The millionaires' problem is an important problem in secure multiparty computation and a basic building block of secure multiparty computation protocols.Secure vector dominance statistic problem is a problem generalized for the millionaires' problem

which can be used to get the number of

y

i

x

i

without leaking further information.In this paper

we first propose an encoding scheme to encode private numbers; then based the new encoding scheme and homomorphic encryption scheme

we design a protocol for millionaires' problem and prove that the protocol is secure in the semi-honest model using the simulation paradigm.Then

we utilize this scheme to propose a solution to secure vector dominance statistic problem.The performance analysis indicates that our protoco

l is simpler and more efficient than the others.Finally

we use the scheme to solve the integer division problem and privately determine the relation between point and lines.