本技术介绍了一种新型量子安全协议，利用圆上双向量子游走技术，安全地计算两个通信方的秘密向量标量积，同时确保秘密信息不外泄。该方法涉及一个半忠诚第三方的参与，以增强安全性。
背景技术
在安全多方计算(Secure Multi-party Computation,SMC)[1]
问题中,若干个互不信任的参与者总是协作计算一个指定的函数,且不存在泄露其秘密输入的风险。安全两方标量积计算被定义为在不泄密的情况下计算两个秘密向量的标量积或点积。标量积计算是SMC的一个重要基础分支,可用于点包含[2]
、距离计算[3]
和k最近邻计算[4]
等各种领域。然而,包括标量积计算在内的SMC的安全性基于计算复杂度假设,存在被量子计算[5-6]
攻破的潜在风险。1984年,Bennett和Brassard[7]
将量子力学基本原理与经典密码学相结合,提出第一个量子密码学方法,即BB84量子密钥分发(Quantum Key Distribution,QKD)方法。此后,学者们开始研究具有理论无条件安全性的量子安全多方计算(Quantum Secure Multi-party Computation,QSMC),包括量子安全多方求和[8-13]
、量子安全多方乘法[12-14]
以及量子标量积(Quantum Scalar Product,QSP)计算[15-18]
。
目前仅存在四种QSP计算方法,即文献[15-18]所描述的方法。2012年,He等人[15]
首次提出一种基于四粒子量子纠缠态的第三方(Third-Party,TP)参与的安全两方量子标量积(Two-party Quantum Scalar Product,TPQSP)计算方法。2018年,Wang和He[16]
提出一种基于连续变量团簇态的安全TPQSP计算方法。2019年,Shi和Zhang[17]
采用单粒子态和七粒子量子纠缠态,提出一种强隐私保护的TPQSP计算方法。2023年,Liu和Li[18]
提出一种基于四粒子量子纠缠态的安全高效TPQSP计算方法。然而,这些QSP计算方法存在一些不足之处。具体来说,文献[15,17,18]的方法需要多粒子量子纠缠态作为初始量子资源,而文献[16]的方法需要连续变量团簇态,但多粒子量子纠缠态以及连续变量团簇态的制备均相当困难；文献[15,16]的方法需要在参与者之间预共享密钥,会消耗额外的量子资源和经典资源；文献[17,18]的方法需要量子傅里叶变换(Quantum Fourier Transform,QFT)或逆量子傅里叶变换(Inverse Quantum Fourier Transform,IQFT),其实施相当具有挑战性[19]
；而且,文献[16]采用复杂的投影测量。
量子游走(Quantum walks,QW)是经典随机游走的量子模拟[20]
,已被广泛应用于众多量子信息处理任务,如量子信息分割[21]
、量子纠缠态生成[22]
、量子身份认证[23]
、量子公钥密码[24]
、量子隐私比较[25]
以及量子秘密共享[26]
等。QW态是一种两粒子乘积态,其相较于量子纠缠态而言易于制备。
基于上述分析,本发明将QW引入到标量积计算,提出一种新颖的基于圆上双向量子游走(Two-Direction Quantum Walks on a Circle,TDQWC)的安全TPQSP计算方法。本发明的方法需要一个半忠诚TP的协助,TP可以按照自己意愿错误行事但不能与其他人共谋[27]
。本发明的方法采用QW态作为初始量子资源,仅需d维和2维单粒子测量而非量子纠缠态测量。本发明的方法不需要QFT或IQFT。此外,本发明的方法不仅具备信息论安全性,还能抵御外部攻击和参与者攻击。
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实现思路