隐私保护整数区间位置关系判定问题

整数区间是指区间的左右端点都是整数，由左右端点及它们之间的所有整数构成的集合。整数区间的位置关系是指两个整数区间在数轴上的位置的相对关系。针对整数区间位置关系提出一种安全两方计算问题，即隐私保护整数区间位置关系判定问题，该问题旨在帮助拥有隐私整数区间的两个用户，在保护输入隐私的前提下，正确地判断出他们的整数区间的位置关系。定义了整数区间的6种位置关系，给出了整数区间的0-1编码方案，并证明了整数区间位置关系的一种判定准则。基于Goldwasser-Micali加密体制在半诚实攻击者模型下设计了解决整数区间位置关系判定问题的一个两方计算协议，证明了协议的正确性和安全性，并对协议的性能进行了分析和说明。

Private-preserving determination problem of integer-interval positional relationship

Integer-interval means the set of the left and right endpoints of the interval (which are integers) and all integers between them. The positional relationship between integer-intervals is the relation between the positions of two integer-intervals. Aiming at the positional relationship between integer-intervals, a secure two-party computation problem was proposed, in other words, a private-preserving determination problem of integer-interval positional relationship was proposed. In this problem, two users with private-preserving integer-intervals were helped to correctly determine the positional relationship between the two integer-intervals of them with the private preserved. Six positional relationships between two integer-intervals were defined, the 0-1 coding scheme of integer-intervals was given, and a determination rule for integer-interval positional relationship was proved. Then, based on the Goldwasser-Micali cryptosystem and semi-honest attacker model, a secure two-party computation protocol for solving the private-preserving determination problem of integer-interval positional relationship was designed. The protocol was proved to be both correct and secure, and the performance of the protocol was analyzed and explained.