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Blueprint Overview

Math Background

Binary Fields Multilinear Polynomials The Sumcheck Oblong-Multilinearization

Constraint Systems

Introduction Shifted Value Indices Constraint Arrays AND Constraints MUL Constraints

The Shift Indicators

The AND Reduction

The MUL Reduction

The Shift Reduction

Public Input Check

Polynomial Commitment

Blueprint

Cryptographic details about our backend

In this site section, we explain the cryptographic backend of Binius64.

Site Directory

We've split this site area into a few sections.

Overview. We start by recording a high-level summary of Binius64, targeting a cryptographic audience.

Math Background. This section contains a crash course on the mathematical objects we use.

Constraint Systems. Constraint systems are how we specify the computations we set about proving and verifying. Think somewhere in between "circuits" and "R1CS".

The Backend. Here, we fully explain our cryptographic backend. We record separate protocols for checking the prover's AND and MUL constraints. These two are very different; the first uses a variant of Gruen's univariate skip, while the second uses GKR. Internally, both protocols reduce to a common internal reduction target, called the shift reduction.

Polynomial Commitment. The "lowermost" layer of our cryptographic stack deals with the assessment of evaluation claims about multilinear polynomials.