This note describes a univariate polynomial interactive oracle proof for multilinear extension evaluation. Unlike prior protocols, (1) the verifier here is given a univariate extension oracle for the same vector of which the multilinear extension is getting evaluated and (2) the prover only has linear complexity. For these reasons, the protocol is well-suited for combining multivariate and univariate sumcheck techniques.

翻译：本笔记描述了一种用于多线性扩展求值的单变量多项式交互式预言证明。与先前协议不同之处在于：(1) 验证者在此获得待求值多线性扩展对应向量的单变量扩展预言；(2) 证明者仅需线性复杂度。基于这些特性，该协议特别适用于结合多变量与单变量求和检验技术。