"In this module, Guillermo Angeris and Muthu Venkitasubramaniam, Co-founder at Ligero Inc, professor at Georgetown University and co-author of the original Ligero paper, deliver a comprehensive technical walkthrough of the Ligero proof system. After situating Ligero within the broader landscape of zero-knowledge proof constructions, Muthu introduces the MPC-in-the-head approach. Using this framework, he explains the Ligero proof system in detail, walking through its use of packed secret sharing, its constraint system, and the three core tests—proximity, multiplication, and linear—that ensure its correctness. Finally, he discusses practical considerations, including how Ligero achieves zero-knowledge, succinct verification, and memory efficiency, making it suitable for client-side proving on resource-constrained devices"

• https://zkhack.dev/whiteboard/s3m5/

This article explains why the FRI protocol is secure, focusing on how the verifier detects dishonest folding through a "prover message graph." It introduces a key property that allows agreement with a Reed-Solomon code to "bubble up" through honest folds. The post simplifies the complex security proof and highlights ongoing research to tighten bounds for more efficient SNARKs.

• https://blog.zksecurity.xyz/posts/fri-security/

This article provides an intuitive explanation of the Bulletproofs protocol, a zero-knowledge proof system that requires no trusted setup or pairings, relying only on the discrete logarithm assumption. It focuses on how Bulletproofs verifiably compresses inner product proofs using Pedersen commitments and recursive vector folding. The post walks through how the prover and verifier reduce vectors and commitments step-by-step, ultimately enabling short, efficient proofs. It also highlights how real-world implementations aggregate checks for performance.

• https://blog.zksecurity.xyz/posts/bulletproofs-intuitions/

This article offers a hands-on, code-driven deep dive into the Bulletproofs Inner Product Argument (IPA) using SageMath. It walks through the protocol step-by-step, starting from basic vector folding and cross terms (L and R), then adds Pedersen commitments to ensure soundness. The post explains how the prover and verifier interact, how challenges are used securely, and how to optimize verification using multiscalar multiplication. Complete with runnable code, it demystifies the math behind Bulletproofs and prepares readers for real-world applications like range proofs.

• https://blog.zksecurity.xyz/posts/bulletproofs-sage/

This article explores the cryptographic mechanisms behind electronic passports (eMRTDs), detailing their file structure, threat model, and protocols like BAC, PA, AA, CA, TA, and PACE. It highlights legacy vulnerabilities, modern enhancements, and the risks of using passports in zero-knowledge proof systems. The post emphasizes the importance of secure handling, as even advanced cryptography can be undermined by poor operational practices.

• https://blog.trailofbits.com/2025/10/31/the-cryptography-behind-electronic-passports/

All Ethereum blocks are now being proven in real time, with an average proof time of about 7.5s

• https://x.com/ziskvm/status/1983221583704445333

• https://snark.express/25q4.pdf

If you're interested in our ZK Insights or have ideas for similar content to share, we highly encourage everyone to head over to our Github repo and submit a Pull Request. Join forces with like-minded ZKPunks to co-create!

✨ Github repo link: https://github.com/ZKPunk-Org/zk-insights
✨ Web collection version: https://insights.zkpunk.pro/

Special thanks to: Kurt

Editor: Purple