Identity-Based Hierarchical Key-Insulated Encryption Without Random Oracles

Key-insulated encryption is one of the effective solutions to a key exposure problem. Recently, identity-based encryption (IBE) has been used as one of fundamental cryptographic primitives in a wide range of various applications, and it is considered that the identity-based key-insulated security has a huge influence on the resulting applications. At Asiacrypt'05, Hanaoka et al. proposed an identity-based hierarchical key-insulated encryption (hierarchical IKE) scheme. Although their scheme is secure in the random oracle model, it has a "hierarchical key-updating structure," which is attractive functionality that enhances key exposure resistance. In this paper, we first propose the hierarchical IKE scheme without random oracles. Our hierarchical IKE scheme is secure under the symmetric external Diffie-Hellman (SXDH) assumption, which is known as the simple and static one. Furthermore, when the hierarchy depth is one (i.e. not hierarchical case), our scheme is the first IKE scheme that achieves constant-size parameters including public parameters, secret keys, and ciphertexts.