在Oblivious RAM (ORAM) 系統中，我們使用的是一個可能被竊聽存取行動的雲端儲存空間，而我們必須同時達到兩個目標：在存取時不會導致資料外洩，並且即使被竊聽了資料存取的行動也不會洩漏任何訊息。Path ORAM[Stefanov et al., 2013] 是一種非常容易建立並且儲存效率很高的ORAM，而這篇論文的主要內容便是將Path ORAM 的分析作得更加緊密。此外，我們提出了在Path ORAM 應用的二元樹上讓每個節點上使用不同儲存容量，使得在不影響安全性的前提下縮小了所需的雲端空間容量。最後，我們也以實驗展示了我們的設計成果。

In an oblivious RAM (ORAM) setting, a remote untrusted server is responsible for storing user data. The major goal is to simultaneously (1) keep the data secure from eavesdroppers during read/write accesses and (2) preserve privacy about the access pattern of the data from the untrusted server. Path ORAM [Stefanov et al., 2013] is a protocol, with extremely simple construction and practical eficiency, that achieves the above goal. In this thesis, we revisit the Path ORAM and show how to improve some of the results by tighter analysis. We also propose a variant of Path ORAM that uses non-uniform bucket size, and show that the server space can be reduced while the client storage remains unchanged. Finally, we perform experiments to demonstrate the practicality of our Path ORAM variant.

1 Introduction. . . . . . . . . . . . . . . . .1
1.1 Path ORAM . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Thesis Organisation . . . . . . . . . . . . . . . . . . . 3
2 Tighter Analysis. . . . . . . . . . . . . . . . .4
2.1 1-ORAM . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Tighter Analysis . . . . . . . . . . . . . . . . . . . . 7
3 Storage Improvement. . . . . . . . . . . . . . . . .11
3.1 Modications in Post-Processing Step . . . . . . . . . 11
3.2 Performance Analysis . . . . . . . . . . . . . . . . . . 13
3.2.1 Further Observation . . . . . . . . . . . . . . 14
4 Experiments. . . . . . . . . . . . . . . . .17
4.1 Maximum Stash Usage . . . . . . . . . . . . . . . . . 17
4.2 Maximum Level Load Usage . . . . . . . . . . . . . . 19
4.3 A Practical Path ORAM . . . . . . . . . . . . . . . . 20
5 Conclusion. . . . . . . . . . . . . . . . .22

E. Stefanov, M. van Dijkz, E. Shi, T.-H. H. Chan, C. Fletcher, L. Ren, X. Yu, and S. Devadas. \Path ORAM: An Extremely Simple Oblivious RAM Protocol." In IACR Cryptology ePrint Archive, 2013.
Oded Goldreich and Rafail Ostrovsky In Software protection and simulation on oblivious RAMs.