Development Paillier's library of fully homomorphic encryption

Abstract

One of the new areas of cryptography considered-homomorphic cryptography. The article presents the main areas of application of homomorphic encryption. An analysis of existing developments in the field of homomorphic encryption carried out. The analysis showed that existing library implementations only allow processing bits or arrays of bits and do not support division and subtraction operations. However, to solve applied problems, support for performing integer operations are necessary. Because of the analysis, the need to implement the homomorphic division and subtraction operations identified, as well as the relevance of developing our own implementation of a homomorphic encryption library over integers. The ability to perform four operations (addition, difference, multiplication and division) on encrypted data will expand the areas of application of homomorphic encryption. A homomorphic division and subtraction methods proposed that allows the division operation performed on homomorphically encrypted data. An architecture for a library of fully homomorphic operations on integers is proposed. The library supports basic homomorphic operations on integers, as well as homomorphic division method. The article also provides measurements of the time required to perform certain operations on encrypted data and analyzes the efficiency of the developed implementation of the library.