在現今數位網路的時代中，如何提供使用者一個安全的通訊管道已成為一項重要的研究議題。為解決安全通訊的問題，近代密碼學（modern cryptography）被廣泛的研究與發展。雖然，近代密碼學(包含對稱密碼系統 (symmetric cryptograph) 與非對稱系統 (asymmetric cryptography) 系統，)已經可以讓使用者在數位網路的環境中安全地傳送訊息，然而，在1994年時，學者Shor使用量子的物理特性，提出一個量子演算法，成功在線性時間中分解大質因數。換言之，一些基於數學難題的非對稱加密演算法在量子電腦的環境下，將面臨被破解的問題。這意味著傳統密碼學在量子電腦的環境下，可能將不再能全然提供使用者安全的通訊管道。因此，如何在量子電腦的環境下建立安全的通訊協定將是未來密碼學研究的重點議題。有鑒於此，本論文試圖利用量子物理的特性來架構量子安全通訊協定(quantum secure communication protocol, QSC protocol)。本論文專著於研究糾結態之量子物理特性。首先，研究三個量子糾結態，包括：對稱式W糾結態 (symmetric W state)，GHZ-like糾結態 (GHZ-like state) 與cluster糾結態 (the cluster state)，針對這三個糾結態提出編碼的方法，並利用這些編碼的方法來建置直接量子通訊協定(direct quantum communication protocol, DQC protocol) 與確定式量子通訊協定 (deterministic quantum communication protocol, DQC protocol)。此外，本論文亦發現了二個具有特殊量測結果的量子糾結態，並利用這二個量子糾結態之量測特性，提出一個高效率的量子祕密分享協定 (quantum secure sharing protocol, QSS protocol)。 最後，本論文利用GHZ-like糾結態建置一個量子隱傳協定(quantum teleportation protocol，QT protocol)，在此協定中，一個純Bell糾結態 (pure Bell state) 可以被完整隱傳，進一步，基於此量子隱傳協定，本論文亦建置一個量子資訊分享協定(quantum information protocol, QIS protocol)。

In the internet age, enabling users to transmit messages securely is an important area of research. Modern cryptography (involving, for example, symmetric and asymmetric cryptographic algorithms) has been developed and extensively applied to achieve this goal. Although it allows users to communicate with each other securely nowadays, it will not be deemed secure from a quantum perspective since Shor (1994) developed an efficient algorithm for integer factorization based on quantum phenomena, in which an integer N can be factored in polynomial time. Hence, some asymmetric cryptographic algorithms that are based on the underlying hardness of a mathematical problem may be cracked. In view of this fact, this thesis attempts to employ the properties of quantum mechanics to develop secure communication protocols in quantum environments. This thesis investigates the properties of entangled states. Firstly, three entangled states are considered. These are the symmetric W state, the GHZ-like state, and the cluster state. Three coding function are developed using the entanglement of these entangled states, and these are used to establish the quantum direct communication protocol (QDC protocol) and the deterministic quantum communication protocol (DQC protocol), respectively. Next, two entangled states with a specific measurement property are identified. They are utilized to establish a quantum secret sharing protocol (QSS protocol). Finally, a teleportation using the GHZ-like state is proposed, in which a pure Bell state can be perfectly teleported via a GHZ-like state. Then, a quantum information sharing protocol (QIS protocol) is developed based on this teleportation.

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