Survey software implementations of homomorphic encryption methods

Abstract

Homomorphic Encryption (HE) is a perspective form of encryption that allows computing on encrypted data. Potential applications include combining sensitive encrypted data in a cloud environment and performing calculations on it in the cloud without compromising data privacy. Due to the active interest in this area, many new schemes of Fully Homomorphic Encryption are being developed. We implement two optimized versions of HE: the Brakersky-Fan-Vercauteren (BFV) and Cheon-Kim-Kim-Song (CKKS) schemes, and evaluate their performance. The most interesting (and also unexpected result of our performance assessment) is that the CKKS variant in practice scales significantly better (usually several times) with an increase in the multiplicative depth of the computational schemes than the BFV, implying that the CKKS variant will always surpass the BFV for most practical applications. The unexpected result was that the decoding and KeyGen functions for 128-bit security settings show the superiority of the BFV scheme, however, if we consider the whole process of encryption, decryption and operation above ciphertexts, CKKS performance exceeds BFV by more than 100 times, which gives a reliable result of our research