Synthesizers and their application to the parallel construction of pseudo-random functions

  • Authors:
  • M. Naor;O. Reingold

  • Affiliations:
  • -;-

  • Venue:
  • FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
  • Year:
  • 1995

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Abstract

We present a new cryptographic primitive called pseudo-random synthesizer and show how to use it in order to get a parallel construction of a pseudo-random function. We show an NC/sup 1/ implementation of pseudo-random synthesizers based on the RSA or the Diffie-Hellman assumptions. This yields the first parallel (NC/sup 2/) pseudo-random function and the only alternative to the original construction of Goldreich, Gold-wasser and Micali (GGM). The security of our constructions is similar to the security of the underling assumptions. We discuss the connection with problems in computational learning theory.