Efficient Privacy-Preserving Matrix Factorization for Recommendation via Fully Homomorphic Encryption

There are recommendation systems everywhere in our daily life. The collection of personal data of users by a recommender in the system may cause serious privacy issues. In this article, we propose the first privacy-preserving matrix factorization for recommendation using fully homomorphic encryption. Our protocol performs matrix factorization over encrypted users' rating data and returns encrypted outputs so that the recommendation system learns nothing on rating values and resulting user/item profiles. Furthermore, the protocol provides a privacy-preserving method to optimize the tuning parameters that can be a business benefit for the recommendation service providers. To overcome the performance degradation caused by the use of fully homomorphic encryption, we introduce a novel data structure to perform computations over encrypted vectors, which are essential for matrix factorization, through secure two-party computation in part. Our experiments demonstrate the efficiency of our protocol.