Efficient Secure Matrix Multiplication over LWE-Based Homomorphic Encryption

Homomorphic encryption enables various calculations while preserving the data confidentiality. In this paper, we apply the somewhat homomorphic encryption scheme proposed by Brakerski and Vaikuntanathan (CRYPTO 2011) to secure matrix multiplication between two matrices. To reduce both the ciphertext size and the computation cost, we propose a new method to pack a matrix into a single ciphertexts so that it also enables efficient matrix multiplication over the packed ciphertexts. Our packing method generalizes Yasuda et al.'s methods (Security Comm. Networks 2015 and ACISP 2015), which are for secure inner product. We also implement our methods and give a comparison with previous packing methods.