An Analysis of the WHIR Interactive Oracle Proof of Proximity

Abstract

Interactive oracle proofs of proximity (IOPPs) play a central role in the construction of modern hash-based zk-SNARKs. Among these, the WHIR protocol introduced in 2024 is one of the most verifier-efficient known IOPPs for testing proximity to multilinear Reed–Solomon codes. Due to its recent introduction and technical complexity, however, the protocol has received little detailed exposition beyond the original paper. In this thesis, we present a comprehensive study of the WHIR protocol. Following the original work, we develop the necessary background on constrained Reed–Solomon codes and list decoding, and analyze key concepts such as folding, mutual correlated agreement, and block relative distance. We then introduce the WHIR protocol itself, analyze its asymptotic parameters, and prove its completeness and round-by-round soundness. Throughout, we clarify the design choices underlying WHIR and correct technical inaccuracies present in the original presentation. Finally, we apply WHIR to transform a concrete polynomial interactive oracle proof into an interactive oracle proof, providing a fully worked example. Our aim is to make WHIR more accessible and to provide a clear and reliable reference for its use in hash-based zk-SNARK constructions