Fast Secure Matrix Multiplications over Ring-Based Homomorphic Encryption

Secure matrix computation is one of the most fundamental and useful operations for statistical analysis and machine learning with protecting the confidentiality of input data. Secure computation can be achieved by homomorphic encryption, supporting meaningful operations over encrypted data. HElib is a software library that implements the Brakerski-Gentry-Vaikuntanathan (BGV) homomorphic scheme, in which secure matrix-vector multiplication is proposed for operating matrices. Recently, Duong et al. (Tatra Mt. Publ. 2016) proposed a new method for secure single matrix multiplication over a ring-LWE-based scheme. In this paper, we generalize Duong et al.\u27s method for secure multiple matrix multiplications over the BGV scheme. We also implement our method using HElib and show that our method is much faster than the matrix-vector multiplication in HElib for secure matrix multiplications