Extend the Concept of Public Key Encryption with Delegated Search

We revisit the concept of public key encryption with delegated search (PKEDS), a concept proposed by Ibraimi et al. A PKEDS scheme allows a receiver to authorize a third-party server to search in two ways: either according to a message chosen by the server itself or according to a trapdoor sent by the receiver. We first show some observations on the primitive formulation and the proposed PKEDS scheme by Ibraimi et al. and point out that the single-server setting may limit the application of this primitive. We then extend the concept to the multiple-server setting and present a new security model. We finally propose a new PKEDS scheme, which is proven secure, and compare it with that by Ibraimi et al.