A Toolbox for Barriers on Interactive Oracle Proofs

Gal Arnon; Amey Bhangale; Alessandro Chiesa; Eylon Yogev

doi:10.1007/978-3-031-22318-1_16

A Toolbox for Barriers on Interactive Oracle Proofs

Gal Arnon, Amey Bhangale, Alessandro Chiesa, Eylon Yogev

Department of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

Interactive oracle proofs (IOPs) are a proof system model that combines features of interactive proofs (IPs) and probabilistically checkable proofs (PCPs). IOPs have prominent applications in complexity theory and cryptography, most notably to constructing succinct arguments. In this work, we study the limitations of IOPs, as well as their relation to those of PCPs. We present a versatile toolbox of IOP-to-IOP transformations containing tools for: (i) length and round reduction; (ii) improving completeness; and (iii) derandomization. We use this toolbox to establish several barriers for IOPs: Low-error IOPs can be transformed into low-error PCPs. In other words, interaction can be used to construct low-error PCPs; alternatively, low-error IOPs are as hard to construct as low-error PCPs. This relates IOPs to PCPs in the regime of the sliding scale conjecture for inverse-polynomial soundness error.Limitations of quasilinear-size IOPs for 3SAT with small soundness error.Limitations of IOPs where query complexity is much smaller than round complexity.Limitations of binary-alphabet constant-query IOPs. We believe that our toolbox will prove useful to establish additional barriers beyond our work.

Original language	English
Title of host publication	Theory of Cryptography - 20th International Conference, TCC 2022, Proceedings
Editors	Eike Kiltz, Vinod Vaikuntanathan
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	447-466
Number of pages	20
ISBN (Print)	9783031223174
DOIs	https://doi.org/10.1007/978-3-031-22318-1_16
State	Published - 2022
Event	20th Theory of Cryptography Conference, TCC 2022 - Chicago, United States Duration: 7 Nov 2022 → 10 Nov 2022

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	13747 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	20th Theory of Cryptography Conference, TCC 2022
Country/Territory	United States
City	Chicago
Period	7/11/22 → 10/11/22

Bibliographical note

Publisher Copyright:
© 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Keywords

Interactive oracle proofs
Lower bounds
Probabilistically checkable proofs

Access to Document

10.1007/978-3-031-22318-1_16

Cite this

Arnon, G., Bhangale, A., Chiesa, A., & Yogev, E. (2022). A Toolbox for Barriers on Interactive Oracle Proofs. In E. Kiltz, & V. Vaikuntanathan (Eds.), Theory of Cryptography - 20th International Conference, TCC 2022, Proceedings (pp. 447-466). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13747 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-22318-1_16

Arnon, Gal ; Bhangale, Amey ; Chiesa, Alessandro et al. / A Toolbox for Barriers on Interactive Oracle Proofs. Theory of Cryptography - 20th International Conference, TCC 2022, Proceedings. editor / Eike Kiltz ; Vinod Vaikuntanathan. Springer Science and Business Media Deutschland GmbH, 2022. pp. 447-466 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

@inproceedings{29a1d29d83584006b0d4700bffbc106d,

title = "A Toolbox for Barriers on Interactive Oracle Proofs",

abstract = "Interactive oracle proofs (IOPs) are a proof system model that combines features of interactive proofs (IPs) and probabilistically checkable proofs (PCPs). IOPs have prominent applications in complexity theory and cryptography, most notably to constructing succinct arguments. In this work, we study the limitations of IOPs, as well as their relation to those of PCPs. We present a versatile toolbox of IOP-to-IOP transformations containing tools for: (i) length and round reduction; (ii) improving completeness; and (iii) derandomization. We use this toolbox to establish several barriers for IOPs: Low-error IOPs can be transformed into low-error PCPs. In other words, interaction can be used to construct low-error PCPs; alternatively, low-error IOPs are as hard to construct as low-error PCPs. This relates IOPs to PCPs in the regime of the sliding scale conjecture for inverse-polynomial soundness error.Limitations of quasilinear-size IOPs for 3SAT with small soundness error.Limitations of IOPs where query complexity is much smaller than round complexity.Limitations of binary-alphabet constant-query IOPs. We believe that our toolbox will prove useful to establish additional barriers beyond our work.",

keywords = "Interactive oracle proofs, Lower bounds, Probabilistically checkable proofs",

author = "Gal Arnon and Amey Bhangale and Alessandro Chiesa and Eylon Yogev",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.; 20th Theory of Cryptography Conference, TCC 2022 ; Conference date: 07-11-2022 Through 10-11-2022",

year = "2022",

doi = "10.1007/978-3-031-22318-1_16",

language = "אנגלית",

isbn = "9783031223174",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Science and Business Media Deutschland GmbH",

pages = "447--466",

editor = "Eike Kiltz and Vinod Vaikuntanathan",

booktitle = "Theory of Cryptography - 20th International Conference, TCC 2022, Proceedings",

address = "גרמניה",

}

Arnon, G, Bhangale, A, Chiesa, A & Yogev, E 2022, A Toolbox for Barriers on Interactive Oracle Proofs. in E Kiltz & V Vaikuntanathan (eds), Theory of Cryptography - 20th International Conference, TCC 2022, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 13747 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 447-466, 20th Theory of Cryptography Conference, TCC 2022, Chicago, United States, 7/11/22. https://doi.org/10.1007/978-3-031-22318-1_16

A Toolbox for Barriers on Interactive Oracle Proofs. / Arnon, Gal; Bhangale, Amey; Chiesa, Alessandro et al.
Theory of Cryptography - 20th International Conference, TCC 2022, Proceedings. ed. / Eike Kiltz; Vinod Vaikuntanathan. Springer Science and Business Media Deutschland GmbH, 2022. p. 447-466 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13747 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - A Toolbox for Barriers on Interactive Oracle Proofs

AU - Arnon, Gal

AU - Bhangale, Amey

AU - Chiesa, Alessandro

AU - Yogev, Eylon

PY - 2022

Y1 - 2022

N2 - Interactive oracle proofs (IOPs) are a proof system model that combines features of interactive proofs (IPs) and probabilistically checkable proofs (PCPs). IOPs have prominent applications in complexity theory and cryptography, most notably to constructing succinct arguments. In this work, we study the limitations of IOPs, as well as their relation to those of PCPs. We present a versatile toolbox of IOP-to-IOP transformations containing tools for: (i) length and round reduction; (ii) improving completeness; and (iii) derandomization. We use this toolbox to establish several barriers for IOPs: Low-error IOPs can be transformed into low-error PCPs. In other words, interaction can be used to construct low-error PCPs; alternatively, low-error IOPs are as hard to construct as low-error PCPs. This relates IOPs to PCPs in the regime of the sliding scale conjecture for inverse-polynomial soundness error.Limitations of quasilinear-size IOPs for 3SAT with small soundness error.Limitations of IOPs where query complexity is much smaller than round complexity.Limitations of binary-alphabet constant-query IOPs. We believe that our toolbox will prove useful to establish additional barriers beyond our work.

AB - Interactive oracle proofs (IOPs) are a proof system model that combines features of interactive proofs (IPs) and probabilistically checkable proofs (PCPs). IOPs have prominent applications in complexity theory and cryptography, most notably to constructing succinct arguments. In this work, we study the limitations of IOPs, as well as their relation to those of PCPs. We present a versatile toolbox of IOP-to-IOP transformations containing tools for: (i) length and round reduction; (ii) improving completeness; and (iii) derandomization. We use this toolbox to establish several barriers for IOPs: Low-error IOPs can be transformed into low-error PCPs. In other words, interaction can be used to construct low-error PCPs; alternatively, low-error IOPs are as hard to construct as low-error PCPs. This relates IOPs to PCPs in the regime of the sliding scale conjecture for inverse-polynomial soundness error.Limitations of quasilinear-size IOPs for 3SAT with small soundness error.Limitations of IOPs where query complexity is much smaller than round complexity.Limitations of binary-alphabet constant-query IOPs. We believe that our toolbox will prove useful to establish additional barriers beyond our work.

KW - Interactive oracle proofs

KW - Lower bounds

KW - Probabilistically checkable proofs

UR - http://www.scopus.com/inward/record.url?scp=85146672142&partnerID=8YFLogxK

U2 - 10.1007/978-3-031-22318-1_16

DO - 10.1007/978-3-031-22318-1_16

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:85146672142

SN - 9783031223174

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 447

EP - 466

BT - Theory of Cryptography - 20th International Conference, TCC 2022, Proceedings

A2 - Kiltz, Eike

A2 - Vaikuntanathan, Vinod

PB - Springer Science and Business Media Deutschland GmbH

T2 - 20th Theory of Cryptography Conference, TCC 2022

Y2 - 7 November 2022 through 10 November 2022

ER -

Arnon G, Bhangale A, Chiesa A, Yogev E. A Toolbox for Barriers on Interactive Oracle Proofs. In Kiltz E, Vaikuntanathan V, editors, Theory of Cryptography - 20th International Conference, TCC 2022, Proceedings. Springer Science and Business Media Deutschland GmbH. 2022. p. 447-466. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-031-22318-1_16