International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: A Toolbox for Barriers on Interactive Oracle Proofs

Gal Arnon , Weizmann Institute
Amey Bhangale , UC Riverside
Alessandro Chiesa , EPFL
Eylon Yogev , Bar-Ilan University
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Presentation: Slides
Conference: TCC 2022
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: \begin{itemize} \item 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. \item Limitations of quasilinear-size IOPs for 3SAT with small soundness error. \item Limitations of IOPs where query complexity is much smaller than round complexity. \item Limitations of binary-alphabet constant-query IOPs. \end{itemize} We believe that our toolbox will prove useful to establish additional barriers beyond our work.
  title={A Toolbox for Barriers on Interactive Oracle Proofs},
  author={Gal Arnon and Amey Bhangale and Alessandro Chiesa and Eylon Yogev},