In this paper, we present a new method to construct RHIBE that implements history-free updates. Our history-free approach renders the scheme simple and efficient. As a second contribution, we redefine the security model for RHIBE to ensure security against insiders, where adversaries are allowed to obtain all internal system information, e.g., state information. In addition, we also consider the decryption key exposure attack, which was considered by Seo and Emura (2013) [23].
Further, we propose two RHIBE schemes with shorter secret keys and constant size ciphertexts that implement the aforementioned history-free updates approach and security model. For revocation, our constructions use the Complete Subtree (CS) method and the Subset Difference (SD) method. Both schemes are selectively secure in the standard model under the q-weak Bilinear Diffie–Hellman Inversion assumption.