Delegating computation: interactive proofs for muggles
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Affine dispersers from subspace polynomials
Proceedings of the forty-first annual ACM symposium on Theory of computing
Short PCPPs verifiable in polylogarithmic time with O(1) queries
Annals of Mathematics and Artificial Intelligence
Sub-linear zero-knowledge argument for correctness of a shuffle
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
Improving exhaustive search implies superpolynomial lower bounds
Proceedings of the forty-second ACM symposium on Theory of computing
Short locally testable codes and proofs: a survey in two parts
Property testing
Short locally testable codes and proofs: a survey in two parts
Property testing
Short locally testable codes and proofs
Studies in complexity and cryptography
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
Verifying computations with streaming interactive proofs
Proceedings of the VLDB Endowment
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Perfectly secure multiparty computation and the computational overhead of cryptography
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
Robust local testability of tensor products of LDPC codes
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Efficient zero-knowledge arguments from two-tiered homomorphic commitments
ASIACRYPT'11 Proceedings of the 17th international conference on The Theory and Application of Cryptology and Information Security
On the power of many one-bit provers
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Resolving the conflict between generality and plausibility in verified computation
Proceedings of the 8th ACM European Conference on Computer Systems
Delegation of computation with verification outsourcing: curious verifiers
Proceedings of the 2013 ACM symposium on Principles of distributed computing
On the concrete efficiency of probabilistically-checkable proofs
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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We show that every language in NP has a probabilistically checkable proof of proximity (i.e., proofs asserting that an instance is "close" to a member of the language), where the verifierýs running time is polylogarithmic in the input size and the length of the probabilistically checkable proof is only polylogarithmically larger that the length of the classical proof. (Such a verifier can only query polylogarithmically many bits of the input instance and the proof. Thus it needs oracle access to the input as well as the proof, and cannot guarantee that the input is in the language 驴 only that it is close to some string in the language.) If the verifier is restricted further in its query complexity and only allowed q queries, then the proof size blows up by a factor of 2^(log n)^c/q where the constant c depends only on the language (and is independent of q). Our results thus give efficient (in the sense of running time) versions of the shortest known PCPs, due to Ben-Sasson et al. (STOC ý04) and Ben-Sasson and Sudan (STOC ý05), respectively. The time complexity of the verifier and the size of the proof were the original emphases in the definition of holographic proofs, due to Babai et al. (STOC ý91), and our work is the first to return to these emphases since their work. Of technical interest in our proof is a new complete problem for NEXP based on constraint satisfaction problems with very low complexity constraints, and techniques to arithmetize such constraints over fields of small characteristic.