A revocation mechanism in cryptosystems for a large number of users is absolutely necessary to maintain the security of whole systems. A revocable identity-based encryption (RIBE) provides an efficient revocation method in IBE that a trusted authority periodically broadcasts an update key for non-revoked users and a user can decrypt a ciphertext if he is not revoked in the update key. Boldyreva, Goyal, and Kumar (CCS 2008) defined RIBE and proposed an RIBE scheme that uses a tree-based revocation encryption scheme to revoke users. However, this approach has an inherent limitation that the number of private key elements and update key elements cannot be constant. In this paper, to overcome the previous limitation, we devise a new technique for RIBE and propose RIBE schemes with a constant number of private key elements. We achieve the following results:
- We first devise a new technique for RIBE that combines hierarchical IBE (HIBE) scheme and a public-key broadcast encryption (PKBE) scheme by using multilinear maps. In contrast to the previous technique for RIBE, our technique uses a PKBE scheme in bilinear maps for revocation to achieve short private keys and update keys.
- Following our new technique for RIBE, we propose an RIBE scheme in 3-leveled multilinear maps that combines the HIBE scheme of Boneh and Boyen and the PKBE scheme of Boneh, Gentry, and Waters. The private key and update key of our scheme have a constant number of group elements. To prove the security of our scheme, we introduce a new complexity assumption in multilinear maps, and prove its security in the selective revocation list model.
- Next, we propose another RIBE scheme that reduces the number of public parameters by using the parallel construction technique of PKBE. We could reduce the number of public parameters by using the fact that only the trusted authority in RIBE can broadcast an update key.