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Why “Fiat-Shamir for Proofs” Lacks a Proof

  • Nir Bitansky
  • Dana Dachman-Soled
  • Sanjam Garg
  • Abhishek Jain
  • Yael Tauman Kalai
  • Adriana López-Alt
  • Daniel Wichs
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7785)

Abstract

The Fiat-Shamir heuristic [CRYPTO ’86] is used to convert any 3-message public-coin proof or argument system into a non-interactive argument, by hashing the prover’s first message to select the verifier’s challenge. It is known that this heuristic is sound when the hash function is modeled as a random oracle. On the other hand, the surprising result of Goldwasser and Kalai [FOCS ’03] shows that there exists a computationally sound argument on which the Fiat-Shamir heuristic is never sound, when instantiated with any actual efficient hash function. This leaves us with the following interesting possibility: perhaps we can securely instantiates the Fiat-Shamir heuristic for all 3-message public-coin statistically sound proofs, even if we must fail for some computationally sound arguments. Indeed, this has been conjectured to be the case by Barak, Lindell and Vadhan [FOCS ’03], but we do not have any provably secure instantiation under any “standard assumption”. In this work, we give a broad black-box separation result showing that the security of the Fiat-Shamir heuristic for statistically sound proofs cannot be proved under virtually any standard assumption via a black-box reduction. More precisely:

–If we want to have a “universal” instantiation of the Fiat-Shamir heuristic that works for all 3-message public-coin proofs, then we cannot prove its security via a black-box reduction from any assumption that has the format of a “cryptographic game”.

–For many concrete proof systems, if we want to have a “specific” instantiation of the Fiat-Shamir heuristic for that proof system, then we cannot prove its security via a black box reduction from any “falsifiable assumption” that has the format of a cryptographic game with an efficient challenger.

Keywords

Hash Function Proof System Random Oracle Security Parameter Argument System 
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

© International Association for Cryptologic Research 2013

Authors and Affiliations

  • Nir Bitansky
    • 1
  • Dana Dachman-Soled
    • 2
  • Sanjam Garg
    • 3
  • Abhishek Jain
    • 4
  • Yael Tauman Kalai
    • 2
  • Adriana López-Alt
    • 5
  • Daniel Wichs
    • 6
  1. 1.Tel Aviv UniversityIsrael
  2. 2.Microsoft Research New EnglandUK
  3. 3.UCLAUSA
  4. 4.MIT and BUUSA
  5. 5.NYUUSA
  6. 6.IBM Research, T.J. WatsonUSA

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