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Math Background

A sketch of the objects we use

In this section, we stash some mathematical background. If the stuff below looks new to you, it might be wise to study it before looking at the rest of this site area.

Section Directory

This section contains the following subsections.

  • Binary Fields. Here, we review binary fields and some of their basic algebraic properties.
  • Multilinear Polynomials. In Binius64, we work throughout with multilinear polynomials. Here, we define these objects and recall a few basic facts about them.
  • The Sumcheck. The sumcheck protocol is classic, and one of our most important building blocks. Here, we sketch that protocol and its proof of security.
  • Oblong-Multilinearization. Here, we describe a generic mathematical transformation that turns a standard, "cubular" multilinear into an oblong one, i.e. which takes prescribed values on a rectangular domain. We will use this thoroughly in our protocol.