Fully secure constructions of spatial encryption with vector privacy

An encryption scheme is a tuple of algorithms used to ensure secrecy while exchanging messages over a public channel. Spatial encryption is a generalized extension of id-based encryption with the ability of partial order role delegation. In this paper, we propose an efficient spatial encryption with vector privacy preservation, which is derived from the technique of static assumption from dual system encryption in composite order groups. The proposed scheme achieves the cryptosystem properties of message confidentiality, recipient anonymity, adaptively full security, and short constant ciphertext. Provable security in our setting consists of three steps: the first one is giving a rigorous definition of security, the second one is giving the construction of a scheme, and the last one is giving a rigorous mathematical proof showing that the scheme satisfies the security definition given in the first stage. Compared with related schemes, our proposed scheme has a comparable advantage in security while it holds an approximate computing efficiency and communicating payload such as public parameters, private keys, and ciphertexts.