在現今網路如此發達的環境中，如何確保傳輸的資訊安全是一個重要的研究議題，目前密碼學家提出了許多安全性基於數學難題的保護機制，讓攻擊者無法在短時間內解得明文訊息，如常見的對稱式金鑰密碼系統以及非對稱式金鑰密碼系統等等。然而目前量子電腦已被證明具有強大的平行運算能力，並且Shor 證實了利用量子演算法，在多項式時間內破解了因數分解之難題。因此，如何在具有強大運算能力的量子電腦下，又能設計出安全的量子密碼技術，是目前密碼學熱門研究領域之一。
許多量子密碼學的應用在近年內被提出，諸如量子金鑰分配、量子安全直接通訊、量子私密比較、量子秘密分享、量子投票等等。其安全性是植基於量子的物理特性，包括海森堡測不準原理、不可複製性等等，使得溝通雙方可以確保傳輸的資訊安全或共享一把到達理論安全的金鑰，即使有監聽者監聽，也可以利用以上的特性來檢查出來。
量子秘密分享(Quantum Secret Sharing)是量子密碼學中一個重要的研究議題，其主要的目標是秘密分享者(boss)持有一把私密金鑰，並且利用量子的特性，將金鑰分成許多子金鑰，之後將每個子金鑰分別安全的傳送給每個成員(agents)，當成員想還原出秘密分享著的私密金鑰時，必須所有拿到子金鑰的成員一起合作，才能還原出密碼分享者的私密金鑰。目前已經存在許多利用不同量子態的量子秘密分享協定被提出，如Einstein-Podolsky-Rosen糾結態、Green-Horne-Zeilinger糾結態、單光子等等。
然而在這些量子秘密分享協定中，大部分的協定皆沒有考慮到動態增減人的特性。當秘密分享者把帶有子金鑰資訊的量子傳給成員時，若在此時有新的成員想要加入，或者是舊有的成員想要離開，秘密分享者必須重新產生帶有子金鑰資訊的量子，並且之前收到量子的成員必須把舊有的量子丟棄，即使成員還尚未量測收到的量子，之後再重新接收新的量子。因此，動態的量子秘密分享(Dynamic Quantum Secert Sharing)即被提出來改善這個問題。
本論文將會對先前的動態量子金鑰分享協定提出一個安全性的問題，必且提出初步的解法。接著也分別使用GHZ糾結態與EPR糾結態來設計出兩個新的動態量子秘密分享協定，且針對現存的一些攻擊與新提出的安全性上的問題來做討論。之後再與現存的動態量子秘密分享協定來做深入的比較，深入探討在整體效率與增減人階段的作法。

The Internet environment is extremely prosperous. Consequently, transmitting a mes-sage securely through the Internet has become a fundamental issue. Cryptographers have proposed numerous protective schemes (i.e., symmetric key encryption and asymmetric key encryption) based on mathematics. An eavesdropper cannot decode a ciphertext message within a short period. However, the quantum computer has proven to be a powerful weapon with parallel computing ability to make the computational task easier. Peter Shor proposed a quantum algorithm to solve the factorization problem in polynomial time. Therefore, how to design a secure quantum cryptography protocol has become a popular research topic.
Numerous recent applications of quantum cryptography have been proposed, such as quantum key distrubtion (QKD), quantum secure direct communication (QSDC), quantum privacy comparision (QPC), quantum secret sharing (QSS), and quantum voting (QV). The security of these applications is based on quantum physics properties, including the Hilbert uncertainty principle of measurement and the no-cloning theorem. Two-party communica-tion ensures the security of the transmission message or the theoretical security key, which can also check the eavesdropper by using these properties.
Quantum secret sharing (QSS) is a crucial research topic in quantum cryptography. A QSS protocol allows a secret key to be shared among several agents by using quantum me-chanics such that the secret key can only be recovered when sufficient legitimate agents cooperate. Numerous QSS schemes have been developed using different quantum states (i.e., EPR pair, GHZ state, and single photon).
However, most QSS schemes do not address the problem of adding and deleting agents. After the boss delivers the shadow key qubits to agents, if an agent wants to join or leave the QSS, the boss must generate new qubits and all agents must abort the qubits in their hand. Therefore, dynamic quantum secret sharing (DQSS) has been proposed to solve this problem.
This thesis first indicates a new security issue in the Hsu et al. DQSS protocol regard-ing the honesty of a revoked agent and proposes a possible solution. Because it does not address this problem, the Hsu et al. DQSS protocol fails to provide a secret sharing func-tion. Two DQSS protocols are then proposed using the GHZ state and the Bell state, fol-lowed by a discussion of certain attacks and a new security on the 2 proposed DQSS protocols. Finally, this thesis presents an analysis of qubit efficiency and the volatility of the agents on the 2 proposed protocols compared with the existing DQSS protocols.

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