在現今量子電腦和量子演算法快速發展的時代中，許多基於因數分解與離散對數之密碼系統都已被證明可以使用量子演算法在多項式時間內破解。因此，基於量子物理之特性的量子密碼就此因應而生。量子密碼學基於量子物理之特性設計通訊協定除了可以達到無條件安全外，更具備兩項優點 : (1) 通訊協定的安全性是基於量子物理之特性，所以不受量子電腦的威脅; (2) 在通訊的過程中，可以偵測出是否有竊聽者的存在。然而現今大多數的量子通訊協定，必須假設量子在傳輸過程當中無雜訊干擾的影響，換言之就是假設量子通道為理想通道，通道內沒有任何雜訊會影響正在傳輸的量子訊息。若是不假設量子通道為理想通道，則這些量子協定在執行竊聽者檢查時，會因為雜訊的干擾而無法得知訊息的錯誤率是由雜訊的干擾所造成或是竊聽者攻擊所造成。再者，竊聽者也可以利用量子通道雜訊所造的錯誤對通訊協定進行攻擊，使協定產生錯誤。讓通訊者在檢查是否有竊聽者存在時，以為錯誤是因為通道內有雜訊所產生之錯誤，而非竊聽者存在之原因。因此如何在有集合雜訊干擾下的量子通道，設計出安全的量子通訊協定將是未來量子密碼學研究的熱門的議題。
本論文專注於研究量子物理與可抗集合雜訊之六顆DFS量子態。首先，結合量子物理之特性來設計可抗雜訊干擾的編碼方式並設計安全的量子通訊協定。最後，利用編碼方式來確保在有雜訊干擾下進行的量子通訊協定都可保持協定的安全性。其中，這些量子協定包含量子私密比較、半量金鑰分配協定、量子直接通訊協定與確定式量子通訊協定

Owing to the rapid development of quantum computing and quantum algorithms, it is believed that many difficult mathematical problems could be easily solved in the near future using quantum computers. Thus, various well known cryptosystems whose security is based on such mathematical problems could be easily compromised. This motivates the conduct of research on quantum computation, and the establishment of quantum cryptography businesses to resolve these security issues. Many quantum security protocols using quantum phenomena (e.g., the no-cloning theorem and the measurement uncertainty principle) have been proposed. In comparison with classical communication protocols, quantum security protocols have the following advantages: (1) their security is built with consideration given to quantum phenomena; therefore, the protocols are secure against attacks using quantum computers; (2) the presence of eavesdroppers can be detected. Moreover, existing quantum security protocols assume that quantum channels are ideal; that is, a quantum channel is considered to be free of any type of noise. However, noise exists in real channels, and an eavesdropper may disguise their attack as noise to avoid being detected during the eavesdropping checking process. Hence, in real applications, quantum security protocols have to be designed for combating noise, which is an important research topic.
Accordingly, the objective of this study was to employ quantum mechanical properties and decoherece-free states and develop fault tolerant quantum secure communication protocols in quantum environments. This thesis investigates the properties of decoherece-free states and its coding functions. First, two decoherece-free states, four-particle decoherece-free states and six-particle decoherece-free states are considered. Three coding functions were developed using six-particle decoherece-free states. Finally, this thesis proposes a fault tolerant semi-quantum key distribution protocol, fault tolerant quantum direct communication protocol, and fault tolerant deterministic quantum communication protocol, respectively.

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