This paper proposes methods for “restricting the message space” of public-key encryption, by allowing a third party to verify whether a given ciphertext does not encrypt some message which is previously specified as a “bad” (or “problematic”) message. Public-key encryption schemes are normally designed not to leak even partial information of encrypted plaintexts, but it would be problematic in some circumstances. This higher level of confidentiality could be abused, as some malicious parties could communicate with each other, or could talk about some illegal topics, using an ordinary public key encryption scheme with help of the public-key infrastructure. It would be undesirable considering the public nature of PKI. The primitive of restrictive public key encryption will help this situation, by allowing a trusted authority to specify a set of “bad” plaintexts, and allowing every third party to detect ciphertexts that encrypts some of the specified “bad” plaintext. The primitive also provides strong confidentiality (of indistinguishability type) of the plaintext when it is not specified as “bad.” In this way, a third party (possible a gateway node of the network) can examine a ciphertext (which comes from the network) includes an allowable content or not, and only when the ciphertext does not contain forbidden message, the gateway transfers the ciphertext to a next node. In this paper, we formalize the above requirements and provide two constructions that satisfied the formalization. The first construction is based on the techniques of Teranishi et al. (IEICE Trans. Fundamentals E92-A, 2009), Boudot (EUROCRYPT 2000), and Nakanishi et al. (IEICE Trans. Fundamentals E93-A, 2010), which are developed in the context of (revocation of) group signature. The other construction is based on the OR-proof technique. The first construction has better performance when very few messages are specified as bad, while the other does when almost all of messages are specified as bad (and only very few messages are allowed to encrypt).