Oblivious Parallel RAM (OPRAM) enables multiple clients to synchronously make read and write accesses to shared memory (more generally, any data-store) whilst hiding the access patterns from the owner/provider of that shared memory. Prior work is best suited to the setting of multiple processors (or cores) within a single client device, and consequently there are shortcomings when applying that work to the multi-client setting where distinct client devices may not trust each other, or may simply wish to minimise - for legal reasons or otherwise - the volume of data that is leaked to other client devices. In prior constructions, obliviousness from the storage provider is achieved by passing accesses between the clients in one or more sorting networks, both before and after the logical access is made to the shared memory: this process inherently leaks the contents of the accesses to those other clients. In this paper we address this issue by introducing the notion of client obliviousness for OPRAM, which asks that clients should only learn as much as is necessary for the scheme to function correctly. We provide an instantiation using established tools, with careful analysis to show that our new notion and regular OPRAM security are met. In the process, we give new insight into the use of the OPRAM model in the context of outsourced storage.
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