Somewhat homomorphic cryptography for matrix multiplication using GPU acceleration

Abstract

Homomorphic encryption has become a popular research topic since the cloud computing paradigm emerged. This paper discusses the design of a GPU-assisted homomorphic cryptograph for matrix operation. Our proposed scheme is based on an n*n matrix multiplication which are computationally homomorphic. We use more efficient GPU programming scheme with the extension of DGHV homomorphism, which prove the result of verification does not leak any information about the inputs or the output during the encryption and decryption. The performance results are obtained from the executions on a machine equipped with a GeForce GTX 765M GPU. We use three basic parallel algorithms to form efficient solutions which accelerate the speed of encryption and evaluation. Although fully homomorphic encryption is still not practical for real world applications in current stage, this work shows the possibility to improve the performance of homomorphic encryption and achieve this target one step closer.