  Private computation, which includes techniques like multi-party computation
and private query execution, holds great promise for enabling organizations to
analyze data they and their partners hold while maintaining data subjects'
privacy. Despite recent interest in communicating about differential privacy,
end users' perspectives on private computation have not previously been
studied. To fill this gap, we conducted 22 semi-structured interviews
investigating users' understanding of, and expectations for, private
computation over data about them. Interviews centered on four concrete
data-analysis scenarios (e.g., ad conversion analysis), each with a variant
that did not use private computation and another that did (private set
intersection, multi-party computation, and privacy preserving query
procedures). While participants struggled with abstract definitions of private
computation, they found the concrete scenarios enlightening and plausible even
though we did not explain the complex cryptographic underpinnings. Private
computation increased participants' acceptance of data sharing, but not
unconditionally; the purpose of data sharing and analysis was the primary
driver of their attitudes. Through collective activities, participants
emphasized the importance of detailing the purpose of a computation and
clarifying that inputs to private computation are not shared across
organizations when describing private computation to end users.
