There were a bunch of CS theses starting in the late 90s along those lines, some of the general labels used were 'trustless computing' and 'fog computing' or something similar. Other keywords are 'enclave' and 'opaque'. David Brin also promoted 'translucent databases' as a way to allow computations on aggregate data without the possibility of revealing individual rows. Intel has a related technology platform called SGX (Software Guard Extensions) in this space that is aimed at being able to run your own trusted code on infra owned and operated by potentially malicious providers.
On the activist front, Doc Searls has been pushing a marketing/commerce twist on the idea of user-owned and controlled data under the labels 'Project VRM' (Vendor Relationship Management) and 'The Intention Economy' but without much traction.