Efficient batch identity‐based fully homomorphic encryption scheme in the standard model

Abstract

Identity-based fully homomorphic encryption (IBFHE) provided a fundamental solution to the problem of huge public key size that exposed in fully homomorphic encryption (FHE) schemes, thus it is significant to make FHE become more practical. In recent years, the construction of IBFHE schemes were mainly based on lattices due to their conjectured resistance against quantum cryptanalysis, however, which makes these cryptosystems further unpractical. The main reason is the trapdoor function on which the scheme was based is rather complex for practical and the ciphertext size is too large. In this study, the authors propose an efficient batch IBFHE scheme, which can be proven secure from the standard LWE assumption in the standard model. The first contribution of this work is that the authors construct an efficient batch version of MP12 preimage sampling algorithm, which can efficiently generate identity keys for multi-bit IBE schemes. Based on that, the authors construct an asymptotically-faster multi-bit IBE scheme as the second contribution. The third contribution is that the authors transform the multi-bit IBE scheme to batch IBFHE scheme which supports to encrypt any message in Z q n . Compared with the similar schemes, the authors show their schemes are essentially improved.