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Combinatorica

, Volume 7, Issue 4, pp 357–363 | Cite as

One way functions and pseudorandom generators

  • Leonid A. Levin
Article

Abstract

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 (a x 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.

Keywords

Polynomial Time Hamiltonian Cycle Probabilistic Algorithm Pseudorandom Generator Bell System Technical Journal 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Akadémiai Kiadó 1987

Authors and Affiliations

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

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