Homomorphic Comparison Methods: Technologies, Challenges, and Opportunities

The use of cloud computing imposes a number of restrictions related to the security and confidentiality of stored and processed data. One of the mechanisms that allows expanding the scope of public cloud services for processing personal and medical data is homomorphic encryption. Homomorphic encryption allows performing arithmetic addition and multiplication operations on encrypted data. To expand the scope of homomorphic encryption, efficient algorithms are needed to implement the operation of comparing encrypted numbers. In this paper we investigate existing algorithms of encrypted numbers comparison for homomorphic encryption schemes operating both with integers and with fixed-precision numbers. We have shown that for homomorphic integer ciphers, there are efficient algorithms for comparing encrypted numbers based on Lagrange interpolation of a function of two variables. We have shown that fixed-precision comparison of encrypted numbers is an open problem.