Random-Index Oblivious RAM.

We study the notion of Random-index ORAM (RORAM), which is a weak form of ORAM where the Client is limited to asking for (and possibly modifying) random elements of the N-items memory, rather than specific ones. That is, whenever the client issues a request, it gets in return a pair (r, x(r)) where r is an element of (R) [N] is a random index and xr is the content of the r-th memory item. Then, the client can also modify the content to some new value x'(r). We first argue that the limited functionality of RORAM still suffices for certain applications. These include various applications of sampling (or sub-sampling) and, in particular, the very-large-scale MPC application in the setting of Benhamouda et al. [2]. Clearly, RORAM can be implemented using any ORAM scheme (by the Client selecting the random r's by itself), but the hope is that the limited functionality of RORAM can make it faster and easier to implement than ORAM. Indeed, our main contributions are several RORAM schemes (both of the hierarchical-type and the tree-type) of lighter complexity than that of ORAM.