* How is it possible to construct all the previous "search tokens" on the server side?

* The client stores does a lot of work (storing a map of all keys, for one). Could the client get away with ONLY generating a new search token when a document is updated/inserted? That is, could the client only be responsible for creating "UTc+1 ← H1(Kw, STc+1)" and "e ← ind ⊕ H2(Kw, STc+1)" (in the update portion of "Algorithm 1")? In other words, could the map W be stored on the server, as well?

Hope these questions make sense!