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computational complexity

, Volume 19, Issue 2, pp 265–304 | Cite as

Are PCPs Inherent in Efficient Arguments?

  • Guy N. RothblumEmail author
  • Salil Vadhan
Article

Abstract.

Starting with Kilian (STOC ‘92), several works have shown how to use probabilistically checkable proofs (PCPs) and cryptographic primitives such as collision-resistant hashing to construct very efficient argument systems (a.k.a. computationally sound proofs), for example with polylogarithmic communication complexity. Ishai et al. (CCC ‘07) raised the question of whether PCPs are inherent in efficient arguments, and if so, to what extent. We give evidence that they are, by showing how to convert any argument system whose soundness is reducible to the security of some cryptographic primitive into a PCP system whose efficiency is related to that of the argument system and the reduction (under certain complexity assumptions).

Keywords.

Probabilistically checkable proof computationally sound proof argument cryptographic reductions 

Subject classification.

68Q05 

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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  1. 1.Computer Science Department, Center for Computational IntractabilityPrinceton UniversityPrincetonUSA
  2. 2.School of Engineering & Applied Sciences and Center for Research on Computation & SocietyHarvard UniversityCambridgeUSA

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