Deterministic and Efficiently Searchable Encryption

We present as-strong-as-possible definitions of privacy, and constructions achieving them,for public-key encryption schemes where the encryption algorithm is deterministic. We obtainas a consequence database encryption methods that permit fast (i.e. sub-linear, and in factlogarithmic, time) search while provably providing privacy that is as strong as possible subjectto this fast search constraint. One of our constructs, called RSA-DOAEP, has the added featureof being length preserving, so that it is the first example of a public-key cipher. We generalizethis to obtain a notion of efficiently-searchable encryption schemes which permit more flexibleprivacy to search-time trade-offs via a technique called bucketization. Our results answer much-asked questions in the database community and provide foundations for work done there.