基于量子纠缠的密码协议理论研究

发布时间：2018-09-04 09:00

【摘要】：量子密码学是以现代密码学和量子力学为基础,用量子力学性质实现密码任务的一门学科。它利用微观粒子的量子属性实现信息保护,理论上被证明是无条件安全的。相比于基于数学困难问题的经典密码学,量子密码学在安全上具有明显的优势,因此受到了越来越多的关注,取得了快速的发展。其中,量子纠缠作为一种资源,常常被用在密码协议的设计和安全性分析中,在量子密码学的研究中起着至关重要的作用。基于此,本文以量子纠缠为背景,主要研究量子同态签名协议,量子私密比较协议和量子匿名排序协议。主要研究内容分为三部分,所取得的主要研究成果如下:1.量子同态签名协议(1)提出了一个基于量子相干态的量子同态签名协议。首先分析现有的量子同态签名协议,结合经典密码学中同态签名的定义,给出了量子同态签名的定义。然后分析量子相干态在平衡分光器中的干涉性质,利用这种干涉性质提出了一个新的量子同态签名协议,并证明了该协议的同态性和分析了该协议的安全性和通信复杂度。通过和现有的量子同态签名协议相比较可以得出,该协议具有更高的效率而且更容易实现。最后论述了该协议中使用的量子相干态和量子指纹识别中使用的量子纠缠态之间的关系。(2)提出了基于完全Bell态测量和基于部分Bell态测量的量子同态签名协议。首先分析了Bell态测量的原理,并阐述了部分Bell态测量怎样用线性光学器件实现。然后基于完全Bell态测量提出了一个量子同态签名协议,进一步论述了该协议基于部分Bell态测量也可以完成,并给出了该协议。再证明了所提协议的同态性并分析了协议的安全性。在安全性分析中,针对现有的量子同态签名协议提出了一种“截获-重传”的攻击策略,并证明了该协议中所使用的诱骗态方法可以有效抵制这种攻击。最后通过和现有的量子同态签名协议比较可以得出,该协议具有更高的安全性和效率。2.量子私密比较协议(1)首次提出了一个多个参与者可以比较他们私有信息大小的量子私密比较协议。首先找到了一个多体高维纠缠态,并对该量子态的性质进行了分析,进一步用群论的方法证明了两个正整数的大小关系可以用模d减法巧妙地描述。然后基于这些性质提出了一个多个参与者可以比较他们私有信息大小的量子私密比较协议。该协议只需执行一次就可以比较l个参与者私有信息的大小,如果使用两个参与者可以比较私密大小的协议则需要执行(?)次。最后较详细地分析了该协议的安全性,并通过分析协议中所使用量子资源的方式分析了协议的效率。(2)提出了一个基于线性光学器件工作原理的量子私密比较协议。针对现有的量子私密比较协议大都是从完全抽象的角度提出和分析,离实际实现相隔较远,首先分析了常用的线性光学器件的工作原理,主要是分光器的工作原理和偏振态在平衡分光器中的后选择纠缠性。然后基于这些工作原理提出了一个两个参与者可以比较他们私有信息是否相等的量子私密比较协议,为在现实环境中实现量子私密比较协议打下了基础。最后较详细地分析了所提协议的安全性。3.量子匿名排序协议提出了一个基于单粒子态的量子匿名多方多数据排序协议。首先分析了量子匿名排序协议的设计原理和安全性要求。然后基于高维单粒子态提出了一个新的量子匿名多方多数排序协议,并分析了该协议的安全性。通过将该协议和现有的基于量子纠缠的匿名排序协议进行比较表明,该协议具有更高的效率。最后论述了该协议也可以通过使用中国剩余定理,用较低维数的单粒子态完成,并给出了具体的方法。
[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.
【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;TN918.1

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