有理数域上集合成员关系的保密判定协议
Privacy Preserving Protocol of Rational Set Membership’s Judge

DOI: 10.12677/CSA.2021.118213, PP. 2080-2087

Keywords: 集合成员关系，安全多方计算，有理数，ElGamal同态加密算法
Set Membership, Secure Multi-Party Computation, Rational Number, ElGamal Homomorphic Encryption Algorithm

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Abstract:

本文通过将有理数按位编码为矩阵，并结合ElGamal同态加密算法，设计了有理数域上集合成员关系的保密判定协议，其中点集成员关系的保密判定协议可适用于 维有理点。其次，应用模拟范例的方法严格证明了协议的安全性，同时协议能够保护集合的势。最后，比较分析表明当参与者的有理数满足一定条件时，本文设计的协议是高效的。
By encoding the rational numbers into a matrix, combined with the ElGamal homomorphic encryption algorithm, this paper designs secure protocol for the rational set membership’s judge, in which the protocol for the point set membership can be applied to n(n≥2) dimensional rational points. Secondly, using the well accepted simulation paradigm proves that the proposed protocols are secure, and at the same time, the protocol can protect the number of elements in the partici2243pant set. Finally, the comparison and analysis show that the efficiency of the proposed protocol when the rational numbers meet certain conditions.

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