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研究生：	李國彰 Lee, Kuo-Chang
論文名稱：	高量子效率之量子金鑰分配 High Qubit Efficiency Quantum Key Distributions
指導教授：	黃宗立 Hwang, Tzonelih
學位類別：	博士 Doctor
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：	2009
畢業學年度：	97
語文別：	英文
論文頁數：	106
中文關鍵詞：	量子效率、量子密碼、金鑰分配
外文關鍵詞：	Qubit efficiency, Quantum cryptography, Key distribution
相關次數：	點閱：97 下載：4
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由於量子電腦的發展，一些傳統電腦難解的數學難題，已經被證明出可以在多項式時間內被量子電腦破解。因而，傳統密碼學中許多安全性植基於解數學難題之金鑰分配協定，未來可能變得不安全而無法使用。相對的，量子密碼學主要是利用量子的物理特性，例如：量子的不可複製性，量子的量測不確定性原理等，來達到資訊安全的應用。

相較於傳統金鑰分配協定，量子金鑰分配協定具有下列兩項優點：1.協定之安全性係植基於量子的物理特性，而非解數學難題上；2.便於檢測金鑰分配過程是否遭人竊聽。即是運用量子物理特性達到安全分配金鑰的目的。然而，探討現有的量子金鑰分配協定，亦存在以下待解決的問題：量子位元利用率低、量子設備昂貴、與假設傳統通信通道具備身分認證的功能。

量子金鑰分配過程，金鑰傳送者與接收者必須透過傳統通信通道進行量測基底資訊之交換，捨棄量測基底不同之量子位元。剩下的分享位元，通訊雙方仍須再次透過傳統通信通道交換資訊檢測金鑰正確性與竊聽者是否存在，並捨棄檢測之位元。兩次的協商過程，需消耗大部份的量子位元，因而造成量子使用率不彰。

此外，根據目前科技的現況，製造量子的相關設備仍是非常昂貴。例如，單顆量子產生儀器、精確的量子狀態量測儀器、長時間的量子儲存儀器、穩定的量子狀態轉換閘道、與長距離的量子傳輸通道等。考量成本，一般使用者並無法負擔與持有大量的量子設備，一些量子金鑰分配協定並無考量成本問題，假設通訊雙方擁有各式量子設備，因而造成其協定可行性降低。

大部分現存的量子金鑰分配協定假設傳統通信通道可達到身分認證功能。意即，傳統通信通道的傳輸信息，可以被竊聽，無法被攻擊者竄改。若屏除身分認證的傳統通信通道的假設，則此類量子金鑰分配協定會遭受到中間人攻擊 (man-in-the-middle attack) 的威脅。

本論文結合古典密碼技術與量子物理特性之優點，提出高效率之量子金鑰分配協定，發展出在量子環境下可以安全執行的量子金鑰分配協定。讓合法的通訊者，在面臨具有量子運算能力之攻擊者時，可以安全的進行金鑰分配作業。除了達到金鑰分配協定的安全要求，還可將量子使用率提升。此外，本論文亦提出資源分配不平均狀況下之量子金鑰分配協定，讓一般通訊者在配備少量的量子設備環境下，仍能進行量子金鑰分配作業，以符合環境現況，而更具實用性。最後，本論文提出可驗證通訊者身份的量子金鑰分配協定。讓合法的通訊者，在沒有身分認證的傳統通信通道環境下，可以安全的進行金鑰分配作業。

The security of key distribution in the classical cryptography is usually based on the fact that an attacker is unable to solve a certain mathematical problem, such as the discrete logarithm problem or the factoring problem. In the environment of quantum computation, the discrete logarithm problem and the factoring problem have been found solvable in the polynomial time. More classical mathematical problems may become insecure against the quantum computation in the future. Without using the mathematical problem, the quantum key distribution provides the unconditional security of key distribution between communicants based on quantum physics, such as the quantum uncertainty principle and the quantum no-cloning theorem.

Compare to the key distribution in the classical cryptography, the quantum key distribution protocol (QKDP) has two merits: (1) quantum mechanism provides a good solution to secure key distribution without the use of mathematical problems; and (2) legitimate participants can detect the eavesdroppings due to the quantum phenomena. Therefore, QKDPs are considered more secure than the classical key distribution protocols. However, there are problems of the current QKDPs, such as the inefficiency of qubit utilization rate, the overhead of equipping expensive quantum devices, and the assumption of authenticated classical channel.

During quantum key distributions, the sender and the receiver must exchange the information of their measuring bases through the classical communication channel, which spends 50% of the distributed qubits. Moreover, users perform the random sampling public discussion for the eavesdropping check, which also use 50% of the shared bits. Consequently, valuable qubits are wasted during the execution of the QKDPs and legitimate participants can share only 25% of the distributed qubits as the secret key. The qubit utilization rate of current QKDPs is inefficient.

The quantum devices, e.g., the qubit generating machine, or the quantum memory, or the qubit measuring machine, or the quantum unitary operator, are expensive to develop based on the current technology because of the difficulties on their constructions. Many QKDPs assume that every communicating party is able to equip with various quantum devices. In this situation, the QKDPs become impractical to implement.

The authenticated classical channel is required in most existing QKDPs for the bases negotiation and the random sampling public discussion. The QKDPs assume that the information transmitted in the authenticated classical channel can be eavesdropped, but cannot be modified by an outsider. However, the assumption of authenticated classical channel is usually unavailable. If there is no authenticated classical channel available, the QKDPs suffer the man-in-the-middle attack. An attacker can impersonate as one legitimate user to perform a QKDP with another legitimate user.

This thesis focuses on designing high qubit efficiency QKDPs in bringing the advantages of classical cryptography to the quantum cryptography, in which legitimate users can securely perform key distributions even an attacker has the ability of quantum computation. The proposed QKDPs not only achieve the security requirements of quantum key distribution, but also increase the qubit efficiency. Moreover, consider expensive quantum devices, the dissertation proposes the resource unbalanced QKDPs, which are suitable for the key distribution of the resource unbalanced environment, e.g., the wealthy center and a normal user. The normal user can perform a QKDP with only a few quantum devices. Finally, to eliminate the requirement of authenticated classical channel, the authenticated QKDP is proposed.

Introduction 1
1 Quantum Key Distribution . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Quantum Key Distribution Protocols . . . . . . . . . . . . . . . . . . . 2
3 Overhead and Performance Evaluation in Quantum Key Distribution . 3
4 Motivation and Contributions . . . . . . . . . . . . . . . . . . . . . . . 5
5 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Review of Classical and Quantum Cryptography 7
1 Review of Classical Cryptography . . . . . . . . . . . . . . . . . . . . . 7
1.1 Symmetric Algorithm . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2 Asymmetric Encryption . . . . . . . . . . . . . . . . . . . . . . 10
1.3 One-way Hash Function . . . . . . . . . . . . . . . . . . . . . . 12
1.4 Summary of Classical Cryptography . . . . . . . . . . . . . . . 14
2 Review of Quantum Cryptography . . . . . . . . . . . . . . . . . . . . 15
2.1 Quantum Mechanisms . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.1 Quantum Bit . . . . . . . . . . . . . . . . . . . . . . . 16
2.1.2 Quantum No-cloning Theorem . . . . . . . . . . . . . 18
2.1.3 Quantum Unitary Operations . . . . . . . . . . . . . . 19
2.1.4 The Einstein-Podolsky-Rosen (EPR) Pair . . . . . . . 20
2.1.5 The Qubit Efficiency . . . . . . . . . . . . . . . . . . . 21
2.2 Review of Quantum Key Distribution Protocols . . . . . . . . . 22
2.2.1 The BB84 Quantum Key Distribution Protocol . . . . 22
2.2.2 The EPR Quantum Key Distribution Protocol . . . . 32
2.3 Summary of Quantum Cryptography . . . . . . . . . . . . . . . 34
100% Quantum Key Distribution Protocol 39
1 The Necessity of the QKDP with High Qubit Efficiency . . . . . . . . . 40
2 Proposed 100% QKDP . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.1 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.2 Proposed QKDP with 100% Qubit Efficiency . . . . . . . . . . . 42
2.3 Security Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.4 Comparison of the High Qubit Efficiency QKDPs . . . . . . . . 51
Modifications of 100% Quantum Key Distribution Protocol 55
1 The Necessity of the Modification of 100% QKDP . . . . . . . . . . . . 55
2 The First Modification of 100% QKDP . . . . . . . . . . . . . . . . . . 56
2.1 The First Modification of 100% QKDP (FMQKDP) . . . . . . . 56
2.2 Security Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3 The Second Modification of 100% QKDP (SMQKDP) . . . . . . . . . . 61
3.1 The Second Modification of 100% QKDP . . . . . . . . . . . . . 61
3.2 Security Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4 Comparison of QKDPs . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Resource Unbalanced Quantum Key Distribution Protocols 69
1 The Necessity of the Resource Unbalanced QKDP (RUQKDP) . . . . . 69
2 Proposed Resource Unbalanced Quantum Key Distribution Protocols . 71
2.1 The 100% Resource Unbalanced Quantum Key Distribution Protocol
(FRUQKDP) . . . . . . . . . . . . . . . . . . . . . . . . . 71
2.2 The Second Resource Unbalanced Quantum Key Distribution
Protocol (SRUQKDP) . . . . . . . . . . . . . . . . . . . . . . . 73
2.3 The Third Resource Unbalanced Quantum Key Distribution Protocol
(TRUQKDP) . . . . . . . . . . . . . . . . . . . . . . . . . 74
3 Performance of Resource Unbalanced QKDPs . . . . . . . . . . . . . . 76
Authenticated Quantum Key Distribution Protocols 79
1 The Necessity of the Authenticated QKDP (AQKDP) . . . . . . . . . . 79
2 The proposed Authenticated QKDP . . . . . . . . . . . . . . . . . . . . 81
2.1 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
2.2 Proposed Two-party Authenticated QKDP . . . . . . . . . . . . 82
2.3 Security Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 85
2.3.1 Security Properties of AQKDP . . . . . . . . . . . . . 85
2.3.2 Security Analysis of the AQKDP . . . . . . . . . . . . 85
3 Performance of AQKDPs . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4 The proposed Three-party Authenticated QKDP . . . . . . . . . . . . . 90
4.1 Proposed Three-party Authenticated QKDP . . . . . . . . . . . 90
4.1.1 Security Analysis of the Three-party AQKDP . . . . . 93
Conclusions 95
Bibliography 99
                                    

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校內：2014-07-22公開
校外：2014-07-22公開

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