Paper 2010/366

Oblivious RAM Revisited

Benny Pinkas and Tzachy Reinman

Abstract

We reinvestigate the oblivious RAM concept introduced by Goldreich and Ostrovsky, which enables a client, that can store locally only a constant amount of data, to store remotely $n$ data items, and access them while hiding the identities of the items which are being accessed. Oblivious RAM is often cited as a powerful tool, which can be used, for example, for search on encrypted data or for preventing cache attacks. However, oblivious RAM it is also commonly considered to be impractical due to its overhead, which is asymptotically efficient but is quite high: each data request is replaced by $O({\log }^{4}n)$ requests, or by $O({\log }^{3}n)$ requests where the constant in the ``$O$'' notation is a few thousands. In addition, $O(n\log n)$ external memory is required in order to store the $n$ data items. We redesign the oblivious RAM protocol using modern tools, namely Cuckoo hashing and a new oblivious sorting algorithm. The resulting protocol uses only $$ external memory, and replaces each data request by only $$ requests (with a small constant). This analysis is validated by experiments that we ran.