In recent years, secure multiparty computation (SMC) is one of research focuses in the field of information security, and a key technology of privacy protecting for distributed users in their jointly evaluating. Researchers have proposed many schemes for SMC problem, however, there are many other secure multi-computation problems needed to be investigated. This study involves private relationship test on number axis, which covers three subproblems: (1) secure test on the relationship between a confidential number and a private interval; (2) multi-dimensional secure test on the relationship between multi-number and multi-interval; (3) secure test on the relationship between two confidential intervals. Private relationship test on number axis has an extensive application in the field of privacy protection, and it can be employed as a basic block to construct other SMC protocols. Based on a variant encryption scheme of Paillier’s homomorphic encryption (in which, who encrypts message who evaluates the base), three protocols for private relationship test on number axis are designed. They are secure test on the relationship between a confidential number and a private interval, multi-dimension secure test on the relationship between multi-number and multi-interval, and secure test on the relationship between two confidential intervals. And their security is analyzed using simulation framework (idea/real) in the standard model. The idea of private ratio calculation in these three protocols can be directly used to solve the millionaire problem within the range of rational numbers. More widely, these three protocols can be employed as a basic block to solve the following SMC problems: private test on relationship between a point and an annulus, private test on relationship between a point and a convex polygon, and private proximity test.