One-Way Trapdoor Permutations Are Sufficient for Non-trivial Single-Server Private Information Retrieval

We show that general one-way trapdoor permutations are sufficient to privately retrieve an entry from a database of size n with total communication complexity strictly less than n. More specifically, we present a protocol in which the user sends O(K) bits and the server sends n− cn K bits (for any constant c), where K is the security parameter of the trapdoor permutations. Thus, for sufficiently large databases (e.g., when K = n for some small 2) our construction breaks the informationtheoretic lower-bound (of at least n bits). This demonstrates the feasibility of basing single-server private information retrieval on general complexity assumptions. An important implication of our result is that we can implement a 1-outof-n Oblivious Transfer protocol with communication complexity strictly less than n based on any one-way trapdoor permutation.