IOPs with Inverse Polynomial Soundness Error

We show that every language in NP has an Interactive Oracle Proof (IOP) with inverse polynomial soundness error and small query complexity. This achieves parameters that surpass all previously known PCPs and IOPs. Specifically, we construct an IOP with perfect completeness, soundness error $1/n$, round complexity $O(\log \log n)$, proof length $poly(n)$ over an alphabet of size $O(n)$, and query complexity $O(\log \log n)$. This is a step forward in the quest to establish the sliding-scale conjecture for IOPs (which would additionally require query complexity $O(1)$). Our main technical contribution is a high-soundness small-query proximity test for the Reed-Solomon code. We construct an IOP of proximity for Reed-Solomon codes, over a field $\mathbb{F}$ with evaluation domain $L$ and degree $d$, with perfect completeness, soundness error (roughly) $\max\{1-\delta , O(\rho^{1/4})\}$ for $\delta$-far functions, round complexity $O(\log \log d)$, proof length $O(|L|/\rho)$ over $\mathbb{F}$, and query complexity $O(\log \log d)$; here $\rho = (d+1)/|L|$ is the code rate. En route, we obtain a new high-soundness proximity test for bivariate Reed-Muller codes. The IOP for NP is then obtained via a high-soundness reduction from NP to Reed-Solomon proximity testing with rate $\rho = 1/poly(n)$ and distance $\delta = 1-1/poly(n)$ (and applying our proximity test). Our constructions are direct and efficient, and hold the potential for practical realizations that would improve the state-of-the-art in real-world applications of IOPs

A Toolbox for Barriers on Interactive Oracle Proofs

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