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Notes on Univariate Sumcheck
arXiv:2505.00554v3 Announce Type: replace
Abstract: 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.
Abstract: 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.
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