Checking computations in polylogarithmic time
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
A note on efficient zero-knowledge proofs and arguments (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Nearly-linear size holographic proofs
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Interactive proofs and the hardness of approximating cliques
Journal of the ACM (JACM)
Finite fields
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Probabilistic checking of proofs: a new characterization of NP
Journal of the ACM (JACM)
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
Handbook of Coding Theory
SIAM Journal on Computing
Randomness-efficient low degree tests and short PCPs via epsilon-biased sets
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Computationally efficient error-correcting codes and holographic proofs
Computationally efficient error-correcting codes and holographic proofs
Robust pcps of proximity, shorter pcps and applications to coding
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Short PCPs Verifiable in Polylogarithmic Time
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
Some 3CNF Properties Are Hard to Test
SIAM Journal on Computing
Locally testable codes and PCPs of almost-linear length
Journal of the ACM (JACM)
The PCP theorem by gap amplification
Journal of the ACM (JACM)
Efficient Arguments without Short PCPs
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
Delegating computation: interactive proofs for muggles
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Short PCPs with Polylog Query Complexity
SIAM Journal on Computing
Succinct NP Proofs from an Extractability Assumption
CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
Fast fourier transform algorithms with applications
Fast fourier transform algorithms with applications
Universal Arguments and their Applications
SIAM Journal on Computing
Short PCPPs verifiable in polylogarithmic time with O(1) queries
Annals of Mathematics and Artificial Intelligence
Combinatorial PCPs with Efficient Verifiers
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Two-query PCP with subconstant error
Journal of the ACM (JACM)
Incrementally verifiable computation or proofs of knowledge imply time/space efficiency
TCC'08 Proceedings of the 5th conference on Theory of cryptography
From secrecy to soundness: efficient verification via secure computation
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Non-interactive verifiable computing: outsourcing computation to untrusted workers
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
Improved delegation of computation using fully homomorphic encryption
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Combinatorial PCPs with Short Proofs
CCC '12 Proceedings of the 2012 IEEE Conference on Computational Complexity (CCC)
Taking proof-based verified computation a few steps closer to practicality
Security'12 Proceedings of the 21st USENIX conference on Security symposium
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Recursive composition and bootstrapping for SNARKS and proof-carrying data
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Recursive composition and bootstrapping for SNARKS and proof-carrying data
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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Probabilistically-Checkable Proofs (PCPs) form the algorithmic core that enables fast verification of long computations in many cryptographic constructions. Yet, despite the wonderful asymptotic savings they bring, PCPs are also the infamous computational bottleneck preventing these powerful cryptographic constructions from being used in practice. To address this problem, we present several results about the computational efficiency of PCPs. We construct the first PCP where the prover and verifier time complexities are quasi-optimal (i.e., optimal up to poly-logarithmic factors). The prover and verifier are also higly-parallelizable, and these computational guarantees hold even when proving and verifying the correctness of random-access machine computations. Our construction is explicit and has the requisite properties for being used in the cryptographic applications mentioned above. Next, to better understand the efficiency of our PCP, we propose a new efficiency measure for PCPs (and their major components, locally-testable codes and PCPs of proximity). We define a concrete-efficiency threshold that indicates the smallest problem size beyond which the PCP becomes "useful", in the sense that using it is cheaper than performing naive verification (i.e., rerunning the computation); our definition accounts for both the prover and verifier complexity. We then show that our PCP has a finite concrete-efficiency threshold. That such a PCP exists does not follow from existing works on PCPs with polylogarithmic-time verifiers. As in [Ben-Sasson and Sudan, STOC '05], PCPs of proximity for Reed-Solomon (RS) codes are the main component of our PCP. We construct a PCP of proximity that reduces the concrete-efficiency threshold for testing proximity to RS codes from 2683 in their work to 243, which is tantalizingly close to practicality.