Circuit ORAM: On Tightness of the Goldreich-Ostrovsky Lower Bound

We propose a new tree-based ORAM scheme called Circuit ORAM. Circuit ORAM makes both theoretical and practical contributions. From a theoretical perspective, Circuit ORAM shows that the well-known Goldreich-Ostrovsky logarithmic ORAM lower bound is tight under certain parameter ranges, for several performance metrics. Therefore, we are the first to give an answer to a theoretical challenge that remained open for the past twenty-seven years. Second, Circuit ORAM earns its name because it achieves (almost) optimal circuit size both in theory and in practice for realistic choices of block sizes. We demonstrate compelling practical performance and show that Circuit ORAM is an ideal candidate for secure multi-party computation applications.