基於中國餘數定理的量子信息多方具權重且有門檻值的量子秘密分享

Multiparty Weighted Threshold Quantum Secret Sharing Based on the Chinese Remainder Theorem to Share Quantum Information

陳星宇(Xing-Yu Chan)

指導教授 ： 周耀新

國立暨南國際大學/科技學院/資訊工程學系/碩士(2019年)

摘要

秘密分享是一個廣為利用的場景，其核心意義是藉由所有人的合作，以還原被加密的資訊，甚至是還原損壞後的訊息，然而，由於量子領域的崛起，有別於傳統訊息的缺陷，其特性確實保證資訊的安全，因此大量研究學著墨於量子密碼學的研究，並落實到日益重要秘密分享場景之上其中具門檻值的量子秘密分享因只需要達門檻值的人合作，導致建立起來非常複雜，大多現有的構建方法，因過於複雜以致於難以真正地實作，除此之外，目前大多數的架構方法都是將量子狀態轉換為量子位元以分享傳統訊息，而不是真正的量子訊息，因此無法建立真正地量子架構，所以傳輸資訊和分享資訊也十分沒有效率。
然而，在具權重門檻值的量子秘密分享中，因必須為了利用量子特性來分配權重值，讓各個參與者擁有不同的權重值，但在賦予量子權重上，時常因為搭配多個量子態的發送，來配置不同的參與者權重，因此量子態的消耗便會隨著權重值而上升，導致在建立權重架構上十分沒有效率甚至十分困難，因此在難度和複雜度方面又上升一個層次，以致於尚未能夠成功構建一個合適的協定。
而本研究發現中國餘數定理的分頻和恢復特性提供發送密鑰的方法，而相移操作的可逆性提供編碼和解碼秘密的方法，藉此讓參與者容易獲得分配者分享的量子訊息。由此可知，相較以往的架構方法，本研究的秘密分享架構方法是一種有效且彈性的具權重門檻值的量子秘密分享，基於中國餘數定理和相移操作，中國餘數定理的分配權重和恢復特性提供了一種發送部分密鑰的簡便方法，而相移操作的可逆性提供了一種編碼和解碼秘密的簡便方法，綜合來說提供一種較好的方法建立協定。而在量子資源的消耗上，相比之下也只需要消耗較少的資源，因此更為簡單，且更容易實作。

關鍵字

量子密碼學 ； 量子計算 ； 安全計算 ； 量子秘密分享 ； 具權重門檻值的量子秘密分享 ； 中國餘數定理 ； 相移操作 ； 量子訊息

並列摘要

Secret sharing is a widely used scenario in which all people cooperate to restore encrypted information. However, due to the rise of the quantum field, its characteristic guarantees the security of information. Therefore, researches are interested in the quantum cryptography. In that field, threshold quantum secret sharing is much complex. Even constructed schemes are so complicated as to be very difficult to implement. In addition, most of these schemes share classical information rather than true quantum information. Therefore, it’s very inefficient to transfer information and share information.
However, in weighted thresholds quantum secret sharing, participant has different weight, but in assigning weights, it often cost multiple states. So the quantum state consumption will increase with the weight. It is very inefficient or even difficult. Therefore, not yet able to successfully build a suitable agreement.
The proposed scheme allocates each participant own weight. The dealer can encodes quantum state with the phase shift operation. This proposed scheme is first based on the CRT and phase shift operation to build weighted threshold quantum secret sharing. The CRT‘s dividing and recovery characteristic offers an easy way to send partial key. The phase shift operation's reversibility offers an easy way to encode and decode the secret, and is more efficient, flexible and simpler to implement than earlier ones.

並列關鍵字

Quantum Cryptography ； Quantum Computing ； Secure Computing ； Quantum Secret Sharing ； Weighted Threshold Quantum Secret Sharing ； Chinese Remainder Theorem ； Phase Shift ； Quantum Information

參考文獻

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