, Volume 7, Issue 4, pp 357–363

One way functions and pseudorandom generators

  • Leonid A. Levin

DOI: 10.1007/BF02579323

Cite this article as:
Levin, L.A. Combinatorica (1987) 7: 357. doi:10.1007/BF02579323


Pseudorandom generators transform in polynomial time a short random “seed” into a long “pseudorandom” string. This string cannot be random in the classical sense of [6], but testing that requires an unrealistic amount of time (say, exhaustive search for the seed). Such pseudorandom generators were first discovered in [2] assuming that the function (ax modb) is one-way, i.e., easy to compute, but hard to invert on a noticeable fraction of instances. In [12] this assumption was generalized to the existence of any one-way permutation. The permutation requirement is sufficient but still very strong. It is unlikely to be proven necessary, unless something crucial, like P=NP, is discovered. Below, among other observations, a weaker assumption about one-way functions is proposed, which is not only sufficient, but also necessary for the existence of pseudorandom generators.

Copyright information

© Akadémiai Kiadó 1987

Authors and Affiliations

  • Leonid A. Levin
    • 1
  1. 1.Massachusets Institute of TechnologyBoston UniversityUSA