Full ZK Whiteboard Sessions - Season 1 playlist here: th-cam.com/play/PLj80z0cJm8QErn3akRcqvxUsyXWC81OGq.html
Full ZK Whiteboard Sessions - Season 2 playlist here: th-cam.com/play/PLzdJdAunCamkxvFeF6McbZGqqSEpWQZ0Q.html
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In this module, Nicolas Mohnblatt and Jim Posen talk about small field SNARKs and their importance. They start with some motivating factors and talk about the performance efficiency that we can get using small field techniques, then walk us through an example of how to construct a Plonky2 proof using the Goldilocks 64-bit field. Finally, they talk about some recent work (Binius) that investigates how small we can make our fields using binary towers, and how to construct SNARKs with them.
What you’ll learn:
00:00 Intro: What does“small” in “small fields” mean?
04:48 Simple STARK Fibonacci example
07:47 The Goldilocks 64-bit prime field
13:11 Error amplification and extension fields
18:10 Back to the STARK: Protocol with Goldilocks extension
28:16 Going even smaller
33:54 Binary fields / Binary towers
37:35 Packing
39:53 Build a SNARK with binary towers
47:41 Summary
Below is an accompanying reading list:
- Polynomial identity testing (PIT) definition (Wikipedia): en.wikipedia.org/wiki/Polynomial_identity_testing
- Vanishing Polynomial definition (ZK Jargon Decoder): zkjargon.github.io/definitions/vanishing_polynomial.html
- Module Two: Building a SNARK, pt 1 by Dan Boneh (ZK Whiteboard Sessions S1, ZK Hack, 2022): th-cam.com/video/J4pVTamUBvU/w-d-xo.html
- Module Three: Building a SNARK, pt 2 by Dan Boneh (ZK Whiteboard Sessions S1, ZK Hack, 2022): th-cam.com/video/vxyoPM2m7Yg/w-d-xo.html
- Anatomy of a STARK, Part 3: FRI (Alan Szepieniec, 2021): aszepieniec.github.io/stark-anatomy/fri
- Fast Fourier transform definition (Wikipedia): en.wikipedia.org/wiki/Fast_Fourier_transform
- Schwartz Zippel Lemma definition (ZK Jargon Decoder): zkjargon.github.io/definitions/schwartz_zippel.html
- Reed Solomon Codes definition (Martyn Riley and Iain Richardson): www.cs.cmu.edu/%7Eguyb/realworld/reedsolomon/reed_solomon_codes.html
- Efficient Prime Fields for Zero-knowledge proof (Kayson Wang, 2024): hackmd.io/@Voidkai/BkNX3xUZA
- S2M2: The Sum-Check Protocol with Justin Thaler (ZK Whiteboard Sessions S2, ZK Hack, 2024): th-cam.com/video/gfy8rotcas4/w-d-xo.html
- The Number Theoretic Transform (NTT) (Ardianto Satriawan, Rella Mareta and Hanho Lee, 2024): eprint.iacr.org/2024/585.pdf
- Binius: highly efficient proofs over binary fields (Vitalik Buterin, 2024): vitalik.eth.limo/general/2024/04/29/binius.html
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ZK Whiteboard Sessions is a weekly video educational series focused on the building blocks of ZK.
Season 2 is presented by ZK Hack and supported by a grant from the ZK Grants Round 2024, a grant initiative that was co-funded by the Ethereum Foundation, Aztec, Polygon, Scroll, Taiko, and zkSync
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Follow along with the series:
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