In this module, Tracy Livengood and Justin Thaler provide a comprehensive introduction to the sum-check protocol and why it is so powerful, beginning with a catch-up on polynomials (univariate, multivariate, multilinear) as well as the important concept of multilinear extensions, and introduce the “equality” function. They go on to explain the mechanics of the sum-check protocol, detailing its goals and process, before walking us through the rounds of the protocol and demonstrating how it is applied. They then highlight the advantages of sum-check over other SNARK systems, and sketch the Spartan polynomial IOP. Toward the end, they delve into the Goldwasser, Kalai and Rothblum (GKR) protocol and discuss the trade-offs between this system and Spartan.

https://zkhack.dev/whiteboard/s2m2/

Deep dive into Circle-STARKs FFT

@ignaciohagopian wrote an article explaining the rationale and the mechanics of the specific fast Fourier transform (FFT) defined in the Circle STARKs paper.

https://ihagopian.com/posts/deep-dive-into-circle-starks-fft

Possible futures of the Ethereum protocol, part 1: The Merge

https://vitalik.eth.limo/general/2024/10/14/futures1.html

Possible futures for the Ethereum protocol, part 2: The Surge

https://vitalik.eth.limo/general/2024/10/17/futures2.html

Vac 101: Transforming an Interactive Protocol to a Noninteractive Argument

https://vac.dev/rlog/vac101-fiat-shamir/

Intro To Math Proofs (Full Course)

https://www.youtube.com/watch?v=3czgfHULZCs

A library for lattice-based multiparty homomorphic encryption in Go

https://github.com/tuneinsight/lattigo

Updates

Plonky3 has gotten 2-4x faster, with M3 Max now proving ~1.7 million Poseidon2 hashes per second.

https://x.com/dlubarov/status/1845862467315920940
https://x.com/_bfarmer/status/1845870877453455403

Overview of Circle STARKs

https://www.youtube.com/watch?v=Xrpi-gO3IpI

Proof is in the Pudding 02: zkTLS

https://www.youtube.com/watch?v=k4fylgnJRPE

ZK12: ZK on Bitcoin - Liam Eagen

https://www.youtube.com/watch?v=BM0dBtyLNNk

ZK12: Myth vs. Reality: Enhancing Proving Time in KZG-Backed Plonkish Systems for zkWASM - Sinka Gao

https://www.youtube.com/watch?v=qFXWbYwqqbM&list=PLj80z0cJm8QFy2umHqu77a8dbZSqpSH54&index=15

House of ZK - Virtual Conference 1.0

https://www.youtube.com/watch?v=wZFlugUR9Qc

Interview with Eli Ben-Sasson - HoZK Virtual Conference 1.0

https://www.youtube.com/watch?v=92EkOmij_Mo

ZK-SecreC

Open sourced ZK-SecreC, a zero knowledge toolkit for building large proofs on computation. Imagine proving to someone that your health records don't have a diagnosis or that you have been staying in some are without leaking the source data.

https://x.com/danbogdanov/status/1847196941102318048
https://github.com/zk-secrec/

On Distributed FRI-based Proof Generation

https://hackmd.io/@nil-research/rJ_NVyiRA

Papers

Glacius: Threshold Schnorr Signatures from DDH with Full Adaptive Security

https://eprint.iacr.org/2024/1628

Sparrow: Space-Efficient zkSNARK for Data-Parallel Circuits and Applications to Zero-Knowledge Decision Trees

https://eprint.iacr.org/2024/1631

RPO-M31 and XHash-M31: Efficient Hash Functions for Circle STARKs

https://eprint.iacr.org/2024/1635

Fiat-Shamir Goes Rational

https://eprint.iacr.org/2024/1645

Curve Forests: Transparent Zero-Knowledge Set Membership with Batching and Strong Security

https://eprint.iacr.org/2024/1647

One-Shot Native Proofs of Non-Native Operations in Incrementally Verifiable Computations

https://eprint.iacr.org/2024/1651

Compressed -protocol Theory from Sum-check

https://eprint.iacr.org/2024/1654

Instance Compression, Revisited

https://eprint.iacr.org/2024/1659

zkFFT: Extending Halo2 with Vector Commitments & More

https://eprint.iacr.org/2024/1661

A Hidden-Bits Approach to Black-Box Statistical ZAPs from LWE

https://eprint.iacr.org/2024/1663

Consensus on SNARK pre-processed circuit polynomials

https://eprint.iacr.org/2024/1664

Multi-party Setup Ceremony for Generating Tokamak zk-SNARK Parameters

https://eprint.iacr.org/2024/1671

Batch Range Proof: How to Make Threshold ECDSA More Efficient

https://eprint.iacr.org/2024/1677

Blind zkSNARKs for Private Proof Delegation and Verifiable Computation over Encrypted Data

https://eprint.iacr.org/2024/1684

GAPP: Generic Aggregation of Polynomial Protocols

https://eprint.iacr.org/2024/1685

On pairing-friendly 2-cycles and SNARK-friendly 2-chains of elliptic curves containing a curve from a prime-order family

https://eprint.iacr.org/2024/1697

Computational Analysis of Plausibly Post-Quantum-Secure Recursive Arguments of Knowledge

https://eprint.iacr.org/2024/1698