An efficient and secure spatial encryption scheme

Spatial encryption was first introduced as an instance of generalized identity-based encryption by Boneh and Hamburg in 2008. Their scheme is only secure in selective model. This paper constructed a full secure and more efficient spatial encryption scheme which differs from Boneh and Hamburg's scheme. The paper introduces a technique to map a vectors to elements of groups. Then it applies the dual system technique. With this technique and the three composite order bilinear groups decision problem, it can prove full security of the scheme in adaptive model. Because of only computing in composite groups without matrix, the efficiency of the scheme is much improved.