Enhancement for Secure Multiple Matrix Multiplications over Ring-LWE Homomorphic Encryption

摘要

Homomorphic encryption allows to perform various calculations on encrypted data without decryption. In this paper, we propose an efficient method for secure multiple matrix multiplications over the somewhat homomorphic encryption scheme proposed by Brakerski and Vaikuntanathan. Our method is a generalization of Duong et al.'s method, which computes only one multiplication between two matrices. In order to minimize both the ciphertext size and the computation cost, our method packs every matrix into a single ciphertext so that it enables efficient matrix multiplications over the packed ciphertexts. We also propose several modifications to obtain practical performance of secure multiplications among matrices with larger size and entries. We show implementation results of our packing method with modifications for secure multiplications among two and three matrices with 32 x 32 and 64 x 64 sizes and entries from 16-bit to 64-bit.