本文選題：量子密鑰分發(fā) + 三值量子加密�。� 參考：《電子科技大學(xué)》2017年博士論文

【摘要】：量子密碼最早起源于Wiesner的“Conjugate Coding”,是量子理論、信息科學(xué)和計算機科學(xué)相結(jié)合的產(chǎn)物。它的研究內(nèi)容包括量子密鑰分發(fā)、量子密鑰管理、量子加密、量子認(rèn)證、量子密碼安全多方協(xié)議、量子密碼信息理論和量子密碼分析等。無條件安全性和對竊聽的可檢測性是量子密碼的兩個重要特征。量子力學(xué)測不準(zhǔn)原理和不可克隆定理是保證量子密碼具有無條件安全性的重要基礎(chǔ)之一。本論文首先提出了一種基于重發(fā)機制的量子密鑰分發(fā)協(xié)議,它能有效提高協(xié)議的密鑰分發(fā)效率;接著,研究了三值量子態(tài)、同態(tài)加密技術(shù)和線路擬合技術(shù),提出了三值量子態(tài)的同態(tài)加密方案,并建立起了量子同態(tài)加密框架,通過二值和三值量子態(tài)的實例,驗證了該框架的正確性和普適性;然后,通過對三值XHZ加密方案的優(yōu)化,得到了一些有趣的結(jié)論;最后,提出了一種實用的量子公鑰加密模型。具體研究內(nèi)容總結(jié)如下:1)重發(fā)機制的量子密鑰分發(fā)協(xié)議。首先研究了BB84協(xié)議的執(zhí)行過程,通過分析發(fā)現(xiàn),發(fā)送光子的“丟失”對QKD協(xié)議的密鑰分發(fā)效率產(chǎn)生了嚴(yán)重的影響;接著提出了新的協(xié)議,并給出了新協(xié)議的工作流程,該流程類似于BB84協(xié)議,不同之處就在于:若發(fā)現(xiàn)丟失光子數(shù)超過了一個閾值的話,就會啟動二次傳輸過程,當(dāng)滿足一定的條件后,重傳過程結(jié)束;然后模擬了該協(xié)議的執(zhí)行過程,同時模擬竊聽者,采用截取后測量重發(fā)策略,將“擾動”過的量子態(tài)序列發(fā)送給接收者,由模擬數(shù)據(jù)可以看出,任何對量子態(tài)的“干擾”都可以在接收端被測試出來;最后,從三個方面分析了該協(xié)議:安全性、數(shù)據(jù)協(xié)商和密性放大。從而得出結(jié)論:該協(xié)議能有效提高密鑰分發(fā)效率,而且分發(fā)過程是無條件安全的。2)三值量子同態(tài)加密方案。首先介紹了相關(guān)三值量子門、三值XHZ加密方案以及QHE;接著,基于三值單量子旋轉(zhuǎn)門,提出第一個TQHE方案;其次,借助于一般的酉變換可以由8種旋轉(zhuǎn)門擬合,我們將其推廣到一般的三值單量子門,提出了第二個TQHE方案;然后,以GCX門作為三值雙量子的通用門,構(gòu)造了第三個TQHE方案,理論上將其推廣到一般三值n量子的情況,并給出它的構(gòu)造過程,得到理論意義上的第四個TQHE方案;最后,從多值量子門的擬合、密鑰安全性和用戶數(shù)據(jù)的私密性三個方面分析了該協(xié)議,得出攻擊者對密文量子態(tài)正確猜對密鑰的最大概率為1/33n,并且該方案可以很好地集成到將來量子遠(yuǎn)程服務(wù)器架構(gòu)中,解決分布式環(huán)境下用戶私密量子數(shù)據(jù)的安全計算問題。3)通用的量子同態(tài)加密模型。首先通過研究量子同態(tài)加密,提出了一種通用的構(gòu)造量子同態(tài)加密算子的方法,進而建立了構(gòu)造量子同態(tài)加密方案的一種框架;其次,通過二值和三值量子態(tài)的酉變換,利用該框架構(gòu)造了相應(yīng)的量子同態(tài)加密方案,與現(xiàn)有文獻構(gòu)造的方案相比,利用該框架構(gòu)造的量子同態(tài)加密方案是正確的,而且更具有普遍性;最后,通過安全性分析,該框架的安全性是基于加密算法的安全性和密鑰的安全性。由于該框架采用了對稱量子加密算法,導(dǎo)致構(gòu)造量子同態(tài)算子時需要加密密鑰。所以,該框架是一種弱的對稱量子同態(tài)加密框架。4)優(yōu)化了三值XHZ加密方案,并得出了一些有趣的結(jié)論。首先,給出了QOTP方案中正交性和最大混合態(tài)的兩個驗證過程,接著又給出了兩個重要的定義:加密算子的正交性和正交率;然后,通過優(yōu)化三值XHZ量子加密方案,提出了4種改進后的三值量子加密方案。通過計算這些改進方案中加密算子的正交率?,得到了方案3中的加密算子kU是完全正交的,而且具有很高的安全性,在所有方案中是最理想的;最后,從兩個方面討論了方案3的安全性。一方面是加密算子kU的安全性。方案3中的加密算子kU在3維Hilbert內(nèi)積空間中是完全正交的,而且具有很高水準(zhǔn)的安全性。另一方面是密鑰源的安全性。通過重發(fā)機制的BB84協(xié)議和自定義的插值函數(shù)f(s,k)或f(s),獲得了無條件安全的、包含數(shù)字0,1和2的密鑰串s。其中,重點介紹了插值函數(shù)的定義,詳細(xì)描述了插值函數(shù)的工作流程以及注意的事項。5)實用的量子公鑰加密模型。該模型主要由可信任的、安全的第三方CA和PKDC,以及客戶端的加解密運算器D/E Adapter(俗稱黑盒子)構(gòu)成。在該模型中,CA和PKDC很關(guān)鍵,是整個模型的骨架。同時,量子單向門限函數(shù)和Holevo界,分別是密鑰生成算法和針對于一個量子公鑰可以發(fā)布的最大拷貝數(shù)。模型中的這些方案或算法是可以被安全地替換,而不影響整個框架的運行。最后,我們希望能夠運用量子區(qū)塊鏈技術(shù),實現(xiàn)去中心化,并能夠給QPKE帶來全新的研究領(lǐng)域。最后,我們總結(jié)了全文的研究內(nèi)容,并給出了下一階段的研究任務(wù):希望構(gòu)建三值量子糾纏的密鑰分發(fā)協(xié)議、三值量子同態(tài)簽名和認(rèn)證協(xié)議、三值量子公鑰加密方案,并希望利用量子區(qū)塊鏈技術(shù),重新研究量子加密的相關(guān)協(xié)議。
[Abstract]:The earliest origin of quantum cryptography is "Conjugate Coding" of Wiesner. It is a product of quantum theory, information science and computer science. Its research contents include quantum key distribution, quantum key management, quantum encryption, quantum authentication, quantum cryptographic security multiparty protocol, quantum cryptography information theory and quantum cryptography. Security and detectability to eavesdropping are two important features of quantum cryptography. Quantum mechanical uncertainty principle and uncloned theorem are one of the important bases to ensure the unconditional security of quantum cryptography. Firstly, a quantum key distribution protocol based on retransmission mechanism is proposed, which can effectively improve the density of the protocol. Key distribution efficiency; then, three valued quantum states, homomorphic encryption technology and line fitting technology are studied. A homomorphic encryption scheme for three valued quantum states is proposed, and a quantum homomorphic encryption framework is established. The correctness and universality of the framework are verified through an example of two value and three value quantum states. Then, the three value XHZ encryption scheme is adopted. Some interesting conclusions are obtained. Finally, a practical quantum public key encryption model is proposed. The specific research content is summarized as follows: 1) the quantum key distribution protocol of the retransmission mechanism. First, the implementation process of the BB84 protocol is studied. Through analysis, it is found that the "loss" of the transmitted photon is strict for the efficiency of the key distribution of the QKD protocol. The new protocol is then proposed and the workflow of the new protocol is presented. The process is similar to the BB84 protocol. The difference is that if the number of lost photons exceeds a threshold, the two transmission process will be started, and the retransmission process is finished when certain conditions are satisfied; then the execution of the protocol is simulated, At the same time, the simulated eavesdropper, using the retransmission strategy after interception, sends the "disturbed" quantum state sequence to the receiver. From the analog data, it can be seen that any "interference" to the quantum state can be tested at the receiver. Finally, the protocol is analyzed from three aspects: Security, data negotiation and density amplification. It is concluded that the protocol can effectively improve the efficiency of key distribution, and the distribution process is an unconditional secure.2 three valued quantum homomorphic encryption scheme. First, the relevant three valued quantum gates, three value XHZ encryption schemes and QHE are introduced. Then, the first TQHE scheme is proposed based on the three value single quantum rotation gate; secondly, the general unitary transformation can be used. By fitting 8 kinds of rotating gates, we generalize it to the general three valued single quantum gates and propose second TQHE schemes. Then, using the GCX gate as the universal gate of the three value double quantum, we construct third TQHE schemes, theoretically generalize it to the case of the general three value n quantum, and give its construction process, and get fourth TQHE in the theoretical sense. In the end, the protocol is analyzed from three aspects: the fitting of multivalued quantum gates, key security and the privacy of user data. The maximum probability of the attacker to the correct guessing key of the ciphertext quantum state is 1/33n, and the scheme can be well integrated into the future quantum remote server architecture to solve the user privacy in the distributed environment. .3, a universal quantum homomorphic encryption model. First, by studying the quantum homomorphism encryption, a general method of constructing the quantum homomorphic encryption operator is proposed, and then a framework for constructing the quantum homomorphic encryption scheme is established. Secondly, the unitary transformation of the two value and three valued quantum states is used to use the frame. The architecture makes the corresponding quantum homomorphic encryption scheme. Compared with the existing scheme, the quantum homomorphic encryption scheme constructed by the framework is correct and more universal. Finally, the security of the framework is based on the security of the encryption algorithm and the security of the key by security analysis. Symmetric quantum encryption algorithm requires encryption key when constructing quantum homomorphism operators. Therefore, the framework is a weak symmetric quantum homomorphic encryption framework.4). The three value XHZ encryption scheme is optimized and some interesting conclusions are obtained. First, two verification processes of orthogonality and maximum mixed state in the QOTP scheme are given, and then the results are given. Two important definitions: the orthogonality and the orthogonality of the encryption operator; then, by optimizing the three value XHZ quantum encryption scheme, 4 improved three value quantum encryption schemes are proposed. By calculating the orthogonality rate of the encryption operators in these improvements, the encryption operator kU in scheme 3 is completely orthogonal and has a very high security. Integrity is the best in all schemes; finally, the security of scheme 3 is discussed from two aspects. One is the security of the encryption operator kU. The encryption operator kU in scheme 3 is completely orthogonal in the 3 dimension Hilbert inner product space and has a high level of security. On the other hand, it is the security of the key source. The retransmission mechanism is through the retransmission mechanism. The BB84 protocol and the custom interpolating function f (s, K) or F (s) obtained the unconditional security, including the digital 0,1 and 2 key string s., focusing on the definition of the interpolating function, detailed description of the workflow of the interpolating function and the notice of the.5) the practical quantum public key encryption model. The model is mainly trusted and secure. Third party CA and PKDC, and the client's encryption and decryption operator, D/E Adapter (commonly known as black box). In this model, CA and PKDC are the key to the whole model. At the same time, the quantum one-way threshold function and Holevo bounds are the key generation algorithms and the maximum number of copies that can be published for a quantum public key. This model is in this model. Some schemes or algorithms can be replaced safely without affecting the operation of the entire framework. Finally, we hope to use quantum block chain technology to centralization and bring new research fields to QPKE. Finally, we summarize the research content of the full text, and give the next stage of research task: hope to build three values. The key distribution protocol of quantum entanglement, three valued quantum homomorphism signature and authentication protocol, three valued quantum public key encryption scheme, and hope to use quantum block chain technology to restudy the related protocols of quantum encryption.
【學(xué)位授予單位】：電子科技大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2017
【分類號】：O413;TN918

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