Cache-oblivious and data-oblivious sorting and applications

Abstract

Although external-memory sorting has been a classi-cal algorithms abstraction and has been heavily studied in the literature, perhaps somewhat surprisingly, when data-obliviousness is a requirement, even very rudimen-tary questions remain open. Prior to our work, it is not even known how to construct a comparison-based, external-memory oblivious sorting algorithm that is op-timal in IO-cost. We make a significant step forward in our under-standing of external-memory, oblivious sorting algo-rithms. Not only do we construct a comparison-based, external-memory oblivious sorting algorithm that is op-timal in IO-cost, our algorithm is also cache-agnostic in that the algorithm need not know the storage hi-erarchy's internal parameters such as the cache and cache-line sizes. Our result immediately implies a cache-agnostic ORAM construction whose asymptotic IO-cost matches the best known cache-aware scheme. Last but not the least, we propose and adopt a new and stronger security notion for external-memory, oblivious algorithms and argue that this new notion is desirable for resisting possible cache-timing attacks. Thus our work also lays a foundation for the study of oblivious algorithms in the cache-agnostic model.