Homomorphic Properties Within Lattice-Based Encryption Systems

Homomorphic encryption allows users to perform mathematical operations on open data in encrypted form by performing homomorphically appropriate operations on encrypted data without knowing the decryption function (key). Nowadays such possibilities for cryptoalgorithm are very important in many areas such as data storage, cloud computing, cryptocurrency, and mush more. In 2009 a system of fully homomorphic encryption was constructed, in the future, many works were done based on it. In this work, is performed the implementation of ideal lattices for constructing homomorphic operations over ciphertexts. The idea, presented in this work, allows to separate relations between homomorphic and security parts of a lattice-based homomorphic encryption system.