基于Greenberger-Horne-Zeilinger态的量子安全布尔函数计算  

Quantum Secure Boolean Function Computation Based on Greenberger-Horne-Zeilinger States

作　　者：田欣莹 林崧[1] TIAN Xin-Ying;LIN Song(College of Computer and Cyber Security,Fujian Normal University,Fuzhou 350117,China;Digital Fujian Internet of Things Laboratory of Environmental Monitoring,Fujian Normal University,Fuzhou 350117,ChinaBoolean functions are widely used in the design and analysis of sequence and block)

机构地区：[1]福建师范大学计算机与网络空间安全学院,福州350117 [2]福建师范大学数字福建环境监测物联网实验室,福州350117

出　　处：《密码学报》2022年第6期1168-1176,共9页Journal of Cryptologic Research

基　　金：国家自然科学基金(62171131,61976053,61772134);福建省自然科学基金(2018J01776)。

摘　　要：布尔函数在序列密码和分组密码的设计与分析中有着广泛的应用.本文利用三粒子Greenberger-Horne-Zeilinger(GHZ)纠缠态中三个粒子测量结果之间的相关性设计了一个量子安全多方计算协议.在协议中,两个参与者可以在一个半可信第三方的帮助下完成对任意布尔函数的运算,并保证双方输入信息的私密性.在初始化阶段,他们分别根据各自的私密输入计算得到一些中间信息,并根据该信息设置对GHZ态粒子的测量基信息.在窃听检测阶段,根据纠缠态的关联性,接收方能够验证其收到的粒子是否正确.在计算阶段,参与者对手中的粒子进行测量,并将测量结果的和告诉第三方.然后,第三方对粒子也进行相应的测量,并根据测量结果和两个参与者的消息,计算并公布其结果.最后,基于第三方的公开信息,两个参与者可以同时获取目标函数的计算结果.安全性分析表明,所提出的量子协议可以抵抗外部窃听者的一些常见攻击以及内部参与者的欺骗攻击.这里值得强调的是,虽然协议引入了一个半可信的第三方,但是他既不能窃取两个参与者所拥有的任何秘密信息,也无法获得最终的计算结果.Boolean functions are widely used in the design and analysis of sequence and block cryptography.In this paper,a quantum secure multi-party computing protocol is proposed by using the correlation between the measurement results of three particles that are in the Greenberger-Horne-Zeilinger states.In this protocol,two participants can complete the computation of any Boolean function with the help of a semi-trusted third party and keep their input confidential.During the initialization phase,they compute some intermediate messages based on their private inputs respectively and determine the measurement base messages of Greenberger-Horne-Zeilinger state particles according to these messages.During the eavesdropping detection phase,the receiver can verify whether the received particles are correct according to the correlation of the entangled state.During the calculation phase,participants measure particles in their hands and tell the third party the sum of their measurement results.Then,the third party measures the particles accordingly.Thereafter,he calculates and publishes the results based on the measurement results and the messages of the two participants.Finally,according to the public messages from the third party,both participants can obtain the computed results of the function simultaneously.The security analysis shows that the proposed quantum protocol can resist some common attacks by external eavesdroppers as well as attacks by internal participants.It is worth emphasizing that although a semi-trusted third party is introduced,he can neither eavesdrop any secret information possessed by either party nor obtain the final results.

关 键 词：安全多方计算 量子密码 Greenberger-Horne-Zeilinger态 布尔函数 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]