基于拉格朗日酉算子的量子安全多方求积  

Quantum secure multiparty multiplication based on Lagrange unitary operator

作　　者：张龙威 宋秀丽 李闯 刘羽 ZHANG LongWei;SONG XiuLi;LI Chuang;LIU Yu(School of Cyber Security and Information Law,Chongqing University of Posts and Telecommunications,Chongqing 400065,China;School of Computer Science and Technology,Chongqing University of Posts and Telecommunications,Chongqing 400065,China)

机构地区：[1]重庆邮电大学网络空间安全与信息法学院,重庆400065 [2]重庆邮电大学计算机科学技术学院,重庆400065

出　　处：《中国科学：物理学、力学、天文学》2022年第6期30-41,共12页Scientia Sinica Physica,Mechanica & Astronomica

基　　金：国家自然科学基金(编号:61772098);重庆邮电大学博士启动基金(编号:A2020211);重庆市研究生科研创新项目(编号:CYS21335)资助。

摘　　要：现有的量子安全多方求积协议大多数利用纠缠态携带秘密信息,然而制备这些量子态难度较大.为了解决这个问题,本文提出一种基于d维拉格朗日酉算子的单粒子量子安全多方求积协议.在该协议中,半可信的第三方和每个参与者共享一个私有密钥,参与者首先将共享密钥、秘密整数和随机数模d相乘,接着使用拉格朗日酉算子将计算的结果编码到无偏基粒子上,第三方测量每一个参与者发送回来的粒子获得编码信息,然后使用所有随机数的模d乘积计算多方参与者秘密整数的求积.性能分析表明,该协议与其他相似协议相比,对实体的量子计算能力要求更低.在安全性方面,该协议能够同时抵抗提出的外部攻击和内部攻击.最后,协议使用Q#量子编程语言结合Python仿真验证了本协议的正确性.Most of the existing quantum secure multiparty multiplications use entangled states to carry secret information.However,the preparation of these quantum states is difficult.In order to solve this problem,a single-particle secure multiparty product protocol based on a d-level Lagrange unitary operator is proposed.In this protocol,a semi-honest third party(Server)and each participant share a private key.The participant first uses the private key and random number to multiply his own secret integer with module d,and then he uses Lagrange unitary operator to encode the calculation result into an unbiased basis particle.The server obtains the encoded information by measuring the particle sent back by each participant.Finally,the server uses the module d product of all the random numbers sent by the participant’s representative to calculate the product corresponding to the secret integers of multiple participants.Performance analysis shows that,compared with similar protocols,the proposed protocol requires less of the entity’s quantum computing capabilities.In terms of security,this protocol can resist both external and internal attacks.Finally,the proposed protocol uses the Q#quantum programming language combined with Python language to simulate and verify its correctness.

关 键 词：量子安全多方乘法 d维拉格朗日酉算子 无偏基粒子 Q#量子编程语言 

分 类 号：O413[理学—理论物理] TN918.4[理学—物理]