近年來，隨著量子電腦與量子演算法的快速發展，許多安全性植基於數學難題的傳統密碼學協定開始面臨被破解的威脅。由於利用量子的物理特性所設計出來的通訊協定可達到無條件安全，因此各種量子密碼學的應用陸續地被提出。本論文專注於量子對話(quantum dialogue, QD)協定及具身份認證的量子對話(authenticated quantum dialogue, AQD)協定的研究與設計。量子對話協定可讓兩個使用者同時交換彼此的訊息，而具身份認證的量子對話協定則是可讓兩個使用者確認彼此的身份且同時交換訊息。在本論文的研究過程中，發現現存的協定存在一些問題：(1)資訊洩露(information leakage)；(2)中間人攻擊(man-in-the-middle attack)；(3)缺乏驗證訊息完整性；(4)耗費大量光子使效率低落。因此，如何設計安全且具高效率的量子對話協定與具身份認證的量子對話協定是相當重要的議題。
首先，本論文將指出許多現存的量子對話協定仍然存在資訊洩露的問題，並且也指出現存的具身份認證的量子對話協定無法抵禦中間人攻擊。基於貝爾糾結態(Bell states)與單光子(single photons)，本論文提出兩個安全的量子對話協定以及兩個具身份認證的量子對話協定。其方法結合了傳統密碼學技術與量子物理特性之優點，將傳統密碼學的單向雜湊函數(one-way hash function)引入協定中，使協定能驗證訊息的完整性且有效防範多種常見的攻擊。此外，提出的協定也不會出現資訊洩露及中間人攻擊。因此，相較於現存的協定，本論文提出的協定不僅安全而且效率高。

The rapid development of quantum computers and quantum algorithms in recent years implies that many communication protocols based on the mathematical difficulties of traditional cryptography will be broken. Because quantum protocols based on physical properties can provide unconditional security, various research areas in quantum cryptography have been proposed. This thesis focuses on the secure design of a quantum dialogue (QD) protocol and an authenticated quantum dialogue (AQD) protocol. QD protocols allow two communicants to exchange their secret messages simultaneously, whereas AQD protocols allow two communicants to perform mutual authentication and to engage in secure bidirectional communication simultaneously via classic public channels. Numerous QD protocols and AQD protocols have been proposed in previous studies; however, these protocols have the following drawbacks: (1) many QD protocols experience the information leakage problem; (2) many AQD protocols are vulnerable to a man-in-the-middle attack; (3) all QD and AQD protocols fail to consider the problem of message integrity; and (4) these protocols have low efficiency because large numbers of photons are wasted. Thus, designing secure and efficient QD and AQD protocols is an important issue. In this thesis, we first demonstrate that existing QD protocols still experience the information leakage problem, and we show that existing AQD protocols are susceptible to man-in-the-middle attacks. Next, we propose two separate QD protocols based on Bell states and single photons, respectively. Finally, we present two separate AQD protocols based on Bell states and single photons, respectively. Our protocols integrate the technique of classical cryptography with the advantages of quantum computing. In the protocols, we use a one-way hash function to verify the integrity of received secret messages and to resist several well-known attacks. Moreover, the proposed protocols are free of the information leakage problem and they are not vulnerable to man-in-the-middle attacks. Thus, the proposed protocols are secure and more efficient compared to existing protocols.

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