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Pseudorandom Generators from One-Way Functions: A Simple Construction for Any Hardness

  • Thomas Holenstein
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3876)

Abstract

In a seminal paper, Håstad, Impagliazzo, Levin, and Luby showed that pseudorandom generators exist if and only if one-way functions exist. The construction they propose to obtain a pseudorandom generator from an n-bit one-way function uses \(\mathcal{O}(n^8)\) random bits in the input (which is the most important complexity measure of such a construction). In this work we study how much this can be reduced if the one-way function satisfies a stronger security requirement. For example, we show how to obtain a pseudorandom generator which satisfies a standard notion of security using only \(\mathcal{O}(n^4log^2(n))\) bits of randomness if a one-way function with exponential security is given, i.e., a one-way function for which no polynomial time algorithm has probability higher than 2 − cn in inverting for some constant c.

Using the uniform variant of Impagliazzo’s hard-core lemma given in [7] our constructions and proofs are self-contained within this paper, and as a special case of our main theorem, we give the first explicit description of the most efficient construction from [6].

Keywords

Polynomial Time Algorithm Random String Pseudorandom Generator Pseudorandom Function Evaluable Function 
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

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Thomas Holenstein
    • 1
  1. 1.Department of Computer ScienceETH ZurichZurich

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