About One Property of Number Rank in RNS

An approximate value of the number rank is used to increase the speed of homomorphic encryption algorithms. The use of an approximate rank of a number allows reducing the computational complexity of the data encryption algorithm, but at the same time leads to a loss of accuracy. In this paper, we investigate the properties of the number rank. We have shown that it is possible to reduce the accuracy of calculating the approximate rank of a number, but the homomorphic encryption scheme will have the same properties.