量子加密相关理论与应用研究

发布时间：2018-06-04 02:48

本文选题：量子密钥分发 + 三值量子加密　；参考：《电子科技大学》2017年博士论文

【摘要】：量子密码最早起源于Wiesner的“Conjugate Coding”,是量子理论、信息科学和计算机科学相结合的产物。它的研究内容包括量子密钥分发、量子密钥管理、量子加密、量子认证、量子密码安全多方协议、量子密码信息理论和量子密码分析等。无条件安全性和对窃听的可检测性是量子密码的两个重要特征。量子力学测不准原理和不可克隆定理是保证量子密码具有无条件安全性的重要基础之一。本论文首先提出了一种基于重发机制的量子密钥分发协议,它能有效提高协议的密钥分发效率;接着,研究了三值量子态、同态加密技术和线路拟合技术,提出了三值量子态的同态加密方案,并建立起了量子同态加密框架,通过二值和三值量子态的实例,验证了该框架的正确性和普适性;然后,通过对三值XHZ加密方案的优化,得到了一些有趣的结论;最后,提出了一种实用的量子公钥加密模型。具体研究内容总结如下:1)重发机制的量子密钥分发协议。首先研究了BB84协议的执行过程,通过分析发现,发送光子的“丢失”对QKD协议的密钥分发效率产生了严重的影响;接着提出了新的协议,并给出了新协议的工作流程,该流程类似于BB84协议,不同之处就在于:若发现丢失光子数超过了一个阈值的话,就会启动二次传输过程,当满足一定的条件后,重传过程结束;然后模拟了该协议的执行过程,同时模拟窃听者,采用截取后测量重发策略,将“扰动”过的量子态序列发送给接收者,由模拟数据可以看出,任何对量子态的“干扰”都可以在接收端被测试出来;最后,从三个方面分析了该协议:安全性、数据协商和密性放大。从而得出结论:该协议能有效提高密钥分发效率,而且分发过程是无条件安全的。2)三值量子同态加密方案。首先介绍了相关三值量子门、三值XHZ加密方案以及QHE;接着,基于三值单量子旋转门,提出第一个TQHE方案;其次,借助于一般的酉变换可以由8种旋转门拟合,我们将其推广到一般的三值单量子门,提出了第二个TQHE方案;然后,以GCX门作为三值双量子的通用门,构造了第三个TQHE方案,理论上将其推广到一般三值n量子的情况,并给出它的构造过程,得到理论意义上的第四个TQHE方案;最后,从多值量子门的拟合、密钥安全性和用户数据的私密性三个方面分析了该协议,得出攻击者对密文量子态正确猜对密钥的最大概率为1/33n,并且该方案可以很好地集成到将来量子远程服务器架构中,解决分布式环境下用户私密量子数据的安全计算问题。3)通用的量子同态加密模型。首先通过研究量子同态加密,提出了一种通用的构造量子同态加密算子的方法,进而建立了构造量子同态加密方案的一种框架;其次,通过二值和三值量子态的酉变换,利用该框架构造了相应的量子同态加密方案,与现有文献构造的方案相比,利用该框架构造的量子同态加密方案是正确的,而且更具有普遍性;最后,通过安全性分析,该框架的安全性是基于加密算法的安全性和密钥的安全性。由于该框架采用了对称量子加密算法,导致构造量子同态算子时需要加密密钥。所以,该框架是一种弱的对称量子同态加密框架。4)优化了三值XHZ加密方案,并得出了一些有趣的结论。首先,给出了QOTP方案中正交性和最大混合态的两个验证过程,接着又给出了两个重要的定义:加密算子的正交性和正交率;然后,通过优化三值XHZ量子加密方案,提出了4种改进后的三值量子加密方案。通过计算这些改进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,从两个方面讨论了方案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维Hilbert内积空间中是完全正交的,而且具有很高水准的安全性。另一方面是密钥源的安全性。通过重发机制的BB84协议和自定义的插值函数f(s,k)或f(s),获得了无条件安全的、包含数字0,1和2的密钥串s。其中,重点介绍了插值函数的定义,详细描述了插值函数的工作流程以及注意的事项。5)实用的量子公钥加密模型。该模型主要由可信任的、安全的第三方CA和PKDC,以及客户端的加解密运算器D/E Adapter(俗称黑盒子)构成。在该模型中,CA和PKDC很关键,是整个模型的骨架。同时,量子单向门限函数和Holevo界,分别是密钥生成算法和针对于一个量子公钥可以发布的最大拷贝数。模型中的这些方案或算法是可以被安全地替换,而不影响整个框架的运行。最后,我们希望能够运用量子区块链技术,实现去中心化,并能够给QPKE带来全新的研究领域。最后,我们总结了全文的研究内容,并给出了下一阶段的研究任务:希望构建三值量子纠缠的密钥分发协议、三值量子同态签名和认证协议、三值量子公钥加密方案,并希望利用量子区块链技术,重新研究量子加密的相关协议。
[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.
【学位授予单位】：电子科技大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：O413;TN918

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