Home	About John	Resume/CV	References	Writing	Research

Zero Knowledge Research

Overview

Here we do a deep dive on Zero Knowledge

• Approach
• Emerging Use Cases
• Proof Systems
• Efficient Signatures
• Proof Aggregation
• Tokenomics

Learning Material

Foundational

• An Introduction to Mathematical Cryptography
• Introduction to Applied Linear Algebra
• Calculus I - Differentiation and Integration
• An Introduction to Mathematical Cryptography: the mathematics behind the theory of public key cryptosystems and digital signature schemes.
• Cryptography Algorithms
• Number Theory
• zkSNARKs in a nutshell
• Quadratic Arithmetic Programs: from Zero to Hero
• Exploring Elliptic Curve Pairings
• Zk-SNARKs: Under the Hood
• The MoonMath Manual to zk-SNARKs
• Elliptic Curve Cryptography: a gentle introduction
• Exploring Elliptic Curve Pairings
• KZG polynomial commitments
• plookup: A simplified polynomial protocol for lookup tables.
• Casting out Primes: a nondeterministic method for bignum arithmetic. It is inspired by the “casting out nines” technique, where some identity is checked modulo 9, providing a probabilistic result.

Zero Knowledge

• Fraud and Data Availability Proofs: Maximising Light Client Security and Scaling Blockchains with Dishonest Majorities. Light clients, also known as Simple Payment Verification (SPV) clients, are nodes which only download a small portion of the data in a blockchain, and use indirect means to verify that a given chain is valid.
• zkBridge: Trustless Cross-chain Bridges Made Practical
• Caulk: Lookup Arguments in Sublinear Time: position-hiding linkability for vector commitment schemes: one can prove in zero knowledge that one or m values that comprise commitment cm all belong to the vector of size N committed to in C.
• HyperPlonk: Plonk with Linear-Time Prover and High-Degree Custom Gates
• SLONK—a simple universal SNARK: a simplification to PLONK called SLONK. We replace the permutation argument (the “P” in PLONK) in favour of a shift argument (the “S” in SLONK). We get a universal SNARK with the smallest known proof size and verification time.
• Kate commitments from the Lagrange basis without FFTs: how to commit, evaluate and open polynomials in the Lagrange basis without FFTs. This is the first part in a series (see part 1, part 2, part 3) showing how to do PLONK-style universal SNARKs without FFTs
• Hadamard checks from the Lagrange basis without FFTs: how to prove Hadamard relations between polynomials in the Lagrange basis without FFTs. This is the second part (see part 1, part 2, part 3) in a series showing how to do PLONK-style universal SNARKs without FFTs.
• PLONK-style SNARKs without FFTs: how to do PLONK-style universal SNARKs without FFTs. This is part 3 in a series (part 1, part 2, part 3).
• An efficient verifiable state for zk-EVM and beyondfrom the Anemoi hash function
• Plonky2: Fast Recursive Arguments with PLONK and FRI

• Bridging the Multichain Universe with Zero Knowledge Proofs
• awesome-zkml
• https://learn.0xparc.org/: ZK Learning Resources
• Delendum ZKP Knowledge base
• https://appliedzkp.org: Privacy and Scaling Exploration
• https://zkp.science/: Zero-Knowledge Proofs
• https://starkware.co/stark-101/: Stark 101: write a STARK prover from scratch
• https://docs.starkware.co/starkex/index.html: - Starkware StarkeEx
• Noir Noir is a Domain Specific Language for developing ZK-provable programs. (Rust based)
  • article
  • tweet
  • Grants
• Arkworks
• zkrepl.dev
• succinct
• ZK BATCH ECDSA
• Batch ECDSA Verification
• Bringing IBC to Ethereum using ZK-Snarks
• MINA docs

• zkPoS: End-to-End Trustless: HyperOracle article on how zkPoS provides the ability of proving the consensus with ZK.
• Succinct Towards the endgame of blockchain interoperability with proof of consensus

Codebases

• Circom a novel domain-specific language for defining arithmetic circuits that can be used to generate zero-knowledge proofs
• DarkForest zkSNARK space warfare
  • Awesome List
  • Our front end code (the game is open source!)
  • Twitter
• Discord
  • Team Blog
    • Dark Forest v0.6
    • Exploiting DF v0.5 Artifact Minting
    • v0.5 Plugins Contest Winners
    • Zero-Knowledge Proofs for Engineers
    • Announcing Dark Forest
    • The Strongest Crypto Gaming Thesis: Why we’re building Dark Forest
  • Community plugins
  • Community-run wiki
  • Player-made content
    • Dark Forest GPU universe explorer
    • Getting started with Dark Forest
    • Setting up a remote miner
    • Dark Forest battle timelapse

• halo2ecc-s: Re-implement an ecc circuits with halo2

• plonky2: a SNARK implementation based on techniques from PLONK and FRI. It has since expanded to include tools such as Starky, a highly performant STARK implementation.
  • plonky2-solidity-verifier
  • plonky2-circom: Plonky2 verifier in Circom
  • plonky2-ed25519: SNARK verification circuits of a digital signature scheme Ed25519 implemented with Plonky2.
  • plonky2-sha256: SNARK circuits of a cryptographic hash function SHA-256 implemented with Plonky2.
  • plonky2-sha512: SNARK circuits of a cryptographic hash function SHA-512 implemented with Plonky2.
  • plonky2-pairing

Presentations

• Devcon VI
• Light Client After the Merge video
• What to Know about Zero Knowledge
• ZK Application ShowCase
• ZK Badges: How to prove that you donated to Gitcoin grants
• ZK Security Self Led Session
• zkEVM Vs EVM: Full Equivalence?
• ZK Application Design Patterns video
• Applied ZK SLS presentations

Additional Information

• Review ENS Bridging Strategy and repo
• Succinct $600K tweet Demo github video built using circom
• circom
• Arkworks, tutorial, twitter, video
• Aztec.network Noir intro, github, twitter, docs
• GNark
• ElectronLabs
• ZKU Learning

• Review matter-labs knowledge base

• zkSNARKS explained like you’re someone who knows some math and some coding

• The Halo2 Book
• A survey of elliptic curves for proof systems
• zkEVM
  • zkSync Era
  • Polygon zkEVM
  • zkSync zkEVM
  • ConsenSys zkEVM