Write-only oblivious RAM-based privacy-preserved access of outsourced data

Abstract

Data outsourcing is plagued with several security and privacy concerns. Oblivious RAM (ORAM) can be used to address one of the many concerns, specifically to protect the privacy of data access pattern from outsourced cloud storage. This is achieved by simulating each original read or write operation with some read and write operations on both real and dummy data items. This paper proposes two single-server write-only ORAM schemes and one multi-server scheme, which simulate only the write operations and protect only the write pattern. The reduction in functionality however allows to build much simpler and efficient (in terms of communication/storage cost) ORAMs. Our schemes can achieve constant communication cost with acceptable storage usage. Write-only ORAM can be used in two situations: (i) only the write pattern is considered to contain sensitive information and needs protection. (ii) In outsourced data sharing, ORAM cannot be used to protect read pattern anyway due to access control issues, and Private Information Retrieval (PIR) has to be used instead. In this paper, we also study how to augment ORAM to support the use of PIR in the latter situation.

Appendix: Maximum bucket load in advanced write-only ORAM

Raab and Steger [52] analyzes the maximum load in the standard balls in bins problem under different settings of ball count and bin count. In advanced write-only ORAM, data item distribution can be seen as a variant of the standard problem. Data items and buckets in ORAM are seen as balls and bins, respectively. In the standard problem, N balls are distributed to K bins uniformly at random. From the Theorem 1 in [52], we can know that the maximum number of balls in any bin is higher than $max(2\times N$/$K,2\times \log K)$ with extremely low probability. If $N\ge K\times \log K$, the maximum load in any bin is not more than $2\times N/K$ with extremely high probability. Then we can set a bucket capacity of $B=2\times N$/K data items, and achieve $O(N\times l)$ server-side storage and extremely rare overflows. If a bucket is overflowed, redistributing overflowed data items makes data item distribution different from the distribution in the standard balls in bins problem. However, a bucket capacity of $2\times N$/K is still big enough to make overflow rare after the redistributing. Assume one bucket is overflowed and overflowed data items are distributed to the other buckets randomly. Then, given this assumption, $N^\prime =N-2\times N$/K data items are distributed to the other $K^\prime =K-1$ buckets randomly. This is a standard balls in bins problem, and the maximum number of balls in any bin is higher than $max(2\times N^\prime /K^\prime ,2\times \log K^\prime )$ with extremely low probability. From below, we can see that the bucket capacity of $2\times N$/K is bigger than $max(2\times N^\prime /K^\prime ,2\times \log K^\prime )$.

$$\begin{aligned}&N\times (K-1) > N \times K -2\times N \\&\quad \Rightarrow N\times (K-1) > (N-2\times N{/}K) \times K \\&\quad \Rightarrow N{/}K > (N-2\times N{/}K)/(K-1) \\&\quad \Rightarrow 2\times N{/}K > 2\times N^\prime /K^\prime \\&N\ge K\times \log K \Rightarrow 2\times N{/}K \ge 2\times \log K > 2\\&\quad \times \log (K-1) = 2\times \log K^\prime \end{aligned}$$

Therefore, if one bucket being overflowed and overflowed data items being redistributed (the probability that these events occur is extremely low), the probability of another bucket being overflowed is still extremely low. To sum up, if $N\ge K\times \log K$, we can set a bucket capacity of $B=O(N{/}K)$ data items to achieve $O(N\times l)$ server-side storage and extremely rare overflows.