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研究生:張庭魁
研究生(外文):Chang,Tyng-Kwei
論文名稱:量子密鑰分配及量子模糊傳送協定之研究
論文名稱(外文):Researches of Quantum Key Distribution and Quantum Oblivious Transfer Protocols
指導教授:李南逸李南逸引用關係
學位類別:碩士
校院名稱:南台科技大學
系所名稱:資訊管理系
學門:電算機學門
學類:電算機一般學類
論文種類:學術論文
論文出版年:2005
畢業學年度:93
語文別:中文
論文頁數:49
中文關鍵詞:密碼學資訊安全量子密鑰分配量子模糊傳送
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隨著資訊的蓬勃發展,資料在網路上的傳輸也越來越頻繁,當遠端雙方需要做秘密通訊時,則必須事先擁有一把共同的密鑰,傳送方才得以先對資料加密,接收方也得以對密文解密,若雙方事先沒有這把共同的密鑰時,就必須透過公鑰密碼系統(public key cryptosystem)先交換出這把共同密鑰。

但是隨著電腦運算速度的不斷提升,密鑰的長度也被迫不斷增長,以延長被破解的時間,未來若量子電腦成功的被發展出來,即使密鑰長度增長,仍然無法抵擋量子電腦快速的平行運算能力,而迅速被破解,所幸Bennett和Brassard在1984年提出BB84的量子密鑰分配協定,配合one-time-pad加密方式,即使是運算能力強大的量子電腦也無法破解,因而使得資料通訊安全再度獲得保障。

自從Bennett和Brassard提出BB84的量子密鑰分配協定後,通訊安全便提升到一個新的里程碑,由於量子的測不準定理(uncertainty principle),因此可以確保密鑰分配的安全性,但是BB84的協定其密鑰分享效率只有50%,也就是會有一半的光子訊息白白被浪費掉,為了減少光子訊息的浪費,本論文中提出兩個新的方法,第一種稱為:基底機率調整(Bases Probability Adjustment:BPA) 之量子密鑰分配協定,第二種則為:預設基底之量子密鑰分配協定,並且證明可以在不影響原BB84協定安全性之下,有效的提升量子密鑰分享的效率。

本論文的另一個研究主題為:量子模糊傳送協定,主要介紹Crépeau在1994年所提出的1-out-of-2量子模糊傳送協定,以及說明如何使用量子位元託付(quantum bit commitment)來防止接收者的儲存式攻擊(storage attack),並提出以分段的方式來達成1-out-of-2、1-out-of-n、m-out-of-n的量子模糊傳送協定。
Due to the rapid development of information technology, data communication is more frequent in the network. When two parties need to communicate in secret, they have to share a secret key in advance. The sender encrypts data, and then delivers it to the receiver. The receiver decrypts it using the same secret key. They can share the secret key by public key cryptography.

In order to against breaking, the length of the secret key has to be increased. However, even the length of the secret key is long, they still cannot against the attacks of quantum computers. Fortunately, Bennett and Brassard in 1984 proposed a BB84 quantum key distribution protocol, which is secure from the attack of quantum
computers.

Since BB84 protocol, the communication security has stepped forward to a new milestone. However, the key sharing efficiency is only 50% in BB84 protocol. Therefore, this master thesis will propose two new protocols: The first one is Bases Probability Adjustment (BPA); The second one is Preset Bases Quantum Key Distribution Protocol. These two protocols can improve the key sharing efficiency without affecting the security of BB84.

Another research topic of this master thesis is quantum oblivious transfer. It will introduce Crépeau’s 1-out-of-2 quantum oblivious transfer protocol in 1994, and show how to use quantum bit commitment mechanism to prevent the storage attack. This thesis also proposes 1-out-of-2, 1-out-of-n, and m-out-of-n quantum oblivious transfer protocols.
中文摘要............................................. iv
ABSTRACT............................................. v
致謝................................................. vi
目次................................................ vii
表目錄............................................... ix
圖目錄................................................ x
第一章 緒論............................................ 1
1.1 研究背景........................................... 1
1.2 研究動機與目的...................................... 1
1.3 章節概要........................................... 3
第二章 文獻探討......................................... 4
2.1 量子訊息簡介........................................ 4
2.2 光子的物理特性...................................... 5
2.3 BB84 量子密鑰分配協定................................ 8
2.3.1 協定............................................. 8
2.3.2 效率分析.......................................... 8
2.3.3 安全性分析........................................ 9
2.4 B92 量子密鑰分配協定.................................10
2.4.1 協定..............................................10
2.4.2 效率分析.......................................... 11
2.4.3 安全性分析........................................ 11
2.5 模糊傳送協定簡介.................................... 14
2.6 Crépeau 之量子模糊傳送協定........................... 15
第三章 提升量子密鑰分配協定之效能.......................... 19
3.1 基底機率調整之量子密鑰分配協定......................... 19
3.1.1 協定............................................. 19
3.1.2 公式推導.......................................... 20
3.1.3 實例驗證.......................................... 21
3.1.4 效率分析.......................................... 22
3.1.5 安全性分析......................................... 22
3.2 預設基底之量子密鑰分配協定............................. 24
3.2.1 協定.............................................. 25
3.2.2 公式推導........................................... 26
3.2.3 實例驗證........................................... 27
3.2.4 效率分析........................................... 28
3.2.5 安全性分析......................................... 29
第四章 分段式之量子模糊傳送協定............................. 32
4.1 1 out of 2 協定...................................... 33
4.2 1 out of n 協定...................................... 35
4.3 m out of n 協定...................................... 38
4.4 安全性分析............................................ 41
第五章 結論與未來研究方向.................................. 44
5.1 結論................................................. 44
5.2 未來研究方向.......................................... 44
參考文獻.................................................. 46
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