Page 300 - 《软件学报》2020年第12期

3966 Journal of Software 软件学报 Vol.31, No.12, December 2020

Table 1 Comparative analysis of secure interval computing protocols
表 1 保密区间计算协议间的对比分析
协议 解决问题的范围 是否彻底解决所提出的问题 是否需要调用百万富翁协议 是否是新问题
文献[20]中的协议 有理数 9 9 ×
文献[21]中的协议 声称实数 × × ×
Π 1 有理数 9 × ×
Π 2 有理数 9 × 9
Π 3 有理数 9 × 9
注:9表示具有某种性能,×表示不具有某种性能

6 结束语

本文首先提出数轴上的保密关系测定问题应当分为 3 个值得研究的子问题:(1) 点与区间关系的保密测定;
(2) 多维点与区间保密关系测定;(3) 区间与区间关系的保密测定.然后采用“两个数的安全比值与 1 的关系判
定两个数的大小”的方法,基于同态加密设计了 3 个高效的保密区间计算协议.最后,采用模拟范例(ideal/real)分
析了 3 个协议的安全性.分析表明:(1) 这 3 个协议突破了 Paillier 等加密方案不能进行保密差值计算的瓶颈;(2)
这 3 个协议还可以作为基础模块用于解决其他若干安全多方计算问题,例如保密点与圆环区域关系判定问题、
点与凸多边形位置关系判定问题、保密近感探测问题等.而如何解决无理数轴上的一个无理数一次同时与两个
无理数的安全比较依然是个开问题,需要进一步探索解决.

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