THE LIBRARY OF FULLY HOMOMORPHIC ENCRYPTION OVER THE INTEGERS
Abstract
The article discusses one of the new directions of cryptography, a homomorphic cryptography. Its distinctive feature is that this type of cryptography allows you to process encrypted data without first decrypting it in such a way that the result of operations on encrypted data is equivalent after decryption to the result of operations on open data. The paper describes the main areas of application of homomorphic encryption. The analysis of existing developments in the field of homomorphic encryption is performed. The analysis showed that existing library implementations only allow processing of bits or arrays of bits and do not support the division operation. However, to solve applied problems, support for performing integer operations is necessary. The analysis revealed the need to implement the operation of homomorphic division, as well as the relevance of developing your own implementation of a library of homomorphic encryption over integers. The ability to perform four operations (addition, difference, multiplication and division) on encrypted data will expand the field of application of homomorphic encryption. A method of homomorphic division is proposed, which allows performing the division operation on homomorphically encrypted data. A library architecture of completely homomorphic operations on integers is proposed. The library supports the basic homomorphic operations on integers, as well as the division operation, thanks to the method of homomorphic division. Based on the proposed method of homomorphic division and library architecture, a library of homomorphic operations on integers was implemented. The article also provides measurements of the time required to perform certain operations on encrypted data and analyzes the effectiveness of the developed library implementation. Conclusions and possible ways of further development are given.
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