Revocable hierarchical identity-based encryption with adaptive security

Hierarchical identity-based encryption (HIBE) can be extended to revocable HIBE (RHIBE) if a private key of a user can be revoked when the private key is revealed or expired. Previously, many selectively secure RHIBE schemes were proposed, but it is still unsolved problem to construct an adaptively secure RHIBE scheme. In this work, we propose two RHIBE schemes in composite-order bilinear groups and prove their adaptive security under simple static assumptions. To prove the adaptive security, we use the dual system encryption framework, but it is not simple to use the dual system encryption framework in RHIBE since the security model of RHIBE is quite different with that of HIBE. We show that it is possible to solve the problem of the RHIBE security proof by carefully designing hybrid games. © 2021 The Author(s)