As a prominent cryptographic tool, geometric searchable encryption (GSE) can be applied in many scenarios, such as location-based services (LBS), social networks and vehicle networks. Unfortunately, most of existing searchable encryption schemes supporting the functionality of geometric range searches suffer from false positives, which will lead people to make a wrong decision and further raise some serious consequences such as financial loss. In addition, some of them are designed under a symmetric system, which is not enough flexible deployed in LBS since in a symmetric system only a private key holder creates ciphertext, whereas in a public-key system anyone who holds a public key can produce ciphertext. In this paper, we intend to design a novel GSE scheme without any false positive under a public-key system supporting arbitrary geometric area searches, which is able to guarantee an accurate query result. Toward this goal, we develop a novel technique in handling the relation betwe
Spatial encryption (SE), which involves encryption and decryption with affine/vector objects, was introduced by Boneh and Hamburg at Asiacrypt 2008. Since its introduction, SE has been shown as a versatile and elegant tool for implementing many other important primitives such as (Hierarchical) Identity-based Encryption ((H)IBE), Broadcast (H)IBE, Attribute-based Encryption, and Forward-secure cryptosystems. This paper revisits SE toward a more compact construction in the lattice setting. In doing that, we introduce a novel primitive called Delegatable Multiple Inner Product Encryption (DMIPE). It is a delegatable generalization of Inner Product Encryption (IPE) but different from the Hierarchical IPE (HIPE) (Okamoto and Takashima at Asiacrypt 2009). We point out that DMIPE and SE are equivalent in the sense that there are security-preserving conversions between them. As a proof of concept, we then successfully instantiate a concrete DMIPE construction relying on the hardness of the dec