Spatial Encryption Revisited: From Delegatable Multiple Inner Product Encryption and More

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 decisional learning with errors problem. In turn, the DMIPE design implies a more compact lattice-based SE in terms of sizes compared with SEs converted from HIPE (e.g., Xagawa’s HIPE at PKC 2013) using the framework by Chen et al. (Designs, Codes, and Cryptography, 2014). Furthermore, we demonstrate that one can also use SE to implement the Allow-/Deny-list encryption, which subsumes, e.g., puncturable encryption (Green and Miers at IEEE S &P 2015).