Private information retrieval (PIR) inherently requires public-key cryptography. A recent line of work suggests that this barrier can be avoided in secret-key PIR, where the client first preprocesses an N-bit database and retains only a short secret key. This line of work has yielded communication O(N^\epsilon) for any constant \epsilon under the Learning Parity with Noise (LPN) assumption in a high-noise regime not known to imply public-key cryptography, and communication O(N^{1/2}) under one-way functions. Whether compression beyond N^{1/2} can be achieved without relying on structured assumptions such as LPN has remained open.

We show that interaction enables polylogarithmic communication in the random oracle model. We construct a secret-key PIR protocol with O(log N ) rounds and polylogarithmic total communication. Alternatively, for any constant \epsilon, we obtain a constant-round protocol with communication O(N^\epsilon). We also obtain protocols with similar communication in
the plain model under the weakest version of LPN, with maximal noise rate 1/2 ? o(1).

Our main idea, inspired by the free-XOR technique for circuit garbling, is to make secret-key preprocessing homomorphic under XOR, while relying on security against related-key attacks.