TY - GEN
T1 - A Toolbox for Barriers on Interactive Oracle Proofs
AU - Arnon, Gal
AU - Bhangale, Amey
AU - Chiesa, Alessandro
AU - Yogev, Eylon
N1 - Publisher Copyright:
© 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.
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
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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 -