臺灣博碩士論文加值系統

現今大部分的密碼系統之安全性是植基於一些計算上困難的數學問題上，如解因數分解問題與解離散對數問題等等，然而，一般相信利用量子電腦可有效率地破解這些難題，因此結合量子物理特性與密碼學技術來發展無條件安全的量子協定去對抗量子電腦與傳統電腦是有其必要性的。

模糊傳送是密碼協定中常被使用的一個重要的模型，並且應用於許多領域中，已經有許多文獻發表各式各樣的模糊傳送，為了對抗量子電腦所帶來的威脅，量子模糊傳送也被提出。

本論文中提出了數個2選1量子模糊傳送協定與n選1量子模糊傳送協定，這些協定擁有以下的優點，(1)不用特別的假設條件與量子儲存設備協助，(2)完成整個協定僅需一次量子傳輸與少量的傳統傳輸，因此這些協定是非常有效率的。

另外，我們設計了安全模型，並且利用它們證明本論文中所提出之協定是符合量子模糊傳送安全需求的。此外，可由比較表中本論文所提出的協定與現有的協定之各項比較得知這些協定的效率。

In most of classic cryptosystems today, the security is based on the computational difficulty of certain number theoretic problems, e.g., solving the discrete logarithm problem and factoring large numbers. However, most people believe that these number theoretic problems can be efficiently solved by quantum computers. Therefore, it is significant to combine the properties of quantum physics with classical cryptography to propose unconditional secure quantum protocols against classical or quantum computers.

The oblivious transfer is used as an important primitive in many cryptographic protocols and is widely adopted in many applications. Many variants of the oblivious transfer protocols had been proposed in the literature. To resist the threat of quantum computers, quantum oblivious transfer was proposed.

This thesis proposed several one-out-of-two quantum oblivious protocols and one-out-of-n quantum oblivious protocols. The newly proposed protocol possesses the following advantages: (1) no special assumptions and quantum memory are required; and (2) only one quantum transmission and few classical communications during the whole protocol execution; Therefore, the proposed protocols are very efficient.

In addition, we design the security models, and then use them to show that the proposed protocols satisfy the security requirements of the quantum oblivious transfer. Besides, the efficiency of these proposals can be known from the comparison tables which compare our protocols with existing quantum oblivious protocols.

摘 要 III
Abstract IV
致謝 VI
頁目錄 VII
圖表目錄 XI
第一章 導論 1
第1.1節 量子力學與密碼學 1
第1.2節 模糊傳送協定與其應用 3
第1.3節 量子模糊傳送協定之演進 6
第1.4節 研究動機與研究貢獻 7
第1.5節 論文架構 8
第二章 相關預備知識 9
第2.1節 量子模糊傳送協定的安全需求 9
第2.2節 量子相關技術簡介 10
第2.2.1節 BB84 10
第2.2.2節 B92 12
第2.2.3節 MB4 14
第2.3節 安全性證明的基本概念 18
第2.3.1節 正確性 18
第2.3.2節 傳送者的隱私 18
第2.3.3節 接收者的隱私 19
第三章 現有的量子模糊傳送協定 20
第3.1節 Bennett等人的量子2選1模糊傳送協定 20
第3.1.1節 架構 20
第3.1.2節 分析 23
第3.2節 Crépeau的量子2選1模糊傳送協定 25
第3.2.1節 架構 25
第3.2.2節 分析 28
第3.3節 Chen與Zhu的量子n選t模糊傳送協定 30
第3.3.1節 架構 30
第3.3.2節 分析 33
第3.4節 Lu等人的量子2選1模糊傳送協定 36
第3.4.1節 架構 36
第3.4.2節 分析 37
第3.5節 Crépeau等人的量子2選1模糊傳送協定 39
第3.5.1節 架構 39
第3.5.2節 分析 42
第3.6節 其他的量子模糊協定 44
第四章 無須使用位元承諾相關技術的2選1量子模糊傳送協定 45
第4.1節 架構 45
第4.2節 分析 49
第五章 有效率的n選1量子模糊傳送 51
第5.1節 有效率的n選1量子模糊傳送協定 51
第5.1.1節 架構 51
第5.1.2節 分析 53
第5.2節 非交談式n選1量子模糊傳送協定 57
第5.2.1節 架構 57
第5.2.2節 分析 58
第5.3節 完全的非交談式n選1量子模糊傳送協定 62
第5.3.1節 架構 62
第5.3.2節 分析 63
第六章 效率比較 67
第6.1節 2選1量子模糊傳送協定比較 67
第6.2節 n選1量子模糊傳送協定比較 68
第七章 結論與未來展望 69
第7.1節 結論 69
第7.2節 未來展望 69
參考文獻 70

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