SIAM J. COMPUT.
Vol. 22, no 6,pp. 1163-1175, December 1993
ON THE EXISTENCE OF PSEUDORANDOM GENERATORS
ODED GOLDREICH , HUGO KRAWCZYK , AND MICHAEL LUBY
Abstract. Pseudorandom generators ( suggested and developed by blum and micali
and yao ) are efficient deterministic programs that expand a randomly selected k-bit
seed into a much longer pseudorandom bit sequence that is indistinguishable in
polynomial time from an (equally long ) sequence of unbiased coin tosses. A
fundamental question is to find simple conditions, as the existence of one-way
functions, which suffice for constructing pseudorandom generators.
This paper consider regular functions, in which every image of a k-bit string has the
same number of preimages of length k. This paper shows how to construct
pseudorandom generators from any regular one-way function.
Key words. Pseudorandom generators, one-way functions, cryptography,
randomness, complexity theory.