Goal
The goal is to reduce the size of proof generated by spartan-parallel
.
Background
Currently we need to open four different set of multilinear polynomials at three different points in spartan-parallel
(details). This requires us to generate 4 polynomial opening proofs. However, we know multilinear polynomial opening proof's size is $O(n)$ (where $n$ is the number of variables). This means the opening proof of ML poly with 16 variables is not significantly shorter than that with 25 variables.
- This implies opening them individually incurs very big overhead.
- As a comparison, FRI based proof system like
plonky3
, it batch the opening of hundreds of polynomials into one.
See more discussion at slack
Proposal (TODO) - Batching