Lattice-based revocable (hierarchical) IBE with decryption key exposure resistance

Abstract

Revocable identity-based encryption (RIBE) is an extension of IBE that supports a key revocation mechanism, which is an indispensable feature for practical cryptographic schemes. Due to this extra feature, RIBE is often required to satisfy a strong security notion unique to the revocation setting called decryption key exposure resistance (DKER). Additionally, hierarchal IBE (HIBE) is another orthogonal extension of IBE that supports key delegation functionalities allowing for scalable deployments of cryptographic schemes. So far, R(H)IBE constructions with DKER are only known from bilinear maps, where all constructions rely heavily on the so-called key re-randomization property to achieve the DKER and/or hierarchal feature. Since lattice-based schemes seem to be inherently ill-fit with the key re-randomization property, no construction of lattice-based R(H)IBE schemes with DKER are known.In this paper, we propose the first lattice-based RHIBE scheme with DKER without relying on the key re-randomization property, departing from all the previously known methods. We start our work by providing a generic construction of RIBE schemes with DKER, which uses as building blocks any two-level standard HIBE scheme and (weak) RIBE scheme without DKER. Based on previous lattice-based RIBE constructions without DKER, our result implies the first lattice-based RIBE scheme with DKER. Then, building on top of our generic construction, we construct the first lattice-based RHIBE scheme with DKER, by further exploiting the algebraic structure of lattices. To this end, we prepare a new tool called the level conversion keys, which enables us to achieve the hierarchal feature without relying on the key re-randomization property. In this full version, we give the formal proofs of our proposed schemes.