發(fā)布時(shí)間：2018-09-04 09:00

【摘要】：量子密碼學(xué)是以現(xiàn)代密碼學(xué)和量子力學(xué)為基礎(chǔ),用量子力學(xué)性質(zhì)實(shí)現(xiàn)密碼任務(wù)的一門學(xué)科。它利用微觀粒子的量子屬性實(shí)現(xiàn)信息保護(hù),理論上被證明是無條件安全的。相比于基于數(shù)學(xué)困難問題的經(jīng)典密碼學(xué),量子密碼學(xué)在安全上具有明顯的優(yōu)勢(shì),因此受到了越來越多的關(guān)注,取得了快速的發(fā)展。其中,量子糾纏作為一種資源,常常被用在密碼協(xié)議的設(shè)計(jì)和安全性分析中,在量子密碼學(xué)的研究中起著至關(guān)重要的作用�；诖�,本文以量子糾纏為背景,主要研究量子同態(tài)簽名協(xié)議,量子私密比較協(xié)議和量子匿名排序協(xié)議。主要研究內(nèi)容分為三部分,所取得的主要研究成果如下:1.量子同態(tài)簽名協(xié)議(1)提出了一個(gè)基于量子相干態(tài)的量子同態(tài)簽名協(xié)議。首先分析現(xiàn)有的量子同態(tài)簽名協(xié)議,結(jié)合經(jīng)典密碼學(xué)中同態(tài)簽名的定義,給出了量子同態(tài)簽名的定義。然后分析量子相干態(tài)在平衡分光器中的干涉性質(zhì),利用這種干涉性質(zhì)提出了一個(gè)新的量子同態(tài)簽名協(xié)議,并證明了該協(xié)議的同態(tài)性和分析了該協(xié)議的安全性和通信復(fù)雜度。通過和現(xiàn)有的量子同態(tài)簽名協(xié)議相比較可以得出,該協(xié)議具有更高的效率而且更容易實(shí)現(xiàn)。最后論述了該協(xié)議中使用的量子相干態(tài)和量子指紋識(shí)別中使用的量子糾纏態(tài)之間的關(guān)系。(2)提出了基于完全Bell態(tài)測(cè)量和基于部分Bell態(tài)測(cè)量的量子同態(tài)簽名協(xié)議。首先分析了Bell態(tài)測(cè)量的原理,并闡述了部分Bell態(tài)測(cè)量怎樣用線性光學(xué)器件實(shí)現(xiàn)。然后基于完全Bell態(tài)測(cè)量提出了一個(gè)量子同態(tài)簽名協(xié)議,進(jìn)一步論述了該協(xié)議基于部分Bell態(tài)測(cè)量也可以完成,并給出了該協(xié)議。再證明了所提協(xié)議的同態(tài)性并分析了協(xié)議的安全性。在安全性分析中,針對(duì)現(xiàn)有的量子同態(tài)簽名協(xié)議提出了一種“截獲-重傳”的攻擊策略,并證明了該協(xié)議中所使用的誘騙態(tài)方法可以有效抵制這種攻擊。最后通過和現(xiàn)有的量子同態(tài)簽名協(xié)議比較可以得出,該協(xié)議具有更高的安全性和效率。2.量子私密比較協(xié)議(1)首次提出了一個(gè)多個(gè)參與者可以比較他們私有信息大小的量子私密比較協(xié)議。首先找到了一個(gè)多體高維糾纏態(tài),并對(duì)該量子態(tài)的性質(zhì)進(jìn)行了分析,進(jìn)一步用群論的方法證明了兩個(gè)正整數(shù)的大小關(guān)系可以用模d減法巧妙地描述。然后基于這些性質(zhì)提出了一個(gè)多個(gè)參與者可以比較他們私有信息大小的量子私密比較協(xié)議。該協(xié)議只需執(zhí)行一次就可以比較l個(gè)參與者私有信息的大小,如果使用兩個(gè)參與者可以比較私密大小的協(xié)議則需要執(zhí)行(?)次。最后較詳細(xì)地分析了該協(xié)議的安全性,并通過分析協(xié)議中所使用量子資源的方式分析了協(xié)議的效率。(2)提出了一個(gè)基于線性光學(xué)器件工作原理的量子私密比較協(xié)議。針對(duì)現(xiàn)有的量子私密比較協(xié)議大都是從完全抽象的角度提出和分析,離實(shí)際實(shí)現(xiàn)相隔較遠(yuǎn),首先分析了常用的線性光學(xué)器件的工作原理,主要是分光器的工作原理和偏振態(tài)在平衡分光器中的后選擇糾纏性。然后基于這些工作原理提出了一個(gè)兩個(gè)參與者可以比較他們私有信息是否相等的量子私密比較協(xié)議,為在現(xiàn)實(shí)環(huán)境中實(shí)現(xiàn)量子私密比較協(xié)議打下了基礎(chǔ)。最后較詳細(xì)地分析了所提協(xié)議的安全性。3.量子匿名排序協(xié)議提出了一個(gè)基于單粒子態(tài)的量子匿名多方多數(shù)據(jù)排序協(xié)議。首先分析了量子匿名排序協(xié)議的設(shè)計(jì)原理和安全性要求。然后基于高維單粒子態(tài)提出了一個(gè)新的量子匿名多方多數(shù)排序協(xié)議,并分析了該協(xié)議的安全性。通過將該協(xié)議和現(xiàn)有的基于量子糾纏的匿名排序協(xié)議進(jìn)行比較表明,該協(xié)議具有更高的效率。最后論述了該協(xié)議也可以通過使用中國剩余定理,用較低維數(shù)的單粒子態(tài)完成,并給出了具體的方法。
[Abstract]:Quantum cryptography is a subject based on modern cryptography and quantum mechanics, which implements cryptographic tasks by quantum mechanical properties. It uses quantum properties of microscopic particles to protect information and is theoretically proved to be unconditionally secure. Quantum entanglement, as a kind of resource, is often used in the design and security analysis of cryptographic protocols and plays an important role in the research of quantum cryptography. Based on this, this paper mainly studies quantum homomorphic signatures with the background of quantum entanglement. The main research contents are as follows: 1. Quantum Homomorphic Signature Protocol (QHSP) proposes a quantum homomorphic signature protocol based on quantum coherent states. Firstly, the existing quantum homomorphic signature protocols are analyzed and combined with the classical cryptography homomorphic signature protocols. The definition of quantum homomorphic signature is given. Then the interference properties of quantum coherent states in a balanced splitter are analyzed. A new quantum homomorphic signature protocol is proposed by using this interference property. The homomorphism of the protocol is proved and the security and communication complexity of the protocol are analyzed. Compared with the homomorphic signature protocol, the protocol is more efficient and easier to implement. Finally, the relationship between quantum coherent states used in the protocol and quantum entangled states used in quantum fingerprint identification is discussed. (2) A quantum homomorphic signature protocol based on complete Bell state measurement and partial Bell state measurement is proposed. Firstly, the principle of Bell state measurement is analyzed, and how some Bell state measurements are implemented by linear optical devices is described. Then, a quantum homomorphic signature protocol based on complete Bell state measurement is proposed. Furthermore, the protocol based on partial Bell state measurements is discussed, and the protocol is given. Finally, the homomorphism of the proposed protocol is proved. In security analysis, an interception-retransmission attack strategy is proposed for existing quantum homomorphic signature protocols, and the Decoy-State method used in the protocol is proved to be effective against this attack. The protocol has higher security and efficiency. 2. Quantum Privacy Comparison Protocol (1) proposes a quantum private comparison protocol in which multiple participants can compare the size of their private information for the first time. Based on these properties, a quantum private comparison protocol is proposed in which multiple participants can compare the size of their private information. Finally, the security of the protocol is analyzed in detail, and the efficiency of the protocol is analyzed by using quantum resources. (2) A quantum private comparison protocol based on the principle of linear optical devices is proposed. From a completely abstract point of view, it is far from the actual implementation. Firstly, the working principle of the common linear optical devices is analyzed, mainly the working principle of the splitter and the post-selective entanglement of the polarized state in the balanced splitter. Finally, the security of the proposed protocol is analyzed in detail. 3. A quantum anonymous multi-party data sorting protocol based on single-particle state is proposed. Firstly, quantum anonymous sorting is analyzed. Then a new quantum anonymous multi-party majority sorting protocol based on high-dimensional single-particle States is proposed and its security is analyzed. Compared with the existing quantum entanglement-based anonymous sorting protocol, the protocol is proved to be more efficient. The protocol can also be implemented in lower dimensional single-particle states by using the Chinese remainder theorem, and a concrete method is given.
【學(xué)位授予單位】：電子科技大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2017
【分類號(hào)】：O413;TN918.1

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