最小值问题的安全多方计算及其应用

安全多方计算是国际密码学界近年来的研究热点.本文主要研究科学计算中最小值问题的安全多方计算，目前尚没有见到关于这个问题的解决方案.本文设计了一种新的编码方法，应用该编码方法和ElGamal乘法同态加密算法，并结合秘密分享以及门限密码体制，在半诚实模型下设计了三个能够抵抗合谋攻击的最小值安全多方计算方案，并应用模拟范例证明了方案的安全性.以最小值解决方案为基础还可以解决最大值安全计算以及并集的安全计算等科学计算问题.效率分析表明所设计的安全计算方案是高效的方案.

Secure Multi-Party Computation for Minimum and Its Applications

Secure multi-party computation is a focus in the international cryptographic community.This paper studies how to privately compute the minimum of some private numbers.We have not read about any a solution to this problem.In this study,we introduce a new encoding scheme,and then,based on this new encoding scheme and ElGamal multiplicatively homomorphic encryption scheme,using secret sharing and threshold decryption,devise protocols for this problem.By using the simulation paradigm,we prove that these protocols are secure in the semi-honest model.These protocols can resist collision attack.Based on the computing methods for minimum problem,secure multi-party computation for maximum and union of sets can also be solved.Efficiency analysis shows that these schemes are efficient.