区间关系保密计算若干问题研究

Some Research on Secure Interval Relation Computation

安全多方计算是密码学界的一个重要研究方向,本文主要研究区间的安全计算问题.首先应用Paillier加密方案设计“点与区间”以及“区间与区间”关系两方保密计算基础协议,协议的特点是判定结果以密文形式输出.将其推广为有理区间关系判定协议时,相比已有协议,本文协议更为安全与高效.在此基础上,进一步研究多维度的“点与区间”以及“区间与区间”关系阈值判定这一类新问题.由于基础协议的输出结果为密文,故以此为基础所设计的多维度问题协议更加安全.最后,应用模拟范例方法严格证明了协议的安全性,并对协议进行了效率分析及模拟实验,理论分析及实验结果都说明本文协议是高效的.

Secure multi-party computation(SMC)is an important research direction of cryptography.In this paper,we study the secure computation of intervals.Using the Paillier encryption scheme,we design the protocols of relationship between an interval and a point(or an interval).Firstly,the outputs of protocols are ciphertexts.If we extend it to rational intervals,the protocols are safer and more efficient than existing protocols.And then,we study the multi-dimensional problems,that is,the threshold problems of multiple points(or intervals)and intervals,which are new problems in SMC.Since the outputs of the basic protocols are ciphertexts,the multi-dimensional problem protocols are more secure.We strictly prove the security of the protocols using the simulation paradigm method,analyze and demonstrate the efficiency of the protocols through experiments,and compare with the related work to illustrate that the protocols are efficient.