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.

As widespread development of biometrics, concerns about security and privacy are rapidly increasing. 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) proposed a new method for secure single matrix multiplication over a ring-LWE-based scheme. In this paper, we generalize Duong et al.’s 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.

With widespread development of biometrics, concerns about security and privacy are rapidly increasing. Homomorphic encryption enables us to operate on encrypted data without decryption, and it can be applied to construct a privacy-preserving biometric system. In this article, we apply two homomorphic encryption schemes based on ideal-lattice and ring-LWE (Learning with Errors), which both have homomorphic correctness over the ring of integers of a cyclotomic field. We compare the two schemes in applying them to privacy-preserving biometrics. In biometrics, the Hamming distance is used as a metric to compare two biometric feature vectors for authentication. We propose an efficient method for secure Hamming distance. Our method can pack a biometric feature vector into a single ciphertext, and it enables efficient computation of secure Hamming distance over our packed ciphertexts.