GPU Acceleration of Chinese Remainder Theorem for Fully Homomorphic Encryption

Abstract

Fully Homomorphic encryption (FHE) is an encryption technique capable of performing data operations without decryption operations on encrypted data. With the development of the Internet and AI technology, concerns about personal information have increased. Therefore, the characteristic of being able to operate in the encrypted state of homomorphic Encryption is suitable for application to personal information security technologies. FHE enables data processing while maintaining security between third parties. However, because the calculation time of FHE is very slow, the high computational cost of homomorphic encryption must be addressed before it can be applied to commerce. We focused on multiplication, the slowest, and the main operation of the homomorphic encryption scheme, Cheon, Kim, Kim, and Song (CKKS). In this paper, we accelerate multiplication operations by assigning blocks and threads of GPUs to FHE polynomials. By implementing Chinese remainder theorem (CRT) operations, one of the detailed kernels of multiplication on the GPU, We achieved about 4x the speed improvement over the CPU.