高效的安全多方半量子求和协议

Abstract

安全多方半量子求和 (SMSQS) 是指多个互不信任且资源受限的参与方, 借助量子第三方 (TP) 的帮助联合计算出他们私有秘密之和, 其求和结果可以根据实际应用场景来设计是否公开, 但是协议需确保参与者输入的隐私性和计算结果的正确性. 本文提出一种第三方 TP 只需制备单量子比特就可对多个资源受限的参与方进行秘密求和的协议. 协议中参与方无论执行直接返回操作或者执行测量返回操作, 协议都可以对参与方的秘密进行求和计算, 从而提高协议中量子比特的使用效率. 其次基于一种 d 维的量子叠加态给出将参与方秘密数值的维度扩展到高维的 SMSQS 协议, 并通过数学证明和具体实例验证其协议的正确性. 通过对所提出的协议进行安全性分析可知它们能够防范拦击重发攻击、测量重发攻击、双 CNOT 门攻击和 TP 攻击等典型的攻击行为.

Alternate abstract:

Secure multi-party semi-quantum summation (SMSQS) allows multiple distrusted and resource-constrained participants to jointly compute the summation of their private secrets with the help of a quantum third party (TP). Whether the result of SMSQS can be disclosed depends on its application. However, the computation must ensure the privacy of the participants' inputs and the correctness of the computation result. This paper proposes an efficient SMSQS protocol where TP only needs to prepare single qubits and can help multiple resource-constrained participants to carry out summation operation on their inputs. Whether or not the participants choose to reflect what they received directly or perform measurements on the received qubits, the protocol can sum up the secrets of the participants, thus the qubit efficiency is greatly improved. In addition, based on a d-dimensional quantum superposition state, a high-dimensional SMSQS protocol which can compute the summation of d-dimensional secrets is presented. The correctness of the protocol is verified through mathematical proofs and specific examples are given. The security analysis of the proposed protocols shows that the proposed protocols can prevent some typical attacks such as the intercept-resend attack, the measure-resend attack, the double CNOT attack and the TP attack.