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References and Further Reading

This page provides resources for learning more about zero-knowledge proofs, the Ligero protocol, and related cryptographic concepts.

Books​

Proofs, Arguments, and Zero-Knowledge​

Author: Justin Thaler Available: Free online

A comprehensive introduction to interactive proofs, probabilistically checkable proofs (PCPs), and zero-knowledge proof systems. This book covers both the theory and practical implementations of modern ZK systems, making it an excellent resource for understanding the foundations of Ligetron.

Topics covered:

  • Interactive proofs and arguments
  • Polynomial commitment schemes
  • SNARKs and STARKs
  • Sum-check protocol
  • Zero-knowledge proofs

A Graduate Course in Applied Cryptography​

Authors: Dan Boneh and Victor Shoup Available: Free online

Comprehensive coverage of modern cryptography including zero-knowledge proofs, with rigorous mathematical foundations.

Building Cryptographic Proofs from Hash Functions​

Authors: Alessandro Chiesa and Eylon Yogev Available: Free online

A comprehensive guide to constructing cryptographic proofs using hash functions, covering SNARGs (Succinct Non-interactive Arguments) and related transparent proof systems.

Research Papers​

Ligero: Lightweight Sublinear Arguments Without a Trusted Setup​

Authors: Scott Ames, Carmit Hazay, Yuval Ishai, Muthuramakrishnan Venkitasubramaniam Published: ACM CCS 2017 Link: ePrint Archive

The original Ligero paper introducing the transparent, post-quantum secure zero-knowledge proof system that forms the basis of Ligetron. Key features include:

  • No trusted setup required
  • Sublinear verification time for uniform computations
  • Based on collision-resistant hash functions
  • Post-quantum security

Ligetron: Lightweight Scalable End-to-End Zero-Knowledge Proofs​

Authors: Ruihan Wang, Carmit Hazay, Muthuramakrishnan Venkitasubramaniam Published: 2024 IEEE Symposium on Security and Privacy (SP) Link: IEEE

The Ligetron paper presenting optimizations and practical implementations of the Ligero protocol, including:

  • GPU acceleration for proof generation
  • WebAssembly-based circuit representation
  • Scalable proof system for large computations

Poseidon: A New Hash Function for Zero-Knowledge Proof Systems​

Authors: Lorenzo Grassi, Dmitry Khovratovich, Christian Rechberger, Arnab Roy, Markus Schofnegger Published: USENIX Security 2021 Link: ePrint Archive

Design and analysis of the Poseidon hash function optimized for arithmetic circuits used in zero-knowledge proofs.

Baby Jubjub Elliptic Curve​

Link: EIP-2494

Specification of the Baby Jubjub twisted Edwards curve used for EdDSA signatures in zero-knowledge circuits.

Online Resources​

ZKProof Community​

Website: zkproof.org

Community-driven standardization effort for zero-knowledge proof systems, including workshops, documentation, and implementation references.

ZK Learning Resources​

Website: zkp.science

Curated list of zero-knowledge proof resources including lectures, tutorials, and implementations.

ZKP MOOC​

Website: zk-learning.org

Massive Open Online Course on zero-knowledge proofs, covering both theory and practice with video lectures from leading researchers.

Technical Background​

Finite Field Arithmetic​

BN254 (Barreto-Naehrig) Curve​

Paper: Pairing-Friendly Elliptic Curves of Prime Order Authors: Paulo S. L. M. Barreto, Michael Naehrig

The BN254 curve family used for efficient pairing-based cryptography in zero-knowledge proofs.

Information-Theoretic Security​

Interactive Oracle Proofs (IOPs)​

Paper: Interactive Oracle Proofs Authors: Eli Ben-Sasson, Alessandro Chiesa, Nicholas Spooner

The IOP model that underlies many modern transparent zero-knowledge proof systems including Ligero.

Polynomial Commitments​

FRI: Fast Reed-Solomon Interactive Oracle Proofs of Proximity​

Paper: Fast Reed-Solomon Interactive Oracle Proofs of Proximity Authors: Eli Ben-Sasson, Iddo Bentov, Yinon Horesh, Michael Riabzev

The FRI protocol used in STARK-based proof systems and related to techniques used in Ligero.

Cryptographic Primitives​

SHA-256​

Specification: FIPS 180-4 Published: NIST, 2015

Official specification of the SHA-2 family of hash functions.

EdDSA (Edwards-curve Digital Signature Algorithm)​

Paper: High-speed high-security signatures Authors: Daniel J. Bernstein, Niels Duif, Tanja Lange, Peter Schwabe, Bo-Yin Yang

Original EdDSA paper introducing Ed25519 signatures.

Implementation References​

WebGPU​

Specification: W3C WebGPU

Official WebGPU specification for GPU acceleration in web and native applications.

WebAssembly​

Specification: W3C WebAssembly

Core WebAssembly specification used as the circuit representation in Ligetron.

Dawn (WebGPU Implementation)​

Repository: dawn.googlesource.com

Google's C++ implementation of WebGPU used in Ligetron for GPU acceleration.

zkSNARKs​

zkSTARKs​

Other Transparent Systems​

Video Lectures​

ZK Whiteboard Sessions​

YouTube: ZK Whiteboard Sessions

Series of educational videos explaining zero-knowledge proof concepts with visual explanations.

zkSummit​

Website: zksummit.com

Regular conferences featuring talks from ZK researchers and practitioners, with recorded sessions available online.

Academic Courses​

Introduction to Zero-Knowledge Proofs​

Instructor: Yupeng Zhang (Texas A&M University) Materials: Available through zk-learning.org

Graduate-level course covering the theoretical foundations and practical implementations of ZK proofs.

Community and Discussion​

Ligero Inc.​

Research Forums​