Efficient amplification of the security of weak pseudo-random function generators

Abstract

We show that given a PRFG (pseudo-random function generator) G which is (Formula Presented) -partially secure, the construction g1 (Formula Presented)produces a strongly secure PRFG, where gi ∈ G and ri are strings of random bits. Thus we present the first “natural” construction of a (totally secure) PRFG from a partially secure PRFG. Using results of Luby and Rackoff, this result also demonstrates how to “naturally” construct a PRPG from partially secure PRPG.