Efficient Implementation of the CKKS scheme using a quadratic residue number system

Abstract

The use of homomorphic encryption to ensure computational security imposes additional overhead associated with encryption and decryption of data. One of the mechanisms that can be used to increase the data coding rate is the quadratic residue number system. The quadratic residue number system reduces the number of decimal multiplications by half when multiplying two complex numbers. However, the use of a quadratic residue number system imposes a number of restrictions related to the representation of a number. In this article, we propose a mechanism for choosing the parameters of a quadratic residue number system and develop an efficient data encoding algorithm