Abstract
We efficiently combine unpredictability and verifiability by extending the Goldreich-Goldwasser-Micali construction of pseudorandom functions fs from a secret seed s, so that knowledge of s not only enables one to evaluate fs at any point x, but also to provide an NP-proof that the value fs(x) is indeed correct without compromising the unpredictability of fs at any other point for which no such a proof was provided.