2-Server PIR with sub-polynomial communication

by Zeev Dvir and Sivakanth Gopi

Oded's comments

This is a fantastic result and I am posting it before reading the proof. It presents a 2-server PIR with communication complexity $n^{o(1)}$, improving over the two-decades old 2-server PIR of communication complexity $n^{1/3}$. Specifically, the communication complexity is $n^{\epsilon(n)}$, where $\epsilon(n)=(\log n)^{-(0.5-o(1))}$.

The original abstract

A 2-server Private Information Retrieval (PIR) scheme allows a user to retrieve the $i$th bit of an $n$-bit database replicated among two servers (which do not communicate) while not revealing any information about $i$ to either server. In this work we construct a 1-round 2-server PIR with total communication cost $n^{O({\sqrt{\log\log n/\log n}})}$. This improves over the currently known 2-server protocols which require $O(n^{1/3})$ communication and matches the communication cost of known 3-server PIR schemes. Our improvement comes from reducing the number of servers in existing protocols, based on Matching Vector Codes, from 3 or 4 servers to 2. This is achieved by viewing these protocols in an algebraic way (using polynomial interpolation) and extending them using partial derivatives.

See ECCC TR14-094.

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