Towards an Information Theoretic Analysis of Searchable Encryption

Searchable encryption is a technique that allows a client to store data in encrypted form on a curious server, such that data can be retrieved while leaking a minimal amount of information to the server. Many searchable encryption schemes have been proposed and proved secure in their own computational model. In this paper we propose a generic model for the analysis of searchable encryptions. We then identify the security parameters of searchable encryption schemes and prove information theoretical bounds on the security of the parameters. We argue that perfectly secure searchable encryption schemes cannot be efficient. We classify the seminal schemes in two categories: the schemes that leak information upfront during the storage phase, and schemes that leak some information at every search. This helps designers to choose the right scheme for an application.