The SMC (Secure Multiparty Computation) of the location relation between rational numbers and intervals

and that between two rational intervals has been investigated. As an important branch of the confidential scientific computing

this problem was widely applied in database matching

positioning search

etc. However

there still exist many problems

for example

current solutions to the location relation between rational numbers are low efficiency and the research on the location relation between two rational intervals is limited. In order to address the above gaps

firstly

we use polynomials to represent the interval

and convert the problem into determining the scalar product signs of two integer vectors. Thus

the new protocol of the problem between rational number and interval is worked out. Secondly

with the proposed scheme as the basic module

we construct the protocol of the location relation between two rational intervals. Finally

the theoretical analysis and experimental results prove that our protocols are safe and efficient

and we give the application of millionaire problem and computational geometry problem in rational domain.