International Association for Cryptologic Research (IACR)
Doi
Abstract
Oblivious RAM (ORAM) has established itself as a fundamental cryptographic building block.
Understanding which bandwidth overheads are possible under which assumptions has been the topic of a vast amount of previous works.
In this work, we focus on perfectly secure ORAM and we present the first construction with sublinear bandwidth overhead in the worst-case.
All prior constructions with perfect security require linear communication overhead in the worst-case and only achieve sublinear bandwidth overheads in the amortized sense.
We present a fundamentally new approach for construction ORAM and
our results significantly advance our understanding of what is possible with perfect security.
Our main construction, Lookahead ORAM, is perfectly secure, has a worst-case bandwidth overhead of O(n), and a total storage cost of O(n) on the server-side, where n is the maximum number of stored data elements.
In terms of concrete server-side storage costs, our construction has the smallest storage overhead among all perfectly and statistically secure ORAMs and is only a factor 3 worse than the most storage efficient computationally secure ORAM.
Assuming a client-side position map, our construction is the first, among all ORAMs with worst-case sublinear overhead, that allows for a O(1) online bandwidth overhead without server-side computation.
Along the way, we construct a conceptually extremely simple statistically secure ORAM with a worst-case bandwidth overhead of O(nloglognlogn), which may be of independent interest