Edited by ZKPunk
Highlights
The Ligero Proof System, w/ Muthu Venkitasubramaniam
"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"
Why does FRI work?
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.
本文探讨了 FRI 协议为何安全，通过「证明者消息图」分析验证者如何识别错误折叠，并提出关键性质使与 RS 码的接近性可逐层传递。文章简化了复杂的安全性证明，并指出当前研究正致力于优化安全边界，以提升 SNARK 效率。
Breaking Down Bulletproofs: No Pairings, No Trusted Setup
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.
本文深入浅出地讲解了 Bulletproofs 协议，这是一种无需可信设置和配对的零知识证明系统，仅依赖离散对数假设。文章重点介绍了如何通过 Pedersen 承诺 和递归的 向量折叠 技术，实现可验证的内积压缩，从而生成简洁高效的证明。最后还提到实际应用中如何将多个验证步骤聚合为一次检查以提升性能。
Unfolding the Bulletproofs Magic: A SageMath Deep Dive
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.
本文通过 SageMath 代码深入解析 Bulletproofs 的内积证明（IPA）协议，从基础向量折叠与交叉项（L 和 R）讲起，逐步引入 Pedersen 承诺 实现安全性。文章详细展示了证明者与验证者的交互流程、挑战值的使用方式，并通过 多标量乘法 优化验证效率。配套代码让读者直观理解 Bulletproofs 的核心机制，并为后续实际应用（如 范围证明）打下基础。
The cryptography behind electronic passports
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.
本文深入解析了电子护照（eMRTD）的密码学机制，包括其文件结构、威胁模型及所用协议（如 BAC、PA、AA、CA、TA 和 PACE）。文章指出传统机制的安全缺陷与现代改进，并警示在零知识证明系统中使用护照可能带来的隐私风险，强调即使加密技术先进，不当使用也会削弱其安全性。
Updates
ZisK has reached a major proving milestone for Ethereum.
All Ethereum blocks are now being proven in real time, with an average proof time of about 7.5s
Papers
SnarkExpress(2025.10)
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