How to Construct Random Functions

Abstract

We assume that functions that are one-way in a very weak sense exist. We prove that in probabilitic polynomial time it is possible to construct deterministic polynomial time computable functions g:{1,…,2^k} -> {1,…,2^k} that cannot be distinguished by an probabilistic polynomial time algorithm from a random function. Loosely speaking, g provides random access to a K2^k -bit long pad whose entries record the outcome of independent coin flips. This complexity theoretic result has many important applications in Cryptography, Protocols, and Hashing.