NodeLeaper: Lower Overhead Oblivious AVL Tree

Abstract

Obliviousness is crypto primitives which intent to hide access pattern. Although ORAM is strongest crypto model, it incurs significant overhead. Elaine Shi et. al. propose Obliviousness Data Structrue (ODS) that makes a great theriotical improvement comparing to general ORAM algorithm, in case of the data blocks exhibit some degree of access predictability. Take AVL tree as an example, when all data blocks are organized as one AVL tree, every nodes (data blocks) contain position information points to both of its child node. As such, the client can immediately obtain the next position to be accessed instead of issuing another ORAM access to the server for a PosMap lookup. Also, the algorithm need extra client space for updating the AVL tree.In this paper, we introduce oblivious AVL tree NodeLeaper, NodeLeaper for short, which enables position information of all child nodes to share part of bits. As such one can store multiple positions for is child and grandson node positions with same block size. In this way, the search can be processed in a leap manner. As a result, NodeLeaper theriotically needs less ORAM accessand client space for node updating than ODS.