# Module binius_core::protocols::gkr_gpa

source · ## Expand description

The grand product argument protocol based on a GKR-instantiation.

Grand Product Argument reduces a grand product claim to a multilinear evalcheck claim. A Grand Product Claim is that a multilinear polynomials evaluations over the hypercube multiply to some claimed final product.

The GKR circuit used here has only one gate type: the fan-in-2 multiplication gate. In the natural way, the 2^n input wires are multiplied together in n layers to produce the output.

Naming Convention for challenges:

- Sumcheck challenge: $r’_k$ $k$-variate sumcheck challenge vector generated during the course of gkr_sumcheck
- GKR Challenge $\mu_k$ 1-variate generated during layer proving after the sumcheck proof is created after the layer k to k+1 sumcheck
- Layer Challenge $r_{k+1} := (r_k, \mu_k)$
$k+1$ variate, materialized as a combination of the above two, used in
`LayerClaim`

See Thaler13 Section 5.3.1 for further background on the GKR polynomial identities for a binary tree circuit.

## Structs§

## Enums§

## Functions§

- Proves batch reduction turning each GrandProductClaim into an EvalcheckMultilinearClaim
- Verifies batch reduction turning each GrandProductClaim into an EvalcheckMultilinearClaim