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Derandomization in Cryptography

  • Boaz Barak
  • Shien Jin Ong
  • Salil Vadhan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2729)

Abstract

We give two applications of Nisan–Wigderson-type (“non-cryptographic”) pseudorandom generators in cryptography. Specifically, assuming the existence of an appropriate NW-type generator, we construct:

1) A one-message witness-indistinguishable proof system for every language in NP, based on any trapdoor permutation. This proof system does not assume a shared random string or any setup assumption, so it is actually an “NP proof system.”

2) A noninteractive bit commitment scheme based on any one-way function.

The specific NW-type generator we need is a hitting set generator fooling nondeterministic circuits. It is known how to construct such a generator if E = TIME(2 O(n)) has a function of nondeterministic circuit complexity 2Ω(n) (Miltersen and Vinodchandran, FOCS ‘99). Our witness-indistinguishable proofs are obtained by using the NW-type generator to derandomize the ZAPs of Dwork and Naor (FOCS ‘00). To our knowledge, this is the first construction of an NP proof system achieving a secrecy property.

Our commitment scheme is obtained by derandomizing the interactive commitment scheme of Naor (J. Cryptology, 1991). Previous constructions of noninteractive commitment schemes were only known under incomparable assumptions.

Keywords

Proof System Commitment Scheme Pseudorandom Generator Interactive Proof Auxiliary Input 
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 2003

Authors and Affiliations

  • Boaz Barak
    • 1
  • Shien Jin Ong
    • 2
  • Salil Vadhan
    • 3
  1. 1.Weizmann Institute of ScienceRehovotIsrael
  2. 2.Massachusetts Institute of TechnologyCambridge
  3. 3.Harvard UniversityCambridge

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