Proving Methods

(To add papers: Work in progress)

• 10 papers to read: Papers that shaped modern ZKPs

Sumcheck Protocol

• Unreasonable power of Sumcheck - Thaler
  • Justin Thaler Lecture
  • Sumcheck Overview
  • Intro to Sumcheck protocol -oxsage
• Inuition behind sumcheck - Wong
• A zeroknowledge sumcheck and applications
• Sumcheck argument and applications
  • The amazing sumcheck protocol - Bootle
• Proving AIR with MultiLinear Sumcheck - Borgeaud
• The Power of Interactive Proofs
• Sumcheck Tutorial
• Sumcheck Slide-Deck
• Introduction to the Sumcheck Protocol
• A Zero Knowledge Sumcheck and its Applications
• Arkworks Sumcheck
• Formal Verification of the Sumcheck Protocol
• Succinct Arguments over Towers of Binary Fields
• Sumcheck over fields of small charecteristic
  • Code
  • Video
  • Part 1 - Lambdaclass
  • Part 2 - Lambdaclass
• Explaining the GKR method - Gabizon
• GKR based ZKP - Kalai

Low degree Testing/Reed-Solomon Proximity testing

• STARK paper
• DEEP - FRI
• Proximity Gaps for Reed-Solomon Codes
• FRI hackernoon
• FRI properties
• FRI erasure code fraud proof
• Barycentric low deg check - Dankrad Feist
• Low Degree Testing
• Data Availability sampling from FRI
• Circle STARKS
  • talk - Gabizon
  • circle starks and mersene primes
• STIR: Reed–Solomon Proximity Testing with Fewer Queries
• Note on adding ZK to starks

Permutation arguments

• PLonk’s permutation - a definitive explanation

Lookup arguments

• A brief history of lookup arguments
• Plonkup blog - lambdaclass

Aggregations and recursions

• Snarkpack: practical snark aggregation
  • blog
  • talk
  • talk -Proof aggregation techniques - lambdaclass

Folding and accumulation schemes

• Algebraic reductions of knowledge
• Resource: Awesome Folding
• How to build a snark that is out of this world - Nat Bunner
• An incomplete guide to FOlding schemes - Lisa
• Algebraic Reductions of Knowledge

General

• Succinct Proofs and Linear Algebra
• SOK: Range proofs