Abstract: We build the first sub-linear (in fact, potentially constant-time) public-key searchable encryption system: − server can publish a public key PK. − anybody can build an encrypted index for document D under PK. − client holding the index can obtain a token zw from the server to check if a keyword w belongs to D. − search using zw is almost as fast (e.g., sub-linear) as the non-private search. − server granting the token does not learn anything about the document D, beyond the keyword w. − yet, the token zw is specific to the pair (D,w): the client does not learn if other keywords w′≠w belong to D, or if w belongs to other, freshly indexed documents D′. − server cannot fool the client by giving a wrong token zw. We call such a primitive Encapsulated Search Index (ESI). Our ESI scheme can be made (t,n)- distributed among n servers in the best possible way: non-interactive, verifiable, and resilient to any coalition of up to (t−1) malicious servers. We also introduce the notion of delegatable ESI and show how to extend our construction to this setting. Our solution — including public indexing, sub-linear search, delegation, and distributed token generation — is deployed as a commercial application by Atakama.