Abstract: In designated verifier searchable public key encryption (dPEKS) schemes, the IND-KGA-SERVER security was proposed to formalize the security against the server. Based on the IND-KGA secure dPEKS, the CA (certificate authority), and the strongly unforgeable and undeniable signature, the solution was proposed to show how to construct dPEKS schemes which are secure against KG (keyword guessing) attacks when the attacker is the server. The solution is a bootstrap from IND-KGA secure to IND-KGA-SERVER secure.