Recently, use of cloud computing has expanded to include tasks such as data sharing among multiple enterprises for open innovations and IoT systems for device management, etc. Public-key searchable encryption is particularly useful for cases requiring protection of shared secret data. However, there is no public-key searchable encryption scheme that simultaneously achieves: (A) efficient search performance, (B) multiuser support and (C) implementation on database management systems, simultaneously. In this paper, we propose a new public-key searchable encryption scheme which (A) provides an index generation mechanism for public-key searchable encryption, and (B) generates different secret keys for multiple users. In our scheme, (A) is achieved by a portion of the deterministic values generated from a keyword, and (B) is achieved by hierarchical inner-product predicate encryption. Our scheme in particular, forms wildcards as the user identity from hierarchical inner-product predicate encryption in order to easily represent hierarchical identities. To achieve (C), we further propose an integration method which implements our scheme into database management systems through a user-defined function so that its search functionality can be easily used via SQL.