臺灣博碩士論文加值系統

近年來基於量子傳輸科技和量子金鑰分配技術不斷地創新與發展，使得先進量子密碼技術可以應用於不同的安全性問題,包括量子認證、量子安全通訊、量子偵測、量子安全傳遞及量子簽章；因為有如此多的應用，使得量子資訊網路可以在未來成為一個實際性的網路。
比較量子密碼學和古典密碼學，主要差異來自物理特性,量子通道是基於物理特性包括不確定原理、不可複製性和量子遠端傳遞，這些物理特性使得量子通道的安全性比古典通道高。因為使用物理特性之量子通道，我們可以查出竊聽行為並且提供安全的直接通信。 然而，古典密碼學不可能查出竊聽行為，特别是在有開放的無線媒介。有關於時間複雜度，量子密碼演算法基於物理原理會比基於數學計算的古典密碼演算法來得好。例如，以因式分解而言，量子密碼演算法的時間複雜度是多項式函數而古典密碼演算法的時間複雜度是指數函數。
和先前的量子研究比較，目前文獻上的應用大多使用量子金鑰分配協定，如BB84和E91，來建立一個保密性的金鑰，進而運用此一金鑰在直接通信的環境中達到確保傳輸機密性的要求。然而，在一般常見的情況下，信息傳遞的連接形式是屬於間接通信方式，在間接通訊環境下，在傳遞過程中，可能遭遇三種型態的攻擊，包括竊聽者、中間攻擊者及惡意節點，這種情形下的傳遞路徑稱為不安全的傳送路徑。在一個不安全的傳送路徑之下，我們不可能尋求一個安全傳送路徑來傳送量子訊息。對量子間接通訊而言，抵抗三種型態的攻擊和獲得安全傳輸的過程是個困難的工作。
對於量子間接通訊而言，我的論文是設計幾個傳遞機制來達到資料保密的目標，其主要分為下列幾個部份。對於量子認證而言，我們提出兩種類型的量子認證機制來解決在不安全的傳送路徑下發令者和接收器之間的識別問題，遠端雙方可以達到安全認證過程並且抵抗竊聽者和惡意節點的攻擊，根據物理特性，這些機制可以達到安全認證過程。對於量子偵測而言，發令者和接收器使用量子糾纏光子和協同合作電路來查出惡意節點之侵入行為，根據協同合作電路，接收器能夠獲得量子的原始狀態，因此可以查出惡意節點之攻擊行為。
對於量子傳輸而言，三個量子傳遞機制被提出，來達到在一個不安全的傳送路徑之傳遞機密性。這些機制可能抵抗攻擊的三種類型，並且讓接收器有判斷能力去決定所接受量子傳送框架是否滿足安全性要求，來決定接受與否，這是一個新的突破。對於量子簽章而言，客戶端和伺服器能使用量子分享密碼技術來獲取間接通訊下的安全簽章。如果量子安全密碼技術的這些應用可以成熟發展，那麼本研究所提出之量子傳遞機制，能夠保證於間接通訊條件下來達到量子訊息安全傳遞。

Recently, on the basis of advanced development in quantum transmission technology and quantum key distribution, the advanced techniques of quantum cryptography can be applied to the different security issues, including quantum authentication, quantum secure communication, quantum detection, quantum secure transmission and quantum signature. These applications let that quantum information networks will become realistic in the future.
Compared with quantum cryptography and classical cryptography, the major difference comes from the laws of physics. Quantum channel is based on the laws of physics such as uncertainty principle, no-cloning theorem and quantum teleportation. These physical properties make quantum channel is more secure than classical channel. By using physical properties of quantum channel, we can detect eavesdropping and support secure direct communication. However, classical cryptography can not detect the presence of eavesdroppers, especially with wireless open medium. In regard to the time complexity, quantum cryptography algorithm based on the laws of physics is better than classical cryptography algorithm based on mathematical computation. For example, in the factoring problem, time complexity of quantum algorithm is polynomial time. Compared with classical cryptography algorithm, its time complexity is exponential.
Compared with previous quantum researches, these applications used quantum key distribution protocols such as BB84 and E91 to generate a secret key which can be used to achieve transmission integrity in the direct communication. However, in general, the connection type of transmitting message is indirect communication. Under the indirect communication, transmitting message from source to destination may pass through several intermediate nodes and communication channels. In the routing path, there are three types of attacks, including eavesdropping, man-in-the-middle attacks and malicious node. It is called an unsafe routing path. Under an unsafe routing path, we can not pursue the secure routing path to transmit quantum message. It is a difficult work to resist the previous attacks and get the secure transmission process for quantum indirect communication.
For quantum indirect communication, this dissertation is to design several transmission mechanisms which are used to achieve the data security. This work includes the following parts. For quantum authentication, we present two types of quantum authentication mechanism that can solve the identification problem between the sender and receiver under the unsafe routing path. Two remote parties can achieve the secure authentication process to resist eavesdropping and malicious node. On the basis of the laws of physics, the secure authentication process can be achieved. For quantum detection, the sender and receiver can use quantum entangled qubits and a collaborative working circuit to detect the intrusive behavior of malicious node. Based on this circuit, the receiver can obtain the original quantum state of sending quantum qubits such that the intrusive behavior of malicious node can be detected.
For quantum transmission, three quantum transmission mechanisms are proposed to achieve transmission integrity under an unsafe routing path. These mechanisms can resist three types of attacks and let the receiver has the capability to judge whether the receiving quantum frame is complied with the security requirement and can be accepted or not. This is a new breakthrough. For quantum signature, client and server can use the property of quantum secret sharing to secure the signature process for indirect communication. If the developed techniques of these applications are mature, then the proposed quantum transmission mechanisms can guarantee that the quantum message can be securely transmitted in the quantum indirect communication.

Contents

Acknowledgments …………………………………..………………… i
Abstract ………………………………………………..……………… ii
Contents …………………………………………………………….… vii
List of Figures …………………………………………………..…….. x
List of Tables ………………………………………………….……… xii
Chapter 1. Introduction …………………………………………..…… 1
Chapter 2. Notations and Preliminaries ……………………..………... 5
2-1. Superposition and Entanglement ……………………..……….. 5
2-1-1. Quantum Superposition State ……………………...……... 5
2-1-2. The EPR Pairs ………………………………………...….. 6
2-1-3. The GHZ States ………….………………………………. 6
2-1-4. Entanglement Swapping ………………………………….. 7
2-2. The Laws of Physics ………………………………………..…. 9
2-2-1. The No-cloning Theorem ……………………………..…. 9
2-2-2. The Uncertainty Principle ……………………………...… 10
2-2-3. The Non-deterministic Theorem ……………………….... 10
2-2-4. Quantum Secret Sharing……………………………….….. 11
2-3. Quantum key Distribution Protocols …………………..…….... 12
2-3-1. The BB84 Protocol …………………………………..….... 12
2-3-2. The E91 Protocol ……………………………………..…... 13
2-3-3. The B92 Protocol …………………………………….…... 14
Chapter 3. The Security of Quantum Indirect Communication …..…... 16
3-1. An Unsafe Routing Path …………………………………….… 16
3-2. Quantum Sharing Table …………………………………….…. 18
3-3. Quantum Indirect Shared Key protocol …………………..….... 19
Chapter 4. Quantum Authentication Mechanism …………………….. 28
4-1. Quantum Identification Operations ………………………….... 28
4-2. Quantum Sharing Table …………………………………….…. 31
4-3. The Authentication Protocols ………………………………..... 33
4-3-1. Superposition State Authentication Protocol …………...... 35
4-3-2. Entangled State Authentication Protocol ……………….... 40
4-3-3. Testing Rules …………………………………………..…. 43
4-4. Security Analysis and Discussion ………………………….…. 45
4-4-1. Attacking Types …………………………………….……. 45
4-4-2. Quantum Sharing Table ……………………………….…. 46
4-4-3. Comparisons of SSAP and ESAP …………………….….. 47
4-5. Summary………………………………………………..……… 48
Chapter 5. Quantum Detection Mechanism …………………….……. 49
5-1. The Mechanism …………………………………………….…. 49
5-1-1. Topology and Quantum Sharing Table ……………….….. 49
5-1-2. Collaborative Working Circuit ………………………..….. 51
5-2. Security Analysis …………………………………………..….. 57
5-2-1. Benefit of Quantum Sharing Table …………………….… 57
5-2-2. Secure Capability ……………………………..………….. 57
5-3. Summary... …………………………………………………...... 58
Chapter 6. Quantum Transmission Mechanism ………………….…... 59
6-1. Quantum Three-communication-phase Transmission for indirect Communication ………………………………..…. 60
6-1-1. Operation Model ……………………………………….… 60
6-1-2. Quantum Authentication Phase ………………………..…. 61
6-1-3. Quantum Communication Phase ……………………….… 66
6-1-4. Quantum Transmission Phase ……………………….…… 69
6-1-5. Security Analysis and Discussion …………………….….. 73
6-1-6. Summary ………………………………………………..… 77
6-2. Quantum Transmission Integrity Mechanism Based on Quantum Reversible Switching Circuits ………….... 78
6-2-1. Quantum verification algorithm ……………………….…. 78
6-2-2. Secure Quantum Transmission Mechanism………………. 86
6-2-2. Secure Analysis ……………………………………..……. 94
6-2-3. Summary……………………………………………..….… 97
6-3. Quantum Transmission Mechanism for Detection ……….…. 98
6-3-1. The Mechanism …………………………………….……. 98
6-3-2. Security Analysis………………….………………….….. 103
6-3-3. Summary ………………………………………………...... 106
Chapter 7. Applications of Quantum Indirect Transmission ………..... 107
7-1.Quantum Signature Mechanism with GHZ States ………….…. 107
7-1-1. Notations and Preliminaries ………………………….…... 108
7-1-2. The Proposed Mechanism ……………………………..…. 109
7-1-3. Security Analysis and Discussion ……………………..…. 115
7-1-4. Summary ……………………………………………..…... 117
7-2.Quantum Switching and Quantum String Matching ……….….. 117
7-2-1. Notations and Preliminaries ………………………..…….. 117
7-2-2. Quantum Control Circuit …………………………….…… 120
7-2-3. Summary ………………………………………………..… 123
Chapter 8 Conclusions and Future Works ………………………….... 125
Bibliography ………………………………………………………….. 129

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