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研究生： 陳佳豪
Chen, Jia-Hao
論文名稱： 量子糾結交換態在密碼學上的應用
The Application of Quantum Entanglement Swapping in Cryptography
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： 2009
畢業學年度： 97
語文別： 中文
論文頁數： 89
中文關鍵詞： 量子木馬攻擊 、量子秘密分享協定 、量子金鑰分配協定 、量子糾結交換態
外文關鍵詞： Entanglement swapping, Quantum key distribution protocol, Quantum secret sharing, Quantum Trojan horse attack
相關次數： 點閱：128  下載：3 
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    • 傳統非對稱式金鑰分配協定都是架構在數學難題上，然而，一般相信當量子電腦發展到一定的程度後，便可以有效的破解，因此有必要性發展出非基於數學難題上的金鑰分配協定。量子金鑰分配協定(Quantum Key Distribution Protocol)，利用量子所擁有的量測不可確定性(The uncertainty of measurement)與不可複製性(no-cloning)的特性，發展出非基於數學難題上的無條件安全金鑰分配協定。
    量子金鑰分配協定為目前量子密碼學中重要的研究課題之一，主要是讓溝通訊息的雙方利用量子的傳送，達到雙方分享出一把金鑰，之後利用這把金鑰進行安全的訊息溝通，而中間若存在竊聽者欲竊聽金鑰的訊息，基於量子的特性，無法正確的得到金鑰的訊息，溝通訊息的雙方利用公開討論(public discussion)的機制，有一定的機率成功的檢測出有竊聽者的存在，重新進行金鑰分配。
    在現今的量子金鑰分配協定，基於量子的量測不可確定性，必須擁有基底(base)才能準確的量測出光子的訊息，因此溝通訊息的雙方必須透過傳統通道來傳送基底的訊息，本論文提出一個特別的方法，套用到量子金鑰分配協定中，使得溝通訊息的雙方不需要透過傳統通道來傳送基底的訊息，也能正確的量測到光子的訊息。2008年 Gao提出量子糾結交換態運用到量子金鑰分配的協定[11]，本論文提出利用不同的量子糾結交換態的特性，讓整體所需使用到的傳統通道位元數降低，使得整題的效能提升。針對在量子協定上，因為量子特性所遭受到的木馬攻擊(Trajan Horse Attack)，本論文也提出了相關的解決方式。
    量子秘密分享協定(Quatnum Secret Sharing)同樣為量子密碼學上重要的一環，參與協定者有三位，分別為老闆(Boss)與兩位代理人(Agent)，老闆要將本身的祕密訊息或金鑰平均分給兩位代理人，但兩位代理人卻可能存在不誠實者，因此協定的主要目標為不讓其中一位代理人獨自擁有所有的秘密訊息或金鑰。本論文利用量子記憶體(quantum memory)，
    提出高效能的量子秘密分享協定。2004年Zhang等人提出了利用量子糾結交換態來實行量子秘密分享協定[16]，本論文利用不同的量子糾結交換態的特性來節省光子的利用率。並在量子秘密分享協定現今的發展上，發現一個常見的問題。

    In tranditional asymmetric key distribution protocols, the security is based on the computational difficulty of certain number theoretic problems. However, most people believe that these number theoretic problems can be efficiently solved by quantum computers. Therefore, it is significant to develop key distribution protocol, where is not based on the computational difficulty of certain number theoretic problems. Quantum Key Distribution Protocol (QKDP), it uses the uncertainty of measurement and no-cloning of quantum property, developing quantum key distribution is unconditional security.
    Quantum key distribution protocol is one of the most devoted researches in quantum cryptography. The object is two parties of communication to share a key, so that they can make use of that key for further secure communication. If eavesdropper wants to eavesdrop key, the quantum property lets he can’t get correct key. The protocol uses public discussion to detect the eavesdropper between two parties of communication, the probability is high to detect the existential eavesdropper, the protocol proceeds renew.
    In most of quantum key distribution protocol today, based on the quantum uncertainty of measurement. If someone wants to get the informations by measuring the photons, he must have the correct bases. Therefore, it needs classical channel to transmit the basis information between two parties of communication. This thesis proposed a special method, two parties of communication can get the correct informations by measuring the photons without transmitting the bases. Gao proposed the quantum key distribution protocol using the entanglement swapping in 2008[11]. This thesis proposed the quantum key distribution protocol using different entanglement swapping property to reduce the number of bit of classical channel and improve the total efficiency. This thesis also proposed the soluation of quantum trojan horse attack on quantum protocol.
    Quantum secret sharing (QSS) is also one of the most devoted researches in quantum cryptography. There are three parties in the protocol, one boss and two agents. The boss wants to share his information of key or secret to two agents, but maybe one of two agents is dishonest. Therefore, the object of protocol is avoiding one of two agents has all the information of key or secret. This thesis proposed the high efficient quantum secret sharing by using quantum memory. Zhang et al proposed the quantum secret sharing by entanglement swapping in 2004[16], this thesis improved photons efficiency by different property of quantum entanglement swapping, and discovered a usually problem in the quantum secret sharing today.

    中文提要 .................................................................................................. III Abstract ..................................................................................................... V 致謝 ......................................................................................................... VII 頁目錄 ....................................................................................................VIII 圖目錄 ....................................................................................................... XI 表目錄 ....................................................................................................XIII 第一章 導論 ............................................................................................... 1 第1.1 節 量子物理特性 .......................................................................................................... 2 第1.1.1 節 單光子的特性 ............................................................................................... 2 第1.1.2 節 雙光子的特性 ............................................................................................... 4 第1.1.3 節 量子運算子 ................................................................................................... 6 第1.1.4 節 量子糾結交換態 ........................................................................................... 8 第1.2 節 CaBello 的量子金鑰分配效率之定義 ..................................................................... 10 第1.3 節 在量子密碼學上的木馬攻擊 ................................................................................... 11 第1.3.1 節 木馬攻擊的環境與方式 ............................................................................... 11 第1.3.1.1 節 存在木馬攻擊的環境 ...................................................................... 11 第1.3.1.2 節 不可見光子攻擊 .............................................................................. 12 第1.3.1.3 節 延遲光子攻擊 .................................................................................. 13 第1.3.2 節 硬體防止木馬攻擊之技術 ........................................................................... 14 第1.4 節 研究動機與研究貢獻 ............................................................................................... 18 第1.5 節 論文架構 ................................................................................................................. 20 第二章 量子在密碼學上的應用 ............................................................. 21 第2.1 節 量子金鑰分配協定 .............................................................................................. 21 第2.1.1 節 量子金鑰分配協定介紹與環境 ................................................................... 21 第2.1.2 節 現有的量子金鑰分配協定技術 ................................................................... 22 第2.2 節 量子秘密分享協定 ................................................................................................... 31 第2.2.1 節 量子秘密分享協定介紹與環境 ................................................................... 31 第2.2.2 節 現有的量子秘密分享協定技術 ................................................................... 33 第三章 可防止木馬攻擊的量子金鑰分配協定 ..................................... 38 第3.1 節 遭受木馬攻擊的量子金鑰分配協定 ....................................................................... 38 第3.2 節 抵禦木馬攻擊的量子金鑰分配協定 ....................................................................... 40 第3.3 節 安全性分析 ............................................................................................................... 45 第四章 在金鑰分配協定上的研究 ......................................................... 49 第4.1 節 不傳送基底之金鑰分配協定 ................................................................................... 49 第4.1.1 節 單光子不傳送基底之金鑰分配協定 ........................................................... 50 第4.1.1.1 節 架構 .................................................................................................. 50 第4.1.1.2 節 安全性分析 ...................................................................................... 53 第4.1.1.3 節 效能分析 .......................................................................................... 55 第4.1.2 節 雙光子不傳送基底之金鑰分配協定 ........................................................... 56 第4.1.2.1 節 架構 .................................................................................................. 56 第4.1.2.2 節 安全性分析 ...................................................................................... 58 第4.1.2.3 節 效能分析 .......................................................................................... 58 第4.2 節 運用量子糾結交換態的金鑰分配協定 ................................................................... 60 第4.2.1 節Gao 的金鑰分配協定 .................................................................................... 60 第4.2.2 節 提高Gao 的效能金鑰分配協定 .................................................................. 62 第4.2.2.1 節 架構 .................................................................................................. 62 第4.2.2.2 節 安全性分析 ...................................................................................... 64 第4.2.2.3 節 效能分析 .......................................................................................... 65 第五章 在量子秘密分享協定上的研究 ................................................. 67 第5.1 節 提高Zhou 等人的效能秘密分享協定 ..................................................................... 67 第5.1.1 節 架構 ............................................................................................................... 67 第5.1.2 節 安全性分析 ................................................................................................... 69 第5.1.3 節 效能分析 ....................................................................................................... 70 第5.2 節 Zhang 等人的量子秘密分享協定 ............................................................................ 71 第5.3 節 提高Zhang 等人的效能秘密分享協定 ................................................................... 74 第5.3.1 節 架構 ............................................................................................................... 74 第5.3.2 節 安全性分析 ................................................................................................... 76 第5.3.3 節 效能分析 ....................................................................................................... 77 第5.4 節 量子秘密分享協定之一方獨佔問題 ....................................................................... 78 第六章 結論與未來展望 ......................................................................... 84 參考文獻 ................................................................................................... 86

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