多重集的保密计算及应用

安全多方计算是近年来国际密码学界研究的热点问题.多重集作为标准集的推广在实际中有广泛的应用，对于多重集的保密计算问题研究具有重要的意义.本文主要研究两方多重集的交集、并集以及基于阈值和集的保密计算问题.首先针对不同问题设计相应的编码方法，结合Paillier加密方案设计保密计算协议，并应用模拟范例方法严格证明协议的安全性.效率分析和实验验证表明本文所设计的协议是简单高效的.

Secure Multiset Operations and Their Applications

Secure multiparty computation is one focus in the international cryptographic community in recent years.The private computation of multisets is also of great practical significance.In order to privately compute on multisets,we first propose two new encoding schemes.Then based on Paillier probabilistic encryption algorithm,we design three simple and efficient secure two party protocols to compute the intersection,the union and the summation of two private multisets.We prove that they are secure in the semi-honest model.We also analyze the computational complexities and communication complexities of the protocols and test the efficiency on a PC.The test result shows that our protocols are efficient.