CRT representation of LWE Based TFHE

Abstract Homomorphic encryption is a special type of encryption that allows you to perform homomorphic operations on encrypted data without decryption, ensuring data security. This is the most important system that needs to be developed for customer and/or patient privacy on behalf of all sectors using a cloud system. In addition, with the increase in the use of IoT systems, one of the biggest problems in these areas is data protection and privacy. Although homomorphic encryption is solution to these problems, using homomorphic encryption schemes is quite costly and slow. Therefore, studies aimed at developing and improving homomorphic schemes are of great importance. But the creation of encryption schemes has remained theoretical due to the cost and computational size of these schemes. For this reason, many studies are being carried out in order to speed up encryption schemes and reduce costs. In this article, we plan to contribute to homomorphic encryption by applying the Chinese remainder theorem (CRT) to the torus fully homomorphic encryption (TFHE) scheme, which has recently achieved a major breakthrough. CRT is used to apply residue number system (RNS) which accelerates schemes to the TFHE scheme. By applying CRT to the scheme, we have achieved an acceleration of about 30% in the encryption and decryption times of the scheme.