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arXiv:2505.00554 · v6

Protocols for Univariate Sumcheck

Malcom Mohamed
cs.CR
首次提交 2025-05-01 22:29
版本更新 2026-11-02 04:03
雷达观测 2026-11-04 23:43
arXiv ↗PDF ↗

摘要

Two candidate approaches for univariate sumcheck over roots of unity are presented. The first takes the form of a multilinear evaluation protocol, which can be combined with the standard multivariate sumcheck protocol. The other consists of a direct reduction from univariate sumcheck to multilinear evaluation, which can be combined with Gemini (Bootle et al., Eurocrypt 2022). Optionally, natural round reductions from $m$ to $\log(m)$ are supported, while retaining linear prover time.

作者备注：Full version of the paper from APKC@AsiaCCS'26

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v6 · 2026-11-02 04:03 · 最新观测版本

Protocols for Univariate Sumcheck

Two candidate approaches for univariate sumcheck over roots of unity are presented. The first takes the form of a multilinear evaluation protocol, which can be combined with the standard multivariate sumcheck protocol. The other consists of a direct reduction from univariate sumcheck to multilinear evaluation, which can be combined with Gemini (Bootle et al., Eurocrypt 2022). Optionally, natural round reductions from $m$ to $\log(m)$ are supported, while retaining linear prover time.

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