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Short PCPPs verifiable in polylogarithmic time with O(1) queries

Author:

Thilo MieAuthors Info & Claims

Annals of Mathematics and Artificial Intelligence, Volume 56, Issue 3-4

Pages 313 - 338

https://doi.org/10.1007/s10472-009-9169-y

Published: 01 August 2009 Publication History

Abstract

In this paper we show for every pair language $L\subseteq \{0,1\}^*\times\{0,1\}^*$ in ${\ensuremath{\mathsf{NTIME}}}(T)$ for some non-decreasing function $T:{{\mathbb Z}}^+\rightarrow {{\mathbb Z}}^+$ there is a ${\ensuremath{\mathsf{PCPP}}}$ -verifier such that the following holds. In time poly (| x |,log| y |,log T (| x | + | y |)) it decides the membership of a purported word ( x , y ) by reading the explicit input x entirely and querying the implicit input y and the auxiliary proof of length T (| x | + | y |)·poly log T(|x| + |y|) in a constant number of positions.

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Freitag CPaneth OPass R(2024)Public-Coin, Complexity-Preserving, Succinct Arguments of Knowledge for NP from Collision-ResistanceAdvances in Cryptology – EUROCRYPT 202410.1007/978-3-031-58737-5_5(112-141)Online publication date: 26-May-2024
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Augot DBordage SNardi J(2023)Efficient multivariate low-degree tests via interactive oracle proofs of proximity for polynomial codesDesigns, Codes and Cryptography10.1007/s10623-022-01134-z91:3(1111-1151)Online publication date: 1-Mar-2023
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Short PCPPs verifiable in polylogarithmic time with O(1) queries
1. Theory of computation
  1. Design and analysis of algorithms

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cover image Annals of Mathematics and Artificial Intelligence

Annals of Mathematics and Artificial Intelligence Volume 56, Issue 3-4

August 2009

146 pages

ISSN:1012-2443

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Copyright © Copyright © 2010 Springer Science+Business Media B.V.

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Kluwer Academic Publishers

United States

Publication History

Published: 01 August 2009

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Cited By

Ron-Zewi NRothblum R(2024)Local Proofs Approaching the Witness LengthJournal of the ACM10.1145/366148371:3(1-42)Online publication date: 25-Apr-2024
https://dl.acm.org/doi/10.1145/3661483
Freitag CPaneth OPass R(2024)Public-Coin, Complexity-Preserving, Succinct Arguments of Knowledge for NP from Collision-ResistanceAdvances in Cryptology – EUROCRYPT 202410.1007/978-3-031-58737-5_5(112-141)Online publication date: 26-May-2024
https://dl.acm.org/doi/10.1007/978-3-031-58737-5_5
Augot DBordage SNardi J(2023)Efficient multivariate low-degree tests via interactive oracle proofs of proximity for polynomial codesDesigns, Codes and Cryptography10.1007/s10623-022-01134-z91:3(1111-1151)Online publication date: 1-Mar-2023
https://dl.acm.org/doi/10.1007/s10623-022-01134-z
Bordage SLhotel MNardi JRandriam H(2022)Interactive oracle proofs of proximity to algebraic geometry codesProceedings of the 37th Computational Complexity Conference10.4230/LIPIcs.CCC.2022.30(1-45)Online publication date: 20-Jul-2022
https://dl.acm.org/doi/10.4230/LIPIcs.CCC.2022.30
Xie TZhang YSong D(2022)Orion: Zero Knowledge Proof with Linear Prover TimeAdvances in Cryptology – CRYPTO 202210.1007/978-3-031-15985-5_11(299-328)Online publication date: 15-Aug-2022
https://dl.acm.org/doi/10.1007/978-3-031-15985-5_11
Bootle JChiesa ALiu S(2022)Zero-Knowledge IOPs with Linear-Time Prover and Polylogarithmic-Time VerifierAdvances in Cryptology – EUROCRYPT 202210.1007/978-3-031-07085-3_10(275-304)Online publication date: 30-May-2022
https://dl.acm.org/doi/10.1007/978-3-031-07085-3_10
Chiesa AZhu Z(2019)Shorter arithmetization of nondeterministic computationsTheoretical Computer Science10.1016/j.tcs.2015.07.030600:C(107-131)Online publication date: 6-Jan-2019
https://dl.acm.org/doi/10.1016/j.tcs.2015.07.030
Ben-Sasson EChiesa AGoldberg LGur TRiabzev MSpooner N(2019)Linear-Size Constant-Query IOPs for Delegating ComputationTheory of Cryptography10.1007/978-3-030-36033-7_19(494-521)Online publication date: 1-Dec-2019
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Santhanam RWilliams R(2018)On Uniformity and Circuit Lower BoundsComputational Complexity10.1007/s00037-014-0087-y23:2(177-205)Online publication date: 26-Dec-2018
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Ben-Sasson EKaplan YKopparty SMeir OStichtenoth H(2016)Constant Rate PCPs for Circuit-SAT with Sublinear Query ComplexityJournal of the ACM10.1145/290129463:4(1-57)Online publication date: 8-Nov-2016
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