Earticle

In traditional hierarchical identity based cryptosystems (HIBC), non-leaf entities as level PKGs are usually capable of deriving private keys for their descendants with use of their private keys, non-leaf entities can therefore act (decrypt or sign) on the behalf of their arbitrary descendants. This is called key escrow problem of HIBC. In order to resolve key escrow problem, a new technique – Identifier Discrimination is proposed in this paper for composing private keys for entities in hierarchy. With the technique, an identity selective secure HIBE scheme is constructed under Decisional Bilinear Diffie- Helleman (DBDH) assumption in standard security model, in which any identity is incapable of deriving private keys for any of its descendants with use of its private key, and the privilege of generating private keys for each individual descendant is delegated by the root PKG through authorization, that we call Authorization Delegation. Moreover, a new hierarchical identity based signature (HIBS) scheme is constructed from our HIBE construction, by applying Naor transformation of an identity-based signature (IBS) out of an IBE. Because of the inability of deriving its descendants’ private keys with use its private key, an entity therefore cannot sign messages on behalf of any of its descendants, thus guaranteeing that authenticity and non-repudiation properties are achieved in our HIBS system.

The main challenge at present in constructing hierarchical identity-based encryption (HIBE) is to solve the trade-off between private-key size and ciphertext size. At least one private-key size or ciphertext size in the existing schemes must rely on the hierarchy depth. In this letter, a new hierarchical computing technique is introduced to HIBE. Unlike others, the proposed scheme, which consists of only two group elements, achieves constant-size private keys. In addition, the ciphertext consists of just three group elements, regardless of the hierarchy depth. To the best of our knowledge, it is the first efficient scheme where both ciphertexts and private keys achieve O(1)-size, which is the best trade-off between private-key size and ciphertext size at present. We also give the security proof in the selective-identity model.