Library of Fully Homomorphic Encryption on a Microcontroller

Abstract

Fully homomorphic encryption technologies allow you to operate on encrypted data without disclosing it, therefore they have a lot of potential for solving personal data storage and processing issues. Because of the increased interest in these technologies, various software tools and libraries that allow completely homomorphic encryption have emerged. However, because this subject of cryptography is still in its early stages, standards and recommendations for the usage of completely homomorphic encryption algorithms are still being developed. The paper presents the main areas of application of homomorphic encryption. The analysis of existing developments in the field of homomorphic encryption is carried out. The analysis showed that existing library implementations do not support the division and subtraction operation. The analysis revealed the need to develop a library of fully homomorphic encryption, which allows performing all mathematical operations on them (addition, difference, multiplication and division), as well as the relevance of developing its own implementation of a library of homomorphic encryption on integers. Then, implement the development of a fully homomorphic encryption library in C++ and on an ESP 32 microcontroller. The ability to perform four operations (addition, difference, multiplication and division) on encrypted data will expand the scope of application of homomorphic encryption. A method of homomorphic division and subtraction is proposed that allows performing the division and subtraction operation on homomorphically encrypted data. The level of security, the types of operations executed, the maximum length of operands, and the algorithm's running time are all described as a consequence of numerical experimentation with parameters.