Understanding Binius, Part II
Make Binius efficiently verifiable
In the previous article, we discussed Ligero-Binius, which is the Binius-family proof system released in 2023 by the Irreducible team.
This year, the Irreducible team released another Binius-family proof system, called FRI-Binius. FRI-Binius is a direct competitor to Plonky3, the proof system from Polygon Zero.
FRI-Binius improves over Ligero-Binius by having a smaller verification overhead, making itself more suitable for recursive proof verification, while the prover efficiency remains competitive.
In the second article, we talk about FRI-Binius. This article is available on HackMD.
https://hackmd.io/@l2iterative/binius2
FRI-Binius is more complicated than Ligero-Binius. Readers who have not read our article on Ligero-Binius should start with that article first, as it provides the background on error-correcting code on binary fields as well as packing small field elements into bigger elements.
In this article, we use animations and visual aids to assist understand the sumcheck protocol and the folding protocols, which are the hard part.
Even if you previously have looked into FRI-based protocols (such as STARK), be careful, the way that FRI-Binius works is very different from several popular FRI-based protocols. For example, Stwo and RISC Zero’s proof systems both use DEEP-FRI (where DEEP refers to “Domain Extending for Eliminating Pretenders”), in which a quotient protocol is used for opening polynomial, instead of the sumcheck and folding protocol used in FRI-Binius, which comes from a recent work, BaseFold. The reason why the quotient protocol does not work well with small fields have been discussed in the Ligero-Binius paper.
We would like to thank Radisav Cojbasic, Jim Posen, and Benjamin Diamond from Irreducible for reviewing the article series and providing feedback.
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Author: Weikeng Chen, Research Partner, L2IV
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