Euclidean Division Method for the Homomorphic Scheme CKKS

The use of cloud computing can reduce the economic costs of maintaining IT infrastructure, but at the same time, the likelihood of confidential data theft increases. To reduce the likelihood of it, cloud computing uses homomorphic encryption. However, a homomorphic cipher only allows adding and multiplying encrypted numbers; in some cases, a division operation is required to implement algorithms. To implement the division operation with encrypted numbers it is necessary to implement the encrypted number comparison operation. Considering that the operation of comparing encrypted numbers is carried out using numerical methods, it is necessary to adapt the existing algorithms for Euclidean division. In this article, we propose a two-stage algorithm for Euclidean division of numbers encrypted using the CKKS scheme and investigate its properties.