An Examination of Multi-Key Fully Homomorphic Encryption and Its Applications

With the rapid development of the Internet of Things (IoT) technology, the security problems it faces are increasingly prominent and have attracted much attention in industry and the academy. Traditional IoT architecture comes with security risks. Illegal intrusion of attackers into the network layer disrupts the availability of data. The untrusted transmission environment increases the difficulty of users sharing private data, and various outsourced computing and application requirements bring the risk of privacy leakage. Multi-key fully homomorphic encryption (MKFHE) realizes operations between ciphertexts under different key encryption and has great application potential. Since 2012, the first MKFHE scheme LTV12 has been extended from fully homomorphic encryption (FHE) and has ignited the enthusiasm of many cryptographic researchers due to its lattice-based security and quantum-resistant properties. According to its corresponding FHE scheme, the MKFHE schemes can be divided into four kinds: Gentry–Sahai–Water (GSW), number theory research unit (NTRU), Brakerski–Gentry–Vaikuntanathan (BGV), and FHE over the tour (TFHE). Efficiency and cost are urgent issues for MKFHE. New schemes are mainly improved versions of existing schemes. The improvements are mostly related to the four parts of MKFHE: security assumption, key generation, plaintext encryption, and ciphertext processing. We classified MKFHE schemes according to the improved partial schemes, and we present some improved techniques and the applications of MKFHE.