Identity-based leveled fully homomorphic encryption over ideal lattices

This paper proposes an efficient identity-based leveled fully homomorphic encryption (IBFHE) scheme over ideal lattice. First, we achieve an identity-based encryption (IBE) scheme in dual-LWE cryptosystem. Then, we take advantage of the eigenvector method to compile the IBE scheme into an IBFHE scheme. Compared with the previous scheme, our scheme is of shorter key size, smaller storage, and higher efficiency, owing to a new trapdoor generation function and algebraic structure of ideal lattice. The security analysis shows that our scheme is selective-identity secure against chosen-plaintext attacks in the standard model.