Multi-key Searchable Encryption without Random Oracle

Multi-Key Searchable Encryption (MKSE) is a new application scenario of searchable encryption, in which any user can search over all encrypted documents stored in untrusted server by submitting only one trapdoor. Firstly, we describe a general model of multi-key searchable encryption and introduce its system model and attack model. Secondly, we define its formulized model and the corresponding security with no ideal Hash function required. Furthermore, we construct a feasible and efficient MKSE scheme without random oracle. Security analysis shows that our scheme is secure.