Single Database Private Information Retrieval with Logarithmic Communication

We study the problem of single database private information retrieval, and present a solution with only logarithmic server-side communication complexity and a solution with only logarithmic user-side communication complexity. Previously the best result could only achieve polylogarithmic communication on each side, and was based on certain less well-studied assumptions in number theory [6]. On the contrary, our schemes are based on Paillier’s cryptosystem [16], which along with its variants have drawn extensive studies in recent cryptographic researches [3, 4, 8, 9], and have many important applications [7, 8].In fact, our schemes directly yield implementations for 1-out-of-N ℓ-bit string oblivious transfer with O(ℓ) sender-side communication (against semi-honest receivers and malicious senders). Note the sender-side communication complexity is independent of N, the constant hidden in the big-O notation is quite small, and ℓ is unrestricted. Moreover, we show a way to do communication balancing between the sender-side and the receiver-side, and show how to handle malicious receivers with small communication overheads.