The millionaire’s problem is the origin of secure multi-party computation. This problem has always been the focus of scholars' research, and it is also the design basis and important part of other secure multi-party computation protocols. An in-depth study of the millionaires’ problem is of great significance to promote the further development of secure multi-party computation. Based on millionaires’ problem and secure vector dominance protocol, we propose an improved protocol and an extended protocol. The improved protocol solves the problem of coarse granularity when comparing elements in the original protocol, and can realize that two parties can compare the relationships of greater than, equal to or less than between their elements by executing the protocol once. The improved protocol and the extended protocol are further applied to solve the problem of finding the cardinality of the intersection of the two-party sets in two cases. In addition, based on the integer division problem, we give a method to privately evaluate the greatest common factor of two integers.
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