The Snowden incident illustrates that an adversary may launch an algorithm substitution attack (ASA) by tampering with the algorithms of protocol participants to obtain users’ secret information. A measure against ASA is to equip the protocol participants with cryptographic reverse firewalls (CRF). Public key encryption with keyword search (PEKS) as a cryptographic primitive allows users to search encrypted file in cloud servers while ensuring the security of the original file. The existing CRF constructions for PEKS does not consider the trust level of CRFs, leaving honest-but-curious CRF to deal with trapdoors that should be sent in the secure channels, which brings new security risks. This article first introduces the notion of malleable designated tester public key encryption with keyword search (M-DPEKS). Based on M-DPEKS, we propose the generic construction of public key encryption with keyword search with cryptographic reverse firewalls to overcome the privacy leakage issue in cloud storage. Security proof indicates the generic construction is secure against ASA. Lastly, we instantiate the generic construction with a concrete M-DPEKS scheme and analyze the computation cost and communication overhead to evaluate the efficiency.