中文摘要：

安全多方计算协议是指拥有秘密输入的n方，在不泄漏各自秘密输入的前提下共同正确地计算1个函数，并且除了输出所反映的信息之外，任何一方的输入信息都不泄漏．基于可交换确定型加密体制，在半诚实模型下给出了判断元素属于集合、集合相等及同一集合上的等价关系相等的安全双方计算协议．给出了利用核、像和核类来判断映射相等的方法，在此基础上进一步提出了判断映射相等的安全双方计算协议，并对协议的正确性、安全性和效率进行了说明．

英文摘要：

Secure multi-party computation protocol allows a set of n-parties to evaluate a joint function of their inputs such that the function is calculated correctly and furthermore no information about their inputs is revealed by the output of the function. Based on the determinate-commutative cryptosystem and under the semi-honest model hypothesis, secure two-party computation protocols for determine whether an element is belong to a certain finite set, whether two finite sets are equal, and whether two equivalence relations are equal are considered. A mathematic method, relates to kernel, image and kernel-classes of mapping, to determine whether two mappings are equal is introduced. Furthermore, two-party computation protocol for determine whether two mappings are equal is given. Correctness, security, and efficiency of our protocols are analyzed.