Evaluation of the Complexity of Fully Homomorphic Encryption Schemes in Implementations of Programs

Dimitar Chakarov, Yavor Papazov

Abstract: This paper shows a thorough examination of fully homomorphic encryption schemes and their performance in programs. We do an extensive analysis of one specific, widely-used scheme -- the Gentry-Sahai-Waters scheme, and its variations -- the libraries TFHE and FHEW. We aim to devise an abstraction level that enables us to assess the real-world speed performance of fully homomorphic operations without actually working with encrypted data. We propose an algorithm that uses the gathered statistical data combined with our mathematical model to evaluate the performance of fully homomorphic implementations of arbitrary computer programs.