Etoram: A More Efficient ORAM for Secure Computation

When scaling a distributed ORAM to a two-party secure computation, the overhead is dominated by the number of pseudo-random generator (PRG) calls in generation and evaluation of a distributed point function (DPF), which are O(logn) and O(n) respectively, where n is the number of data blocks. We propose a distributed ORAM scheme, in which the PRG calls are reduced to O(log(zn/λ)) for generation and O(2
^log(zn/λ)
) for evaluation, where λ is the secure parameter and z is the length of outputs in DPF. Technically, we first extend the optimization of Function Secret Sharing (FSS), early termination for functions with small output groups, to the context of ORAM for secure computation. Then, we design a scheme named etoram to exploit the high efficiency achieved by early termination. In etoram, we introduce an access counter for each data block. Then, instead of {0,1}
^λ
, the output of the point function becomes the maximum value of these counters, i.e.,{0,1}
^z
. Data blocks are privately updated by masking random strings generated by their counters. In practice, according to different access rates, z ranges from 1 to logn in sequential mode and from 3 to logn in random mode if the total number of accesses is n.