Efficient multivariate low-degree tests via interactive oracle proofs of proximity for polynomial codes

In STARK-like zero -knowledge proofs, like those of the Starware company, the major algorithmic and mathematical breakthrough which enables such great performance in applications is the invention of very efficient « low degree test » of univariate polynomials. Our work enables to perform such low degree test for multivariate polynomials, with the same efficiency. This is a first layer, and we think it can lay ground for still more optimization of  STARKs.