近年來，隨著量子力學的研究日趨成熟，許多安全性植基於傳統密碼學的通訊技術開始遭受威脅。舉現今常見的密碼系統RSA為例，其安全性植基於質因數分解的數學難題，目的是要讓破密者無法於短時間內解出明文。然而，在量子通訊的環境中，量子電腦被證明具有強大的平行處理能力，可利用有效率的演算法，使其傳統的數學難題在多項式時間內被破解。因此，如何設計出既安全又實用的量子密碼技術，是近年來密碼學家主要研究的課題之一。
　　近年來提出了許多量子密碼學的應用，像是量子金鑰分配、量子直接通訊、量子模糊傳輸、量子對話等等。有別於傳統密碼學，量子密碼學(Quantum Cryptography)的安全性植基於量子的物理特性，如：海森堡測不準原理、不可複製性等等。利用這些特性，可以使通訊的雙方分享一把符合理論安全的金鑰，使得破密者破解密文的難度相當於直接猜測金鑰的難度；而在傳輸過程中，利用量子的量測不確定性，竊聽的一方也可輕易地被偵測出來。
　　量子秘密分享(Quantum Secret Sharing)是量子密碼學中一門重要的應用，其主要精神為一祕密分享者將其私密金鑰利用量子特性拆解成數個子金鑰，並安全地分派給其他成員(agents)，而還原分享者的秘密訊息時，必須所有成員的共同合作，缺少任何一位成員皆無法解得該秘密訊息。現存許多量子秘密分享協定利用量子糾結態的特性而被提出，包括EPR糾結態、GHZ糾結態與GHZ-like糾結態等，也有少數協定利用單光子傳輸來達到祕密分享之目的。
　　依傳輸策略的不同，量子祕密分享可以分成三種類型：來回式傳輸、環繞式傳輸以及一次性傳輸。本論文將會對這些傳輸模式作深入地討論與分析其優缺點，也試圖在這些模式中，找尋較有效率的方法來提升量子位元的利用率，以減輕不必要的計算及設備，並在設計過程中防止常見的量子攻擊，例如木馬攻擊或是攔截重送攻擊等。此外，由於現實環境中，量子通道上存在某些特定的雜訊，使量子在傳輸過程中可能改變其原本的狀態，故在本論文中，亦會提出可容錯之量子秘密分享協定來抵抗這些雜訊。

　　In recent years, the rapid development of quantum mechanics has threatened the security of many communication protocols of classical cryptography. For example, the security of the present well-known cryptosystem RSA is based on the difficulty of factorization problem, which an eavesdropper cannot decode the cipher text within a short time. However, in quantum environment, the quantum computer is proven to have powerful parallel processing ability that can utilize some efficient quantum algorithm to crack the classical difficult math problems in polynomial time. Therefore, how to design a secure and practical quantum cryptographic technique is the dominant research topic for cryptographers.
　　Recently, many applications in quantum cryptography have been proposed such as quantum key distribution (QKD), quantum secure direct communication (QSDC), quantum oblivious transfers (QOT), quantum dialogue (QD), and so on. Different from classical cryptography, the security of quantum cryptography is based on the properties of quantum physics like Hilbert uncertainty principle of measurement and no-cloning theorem. By using these properties, two parties of communication can share a common key that is consistent with the theoretical security. The difficulty in cracking the cipher text is equivalent to directly guessing the key bits. Moreover, based on the uncertainty measurement of quantum, the eavesdropper can be easily detected.
　　Quantum secret sharing (QSS) is an important branch of quantum cryptography. The main idea of QSS is to split a dealer's secret into several shadows, which are then securely delivered to the agents, one for each. Enough agents are required to collaborate together in order to recover the dealer’s secret. The agent can not individually retrieve the dealer’s secret. So far, most of the present QSS protocols are proposed according to the properties of quantum entangled states such as EPR pair, GHZ state and GHZ-like state, though there are also some protocols based on the single photons.
　　According to the transmission strategies, QSS protocols can be classified into three types: the round-trip transmission QSS, the quantum-relay QSS, and the one-way transmission QSS. In this thesis, we will discuss and analyze the advantages and disadvantages of each transmission strategy. In these modes, a more efficient protocol will be proposed to enhance the quantum bit efficiency, and to reduce the unnecessary cost of computing and devices. The proposed QSS schemes are robust against some well-known quantum attacks like the Trojan horse attack and the Intercept-resend attack. In practice, there are some specific noises existing in the quantum channel that will change the original state of quantum during transmission. Hence, in this thesis, the fault-tolerant QSS protocols will also be proposed to resist the disturbance of these noises.

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