditional Security Proof 47 7.2.2.1 Entanglement Distillation Protocol 47 7.2.2.2 Estimation of the Phase Error Rate 48 Chapter 8 Conclusion 50 Bibliography 52 Appendix A Creation and Annihilation Operators 56 Appendix B Principle of Beam Splitter 57 Appendix C Principle of Inoue et al.'s DPS-QKD 59

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