• Corpus ID: 16892153

Incrementally verifiable computation or knowledge implies time/space efficiency

  title={Incrementally verifiable computation or knowledge implies time/space efficiency},
  author={Paul Valiant},
The probabilistically checkable proof (PCP) system enables proofs to be verified in time polylogarithmic in the length of a classical proof. Computationally sound (CS) proofs improve upon PCPs by additionally shortening the length of the transmitted proof to be polylogarithmic in the length of the classical proof. In this thesis we explore the ultimate limits of non-interactive proof systems with respect to time/space efficiency and the new criterion of composability. We deduce the existence of… 



Computationally Sound Proofs

  • S. Micali
  • Computer Science, Mathematics
    SIAM J. Comput.
  • 2000
If a special type of computationally sound proof exists, it is shown that Blum's notion of program checking can be meaningfully broadened so as to prove that $\cal N \cal P$-complete languages are checkable.

Communication-Efficient Non-interactive Proofs of Knowledge with Online Extractors

A superlogarithmic lower bound on the number of hash function evaluations for such online extractable proofs is given, matching the number in the construction, and how to enhance security of the group signature scheme suggested recently by Boneh, Boyen and Shacham with its construction is shown.

The knowledge complexity of interactive proof-systems

A computational complexity theory of the “knowledge” contained in a proof is developed and examples of zero-knowledge proof systems are given for the languages of quadratic residuosity and 'quadratic nonresiduosity.

Probabilistic checking of proofs; a new characterization of NP

  • Sanjeev AroraS. Safra
  • Mathematics, Computer Science
    Proceedings., 33rd Annual Symposium on Foundations of Computer Science
  • 1992
The authors give a new characterization of NP: the class NP contains exactly those languages L for which membership proofs can be verified probabilistically in polynomial time using logarithmic number of random bits and sub-logarital number of queries to the proof.

Linear Zero-Knowledgde. A Note on Efficient Zero-Knowledge Proofs and Arguments

Two protocols based on a Boolean formula Phi containing and- , or- and not-operators which verifies an NP-witness of membership in L have the smallest known asymptotic communication complexity among general proofs or arguments for NP.

Linear zero-knowledge—a note on efficient zero-knowledge proofs and arguments

The protocols presented have the smallest known asymptotic communication complexity among general proofs or arguments for NP, and are also proofs of knowledge of an NP-witness of membership in the language involved.

Proof verification and hardness of approximation problems

The authors improve on their result by showing that NP=PCP(logn, 1), which has the following consequences: (1) MAXSNP-hard problems do not have polynomial time approximation schemes unless P=NP; and (2) for some epsilon >0 the size of the maximal clique in a graph cannot be approximated within a factor of n/sup ePSilon / unless P =NP.

On Deniability in the Common Reference String and Random Oracle Model

  • R. Pass
  • Computer Science, Mathematics
  • 2003
It is shown that there exist a specific natural security property that is not captured by these definitions of zero-knowledge, and the notion of deniable zero- knowledge is formally defined in these models.

Robust pcps of proximity, shorter pcps and applications to coding

The techniques include the introduction of a new variant of PCPs that are called "Robust PCPs", which facilitate proof composition, which is a central ingredient in construction of PCP systems.

Locally testable codes and PCPs of almost-linear length

  • Oded GoldreichM. Sudan
  • Computer Science
    The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings.
  • 2002
It is shown that certain PCP systems can be modified to yield locally testable codes and PCPs of almost-linear length, and novel techniques in use include a random projection of certain codewords and PCP-oracles, an adaptation of PCP constructions to obtain "linear PCP -oracles" for proving conjunctions of linear conditions, and a direct construction of local testable (linear) codes of sub-exponential length.