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研究生：	張智閎 Chang, Chih-Hung
論文名稱：	基於GHZ量子態之可抗集合雜訊之量子安全協定 Collective Noise Resistant Quantum Security Protocols Using GHZ States
指導教授：	黃宗立 Hwang, Tzonelih
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：	2014
畢業學年度：	102
語文別：	英文
論文頁數：	102
中文關鍵詞：	量子密碼學、集合雜訊、隨機量子金鑰分配、量子私密比較、量子對話、GHZ量子態、GHZ-like量子態
外文關鍵詞：	Quantum Cryptography, Collective noise, Probabilistic Quantum Key Distribution, Quantum Private Comparison, Quantum Dialogue, GHZ state, GHZ-like state
相關次數：	點閱：182 下載：0
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近年來，基於量子力學的研究發展，量子電腦與量子演算法的研究也日益興起。然而，許多安全性植基於因數分解或離散對數難題之密碼學系統，皆已被證明可被量子演算法在多項式時間內破解。因此，隨著量子電腦的成熟，近代密碼學所提供的安全技術將面臨重大威脅。有鑑於此，一門結合量子力學與密碼學之研究-量子密碼學因應而生，不同於以複雜的計算過程或數學難題為基礎的設計方式，量子密碼學植基於量子物理的特性來設計安全的協定，故可免於量子電腦所帶來的危害。
在這幾年來，量子密碼學主要著重於量子金鑰分配和量子通訊相關之研究，其應用可分為：量子金鑰分配、量子金鑰協商、隨機量子金鑰分配、量子直接通訊、確定式量子通訊、量子對話、量子秘密分享、量子私密比較以及量子簽章等協定。然而，大多數這些現存的量子協定必須假設量子通道是理想通道，也就是假設量子傳輸在這些量子通道中，不會受到雜訊的干擾影響。然而，實際上，合法的通訊雙方執行量子通訊時，必須透過光纖來傳輸光子。但在光子傳輸的過程中，光纖的雙折射波動會導致集合雜訊產生。倘若不假設量子通道為理想通道，則這些量子協定在進行竊聽者檢查時，將無法分辨其錯誤率是由此集合雜訊干擾所造成，抑或是竊聽者攻擊所造成的。基於此弱點，竊聽者就可以藉由雜訊來隱蔽其攻擊所造成的錯誤率，讓合法的通訊者在公開討論中誤以為其錯誤率是通道上的雜訊干擾所造成的。因此，如何在量子通道受到集合雜訊干擾下，設計出安全的量子協定成為量子密碼學中近年來熱門的議題。
基於此，本論文利用可抗集合雜訊之GHZ量子態與GHZ-like量子態，結合量子物理的特性來設計編碼方法並建置量子協定，以確保當量子通道受到雜訊干擾時，仍能保持量子協定的安全性。其中，這些量子協定包含隨機量子金鑰分配、量子私密比較和量子對話。

Recently, the research in quantum computer and quantum algorithm is prospering due to the development of quantum mechanics. With quantum algorithm, the cryptosystems whose security is based on the problems of factorization and discrete logarithm can be bro-ken with polynomial time. As development on quantum computer area keeps maturing, se-curity technique based on modern cryptography will face a sever threat. In this regard, Quantum cryptography is a novel area coming after quantum physics and cryptography. Different from the modern cryptography that is designed on the basis of intricate calcula-tion and intractable mathematical problems, quantum cryptography can be utilized to de-sign security protocols according to the property of quantum physics.
In recent years, research about quantum key distribution, quantum communication has been the focus in the area of quantum cryptography, and the research is applied to many areas including quantum key distribution, quantum key agreement, probabilistic quantum key distribution, quantum secure direct communication, deterministic secure quantum communication, quantum dialogue, quantum secret sharing, quantum private comparision and quantum signature are widely studied.
Nevertheless, most of existing quantum protocols are arranged under the assumption that quantum channel is an ideal channel. In other words, a quantum channel is not affected by any noise while the photons are transmitted through the quantum channel. However, in realilty, two legitimate communicants need to transmit photons through optical fiber. But during the transmission process, the collective noise is generated because of the fluctuation of the birefringence in optical fiber. If the quantum channel is not assumed to be ideal, it is difficult to discern between mistakes caused by the collective noise and mistakes caused by malicious eavesdropper when the eavesdropper checking process are performed in the quantum protocols. Aiming to exploit this weak point, an eavesdropper is able to cover its attack by this kind of noise, which misleads legitimate communicants into believing that mistakes are caused by the noise during their public discussion procedure. As a result, how to design a secure quantum protocol under the condition that quantum channel is disturbed by the collective noise is being the most widely discussed issue in quantum cryptography.
This thesis focuses on designing secure quantum protocols based on the proposed coding methods by using the GHZ states and the GHZ-like states in order to repel the col-lective noise. The purpose of this thesis is providing a way to improve security of quantum protocols under the condition that the quantum channel suffers from the collective noise. Here, the quantum protocols include probabilistic quantum key distribution, quantum pri-vate comparision and quantum dialogue.

中文摘要		III
Abstract		V
誌謝		VII
Content		VIII
List of Tables	XI
List of Figures	XII
Chapter 1	Introduction	1
1	Probabilistic Quantum Key Distribution Protocol	1
2	Quantum Private Comparison Protocols	2
3	Quantum Qialogue Protocols	3
4	Motivation and Contributions	3
5	Thesis Structure	7
Chapter 2	Quantum Background	8
1	Quantum Properties	8
1.1	The Qubit and Its Properties	8
1.2	Unitary Operations	10
1.3	Entangled States and Their Properties	12
1.4	Efficiency Evaluation Function	16
2	Quantum Properties resistant to Collective Noises	16
2.1	The Properties of Collective Noises	16
2.2	The Quantum States resistant to Collective Noises	17
2.2.1	The Logical Qubit resistant to Collective-dephasing Noise	17
2.2.2	The Logical Qubit resistant to Collective-rotation Noise	19
Chapter 3	Encoding and Decoding for Collective Noises	23
1	The Properties of four-particle Entangled States	23
1.1	The the measurement result of four-particle GHZ state	23
1.2	The the measurement result of four-particle GHZ-like state	25
2	Entanglement Swapping via two three-particle Entangled States	26
3	Entanglement Swapping via three three-particle Entangled States	28
4	Coding Functions for three-particle Entangled States	33
4.1	Coding Function for a GHZ State	33
4.2	Coding Function for a GHZ-like State	37
Chapter 4	PQKD with Third Parties immune to Collective Noises	42
1	The Proposed PQKD Protocol via four-particle Entangled States	42
1.1	PQKD immune to Collective-dephasing Noise	42
1.1.1	PQKD protocol using four-particle GHZ state with one TP	43
1.1.2	PQKD protocol using four-particle GHZ state with two TPs	47
1.2	PQKD immune to Collective-rotation Noise	48
1.2.1	PQKD protocol using four-particle GHZ-like state with one TP	49
1.2.2	PQKD protocol using four-particle GHZ-like state with two TPs	50
1.3	Security Analysis	50
1.3.1	Eavesdropping attacks	50
1.3.2	Insider attack	51
2	The Proposed PQKD Protocol via three-particle Entangled States	55
2.1	PQKD immune to Collective-dephasing Noise	55
2.1.1	PQKD protocol using GHZ state with one TP	56
2.1.2	PQKD protocol using GHZ state with two TPs	60
2.2	PQKD immune to Collective-rotation Noise with third parties	61
2.3	Security Analysis	62
2.3.1	Outsider attack	62
2.3.2	Insider attack	63
3	Comparison	72
Chapter 5	QPC Protocols immune to Collective Noises	74
1	Extended Liu et al.’s Protocol for Collective Nosies	74
1.1	Review of Liu et al.’s scheme	74
1.2	The Extended Liu et al.’s scheme immune to Collective Noises	76
2	The Proposed QPC Protocols immune to Collective Nosies	80
2.1	The Proposed QPC Protocols immune to Collective-dephasing Noise	80
2.2	The Proposed QPC Protocols immune to Collective-rotation Noise	84
2.3	Security Analysis	84
3	Comparison	87
Chapter 6	QD Protocols immune to Collective Noises	89
1	The Proposed QD immune to Collective-dephasing Noise	90
2	The Proposed QD immune to Collective-rotation Noise	93
3	Security Analysis	93
3.1	Security against eavesdropping attacks	94
3.2	Security against Trojan horse attack	94
3.3	Security analysis of information leakage	95
Chapter 7	Conclusion	96
Bibliography	98
                                    

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