Collaborative calculation and application of interreal and real interval relations to protect privacy

The determination of the relation between a number and a numerical interval is one of the core problems in the scientific calculation of privacy protection. The calculation of the relationship between two numbers and a numerical interval to protect privacy is also the basic problem of collaborative computing. It is widely used in data queries, location search and other fields. At present, most of the solutions are still fundamentally limited to the integer level, and there are few solutions at the real number level. To solve these problems, this paper first uses Bernoulli inequality generalization and a monotonic function property to extend the solution to the real number level and designs two new protocols based on the homomorphic encryption scheme, which can not only protect the data privacy of both parties involved in the calculation, but also extend the number domain to real numbers. In addition, this paper designs a solution to the confidential cooperative determination problem between real numbers by using the sign function and homomorphism multiplication. Theoretical analysis shows that the proposed solution is safe and efficient. Finally, some extension applications based on this protocol are given.