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.

如果在私钥泄露或过期时可以撤销用户的私钥，则基于分层身份的加密 (HIBE) 可以扩展为可撤销的 HIBE (RHIBE)。此前，人们提出了许多选择性安全的 RHIBE 方案，但构建自适应安全的 RHIBE 方案仍然是一个悬而未决的问题。在这项工作中，我们在复合阶双线性群中提出了两个 RHIBE 方案，并在简单的静态假设下证明了它们的自适应安全性。为了证明自适应安全性，我们使用了双系统加密框架，但是在RHIBE中使用双系统加密框架并不简单，因为RHIBE的安全模型与HIBE的安全模型有很大的不同。我们表明通过精心设计混合游戏可以解决 RHIBE 安全证明的问题。