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系統識別號 U0026-2008201013222800
論文名稱(中文) 信任不均衡的量子秘密分享
論文名稱(英文) Trust Unbalanced Quantum Secret Sharing
校院名稱 成功大學
系所名稱(中) 資訊工程學系碩博士班
系所名稱(英) Institute of Computer Science and Information Engineering
學年度 98
學期 2
出版年 99
研究生(中文) 黃正傑
研究生(英文) Cheng-Chieh Hwang
學號 p7697427
學位類別 碩士
語文別 英文
論文頁數 56頁
口試委員 指導教授-黃宗立
口試委員-李南逸
口試委員-王智弘
中文關鍵字 量子金鑰分配協定  量子秘密分享協定  偽裝光子  區塊傳輸 
英文關鍵字 Quantum key distribution protocol  Quantum secret sharing protocol  Decoy photons  block-transmission 
學科別分類
中文摘要 現今的資訊安全技術都是基於密碼學相關理論所發展出來的,例如:DES、AES、RSA、ElGamal密碼系統等等,其安全性皆屬於計算安全,目的在於讓破密者在一定時間內無法破解這些密碼系統,所以這些密碼系統並不是永久安全的。隨著量子電腦的發展,一些基於數學難題的密碼系統,例如RSA(基於因式分解數學難題),已經被證實可以在多項式的時間內被量子電腦破解(Shor演算法)。因此在傳統密碼學中,許多基於解數學難題的密碼系統,未來可能變的不安全而無法使用,所幸的是,量子電腦除了用來破解傳統密碼系統之外,我們還可以利用量子電腦來發展出建構在量子物理上的密碼系統。
量子密碼學(Quantum Cryptography)為近代重要的研究領域之一,主要是根據量子物理的法則,例如:海森堡測不準原理、不可複製性等等,所發展出來的一門科學,其安全性皆架構在這些量子物理特性上;量子密碼的基本特徵有兩點:無條件安全、竊聽可檢測性,所謂的無條件安全指的是,破密者在具有無限資源的條件下仍無法破解該密碼系統;竊聽可檢測性指的是,通訊的雙方可以根據量測不確定性來檢測出是否存在此攻擊。
量子金鑰分配協定(Quantum Key Distribution Protocol)是目前量子密碼學中重要的研究課題之一,其目的在於讓通訊的雙方利用量子的傳輸來分享出一把共享的金鑰,之後再利用此金鑰來進行訊息的溝通。而為了確定在量子的傳輸過程中是否存在竊聽者,在基於量子物理的特性下,通訊的雙方利用公開討論(public discussion)的機制,來檢測出是否有竊聽者的存在。
量子秘密分享協定(Quantum Secret Sharing Protocol)同樣為量子密碼學上重要的一環。秘密分享目的在於將一個秘密訊息分割成數個次密鑰(shadows)。每一個次密鑰都不能單獨地復原此秘密訊息,但是當有足夠的次密鑰時,則可以做到。以一個簡單的例子來看,在三方的量子秘密分享中,老闆將他的秘密訊息分成兩個次密鑰,然後分別分給他的兩個代理人,任何一個代理人都不能單獨的復原老闆的秘密訊息,只有當他們合作時,老闆的秘密訊息才能被還原回來,所以不誠實的代理人沒有辦法單獨的還原老闆的秘密訊息。2006年Deng等人利用GHZ states提出一個量子秘密分享協定,2009年Gao利用三維的EPR pairs提出另一個量子秘密分享協定。本論文將利用decoy photons、block-transmission等技術來提升量子的利用率、減少不必要的運算和設備。更進一步,本論文將提出另一種用途的量子秘密分享協定,信任不均的量子秘密分享協定,根據擁有不同權利、階級和信賴度的代理人,來分配次密鑰的數量,擁有越高權利、階級和信賴度的代理人,將擁有更多的次密鑰數量。因此擁有越高權利、階級和信賴度的代理人,將有越高的機率猜到秘密分享者的資訊。並且擁有越高權利、階級和信賴度的代理人能夠自己就解得秘密分享者一半的資訊,另一半的訊息必須跟另一個代理人合作才能解出來。
英文摘要 Today, information security techniques such as DES, AES, RSA, and ElGamal are based on the cryptography theory. These cryptosystems are computationally secure. The purpose of these cryptosystems is to prevent attackers from breaking them in a certain period of time. Therefore, such cryptosystems are not perfectly secure. The development of the quantum computer has called into question the security of cryptosystems that are based on the fact that an attacker is unable to solve mathematical problems such as RSA (based on the factoring problem), because such problems have been found to be solvable in polynomial time. Therefore, a number of classical mathematical problems in cryptography may render them insecure in the future because of quantum computation. Fortunately, the quantum computer can be used not only to break traditional cryptosystems but also to develop quantum cryptography based on quantum mechanics.
Quantum cryptography is an important research area wherein quantum phenomena such as the Heisenberg uncertainty principle and the no-cloning theorem are used to ensure secure communication over quantum channels.
Quantum cryptography has two basic characteristics: unconditional security and eavesdropping detectability. Unconditional security means an attacker cannot break the cryptosystem, even using infinite resources. Eavesdropping detectability means the communicators can use the measurement uncertainty to check for the presence of eavesdropping.
The quantum key distribution protocol (QKDP) is one of the most important research topics in quantum cryptography. In this protocol, two communicators use the quantum state and quantum channel to share a common secret key. Then, they use this common secret key to communicate. In order to check for the presence of eavesdropping in quantum transmission, the two communicators use a public discussion channel to detect this attack on the basis of the principles of quantum mechanics.
The quantum secret sharing (QSS) protocol is another important research topic. In this protocol, secret information is split into several shadows. A single shadow alone cannot be used to recover the secret, but a sufficient number of shadows can be used to do so. For example, in three-party QSS, an employer splits a secret into two shadows and then sends one to each of her two agents. Neither agent alone can recover the employer’s secret information. Only when they collaborate, the employer’s secret can be recovered. Therefore, a dishonest agent cannot recover the employer’s secret information on his/her own. In 2006, Deng et al. used the GHZ states to propose a quantum secret sharing protocol. In 2009, Gao proposed a quantum secret sharing protocol based on three-dimensional Bell states. In our thesis, we will use the techniques of decoy photons, block-transmission, etc., to increase the qubit efficiency and reduce the number of unnecessary operations and quantum devices. Moreover, we will propose another quantum secret sharing protocol, an unbalanced-trust quantum secret sharing protocol, for applications in which one agent has more power (trust) than the other. In this protocol, an agent with more power (trust) also acquires more information. As a result, there is a high probability that this agent will be able to guess the secret holder’s information. Moreover, the agent with more power (trust) can recover half of the secret holder’s information alone, but must cooperate with the other agent to recover the other half.
論文目次 Contents IX
Chapter 1 Introduction 1
1.1 Overview 1
1.2 Motivation and Contribution 3
1.3 Thesis Structure 4
Chapter 2 Background 5
2.1 Quantum Theory and The properties of Quantum Mechanics 5
2.1.1 The Properties of Single Photons 5
2.1.2 The Quantum Unitary Operations 8
2.1.3 The Properties of Bell States 9
2.1.4 The Properties of GHZ States 11
2.1.5 The Properties of Three-Dimensional Bell States 14
2.2 Current Research on Quantum Secret Sharing 15
2.2.1 HBB99 Protocol 16
2.2.2 Efficient Multiparty Quantum Secret Sharing with GHZ States 18
2.2.3 Three-party Quantum Secret Sharing Using Two-Photon Three-Dimensional Bell States 21
2.2.4 Xue et al.’s Quantum Secret Sharing Protocol 24
Chapter 3 The Improvement Research in Quantum Secret Sharing Protocol 28
3.1 The Improvement of Efficient Multiparty Quantum Secret Sharing with GHZ States 28
3.1.1 Notation 28
3.1.2 Structure 29
3.1.3 Security analysis 32
3.1.4 Efficiency analysis 33
3.2 The Improvement of Multiparty Quantum Secret Sharing Using Two-Photon Three-Dimensional Bell States 34
3.2.1 Notation 35
3.2.2 Structure 35
3.2.3 Security analysis 37
3.2.4 Comparison 38
Chapter 4 Trust Unbalanced Quantum Secret Sharing Protocol 40
4.1 Trust Unbalanced Quantum Secret Sharing Protocol Using GHZ States 40
4.1.1 GHZ states with Bell measurement and X-basis measurement 41
4.1.2 Notation 42
4.1.3 Strucutre 43
4.1.4 Security analysis 45
4.1.5 Comparison 46
4.2 Trust Unbalanced Quantum Secret Sharing Protocol Using GHZ States and GHZ Measurement 47
4.2.1 Notation 47
4.2.2 Structure 47
4.2.3 Security analysis 50
4.2.4 Comparison 51
Chapter 5 Conclusions 52
Bibliography 54

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