Analysis on Matrix GSW-FHE and Optimizing Bootstrapping

With the rapid development of multimedia technologies, the multimedia data storage and outsource computation are delegated to the untrusted cloud, which has led to a series of challenging security and privacy threats. Fully homomorphic encryption can be used to protect the privacy of cloud data and solve the trust problem of third party. In this paper, we analyse circular security of matrix GSW-FHE scheme. We derive a sufficient condition of circular security for matrix GSW-FHE scheme. It allows us to choose a good secret key via “reject sample” technique and furthermore obtain circular secure matrix GSW-FHE scheme. We also give an extended version of matrix GSW-FHE by defining deterministic asymmetric encryption algorithm and propose hybrid homomorphic plaintext slot-wise switching method, which significantly reduces computation and storage complexity of bootstrapping key generation, thus optimizing the bootstrapping procedure.