A Geometric Approach to Information-Theoretic Private Information Retrieval

A t-private private information retrieval (PIR) scheme allows a user to retrieve the ith bit of an n-bit string x replicated among k servers, while any coalition of up to t servers learns no information about i. We present a new geometric approach to PIR, and obtain • A t-private k-server protocol with communication O k2 t log k n1/ (2k−1)/t , removing the k t term of previous schemes. This answers an open question of [14]. • A 2-server protocol with O(n1/3 ) communication, polynomial preprocessing, and online work O(n/ logr n) for any constant r. This improves the O(n/ log2 n) work of [8]. • Smaller communication for instance hiding [3, 14], PIR with a polylogarithmic number of servers, robust PIR [9], and PIR with fixed answer sizes [4]. To illustrate the power of our approach, we also give alternative, geometric proofs of some of the best 1-private upper bounds from [7].

• Type: Conference
• Year: 2005
• Where: COCO
• Authors: David P. Woodruff, Sergey Yekhanin
• Keywords: COCO 2005, N-bit String, T-private K-server Protocol, T-private Private Information