Locality Aware Path ORAM: Implementation, Experimentation and Analytical Modeling

Abstract

In this paper, we propose an advanced implementation of Path ORAM to hide the access pattern to outsourced data into the cloud. This implementation takes advantage of eventual data locality and popularity by introducing a small amount of extra storage at the client side. Two replacement strategies are used to manage this extra storage (cache): the Least Recently Used (LRU) and the Least Frequently Used (LFU). Using the same test bed, conducted experiments clearly show the superiority of the advanced implementation compared to the traditional Path ORAM implementation, even for a small cache size and reduced data locality. We then present a mathematical model that provides closed form solutions when data requests follow a Zipf distribution with non-null parameter. This model is showed to have a small and acceptable relative error and is then well validated by the conducted experimental results.

Radix Path: A Reduced Bucket Size ORAM for Secure Cloud Storage

“…Al-Saleh and Belghith [26] proposed an enhanced version of Path ORAM that they called Locality Aware Path ORAM. Their new version is used for outsourced data and takes advantage of any eventual locality and popularity in the data itself.…”

“…The harmonic of degree 2, H n (2) = n i=1 1 i 2 can be readily approximated for very large values of n using equation 9 of [26] where we put α = 2:…”

Practical Suitability and Experimental Assessment of Tree ORAMs

“…However, Path ORAM tries to solve the logarithmic storage complexity of the Tree ORAM by fixing the number of blocks a bucket can hold to a constant number, say [9]. In Path ORAM [9,16,27], each block is mapped to a leaf of the binary tree. This mapping is stored in a leaf map at the client called the position map.…”

“…As such, these studies often overlooked the values of the complexity constants in the Big-O notation that can be very large and therefore greatly affects the overall real performance of an ORAM. Moreover, many of the ORAMs have never been tested with large amounts of data [14][15][16]. Only few studies conducted experimental investigations, even though being limited to some ORAMs, like the work by Chang et al [15].…”

“…In this paper, we investigate the practical performance of the latest and main tree based ORAMs. Using a unified platform, we implemented and compared Path [9], Ring [12], XOR Ring [11,12], and Onion ORAMs [13], while Path ORAM was compared in one experimental study by Chang et al [15] to some earlier ORAMs, to the best of our knowledge, there exists no experimental investigation to later and more advanced ORAMs such as Ring, XOR Ring, and Onion ORAMs, yet there is still a lack of open source implementations of ORAMs [16,17].…”