Protocols for Univariate Sumcheck
This work addresses a specific technical challenge in cryptographic protocols, likely for researchers in zero-knowledge proofs or verifiable computation, and appears incremental as it builds on existing methods like Gemini.
The paper tackles the problem of univariate sumcheck over roots of unity by presenting three candidate approaches, including a multilinear evaluation protocol and reductions to multivariate evaluation, with results showing optional round reductions to log(m) or O(sqrt(m) while maintaining linear prover time.
Three 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 two are reductions from univariate domain identity and univariate sumcheck to multivariate evaluation, respectively, and each can be combined with Gemini (Bootle et al., Eurocrypt 2022). Optionally, natural round reductions from $m$ to $\log(m)$ or $O(\sqrt{m})$ are supported, while retaining linear prover time.