SEASON 2 MODULE 6
An Update on Folding w/ Albert Garreta
In this module, Nicolas Mohnblatt and Albert Garreta start by reviewing the definition of folding schemes and going over what they are. They proceed to give an overview of the advances made since the Nova scheme was introduced in 2022, and dive deep into one of these schemes, Hypernova.
What you’ll learn:
- 00:00 – Introduction and definitions
- 04:25 – Properties of folding schemes
- 08:14 – Benefits of folding and applications (IVC, PCD)
- 12:37 – What has changed since Nova
- 19:47 – Definitions of Hypernova’s relation and accumulated relation
- 29:20 – Multilinear extensions and Schwartz-Zippel lemma
- 32:54 – First step of the Spartan scheme
- 35:33 ↳ Matrix-vector multiplications in polynomial terms
- 38:35 ↳ Indexing trick to build the MLE of a matrix
- 43:25 ↳ Reducing the claim about the R1CS relation Az ○ Bz = Cz
- 49:15 ↳ Running the zerocheck protocol
- 56:20 – The full Hypernova folding protocol
Below is an accompanying reading list:
- Nova: Recursive Zero-Knowledge Arguments from Folding Schemes, by Abhiram Kothapalli, Srinath Setty, and Ioanna Tzialla, 2021.
- HyperNova: Recursive arguments for customizable constraint systems, by Abhiram Kothapalli and Srinath Setty, 2023.
- ProtoGalaxy: Efficient ProtoStar-style folding of multiple instances, by Liam Eagen and Ariel Gabizon, 2023.
- Mova: Nova folding without committing to error terms, by Nikolaos Dimitriou, Albert Garreta, Ignacio Manzur and Ilia Vlasov (Nethermind Research, 2024).
- Sangria: a Folding Scheme for PLONK, by Nicolas Mohnblatt (Geometry Research, 2023).
- ProtoStar: Generic Efficient Accumulation/Folding for Special Sound Protocols, by Benedikt Bünz and Binyi Chen (Espresso Systems, 2023).
- KiloNova: Non-Uniform PCD with Zero-Knowledge Property from Generic Folding Schemes, by Tianyu Zheng, Shang Gao, Yu Guo and Bin Xiao, 2023.
- Accumulation without Homomorphism, by Benedikt Bünz, Pratyush Mishra, Wilson Nguyen and William Wang, 2024.
- LatticeFold: A Lattice-based Folding Scheme and its Applications to Succinct Proof Systems, by Dan Boneh and Binyi Chen (Stanford University, 2024)
- Spartan: Efficient and general-purpose zkSNARKs without trusted setup, by Srinath Setty (Microsoft Research, 2019).
ZK Whiteboard Sessions is an educational series on all things zero knowledge. Presented by ZK Hack.
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