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In this paper, the authors investigate the security for integrated Public-Key Encryption (PKE) and Public-key Encryption with Keyword Search (PEKS) schemes. They observe that the security notions for integrated PKE and PEKS schemes considered in the existing literature are not strong enough to capture practical attacks, thus define a new notion named joint CCA-security, which is shown to be stronger than the previous ones. They also propose two simple and efficient constructions of jointly CCA-secure integrated PKE and PEKS schemes from anonymous (hierarchical) identity-based encryption schemes. Besides, they review the consistency for PEKS schemes and improve previous results.
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