[0002] 传统密码学的安全性依赖于数学问题的计算复杂性,易受具有强大计算能力的量子并行计算的影响。幸运地是,Bennett和Brassard[1]在1984年提出的量子密码基于量子力学原理可以实现无条件安全性。量子密码引起了广泛的关注,并建立了许多有趣的分支,如量子密钥分发(Quantum key distribution,QKD)[1-7],量子安全直接通信(Quantum secure direct communication,QSDC)[8-11],量子秘密共享(Quantum secret sharing,QSS)[12-18]等。
[0003] 隐私比较方法可以追溯到Yao[19]提出的百万富翁问题。在百万富翁问题中,两位百万富翁想要在不了解彼此实际财产的情况下判断谁更富有。之后,Boudot等[20]提出了一个判断两位百万富翁是否同样富有的隐私比较方法。不幸地是,Lo[21]指出,在两方隐私比较中构建一个安全的相等函数是不可能的。因此,需要考虑引入一些额外的假设,例如第三方(Third party,TP),来实现隐私比较。
[0004] 量子隐私比较(Quantum private comparison,QPC),可以看作经典隐私比较在量子力学领域的扩展,最初由Yang和Wen[22]提出。QPC的目标是通过利用量子力学的原理来判断来自不同方的隐私输入是否相等,并且它们的真实内容不会被泄露出去。近年来,QPC方法的设计和分析成功引起了人们的广泛关注。因此,许多两方QPC方法[22-35]已经被提出来。
[0005] 但是,上述QPC方法仅适用于两方的隐私比较。幸运地是,在2013年,Chang[36]等首次提出基于多粒子GHZ类态的多方量子隐私比较(Multiparty quantum private comparison,MQPC)方法,可以只执行一次方法就完成任意一对参与者之间秘密相等性的比较。在这之后,许多基于多级系统的MQPC方法[37-42]被构建出来。例如,Liu等[37]在2014年提出一个基于d级基态的不需要纠缠交换的MQPC方法;在2017年,Ji和Ye[39]提出一个基于d级Bell态和d级Cat态纠缠交换的MQPC方法。
[0006] 基于上述分析,本发明提出一种新颖的基于n级单粒子的环型MQPC方法。本发明的方法以环型方式传输粒子,并且在半忠诚TP的帮助下可以只执行一次方法就实现n个参与者秘密相等性的比较。这里,TP是半忠诚的,意味着她被允许按照自己意愿错误行事,但不允许与其他任何人勾结。
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